Advances in Metal and Semiconductor Clusters Volumes 1–4 published by JAI Press Inc., available from Elsevier Science. Series Editor M.A. Duncan, Department of Chemistry, University of Georgia, Athens, Georgia, USA Volume 1 Spectroscopy and Dynamics (1993) ISBN 155938171X Volume 2 Cluster Reactions (1994) ISBN 1559387041 Volume 3 Spectroscopy and Structure (1996) ISBN 1559387882 Volume 4 Cluster Materials (1998) ISBN 0762300582
ADVANCES IN METAL AND SEMICONDUCTOR CLUSTERS Volume 5
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2001
METAL ION SOLVATION AND METAL–LIGAND INTERACTIONS
ADVANCES IN METAL AND SEMICONDUCTOR CLUSTERS METAL ION SOLVATION AND METAL–LIGAND INTERACTIONS Editor: MICHAEL A. DUNCAN Department of Chemistry University of Georgia
VOLUME 5
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2001
2001
ELSEVIER AMSTERDAM - LONDON - NEW YORK - OXFORD - PARIS - SHANNON - TOKYO
ELSEVIER SCIENCE B.V. Sara Burgerhartstraat 25 P.O. Box 211, 1000 AE Amsterdam, The Netherlands © 2001 Elsevier Science B.V.. All rights reserved. This work is protected under copyright by Elsevier Science, and the following terms and conditions apply to its use: Photocopying Single photocopies of single chapters may be made for personal use as allowed by national copyright laws. Permission of the Publisher and payment of a fee is required for all other photocopying, including multiple or systematic copying, copying for advertising or promotional purposes, resale, and all forms of document delivery. Special rates are available for educational institutions that wish to make photocopies for non-profit educational classroom use. Permissions may be sought directly from Elsevier Science Global Rights Department, PO Box 800, Oxford OX5 1DX, UK; phone: (+44) 1865 843830, fax: (+44) 1865 853333, e-mail:
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∞ The paper used in this publication meets the requirements of ANSI/NISO Z39.48-1992 (Permanence of Paper). Printed in The Netherlands.
CONTENTS
LIST OF CONTRIBUTORS
vii
PREFACE
xi
SOLVATION OF SODIUM ATOM AND AGGREGATES IN AMMONIA CLUSTERS Kiyokazu Fuke, Kenro Hashimoto and Ryozo Takasu
1
ELECTRONIC AND GEOMETRIC STRUCTURES OF WATER CLUSTER COMPLEXES WITH A GROUP 1 METAL ATOM: ELECTRON–HYDROGEN BOND IN THE OH{e}HO STRUCTURE Suehiro Iwata and Takeshi Tsurusawa 39 DETERMINATION OF SEQUENTIAL METAL ION–LIGAND BINDING ENERGIES BY GAS PHASE EQUILIBRIA AND THEORETICAL CALCULATIONS: APPLICATION OF RESULTS TO BIOCHEMICAL PROCESSES Michael Peschke, Arthur T. Blades and Paul Kebarle
77
DOUBLY CHARGED TRANSITION METAL COMPLEXES IN THE GAS PHASE Anthony J. Stace
121
MICROSOLVATION OF COORDINATED DIVALENT TRANSITION-METAL IONS: ESTABLISHING A SPECTROSCOPIC CONNECTION WITH THE CONDENSED PHASE Lynmarie A. Posey 145 ZERO ELECTRON KINETIC ENERGY PHOTOELECTRON SPECTRA OF METAL CLUSTERS AND COMPLEXES Dong-Sheng Yang
v
187
vi
STABILITY, STRUCTURE AND OPTICAL PROPERTIES OF METAL ION-DOPED NOBLE GAS CLUSTERS Michalis Velegrakis
Contents
227
PHOTODISSOCIATION SPECTROSCOPY AS A PROBE OF MOLECULAR DYNAMICS: METAL ION–ETHYLENE INTERACTIONS Paul D. Kleiber 267 SOLVATED METAL IONS AND ION CLUSTERS, AND THE EFFECT OF LIGANDS UPON THEIR REACTIVITY Vladimir E. Bondybey, Martin Beyer, Uwe Achatz, Brigitte Fox and Gereon Niedner-Schatteburg
295
TRANSITION METAL MONOHYDRIDES Peter F. Bernath
325
THE BINDING IN NEUTRAL AND CATIONIC 3d AND 4d TRANSITION-METAL MONOXIDES AND -SULFIDES Ilona Kretzschmar, Detlef Schröder, Helmut Schwarz and Peter B. Armentrout
347
INDEX
397
LIST OF CONTRIBUTORS
Uwe Achatz
Institut für Organische Chemie Technische Universität Berlin Berlin, GERMANY
Peter Armentrout
Department of Chemistry University of Utah Salt Lake City, Utah, USA
Peter F. Bernath
Department of Chemistry University of Waterloo Waterloo, Ontario, CANADA
Martin Beyer
Institut für Physikalische und Theoretische Chemie Technische Universität München Garching, GERMANY
Arthur T. Blades
Department of Chemistry University of Alberta Edmonton, Alberta, CANADA
Vladimir Bondybey
Institut für Physikalische und Theoretische Chemie Technische Universität München Garching, GERMANY
Brigitte Fox
Institut für Physikalische und Theoretische Chemie Technische Universität München Garching, GERMANY
Kiyokazu Fuke
Department of Chemistry Kobe University Kobe, JAPAN
vii
viii
List of Contributors
Kenro Hashimoto
Department of Chemistry Kobe University Kobe, JAPAN
Suehiro Iwata
Institute for Molecular Science Okazaki, JAPAN
Paul Kebarle
Department of Chemistry University of Alberta Edmonton, Alberta, CANADA
Paul Kleiber
Department of Physics University of Iowa Iowa City, Iowa, USA
Ilona Kretzschmar
Institut für Organische Chemie Technische Universität Berlin Berlin, GERMANY
Gereon Niedner-Schatteburg
Institut für Physikalische und Theoretische Chemie Technische Universität München Garching, GERMANY
Michael Peschke
Department of Chemistry University of Alberta Edmonton, Alberta, CANADA
Lynmarie Posey
Department of Chemistry Michigan State University East Lansing, Michigan, USA
Detlef Schröder
Institut für Organische Chemie Technische Universität Berlin Berlin, GERMANY
Helmut Schwarz
Institut für Organische Chemie Technische Universität Berlin Berlin, GERMANY
Anthony J. Stace
School of Chemistry, Physics and Environmental Science University of Sussex Falmer, Brighton, UNITED KINGDOM
List of Contributors
ix
Ryozo Takasu
Department of Chemistry Kobe University Kobe, JAPAN
Takeshi Tsurusawa
Institute for Molecular Science Okazaki, JAPAN
Michalis Velegrakis
Foundation for Research &Technology Institute of Electronic Structure and Lasers Heraklion, Crete, GREECE
Dong-Sheng Yang
Department of Chemistry University of Kentucky Lexington, Kentucky, USA
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PREFACE
In previous volumes in this series, we have focused on atomic clusters of metals, semiconductors and carbon. Fundamental gas phase studies have been surveyed, and most recently we explored new materials which can be produced from clusters or cluster precursors. In the present volume, we shift the focus to clusters composed primarily of non-metal molecules or atoms which have one or more metal atoms seeded into the cluster as an impurity. These clusters provide model systems for metal ion solvation processes and metalligand interactions. Metal-ligand bonding underlies the vast fields of organometallic chemistry, transition metal chemistry and homogeneous catalysis. Catalytic activity, ligand displacement reactions and photochemical activity depend on the specific details of metal-ligand bonding. Likewise, metal ions are ubiquitous in chemistry and biology and weaker electrostatic interactions play a leading role in their function. In solution, metals exist in different charge states depending on the conditions, and the solvation environment strongly influences their chemistry. Many enzymes have metal ions at their active sites, and electrostatic interactions influence the selectivity for metal ion transport through cell membranes. Metal ions (e.g., Mg+, Ca+) are deposited into the earth's atmosphere by meteor ablation, resulting in a rich variety of atmospheric chemistry. Similarly, metal ions (Mg+) have been observed in planetary atmospheres and in the impact of the comet Shoemaker-Levy 9 on Jupiter. In various circumstances, the electrostatic interactions of metal ions xi
xii
Preface
determine the outcome of significant chemistry. Cluster chemistry has made significant contributions to the understanding of these stronger metal ligand interactions and weaker metal ion solvation interactions. In this volume, we explore a variety of work in these general areas, where new cluster science techniques in the gas phase have made it possible to synthesize new kinds of complexes with metals and to measure their properties in detail. Michael A. Duncan Athens, Georgia
1 SOLVATION OF SODIUM ATOM AND AGGREGATES IN AMMONIA CLUSTERS Kiyokazu Fuke, Kenro Hashimoto and Ryozo Takasu
I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 II. Alkali metal atom–ammonia clusters . . . . . . . . . . . . . . . . . . . . . . 3 A. Experimental study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Photodetachment transition to the neutral ground state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Photodetachment transitions to the low-lying excited states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 B. Theoretical study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Geometry and energetics . . . . . . . . . . . . . . . . . . . . . . . . 10 Electron density distribution in Na–(NH3)n (n = 1–4) . 11 Vertical detachment energies and assignment of PES bands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Electronic state of neutral Na(NH3)n . . . . . . . . . . . . . . 14 III. Sodium dimer–ammonia clusters . . . . . . . . . . . . . . . . . . . . . . . 14 A. Experimental study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Photodetachment transition to the neutral ground state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Photodetachment transitions to the low-lying excited states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 B. Theoretical study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Geometry and energetics . . . . . . . . . . . . . . . . . . . . . . . . 23 Excess electron distribution in Na2–(NH3)n . . . . . . . . . . . . . . .24 Advances in Metal and Semiconductor Clusters Volume 5, pages 1–37 © 2001 Elsevier Science B.V. All Rights Reserved. ISBN: 0-444-50726-4
1
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Kiyokazu Fuke, Kenro Hashimoto and Ryozo Takasu
Vertical detachment energies . . . . . . . . . . . . . . . . . . . . .25 Comparison between Na–(NH3)n and Na2–(NH3)n . . . .27 IV. Sodium trimer–ammonia clusters . . . . . . . . . . . . . . . . . . . . . . .30 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .35 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .35 I. INTRODUCTION Excess electrons in liquids are encountered in a variety of solution systems of widely different physical and chemical behavior. The localization modes of electrons and the nature of the resulting electron–solvent molecular entity have been the subject of extensive studies in solution chemistry for many years.1,2 Increasing interest in the structure and dynamics of solvated electrons in polar solvents has led to renewed efforts to unveil the electron localization mode in microclusters.3–10 In polar solvents such as ammonia, alkali metal is dissolved freely and forms solvated electrons spontaneously. The properties of the solvated electrons in dilute condition have been considered to be dominated by electron–solvent interaction, while at high densities, transition from a localized to a delocalized metallic state occurs, where both electron–solvent and interelectronic interactions become important.1 Solvent clusters containing alkali atom and/or alkali metal clusters are expected to serve as a good model for linking the macroscopic properties of alkali metal–solvent systems to their microscopic nature. The aforementioned bulk behavior of an alkali atom in polar fluids lead us an expectation that the valence electron of alkali metal atom is moved onto a solvent cluster and the ground state has an ion-pair character with increasing cluster size n. The photoionization threshold as a function of n provides us size-dependent information on the above change, and also on the excess electron state in clusters. From this point of view, the ionization potentials (IPs) of M(NH3)n and M(H2O)n (M = Li,11 Na,12–14 and Cs15) have been investigated as a function of n by the photoionization threshold measurements. The IPs of M(H2O)n are found to converge rapidly to the estimated photoelectric threshold of ice at n = 4 (3.2 eV).7 On the other hand, the IPs of Li(NH3)n (5 ≤ n ≤ 28) decrease almost linearly with n–1/3 and give the limiting value at n–1/ 3 = 0 (n → ∞) as 1.47 eV. This value agrees with the limiting values for Cs(NH3)n and Na(NH3)n and also with the photoelectric threshold of liquid ammonia (1.45 eV).7 These features in IPs have been discussed in relation to the formation of the ion-pair state, which is a counterpart of the solvated-electron state in bulk solution.13,15 Several theoretical groups have also made efforts to correlate the IP behaviors with the solvation state of alkali atoms.16–19 In order to explore the electronic structure of the neutral clusters, the photoabsorption experiments
Solvation of Sodium Atom and Aggregates in Ammonia Clusters
3
have also been conducted using two-color photoionization and photodepletion techniques.20,21 The photoelectron spectroscopy of negatively-charged clusters such as M–(NH3)n is also a powerful technique to probe the low-lying electronic states of neutral clusters.22 The anion clusters have been successfully produced by a laser vaporization method. The ions produced in the source are mass-separated in a Wiley–McLaren type TOF mass spectrometer. For the photoelectron kinetic energy measurement, negative ions with a given mass-to-charge ratio are selected with a pulsed mass gate, and are decelerated to several tens of eV with a pulsed potential switching method. The ions are irradiated with the fundamental, second harmonic, and third harmonic of a Nd:YAG laser. The kinetic energy of the detached electrons is analyzed by the magnetic-bottle type photoelectron spectrometer. Using these techniques, the photoelectron spectra (PESs) of Li–(NH3)n, Na–(NH3)n, and Li–(H2O)n, have been investigated.11,23–25 The electronic and geometrical structures of these clusters both in the neutral and anion forms have also been examined using the ab initio MO method.26,27 For Li–(H2O)n, the PESs have been found to change extensively due to the spontaneous ionization of Li in water clusters. Both the experimental and theoretical results on Li–(H2O)n suggest the formation of a two-center ion-pair state for n ≥ 5.25,26 The large spectral changes observed in the PESs of alkali atom–ammonia systems have also been ascribed to the delocalization of valence electron of alkali atom over and beyond the ammonia molecules with increasing n and the formation of an one-center ion-pair state.11,23,27 The PESs and ab initio calculations for the ammoniated Na2 and Na3 anions have also been investigated to explore the solvation process of alkali metal aggregates in ammonia clusters. In the present chapter, we summarize the results on the photoelectron spectra of negatively-charged NH3 clusters containing Nam (m ≤ 3) and on the calculation of the geometries, binding energies, and vertical electronic energies of these clusters using the ab initio MO method.28,29 On the basis of these results, we discuss the stepwise solvation of alkali–metal aggregates in ammonia clusters. II. ALKALI METAL ATOM–AMMONIA CLUSTERS A. Experimental study Photodetachment transition to the neutral ground state Fig. 1 shows the photoelectron spectra (PESs) of Na–(NH3)n (n ≤ 7) recorded with the YAG fundamental at 1064 nm (1.17 eV). The
4
Kiyokazu Fuke, Kenro Hashimoto and Ryozo Takasu
Figure 1: Photoelectron spectra of Na–(NH3)n (n ≤ 7) recorded at a detachment energy of 1.17 eV (1064 nm). The FWHM of the 2S(Na)–1S(Na–) transition at 0.55 eV is ca. 80 meV. This figure is cited from ref. 29.
Solvation of Sodium Atom and Aggregates in Ammonia Clusters 2
5
S–1S transition of free Na anion to the neutral ground state is observed at 0.55 eV with the bandwidth of about 80 meV as shown in Fig. 1a. The PES of Na–(NH3) exhibits three peaks at 0.43, 0.52, and 0.67 eV in the energy region corresponding to the transition to the neutral ground state. The spectrum clearly shows the coexistence of isomers. Ab initio calculations at the MP2 level with extended basis sets predict two geometrical isomers for Na–(NH3). In these isomers, ammonia molecule has been found to bind with Na– anion through N (type A1a) and H atom (type A1b), respectively, as shown in Fig. 2. The structure similar to the type-A1b isomer has been well known for the other hydrated anions such as Na–(H2O)n,24 Cu–(H2O)n,22 and X–(H2O)n (X = Cl, Br, and I).30–32 Unexpectedly, this isomer is less stable than the type-A1a isomer (Na–N bond) which has been known to be the stable structure in the neutral form. The vertical detachment energies (VDEs) to the neutral ground state have been calculated to be 0.36 and 0.67 eV for isomers A1a and A1b, respectively (see Table 1). With the aid of these theoretical results, the peaks at 0.43 eV and 0.67 eV have been assigned to the 32S-type transitions of more stable and less stable isomers, respectively. These bands are shifted by –0.12 and + 0.12 eV with respect to that of Na–. The blue shift of the transition for isomer A1b is due to a large geometrical change in the photodetachment process because the neutral complex has a potential minimum only at the type-A1a configuration. Although the amount of the observed shift of isomer A1a is not so large as that expected theoretically, the observed red shift clearly indicates that the binding energy in the neutral form is larger than that in the anion state. The spectrum in Fig. 1b also exhibits another band at 0.52 eV. This band has been tentatively assigned to the transition to the lower vibrational level of isomer A1a since only two isomers are theoretically expected for the 1:1 complex. Figs. 1c–g show the PESs of the 32S-type transition for larger clusters recorded with the 1.17 eV detachment energy. The spectrum of n = 2 has not been recorded due to its low abundance in the cluster beam. The spectrum of Na–(NH3)3 consists of a shoulder (0.41 eV) and a peak (0.51 eV) and is very similar to that of A1a. The calculations have predicted six stable structures for Na–(NH3)3. Among them, a C3h structure in which three NH3 molecules are bound directly to the Na atom by the N atoms has been found to be the most stable. Total binding energy (TBE) and the lowest VDE to the neutral ground state have been calculated to be –21 kcal/mol and 0.37 eV, respectively. Other isomers with fewer Na–N bonds are less stable by more than 5 kcal/mol. For larger clusters, the spectral features and the VDEs of the first bands are almost the same as that
6 Kiyokazu Fuke, Kenro Hashimoto and Ryozo Takasu
Figure 2: Selected sets of optimized geometries of Na– (NH3)n (n = 1–4) at MP2 level with extended basis sets. Geometrical parameters are given in Å and degrees. Molecular symmetry and total binding enthalpies (kcal/mol) at 0 K (ΔH0) with CPC are given under each structure. Values in curved brackets are without CPC. Total binding energies without CPC are also presented in square brackets.
Table 1. n=0
Na anion
Exp.
State
0.55
2
Calc.b)
3 S
0.53
n=1
A1a
Exp.
State
0.43
2
A1b Calc.
1 A1
3 2P
1 2E
2.59
n=2 Calc.
0.36
0.67 2.65
State
1.84
1 2A1
0.67
1 2E
2.65
State
0.4
2
n=3
A3a
n=4
Exp.
State
0.41
2
1 A'
0.37
1 2E'
1.08
1.38
1 2A"
Calc.
1.08
1.94
A4a
Exp.
State
Calc.
0.42
2
1 A1
0.39
1 2B1
0.95
1 2B2
0.95
2 2A1
1.02
1.26
a) Molecular structures are shown in Fig. 2. b) Only 1s orbital of Na was frozen in CI.
2 2A1
2.70
1 A
A2b
A2c
Calc.
State
Calc.
0.35
2
0.26
1 A'
0.6 2 2A
2.4 2 2A1
A2a
Exp.
1.65
State
Calc.
1 2A
0.79
1.36
2 2A'
1.71
2 2A
2.79
2
1 B
1.39
2
1 A"
1.72
1 2B
2.77
2 2B
1.46
3 2A'
2.02
2 2B
2.85
Solvation of Sodium Atom and Aggregates in Ammonia Clusters 7
Vertical detachment energies (eV) corresponding to transitions from anionic ground state to ground and low-lying excited states of various isomers of Na–(NH3)n (n = 0–4)a) at MRSDCI level.
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Kiyokazu Fuke, Kenro Hashimoto and Ryozo Takasu
of n = 3; 0.42, 0.41, 0.40, and 0.40 eV for n = 4–7, respectively. These results seem to be consistent with the theoretical predictions that the most stable isomers with maximum numbers of M–N bonds and the lowest VDEs for the 2S-type transition are predominantly observed in the PESs for n ≥ 2. Although the theoretical calculations are not available for n ≥ 5, these bands are tentatively assigned to the 2 S-type transitions of the isomers with maximum numbers of M–N bonds. The spectra also show the second peaks (or shoulders) at around 0.5 eV and their energy separation from the first band is found to be 800 ± 100 cm–1, which is close to that of the 1:1 complex. From the similarity in energy separation, the 0.5 eV bands are tentatively assigned to the vibronic transition as in the case of n = 1, though the assignment to the 2S-type transition of the other isomer cannot be ruled out. Photodetachment transitions to the low-lying excited states Fig. 3 shows the PESs of Na–(NH3)n (n ≤ 8) recorded at the photodetachment energy of 3.50 eV. The photoelectron spectrum of Na– exhibits a weak transition at 2.65 eV corresponding to the transition to the first excited (32P) state as well as that to the ground state at 0.55 eV (Fig. 3a). The spectral bandwidth for the transition to the neutral ground state becomes significantly broader as seen in Fig. 3, because of the loss of the spectral resolution as a result of an increase in electron kinetic energy. A very weak band at around 2.4 eV in the spectrum of the 1:1 complex shown in Fig. 3b has been assigned to the 32P-type transition, which splits into two bands due to the coexistence of the aforementioned isomers such as type-A1a and A1b. For n = 2, the VDE to the 32P-type state peaks at about 1.7 eV (Fig. 3c), being shifted further to the lower electron binding energy (EBE). This transition is shifted further to the lower EBE for n ≤ 4; the amount of shift is more than 1.4 eV at n = 5 with respect to that of Na– (2.65 eV). The large decrease in the 32P–32S energy separation suggests the drastic change in the electronic structure of Na in clusters. It is interesting to notice that the successive changes in VDEs of the 32P-type state are more than 0.2 eV for Na–(NH3)n (n ≤ 4), while those are negligibly small for n = 5–8. The rapid change in the rate of shift for this transition between n = 4 and 5 may indicate the filling of the first solvation shell about Na–. The PESs of Li–(NH3)n have also been investigated and found to exhibit the similar spectral changes.23 In order to interpret these spectral features, the electron distribution in Na–(NH3)n (n ≤ 4) has been analyzed by ab initio methods as mentioned later. For n ≥ 4, the SOMO electron densities of Na(NH3)n have been calculated to
Solvation of Sodium Atom and Aggregates in Ammonia Clusters
9
Figure 3: Photoelectron spectra of Na–(NH3)n (n ≤ 8) recorded at a detachment energy of 3.50 eV (355 nm). This figure is cited from ref. 12.
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Kiyokazu Fuke, Kenro Hashimoto and Ryozo Takasu
extend in space on and between the ammonia molecules because of the strong metal atom–N interaction.19 The observed redshift of the 2 S-type bands, as well as the rapid decrease in the 2P–2S energy separation seen in Fig. 3, are consistent with the theoretical results; the Na atom is spontaneously ionized and forms the one-center ion-pair state in the neutral clusters. B. Theoretical study Theoretical investigation of solvation of atomic alkali cations has been pioneered by Klein’s group by molecular dynamic simulation.33–38 Though the calculations of ammoniated alkali atoms and cations have been limited to the 1:1 complex,39,40 the interesting findings of the size dependence of ionization potentials for neutral M(NH3)n type clusters have motivated new theoretical challenges to explore relationship between the structure and the electronic state for larger clusters.41,42 The excited state of the isoelectronic system such as ammoniated alkali-earth mono cations has been studied by the quantum chemical methods.43 On the other hand, the photoelectron spectra of negatively charged alkali metal atoms embedded in water and ammonia clusters by Fuke’s group have been also a target to ab initio molecular orbital calculation.27,44–46 In this section, the works on Na–(NH3)n (n = 0–4) are summarized. Geometry and energetics Selected sets of the lowest-energy structures of Na–(NH3)n (n = 1–4) are shown in Fig. 2. Total binding enthalpies at 0 K (ΔH0(n)) defined by the following formula are also given for each optimized structure.
ΔH0(n) = H0 (Na–(NH3)n) – H0(Na–) – n×H0(NH3)
(1)
Two stable structures have been found for n = 1. An NH3 molecule is bound to Na– from N side in A1a and from H side in A1b. They are almost isoenergetic and their ΔH0(1) are –2.5(–4.3) and –3.0(–2.9) kcal/mol with (without) counterpoise correction (CPC). Three minimum structures have been found for n = 2. A2a has two equivalent Na–N bonds and A2b has an Na–N bond and a hydrogen bond. On the other hand, both two NH3 molecules are bound to Na– via Na–H interaction in A2c. The ΔH0(2) with CPC for A2a is –8.2 kcal/ mol and is lower than those of A2b and A2c by a few kcal/mol. A3a in which all NH3 molecules are bound to Na– by N atoms is the most stable for n = 3. The isomers with fewer Na–N bonds and with
Solvation of Sodium Atom and Aggregates in Ammonia Clusters
11
hydrogen- or ionic Na–H bond(s) are less stable than A3a by more than 4 kcal/mol. Since the structures with the maximum numbers of Na–N bonds are the most stable for n = 2 and 3, and the energy difference between the most stable complex and the local minimum structures tends to increase as n grows, only the structure with four Na–N bonds has been optimized for n = 4. The ΔH0(4) value for A4a is about –25 kcal/mol with CPC. This structure is similar to the neutral and cationic Na(NH3)4 in such a sense that Na is ligated almost tetrahedrally by NH3 molecules. Electron density distribution in Na–(NH3)n (n = 1–4) The electronic nature of Na–(NH3)n with Na–N bonds is interesting since we usually expect the repulsive interaction between the negative charge on Na and lone-pair electrons of NH3 molecules in these clusters. Fig. 4a shows the radial distribution functions, ρ(r)’s, for the structures with n Na–N bonds together with those for bare Na atom and anion. They are evaluated by having Na at the origin. The r values giving the maximum ρ(r) for each Na–(NH3)n are 4.60 (A1a), 7.53 (A2a), 8.77 (A3a) and 9.68 (A4a), Bohr indicating that the diffusion of the valence electrons proceeds with stepwise ammoniation. It should be worth emphasizing that the r with the maximum ρ(r), which we call the rρmax hereafter, is greater than the average Na–H distance for each n ≥ 2 (5.58–5.63 Bohr). Further analysis of ρ(r) shows that the valence electrons of Na– are polarized by the presence of NH3 and more than half of them are distributed in space opposite to the solvent in A1a.46 The number of electrons, N(r), distributed inside the sphere whose radius is r, is given in Fig. 4b. At r = 4.5 Bohr, which is slightly shorter than the Na–N distance in A1a, the N(r) values are 0.56(Na–), 0.36 (A1a), 0.18 (A2a), 0.06 (A3a), and 0.02 (A4a). On the other hand, at r = 6.0 Bohr, being a little longer than the Na–H distances in A4a, they become 1.2 (Na–), 0.82 (A1a), 0.52 (A2a), 0.27 (A3a), and 0.17 (A4a). These numbers indicate that the most valence electrons are distributed outside the solvation shell rather than in space between Na and NH3 ligands for n ≥ 2. If we examine the electron density distribution on the spherical surface whose radius is rρmax, the density range is 0.00074–0.00032 (A2a), 0.00052–0.00042 (A3a), and 0.00040–0.00032 (A4a) Bohr–1/3. Thus, the excess electrons are not very localized around hydrogen atoms in NH3 molecules but spread widely in space outside the solvent ammonia molecules. In Na–(NH3)n with n ≥ 2, the diffuse and delocalized excess electrons are surrounding Na+(NH3)n core where NH3 ligands point their lone pairs to Na+.
12
Kiyokazu Fuke, Kenro Hashimoto and Ryozo Takasu
Figure 4: (a) Radial distribution functions of valence electrons, ρ(r) of Na–(NH3)n (n = 1–4) together with those of bare Na atom and anion. Na is at the origin. (b) Number of valence electrons, N(r), in the sphere whose radius is r.
Solvation of Sodium Atom and Aggregates in Ammonia Clusters
13
Vertical detachment energies and assignment of PES bands The calculated and experimental VDEs of Na–(NH3)n (n = 0–4) are listed in Table 1. For A1a, the VDEs of the 32S- and 32P-type transitions are calculated to be 0.36 and ~1.9 eV, respectively. The corresponding values for A1b are 0.67 eV and ~2.7 eV. These theoretical results are consistent with the observed PES of n = 1 exhibiting the coexistence of isomers in the cluster beam as mentioned previously. The band at 2.11 eV is considered to stem from the 32P-type transitions of A1a observed at the VDE of 2.65 eV for n = 0. The calculated VDEs for A2a are 0.35 (32S-type) and ~1.4 (32P-type) eV. For A2b, the calculated VDE of the 32S-type transition is less than the lowest VDE of A2a by ~0.1 eV and those of the 32P-type transitions are 1.7–2.0 eV. On the other hand, the VDEs of both 32S- and 32P-type transitions of A2c are shifted to the blue from the bare Na– by ~0.2 eV. The calculation also suggests that the observed weak bands at ~1.7 eV are derived from A2a because the VDEs of the 32P-type transitions are lowered by ~1.0 eV from n = 0 only in this isomer. The VDE of the 32S-type transition for A3a is very close to the lowest VDE of A2a and those of the 32P-type transitions are shifted to the red by ~0.3 eV from A2a. For isomers with one or two Na–N bonds and with hydrogen bond(s) among NH3 molecules, the VDE to the neutral ground state decreases and those to the excited states increase compared to A3a. The VDEs of the other n = 3 isomers where all NH3 molecules are bound to Na from H side are shifted to the higher EBE from the corresponding values of Na– for all transitions examined. On the other hand, the VDEs to the 32S-type state of A4a is calculated to be close to that of A3a, while the VDEs to the 2P like states are 0.95–1.02 eV being again lowered from the corresponding values of A3a. Greer et al. have studied the potential energy curves of Na(NH3)n (n = 1 and 2) along Na–N distance and N–Na–N bond angle for the ground and several low-lying excited states at CASSCF level.47 The differences in the VDEs between the 2S–1S and 2P–1S type transitions should be approximately close to their transition energies to the 2Plike states. The values by Greer et al. are 1.50 (12E) and 1.83(22A1) eV for n = 1 and 1.05 (12B1), 1.09 (22A1) and 1.16(12B2) eV for the n = 2 complex with C2v symmetry. The corresponding transition energies estimated by using the VDEs in Table 1 are 1.48 (2E) and 1.58(22A1) eV for n = 1 and 1.04 (12B), 1.01 (22A) and 1.11(22B) eV for n = 2. The agreement between the two theoretical results is reasonable.
14
Kiyokazu Fuke, Kenro Hashimoto and Ryozo Takasu
Electronic state of neutral Na(NH3)n There are two important features in the PES bands, which can be attributed to the structures having as many Na–N bonds as possible for each n. One is that the position of the first band is slightly shifted to the lower EBE from n = 0 to n = 1 and becomes relatively constant against n ≥ 2. This feature has been ascribed to the fact that total binding energies of the neutral clusters at their anionic geometries are by 0.12 (n = 1)–0.08 (n = 3) eV larger than the corresponding values of the anions for each n. Another characteristic size dependence of the PES bands, the rapid red shift of the second band with increasing n, has been analyzed in terms of the valence electron distribution. The expectation values of the radial distribution (RD) for the unpaired electron of Na(NH3)n (n = 0–4) at their anionic geometries are listed in Table 2. These values are calculated by having Na at the origin. The RD values of 32S-like state for A1a–A4a become larger as n grows, and are over the average Na–H distance in each cluster for n ≥ 2. The RD values for the excited states of the four structures also increase by stepwise additions of NH3 molecules. As a result, the RDs for 32S- and 32P-type states in A4a are about 2.0 and 1.7 times greater than the corresponding atomic values, respectively. The unpaired electron is diffused by the ammoniation not only in the ground state but also in the excited states. In other words, the electronic nature of these neutral clusters with maximum numbers of Na–N bonds changes from atomic state to the one-center Rydberg-like ion-pair state with increasing n, which is considered to be responsible for the rapid decrease of the VDEs of the transitions to the low-lying excited states. III. SODIUM DIMER–AMMONIA CLUSTERS A. Experimental study Photodetachment transition to the neutral ground state Fig. 5 shows the PESs of Na2–(NH3)n (n ≤ 3) recorded at the detachment energy of 1.17 eV (1064 nm). For bare Na2–, the transition to the neutral ground state (11Σg+) is observed at 0.55 eV. This value is very close to that reported by Bowen and co-workers.48 With addition of an ammonia molecule, the spectrum is significantly affected and exhibits two peaks at 0.31 and 0.71 eV as shown in Fig. 5b. These bands are shifted by –0.24 and 0.16 eV, respectively, with respect to those of Na2–. Three structures calculated by the ab initio method have been reported for Na2–(NH3) (see Fig. 6). The most stable
Expectation values of radial distribution of unpaired electron (RD, Bohr) for neutral ground and low-lying excited states of Na(NH3)n (n = 0–4) at their anioic geometries.a)
n=0
n=1
Na atom 2
3 S 3 2P
n=2
A1a
4.486
2
1 A1
6.459
1 2E 2 2 A1
A1b
5.213
2
1 A1
7.263
1 2E
8.613
2 2A1
A2a
4.544
2
1 A
6.375
2 2A
6.364
1 2B 2
2 B a) Geometries are given Fig. 2.
n=3
A2b
6.311
2
1 A'
9.296
2 2A'
8.379
1 2A"
9.483
2
3 A'
A2c
n=4
A3a
5.229
1 A
4.536
1 A'
8.095
1 A1
9.353
7.441
2 2A
6.303
1 2E'
10.399
1 2B1
10.944
9.134
1 2B
6.304
1 2B2
10.944
7.341
2
2 2A1
10.764
2 B
6.296
2
A4a
2
2
2 A"
9.544
2
Solvation of Sodium Atom and Aggregates in Ammonia Clusters 15
Table 2.
16
Kiyokazu Fuke, Kenro Hashimoto and Ryozo Takasu
Figure 5:
Photoelectron spectra of Na2–(NH3)n (n ≤ 3) at a detachment energy of 1.17 eV (1064 nm).
complex D1a has a C3v structure, where NH3 molecule is bound to Na2– colinearly via N atom. On the other hand, the isomers with triangular (D1b, Cs) and linear (D1c, C3v) configurations are less stable than D1a by ~2 kcal/mol. As in the case of Na–(NH3), the
Solvation of Sodium Atom and Aggregates in Ammonia Clusters
17
–
Figure 6: Selected sets of optimized geometries of Na2 (NH3)n (n = 0–3) at CASSCF(3E/10+3n MO)/6-31++G(d,p) level. Geometrical parameters are given in Å and degrees. Total binding energies (kcal/mol) without CPC and zero point vibrational correction are also given in square brackets.
VDE of the 11Σg+-type transition (0.21 eV) for the isomer with Na–N bond is calculated to be much smaller than those for the isomers with Na–H bonds (0.62(D1b) and 0.61(D1c) eV). Thus, the 0.31 eV band can be ascribed to the transition of D1a. The red shift of this transition with respect to that of Na2– clearly indicates that the binding energy in the neutral ground state is larger than that in the anion as in the case of Na(NH3). The calculated VDEs of D1b and
18
Kiyokazu Fuke, Kenro Hashimoto and Ryozo Takasu
D1c suggest that the 0.71 eV band in Fig. 5b is ascribed to the isomers with Na–H interaction. However, it is difficult to specify which isomer is responsible for this band since their binding energies and VDEs are almost the same. The PES of Na2–(NH3)2 displays two bands at 0.37 and 0.55 eV with an energy separation of about 1450 cm–1 as shown in Fig. 5c. Since the first excited state of the clusters containing Na2– is located at ca. 1 eV above the ground state as mentioned later, the 0.55 eV bands may correspond to either the vibronic band of neutral form or that for the different geometrical isomer. Although the free ammonia molecule has a degenerate bending vibration with the frequency rather close to the observed energy separation, this vibrational mode seems to be inactive in the PESs of Na(NH3)n and Na2–(NH3). Thus, the 0.37 and 0.55 eV bands are considered to be the transitions of the different isomers. Ab initio calculations predict that the most stable form for n = 2 has a structure where both NH3 molecules are bound to one of the Na atoms via Na–N bonds as shown in D2a (see Fig. 6). The calculated VDE to the neutral ground state of this isomer (0.25 eV) is close to the observed VDE, which strongly supports the assignment of the 0.37 eV band to the transition of the most stable isomer D2a. The isomers with Na–H bonds have been calculated to be less stable than D2a by more than 8 kcal/mol. In addition, their VDEs to the neutral ground state are shifted to the blue with respect to that of Na2– as in the case of Na2–(NH3). Therefore, these structures should be ruled out as the candidate for the observed bands. The calculations also show that the structures with Na–N bond(s) (D2b–D2d in Fig. 6) are higher in energy than D1a by ~5 to ~7 kcal/mol but have close TBEs to one another. In these complexes, the second NH3 is bound to the different sites in D1a. The calculated VDEs of D2b and D2c are too small to explain the observed spectral trend. On the other hand, the D2d seems to be the most probable candidate for the second transition by taking into account the calculated VDE (0.27 eV) being close to the observed one. Since the isomer D2d has been calculated to be slightly unstable compared with D2b and D2c, further theoretical efforts are necessary to resolve the second band definitely. As it is expected from the computational results on Na2–(NH3)n, the number of local minimum structures increases rapidly as n grows. As a result, it becomes difficult to examine all possible structures and their VDEs. However, the experimental and theoretical results on Na2–(NH3)n (n = 1 and 2) indicate that the isomers with maximum numbers of Na–N bonds at one Na site in Na2– become increasingly stable and dominate the spectrum, which provides us a guide to analyze the larger clusters. In fact, ab initio
Solvation of Sodium Atom and Aggregates in Ammonia Clusters
19
CASSCF calculations show that the C3 structures D3a and D3b in which all NH3 molecules are bound to one of the Na atoms from N side are more stable than the other isomers such as D3c and D3d (see Fig. 6). Based on these theoretical results, the PES band at 0.45 eV in the spectrum of Na2–(NH3)3 shown in Fig. 5 is assigned to the transition to the neutral ground state of the isomer D3a. The spectrum of n = 3 also displays a peak as 0.54 eV. However, it is difficult to assign this peak definitively without the calculated VDEs for the other isomers. Photodetachment transition to the low-lying excited states Fig. 7 shows the PESs of Na2–(NH3)n (n ≤ 8), which are recorded at the photodetachment energy of 3.50 eV. As for Na2–, the PES shows the bands at 1.38 and 2.32 eV corresponding to the transitions to the low-lying excited states of the neutral form in addition to that for the ground state at 0.55 eV as discussed in the previous section. Bowen and co-workers48 have also reported the similar spectrum to that in Fig. 7a. Bonacic-Koutecky and co-workers have theoretically analyzed the spectrum reported by Bowen’s group.50, 51 They have assigned the 1.38 and 2.32 eV bands to the transitions from the anion state (1– 2Σ u) to the first excited (13Σu+) state correlating to the Na(32S) + Na(32S) asymptote and to the 13Πu and 11Σu+ states correlating to the Na(32S) + Na(32P), respectively; the transitions to the latter states are accidentally degenerate at the anion geometry. We have also carried out the ab initio CI calculations and confirmed these assignments as shown in the later section.28 For the transitions to the excited states of Na2NH3, four bands are observed at 1.36, 1.86, 2.11, and 2.40 eV as shown in Fig. 7b. Based on the arguments in the previous section, these bands are ascribed mainly to the transitions for the isomer with Na–N bond. The 13Σu+–1– 2Σu-type transition is not affected by complexation and is observed at 1.36 eV. The calculations have predicted the VDEs of this transition to be 1.19 eV for the isomer with Na–N interaction and reproduced the experimental VDE fairly well.29 The spectral feature of the complex in the energy region above 1.5 eV is substantially different from that of Na–; the spectrum displays the shoulder at 1.86 eV and two peaks at 2.11 and 2.40 eV as seen in Fig. 7b. The former two bands may be assigned to the 13Πu - and 11Σu+-type states from the comparison with the calculated VDEs such as 1.58 and 1.90 eV, respectively.29 The accidental degeneracy of these bands in Na2– is removed in D1a because of the larger stabilization of the 2πu orbitals of Na2 than 4σu by mixing with the σ* orbitals of N–H bond owing to the smaller separation in orbital
20
Kiyokazu Fuke, Kenro Hashimoto and Ryozo Takasu
Figure 7: Photoelectron spectra of Na2–(NH3)n (n ≤ 8) recorded at a detachment energy of 3.50 eV (355 nm). The intensities of each spectrum are normalized at the bands corresponding to the 13Σu+–1– 2Σutransition of Na2–. This figure is cited from ref. 29.
Solvation of Sodium Atom and Aggregates in Ammonia Clusters
21
energy. In addition, the 4σu orbital may be destabilized by the mixing of the lone pair orbital of NH3. The spectrum also displays the relatively strong band at 2.40 eV, which probably corresponds to the transition to the higher excited state correlating to the 32S + 32P asymptote. This band has been tentatively assigned to the transition to the 13Σg+-type state by taking into account the calculated VDE of 2.16 eV as shown in Table 3. For Na2–(NH3)2, three bands are observed at 1.39, 1.90, and 2.17 eV as shown in Fig. 7c, which correspond to the transitions to the low-lying excited states. These bands are mainly ascribed to the isomer D2a rather than D2d by taking into account the strong intensity of the 0.36 eV band in Fig. 7c as mentioned previously. The spectrum clearly shows that the transitions to the states correlating to the 32S + 32P asymptote are strongly affected with the addition of the second ammonia molecule; the 2.11 and 2.40 eV bands in the PES of n = 1 are shifted to the lower EBE by 0.21 and 0.23 eV, respectively. On the other hand, the 13Σu+-type transition correlating to the 32S + 32S asymptote is not shifted appreciably. The 1.39 eV band is assigned to the transition to the 13A1 state in D2a (C2v symmetry) derived from the 13Σu+–1– 2Σu transition of Na2–, while two bands at 1.90 and 2.17 eV are ascribed to the transitions to the 21A1 and 23A1 states derived from the 11Σu+- and 13Σg+-type states of dimer anion, respectively. As in the case of the photodetachment transition of Na2–(NH3)3 to the neutral ground state mentioned previously, the most stable isomer D3a may be responsible for the observed PES of the excited states shown in Fig. 7d. The VDE to the first excited state is almost unchanged from n = 2, while the higher-energy transitions to the states correlating to the Na (32P) + Na (32S) asymptote keep redshifting. Since the spectral features in Fig. 7d are very similar to those of n = 2, the observed bands at 0.51, 1.39, 1.71, and 2.07 eV are tentatively assigned to the 11Σg+-, 13Σu+-, 11Σu+, and 13Σ+g-type transitions of the most stable isomer. The extensive red-shifting of the 11Σu+- and 13Σ+g-type transitions correlating to the Na(2S) + Na(2P) asymptote is coincident with the rapid decrease in the observed VDE to the Na(2P)-type state (n ≤ 4) for Na(NH3)n (see Fig. 1). In the latter clusters, this change has been attributed to the delocalization of unpaired electrons as well as the large destabilization of the 3s orbital by the strong Na–N interaction. For Na2– (NH3)n (n ≤ 3), both experimental and theoretical results indicate that ammonia molecules bind preferentially to one of the Na atoms by N atoms. And also, the VDE to the neutral ground state, exhibiting the redshift from that of bare Na2–, indicates the larger solvation energy of the neutral form than that of anion. All these results suggest that
Exp.
State
Exp.
0.55(0.00)
1 Σg
+
0.53(0.00)
1.38(0.83)
1 3Σu+
1.22(0.69)
1 3 Πu
2.11(1.58)
2.32(1.77)
1
1 1Σu+ 1 Σg 3
2.13(1.60)
+
2.55(2.02)
1 1 Πu
2.95(2.42)
2 1Σg+
Calc.
State
State
State
Calc. b)
1
0.37(0.00)
1 A1
0.21(0.00)
1 A’
0.62(0.00)
1 A1
0.61(0.00)
1.36(0.99)
1 3A1
1.19(0.98)
1 3A’
1.33(0.71)
1 3A1
1.31(0.70)
1.86(1.49)
1 3E
1.58(1.37)
1 3A”
2.19(1.57)
1 3E
2.20(1.59)
2 3A’
2.20(1.58)
2.11(1.74)
2 1A1
1.90(1.69)
2 1A’
2.24(1.62)
2 1A1
2.21(1.60)
2.40(2.03)
3
2 A1
2.16(1.95)
3
3 A’
2.67(2.05)
2 3A1
2.65(2.04)
1 1E
2.38(2.17)
1 1A”
3.04(2.42)
1 1E
3.06(2.45)
4 1A’
3.06(2.44)
3 1A’
3.00(2.38)
3 1A1
2.96 (2.35)
3 1A1
Calc.
2.52(2.31)
D2c a) b)
Calc.
State
D3a a)
n=3 Exp.
State
Calc. b)
0.27(0.00)
0.45(0.00)
1 1A
0.27 (0.00)
1.25(0.98)
1.39(0.94)
1 3A
1.24 (0.97)
1 3E
1.34 (1.07)
1.71(1.26)
2 1A
1.59 (1.32)
2.07(1.62)
2 3A
1.68 (1.41)
1 1E
1.86 (1.59)
Calc.
b)
State
0.37(0.00)
1 1A1
0.25(0.00)
1 1A1g
0.03(0.00)
1 1A’
0.08(0.00)
1 1A’
1.39(1.02)
1 3A1
1.24(0.99)
1 3A2u
1.17(1.14)
1 3A’
1.11(1.03)
1 3A’
1 3B2
1.46(1.21)
1 3Eu
1.14(1.11)
1 3A”
1.44(1.36)
1 3A”
1.64(1.37)
1 3B1
1.51(1.26)
2 3A’
1.44(1.36)
2 3A’
1.64(1.37)
1.90(1.53)
2 1A1
1.77(1.52)
1 1A2u
1.53(1.50)
2 1A’
1.84(1.76)
2 1A’
1.98(1.71)
2.17(1.80)
2 3A1
1.88(1.63)
1 3A1g
1.63(1.60)
3 3A’
2.09(2.01)
3 3A’
2.26(1.99)
1 1B2
2.11(1.86)
1 1Eu
1.86(1.83)
3 1A”
2.23(2.15)
1 1A”
2.45(2.18)
1 1B1
2.13(1.88)
3 1A’
2.23(2.15)
3 1A’
2.46(2.19)
3 1A1
2.31(2.06)
4 1A’
2.42(2.34)
4 1A’
2.62(2.35)
1.93(1.90)
State
D2d a) b)
Exp.
2 1A1g
D1c a) Calc. b)
1
D2b a) b)
D1b a) Calc. b)
State
2.87(2.34)
D2a a)
n=2
D1a a)
n=1 Calc. b)
a) Molecular structures are shown in Fig. 6. b)Values in parentheses are energy difference from neutral ground state.
Kiyokazu Fuke, Kenro Hashimoto and Ryozo Takasu
D0a a)
n=0
22
Table 3. Vertical detachment energies (eV) corresponding to transitions from anionic ground state to ground and low-lying excited states of various isomers of Na2¯ (NH3)n (n = 0 - 3) at MRSDCI level.
Solvation of Sodium Atom and Aggregates in Ammonia Clusters
23
the similar delocalization of the 3s valence electron on the ammoniated Na atom in Na2 occurs as in the case of Na(NH3)n, and as a result, the Na–N bond becomes to some extent ionic. For larger clusters, the VDEs to the higher excited states decrease further, while that to the 13Σu+-type state starts increasing for n ≥ 4 as shown in Fig. 7. Although it is not shown, the PESs recorded with the photodetachment energy of 2.33 eV (532 nm) also show the similar spectral trends including the appearance of new transitions.29 Since the detailed theoretical calculations on Na2–(NH3)n for n ≥ 4 are not available at present, it is difficult to interpret the observed spectral change definitively. However, the large spectral change such as the appearance of the new band as well as the switching of the direction of spectral shift for the 13Σu+-type transition may suggest the coexistence of a new isomer, in which the extra ammonia molecules are bound directly to Na atom even for Na2–(NH3)n for n ≥ 4. If we consider the fact that the first solvation shell of Na(NH3)n is filled with 4 or 5 NH3 molecules as mentioned previously, the bonding of the ligated Na atom in Na2–(NH3)n, is expected to be saturated with three NH3 molecules and then further ammonia molecules may form the second shell or may be directly bound to the second Na atom. The observed rapid redshifting of the 11Σu+- and 13Σ+g-type transitions as well as the sudden commencement of the blue shift for the 13Σu+-type transition at n = 4 may be partially ascribed to this stepwise solvation around Na2 core. Interestingly, we have recently found a new structure for n = 4, where Na– is bound to A4a with N–H bond.49 This isomer is very important when considering a dissolution of Na dimer anion in ammonia clusters as in the case of Na trimer mentioned later. To correlate the structure and the VDEs for n ≥ 4, further theoretical studies are needed. B. Theoretical study Geometry and energetics Fig. 6 shows the selected sets of the low-energy structures for Na2–(NH3)n (n = 0–3) calculated at ab initio CASSCF level together with their TBEs. A C3v structure (D1a) in which an NH3 molecule is bound to one of Na atoms with an Na–N bond is the most stable for n = 1. Its calculated TBE is –4.4 kcal/mol without the correction of the basis set super position error. Two other isomers where an NH3 molecule interacts with Na2– from the H side are less stable than D1a by about 2 kcal/mol. A C2v structure D2a in which both NH3 molecules are bound to one Na atom from N sides is the most stable for
24
Kiyokazu Fuke, Kenro Hashimoto and Ryozo Takasu
n = 2, and its TBE is ca. –13 kcal/mol. The energy gain by forming the second Na–N bond from D1a is about 8 kcal/mol. TBE of the D3d isomer (D2b) where each Na atom is bound by an NH3 molecule from the N side is –7.9 kcal/mol. Other structures (D2c and D2d) with fewer Na–N bonds but with hydrogen- or ionic Na–H bond(s) are higher in energy than D2a by over 6 kcal/mol. For Na2–(NH3)3, D3a with C3 symmetry is the most stable; one Na atom is selectively solvated having three Na–N bonds in this complex. TBE for this structure is calculated to be ca. –21 kcal/mol and stabilization energy per NH3 molecule increases slightly compared to those of D1a and D2a. We have also found another C3 isomer (D3b) whose TBE is –19.4 kcal/mol. In this complex, one Na atom has three equivalent Na–N bonds similarly to D3a but the umbrella structure consisting of an Na and three N atoms in D3a is inverted. In addition, the Na–Na bond is much longer than that in D3a. Three structures where the third NH3 molecule is bound to D2a through hydrogen bond(s) are local minima and less stable than D3a by ~4 kcal/mol; the typical form is given in D3c. The isomer D3d in which one Na atom has two Na–N bonds and another Na has a single Na–N bond is less stable than D3a by 6 kcal/mol. Thus, the clusters in which one of the two Na atom is selectively solvated by having as many Na–N bonds as possible are the most stable for each n ≤ 3. Excess electron distribution in Na2–(NH3)n Fig. 8 represents the distribution of the excess electron in the most stable forms of Na2(NH3)n– (n = 0–3) as a function of z; the z-axis is taken on the line passing through two Na atoms and the origin is at the mid point of the Na–Na bond. 2 D(z) =òòφSOMO (x,y,z)dxdy
(2)
The “solvated” Na is located at z = 3.47(D0a), 3.24(D1a), 3.35(D2a) and 3.56(D3a) Bohr, while the largest z values for the hydrogens are 8.51, 7.53, and 7.11 Bohr for D1a–D3a. The excess electron distribution of the bare Na2– reflects the antibonding character of 4σu orbital. When an NH3 molecule is bound to one Na atom, about 25% of the excess electron moves from around the “solvated” Na to around the “free” Na and the electron distribution near the “free” Na extends in the space where the NaNH3 does not exist. With more than two NH3 molecules, the excess electron density around the “solvated” Na decreases further. However, it is not distributed either between two Na atoms or in the
Solvation of Sodium Atom and Aggregates in Ammonia Clusters Figure 8:
25
–
Density of unpaired electron as function of z for Na2 (NH3)n (n ≤ 3), D(z). See text.
vicinity of the “free” Na. The D(z) becomes maximal at the z value greater than those of the H atoms in the ligating NH3 molecules for each n ≥ 2. In other words, the most excess electron is in the space outside the solvents extended in the direction opposite to Na2. The electron is considered to be photodetatched from around solvents rather than Na2 for n ≥ 2; the ejection of the “solvated” electron takes place. Vertical detachment energies The calculated VDEs for Na2–(NH3)n (n = 0–3) together with the experimental values are listed in Table 3. For a bare Na2–, the calculations predict the VDEs for the transitions from the ground-state anion (1– 2Σu) to the neutral ground (1 1Σ+g) and the first excited (13Σu+) states to be 0.53 and 1.22 eV, respectively. The calculated VDEs for the transitions to the next lowest-excited states are 2.11 (13Πu) and 2.13(11Σu+) eV. These results are consistent with those by Bonacic-Koutecky and coworkers.50,51 Though the VDEs to the other higher states correlating to the 32S(Na) + 32P(Na) asymptote are calculated to be 2.55–2.95 eV, no band has been observed in this energy region. It is probably
26
Kiyokazu Fuke, Kenro Hashimoto and Ryozo Takasu
because of low electron collection efficiency at the energy range close to the detachment energy. For the 1:1 complex, the VDEs of the lowest-energy band derived from the 1 1Σ+g–1 –2Σu transition of Na2– are calculated to be 0.21 eV for D1a and ~0.6 eV for D1b and D1c, respectively. The VDE is shifted to the red from the bare Na2– in D1a and to the blue in D1b and D1c by an addition of NH3. Thus, the observed first band for Na2–(NH3) is considered to stem from the complex with a single Na–N bond based on the energy relation between isomers as well as the red shift from n = 0 to n = 1, though the calculated VDE underestimates the experiment. In addition, the observed energy difference between the two lowest bands (0.99 eV) is better reproduced by the D1a (0.98 eV) than the other two (~0.7 eV). These results support the previous assignments that the first two bands can be ascribed to the 11A1–2A1 and 13A1–2A1 transitions of the N-bonded cluster derived from the 11Σ+g–1– 2Σu and 13Σu+–1 – 2Σu transitions of the bare dimer. On the other hand, the shoulder at 1.86 eV and the peak at 2.11 eV can be assigned to the transitions to the 13E and 21A1 states in D1a though the calculated VDEs for these transitions deviate from the experimental values by 0.2–0.3 eV. The calculations also predict that the VDEs to the 23A1 and 11E states are below 2.50 eV. Since our calculations tend to underestimate the VDEs to the higher excited states correlating to the Na(32S) + Na(32P) asymptote, we have tentatively assigned the 2.40 eV band to the transition to the 23A1 state derived from Na2(13Σ+g). As for n = 2, the calculated VDEs to the neutral ground states of D2b and D2c decrease further from 1:1 complex. These trends are inconsistent with the experimental findings shown in Fig. 7 and suggest that these structures may not contribute to the PES bands. The VDEs of the same transition for the high-energy structures where all NH3 molecules are bound to Na2– from H sides are shifted to higher EBE by the addition of the second ligand. This change is also contradicted with the experimental observation and these structures should be also ruled out. On the other hand, the calculated VDEs to the two lowest states of D2d are close to those of the most stable D2a, while the VDEs to the higher states are large in D2d compared to D2a. Based on the redshifts from n = 1, the observed 1.90 and 2.17 eV bands are assigned to the 11Σu+–1– 2Σu and 13Σ+g–1– 2Σu type transitions of D2a. For the n = 3 cluster, the calculated VDEs of the most stable structures D3a for the transitions to the ground and the lowest excited states are almost unchanged from n = 2, while those of the transitions to the higher states keep decreasing. These theoretical results are consistent with the observed spectral change from n = 2 to n = 3,
Solvation of Sodium Atom and Aggregates in Ammonia Clusters
27
and thus, the PES band for Na2–(NH3)3 can be ascribed to the most stable structure that maximum number of NH3 are bound to a single Na atom by Na–N bonds. On the other hand, it becomes difficult to assign the higher bands definitely because the observed bands are broad and the separations in the calculated VDEs for the states correlating to the ground state Na and the 32P like state of Na(NH3)3 become small compared to the smaller clusters. Comparison between Na–(NH3)n and Na2–(NH3)n The potential energy curves along Na–Na distance for the ground and low-lying excited states of anionic and neutral Na2(NH3)n (n = 0 and 1) are shown in Fig. 9. For a bare Na2–, the curves for the ground 12Σu and the first excited 12Σg states correlating to Na(32S) + Na–(31S) asymptote are shown in Fig. 9a. For the neutral, 16 curves are given; two states correlate to Na(32S) + Na(32S), eight to Na(32S) + Na(32P), and four to Na(32S) + Na(42S). Near the equilibrium distance of Na2–, the curves of 11Σu+ and 13Πu+ states for the neutral Na2 cross each other, which is consistent with the assignment of the second PES band in the previous section. On the other hand, at R Na–Na = 30 Å, the energies of each potential curve converge to four values according to the dissociation limit. The energy difference between the anionic states and the lowest neutral states is close to the lowest VDE of Na–. And also, the energies of the states derived from the ground and excited Na atoms relative to the neutral ground state are close to the transition energies to the 32P and 42S states of the bare Na atom. Fig. 9b indicates that the ground state D1a dissociates to Na– and NaNH3; the VDE of Na– is larger than that of Na–NH3 by ca. 0.2 eV. At RNa–Na = 30 Å, the states correlating to Na (32S) and 32P-like state NaNH3 are located below the states dissociating to Na (32P) and ground state NaNH3 due to the energy lowering of the 32P-like state in NaNH3. This energetic change is seen not only at the dissociation limit but also at molecular region. As a result, the VDEs to the states of which dissociation limit is the ground state Na and the excitedstate NaNH3 decrease by ammoniation. The energy levels of the anionic and low-lying states of Na2(NH3)n (n = 0–3) at equilibrium structure of Na2–(NH3)n for each n are presented in Fig. 10a; the energy values are the VDEs of Na2–(NH3)n. The corresponding levels calculated by fixing Na–Na length at 30 Å and other geometrical parameters at those of D1a–D3a are given in Fig. 10b. The energy differences between the neutral levels and the 12Σu-like state (shown in bold) correspond approximately to the VDEs of Na–(NH3)n.
Potential curves along Na–Na distance for the ground and low-lying excited states of anionic and neutral Na2(NH3)n (n = 0 and 1).
28
Figure 9:
Kiyokazu Fuke, Kenro Hashimoto and Ryozo Takasu
Figure 10: Energy level diagram of low-lying states for anionic and neutral Na2(NH3)n (n = 0–3) at the equilibrium Na–Na lengths (a) and at the dissociation limit (b). Levels of the 2Σu like states for Na2–(NH3)n are not shown for brevity in (a).
Solvation of Sodium Atom and Aggregates in Ammonia Clusters 29
30
Kiyokazu Fuke, Kenro Hashimoto and Ryozo Takasu
Fig. 10 clearly indicates (i) the VDE to the ground 11Σg+-like state of the neutral decreases from n = 0 to n = 1 and increases very slightly for n = 2–3, (ii) the levels of 13Σu+-like states are almost constant irrespective of n, and (iii) all excited states having the Na(32S) + Na(NH3)n (32P) asymptote are lowered as n grows and their energy levels become close to that of 13A1 state at n = 3. The energy levels of 11Πu-like states at the equilibrium structures change against n in a similar manner to those of the state for Na(32S) + Na(NH3)n (32P) asymptote at RNa–Na = 30 Å. The other states having the same dissociation limit are located below 11Πu-like states, and their energies split depending on the strength of the interaction between Na and Na(NH3)n in each state at the molecular region. In the case of Na(NH3)n, the large decrease in VDEs for the transitions to 32P-like states has been ascribed to the spreading of the 3s electron over the space outside the ligand NH3 molecules giving rise to one-center ion-pair states. It is expected from the above results that the similar delocalization of the unpaired electron occurs in the lowlying excited states of Na2(NH3)n due to the “selective” solvation of one Na atom and thus the Na–N bonds are considered to become to some extent ionic. The slight red-shifting of the transition to the neutral ground state, indicating the larger solvation energy of the neutral form than that of anion, strongly supports this conclusion. IV. SODIUM TRIMER–AMMONIA CLUSTERS In the previous sections, we have discussed the ammoniated clusters containing solvation cores such as Na atom and its dimer. Both experimental and theoretical results show various kinds of isomers for these clusters. They originate from the difference in the solvation structures surrounding the metal atom or dimer. In contrast to these systems, the situation for the ammonia clusters containing a metal trimer seems to be different because there may exist isomers even for the core itself in the latter system. For alkali metal trimer, the electronic and geometrical structures have been extensively studied using theoretical methods.50–55 It has been known that the most stable neutral trimer has an isosceles triangle structure, while the linear configuration is less stable. On the other hand, negatively-charged alkali metal trimer is the most stable in the linear form and has no minimum at a triangular geometry. The electronic structures of neutral and anion trimer in the low-lying states are expressed in terms of the valence-type molecular orbitals such as the bonding (σg), nonbonding (σu), and anti-bonding (σ*g) orbitals, which arise from the mixing of the 3s orbital of the Na atom with the σg and σu orbitals of Na2. These molecular orbitals
Solvation of Sodium Atom and Aggregates in Ammonia Clusters
31
may take part in the electron configurations of various states observed in the lower-energy photodetachment process. Fig. 11 shows the PESs of Na3–(NH3)n (n = 0–3) by the photodetachment energy of 3.50 eV. The PES of Na3– exhibits three-bands Figure 11: Photoelectron spectra of Na3–(NH3)n (n ≤ 3) at a detachment energy of 3.50 eV. The intensities of each spectrum are normalized at the transitions derived from that to the 2Σ+g state of linear Na3. The newly appeared band for n ≥ 2 is marked by an asterisk. This figure is cited from ref. 29.
32
Kiyokazu Fuke, Kenro Hashimoto and Ryozo Takasu
peaked at 1.20, 1.90, and 2.74 eV as shown in Fig. 11a and is essentially the same as that reported by Bowen and co-workers.48 Using the ab initio CI method, Bonacic-Koutecky and co-workers have predicted a linear (D∞h) structure for Na3– with bond length of 3.58 Å. They have also calculated the VDEs for the transitions from the anion state (1Σ+g) to the neutral ground (2Σu) and first excited (2Σg) states to be 1.17 and 1.74 eV, respectively, and assigned the observed bands at 1.20 and 1.90 eV to these transitions. As it is clearly seen in the PESs, the VDE of the Na3(2Σu)–Na3– (1Σ+g) transition is much larger than that of the 1Σ+g–2Σu transition of Na2–. The large increase in VDE of the Na3– is mainly due to an enhanced charge delocalization resulting from the addition of excess electron in a nonbonding occupied orbital in contrast to the case of Na2–, in which the electron is added to an anti-bonding orbital.55 Because the theoretical calculations on the higher excited states of neutral trimer are not available at present, the 2.74 eV band in Fig. 11a cannot be assigned definitively The PES of Na3–(NH3) shows the distinct bands at 1.26 and 1.87, and a much weaker one at 2.42 eV as shown in Fig. 11b. The first band shifts to the higher EBE by 0.06 eV with respect to those of the bare Na3–, while the second and third bands are shifted to the lower EBE by 0.03 and 0.32 eV, respectively. In order to analyze the spectra, we have conducted the preliminary calculations on the structure and energetics of Na3–(NH3)n (n = 0–4) at MRSDCI // MCSCF level.55 They have also found the stable linear structure for free Na3– and calculated the VDEs to the ground (2Σu) and first excited (2Σg) states as 1.16 and 1.74 eV, respectively. For Na3–(NH3), a T-shaped structure with a slightly bent Na–Na–Na bond has been found to be the most stable, where NH3 molecule binds to the central Na atom with the N atom (see T1a in Fig. 12). The VDEs to the ground and first excited states are calculated to be 1.14 and 1.57 eV, respectively, and agree well with the experimental VDEs. On the basis of these results, the 1.26 and 1.87 eV bands in Fig. 11b have been assigned to the transitions to the 2Σu- and 2Σg-type states, respectively. With the addition of a second ammonia molecule, two strong bands of Na3–(NH3)2 are slightly shifted to higher and lower EBE from those of Na3–(NH3) as shown in Fig. 11c and observed at 1.43 and 1.86 eV, respectively. From the spectral similarity, these bands are assigned to the transitions to the ground (2Σu-type) and first excited (2Σg-type) states. In addition to these bands, the spectrum of Na3–(NH3)2 exhibits an extra band at 0.61 eV. Although it is not shown here, the similar band has also been observed at 0.55 eV for free Na3– in addition to the above two bands.29 In the case of Na3–, its
Solvation of Sodium Atom and Aggregates in Ammonia Clusters
33
Figure 12: Optimized geometries and total binding energies (kcal/mol) of Na3–(NH3)n (n = 0–3). Geometrical parameters are given in Å and degrees and total binding energies are without CPC and zero point vibrational correction
relative intensity has been found to change with expansion condition and suggest the appearance of a new transition of another isomer. As mentioned previously, we cannot expect the other singlet isomer because the potential energy surface of the singlet Na3– along the bending coordinate has a single minimum at linear configuration. The observed new band at 0.55 eV may be ascribed to the transition to the 2B2(Na3) state of the isomer with nearly-equilateral triangular geometry. For Na3–(NH3)2, the population labeling study has been conducted in order to confirm the involvement of the different isomer.29 In this experiment, PES has been recorded by irradiating with the fundamental of a YAG laser at 1064 nm (1.17 eV) in addition to the 355 nm detachment laser; the 1064 nm pulse is irradiated about 10 ns in advance to the 355 nm radiation to deplete the isomer contributing to the 0.61 eV band. The results clearly show that the first band in Fig. 11c is selectively depleted with the 1064 nm radiation and originated from the isomer other than the linear isomer mentioned previously. Since the VDE of this band is close to that for the bare Na3–, the 0.61 eV band is tentatively
34
Kiyokazu Fuke, Kenro Hashimoto and Ryozo Takasu
assigned to the transition correlated to the 2B2(Na3) state of the isomer with nearly-equilateral triangular geometry. The PESs in Fig. 11 also seem to indicate that the successive stabilization energy of this isomer is larger than the isomer with linear Na3– core. The PES of Na3–(NH3)3 exhibits three distinct bands at 0.50, 1.40, and 1.80 eV as shown in Fig. 11d. The first band has almost the same VDE as that of Na3–(NH3)2 and is assignable to the transition derived from the 2B2(Na3) state of the triangular isomer. As mentioned previously, the 2Σu- and 2Σg-type transitions are shifted gradually to higher and lower EBE from free Na3– to n = 2. However, these transitions are almost superimposed upon each other for n = 3 as seen in Fig. 11d. The preliminary results on the PESs of n = 4 and 5 display a single band peaked at about 1.70 eV. Since these two bands correspond to the transitions derived from the 2Σu and 2Σg states of bare Na3, the degeneracy of these two states may imply the dissociation of the linear-type Na3– core in n = 4 (and possibly in n = 3 too) upon ammoniation as follows. The optimized structures of Na3–(NH3) n (n = 0–4) where all NH3 molecules are bound to the central Na in Na3– are shown in Fig. 12. The ligation of an NH3 molecule to the central Na results in a slight bending of Na3 as shown in T1a. Its TBE is found to be –5.3 kcal/mol. When the second NH3 is attached to the central Na, both NH3 molecules are pushed into an Na–Na bond. As a result, the third Na atom is bound to two ammonia molecules through Na–H bonds (see T2a). The energy gain by the addition of the second NH3 is 9 kcal/mol. A similar geometrical feature is also found for T3a, and further selective solvation of the central Na with four Na–N bonds results in the structure where two Na–Na bonds are almost dissociated; the central Na is surrounded by four NH3 molecules in a tetrahedral fashion in T4a. The elongation of Na–Na bond results in the gradual energy lowering of HOMO derived from the nonbonding σu orbital of the linear Na3–. It also causes the destabilization of the next HOMO, which is originally the bonding σg orbital of Na3– especially for n ≥ 3. Since the PES bands in question correspond to the electron detachment from the HOMO and the next HOMO, the decrease in the energy separation between these orbitals in the solvated structures qualitatively explains the size dependence of the observed bands in the spirit of the Koopmans theorem. These results suggest that the observed extensive changes in the electronic structure of Na3– upon ammoniation are related to the dissociation of the anion core. In order to explore further the dissolution of Na3– core in ammonia clusters, we are performing the similar experiments for larger clusters and extending the theoretical calculations.
Solvation of Sodium Atom and Aggregates in Ammonia Clusters
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ACKNOWLEDGMENTS Most of our own works in this review have been done by the collaborations with Prof. F. Misaigu (Tohoku University), Mr. T. Taguchi (Kobe University), Mr. H. Ito (Kobe University), Ms. K. Nishikawa (Kobe University), Mr. T. Kamimoto (Tokyo Metropolitan University), Ms. R. Okuda (Tokyo Metropolitan University), Mr. K. Daigoku (Tokyo Metropolitan University) and Dr. N. Miura (Tokyo Metropolitan University). This work was partially supported by Grant-in-aid from the Ministry of Education, Science, Sports and Culture of Japan. We are also thankful to the Japan Society for the Promotion of Science for financial support. A financial support by Research and Development Applying Advanced Computational Science and Technology, Japan Science and Technology Corporation (ACT-JST) is also acknowledged. We are also grateful to the Aichi Science and Technology Foundation, Japan Society for Promotion of Science, and the Hyogo Science and Technology Association for financial support. All computations were carried out at Computer Centers, at Tokyo Metropolitan University and at the Institute for Molecular Science. REFERENCES (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14)
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(46) Hashimoto, K., Kamimoto, T., and Daigoku, K. (2000) J. Phys. Chem., A. 104: p. 3299. (47) Greer, J.C., Huglin, C., Hertel I.V., and Ahlrichs R. (1994) Z. Phys. D., 30: p. 69. (48) McHugh, K.M., Eaton, J.G., Lee, G.H., Sarkas, H.W., Kidder, L.H., Snodgrass, J.T., Manaa, M.R., and Bowen, K.H. (1989) J. Chem. Phys., 91: p. 3792. (49) Hashimoto, K., Okuda, R., and Miura, N. (2001) Submitted for publication. (50) Bonacic-Koutecky, V., Fantucci, P., and Koutecky, J. (1989) J. Chem. Phys., 91: p. 3794. (51) Bonacic-Koutecky, V., Fantucci, P., and Koutecky, J. (1990) J. Chem. Phys., 93: p. 3802. (52) Martina, R.L. and Davidson, E.R. (1978) Mol. Phys., 35: p. 1713. (53) Gole, J.L., Childs, R.H., Dixon, D.A., and Eades, R.A. (1980) J. Chem. Phys., 72: p. 6368. (54) Martins, J.L., Car, R., and Buttet, J. (1983) J. Chem. Phys., 78: p. 5646. (55) Hashimoto, K., Okuda, R., and Miura, N. Unpublished results.
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2 ELECTRONIC AND GEOMETRIC STRUCTURES OF WATER CLUSTER COMPLEXES WITH A GROUP 1 METAL ATOM: ELECTRON–HYDROGEN BOND IN THE OH{e}HO STRUCTURE Suehiro Iwata and Takeshi Tsurusawa
I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 II. Computational Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 III. OH{e}HO Structure in Water Cluster Anions . . . . . . . . . . . . . . 43 IV. Electronic and Geometric Structure of M(H2O)n. . . . . . . . . . . 46 A. M(H2O)1, M(H2O)2 and M(H2O)3 . . . . . . . . . . . . . . . . . . . 48 B. M(H2O)4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 C. M(H2O)5 and M(H2O)6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 D. The Frequency Shifts of the OH Stretching Modes in M(H2O)n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 E. Spectral Patterns for OH Stretching Mode and Geometric Structures of M(H2O)n . . . . . . . . . . . . . . . . . . . 59 F. The Frequency Shifts of the OH Stretching Modes in Hexamer Anion (H2O)6–. . . . . . . . . . . . . . . . . . . . 61 G. The Correlation of the Shift ΔνOH with the Lengthening of OH Bonds in Hydrogen Bonds and in OH{e}HO Structure . . . . . . . . . . . . . . . . . . . . . . . . . 61 Advances in Metal and Semiconductor Clusters Volume 5, pages 39–75 © 2001 Elsevier Science B.V. All Rights Reserved. ISBN: 0-444-50726-4
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40
Suehiro Iwata and Takeshi Tsurusawa
H. Vertical Ionization Energies (VIEs), and their Size- and Metal Dependencies . . . . . . . . . . . . . . . . . . . . . . .67 I. Electron–Hydrogen Bond in OH{e}HO Structure and its Similarity and Difference With the Usual Hydrogen Bond . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .71 V. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .72 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .73 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .73 I. INTRODUCTION The ionization threshold energies (ITEs) of water clusters containing a group 1 metal atom, M(H2O)n (M = Li, Na and Cs), have been reported by Takasu et al.,1 Hertel et al.2 and Misaizu et al.3 The observed ionization threshold energies of these clusters show several remarkable features. For n ≤ 3, the ITE decreases rapidly as n increases. But for n ≥ 4, it becomes constant, and the converged values are common for Li, Na and Cs; the value is nearly equal to the estimated photoelectric threshold of bulk ice (about 3.2 eV 4). To explain this behavior, the experimentalists assumed that the solvated metal atom is completely ionized and screened by four water molecules. In their model, the excess electron is ejected outside the first solvation shell, and the state of the excess electron is not affected by the solvated metal ion. Theoretical calculations were also performed to explore the anomalous features. Barnett et al.5 showed by the local-spin-density functional method for Na(H2O)n, that the Na atom becomes ionized at n = 4 and that for n ≥ 4 the structures of Na(H2O)n resemble Na(H2O)n+ with a Rydberglike excess electron. Hashimoto and Morokuma (HM) also performed ab initio MO calculations for Na(H2O)n.6–8 They showed that the most stable structure was the surface-metal structure, where an Na atom sits on the cluster surface. Because this type of structure cannot have more than four water molecules in the first solvation shell, the behavior of the ionization threshold changed at n = 4. The excess electron distribution in the surface structure is localized near the Na atom at the opposite side of the water molecules. Hashimoto and Kamimoto (HK)9,10 have also reported ab initio MO calculations for Li(H2O)n. They showed that the interior-metal structure is most stable, where the metal is surrounded by four water molecules, and that it cannot have more than four water molecules in the first solvation shell. They suggested that this is the origin of the change in the ionization threshold of Li(H2O)n at n = 4. However, the excess electron density is distributed on and between the water molecules in the second solvation shell, which is different
Electronic and Geometric Structures of Water Cluster Complexes
41
from that in Na(H2O)n. Most of the theoretical work indicated that the clusters have four water molecules in the first solvation shell and the metal atom becomes ionized at n = 4. We also examined why the ionization threshold energy becomes nearly constant for n ≥ 4, independently of the metal elements.11,12 Recently, we have performed a series of ab initio MO calculations on the water cluster anions, (H2O)n–, and showed that the excess electron can be trapped inside water clusters as small as n = 2, 3, 4 and 6.13,14 The electron cloud is surrounded by two or more HO bonds of water molecules, whose structure we denote OH{e}HO hereafter. Kim et al.15,16 also found a similar structure in the excess electron of the most stable isomer of (H2O)6–. This type of structure for the excess electron stimulates us to think that the OH{e}HO structure might be present also in a group 1 metal–water clusters, M(H2O)n. If M(H2O)n is an ion pair with an OH{e}HO structure and a solvated metal atomic ion, the ionization energy might not be affected by the metal cation. Furthermore, the structure OH{e}HO might remain unchanged when n increases, and consequently the ionization energy could become n-independent. This review is based on our recent theoretical studies of (H2O)n– and M(H2O)n.11–14 We have examined M(H2O)n (M = Li and Na) in a systematic way, keeping an OH{e}HO structure in mind.11 We introduce the OH{e}HO structure we found in the study of (H2O)n– and then describe the geometric structures of the optimized isomers of M(H2O)n. The isomers are classified by introducing a set of measures to characterize the singly occupied molecular orbital (SOMO). The determining factor of the vertical ionization energy (VIE) is analyzed, and we present a model to explain why the ionization threshold energy converges at an energy beyond n = 4, independently on the metal element. By looking back the past research on water clusters interacting with a negatively charged atom or a molecule, we can find the structures similar to the OH{e}HO structure. One of the examples is the X–(H2O)n (X = F, Cl, Br, I and Cu)17–22 complexes, in which the socalled ion-internal isomers become more stable for larger n than the ion-surface isomers. In particular, for X = F, the observed vibrational spectrum for n = 3 shows only the ion-HO hydrogen bonds.21 The model studies of the solvated electron in liquid water and methanol23–28 are the other examples, where the geometric configurations of water (methanol) molecules were assumed; therefore, the effects of the solvated electron on the intramolecular potential of solvent molecules were not fully taken into account. In this review, we scrutinize the excess electron {e}–HO interaction in the anion part of M(H2O)n and show the uniqueness of the
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Suehiro Iwata and Takeshi Tsurusawa
electron distribution, which is localized by the surrounding OH bonds and has no positive charge near the center of the distribution.12 In particular, we demonstrate how the surrounding OH bonds are changed when they interact with the excess electron. The harmonic frequencies are calculated for many isomers of M(H2O)n (M = Li and Na) as well as for water cluster anions (H2O)n–.14 The strong correlation between the frequency shifts and a few geometric parameters are found; if the infrared absorption or Raman scattering spectra are measured, they help identifying the detected isomers. The magnitude of the shift indicates that the electron {e}–HO interaction in the OH{e}HO structure is as strong as the ordinal hydrogen bonds and that the characteristics of the OH{e}HO structure in M(H2O)n are found to be the same in (H2O)n–. The electron–HO interaction in this structure can be called electron–hydrogen bond, as is called X–(H2O)n ion–hydrogen bond. Finally we discuss the similarity and difference in the electron–hydrogen bond and the ordinal hydrogen bond, and comment on the ubiquitousness of the electron–hydrogen bond and the chemical and physical implications of a “trapped electron” under a potential field corporately created by a few OH and XH bonds. II. COMPUTATIONAL DETAILS For the geometry optimization, the MP2/6-311++G(d,p) level of approximation is used. For pure water cluster anions, extensively diffuse basis sets are augmented to describe the excess electron. The convergence of the diffuse basis set was tested.13 Because we found that in the study of (H2O)n– the electron correlation have a large effect on the OH{e}HO structure, at least the MP2 level of approximation is required in optimizing the structure of M(H2O)n which have an OH{e}HO structure in a key unit. Some of the isomers for M(H2O)n determined by Hashimoto and Kamimoto,9,10 and by Hashimoto and Morokuma6–8 are re-optimized at the MP2 level. Although the basis set superposition error (BSSE) has to be corrected to estimate the total binding energy, we discuss in the present chapter only on the relative energy among the isomers of the same size n, and therefore we do not take account of BSSE. In most cases the energy differences are small among the clusters with the same n, and hence we cannot claim the identification of the most stable isomer in terms of their relative energy in the present level of calculations. The harmonic vibrational frequencies are calculated with the same level of approximation as in geometry optimization steps. For n = 3 and 4, the harmonic frequencies were
Electronic and Geometric Structures of Water Cluster Complexes
43
calculated with the analytical derivative method. For n = 5 and 6, because of the time limit even for the largest job class on the NEC SX-3 in our computer center, we had to employ the numerical derivative method, which allowed us to restart the job a few times. All calculations are carried out with Gaussian 9429 and Gaussian 9830 program packages registered at the computer center of the Institute for Molecular Science. The S 2 expectation values both in UHF and MP2 wave functions are 0.750 for (H2O)n– and M(H2O)n. To characterize the singly occupied molecular orbital (SOMO), three measures are defined as follows: 1. SOMO extent measure (SEM): The volume (in Å3) of the sphere, which contains a half of electron in SOMO. To define the sphere, at first, ψSOMO(rijk) at the cubic grids rijk = (xi, yj, zk) for i = 1, …, L, j = 1, …, M and k = 1, …, N is calculated. The spacings of these grids (Δx, Δy and Δz) are fixed. Next they are sorted in descending order such that |ψSOMO(1)|≥|ψSOMO(2)|≥…≥ |ψSOMO(p)|≥…≥|ψSOMO(LMN)|. Finally, the index P such that ΣPp=1|ψSOMO(p)|2×ΔxΔyΔz ≈ 0.5 is looked for. The surface of the sphere is defined such that |ψSOMO(r)| = |ψSOMO(P)|. The sphere so defined is unique and has a volume P × ΔxΔyΔz which we call SEM. 2. R({e}–M): The distance between the center of the electron density of SOMO (R{e}) and the metal atom. R{e} is evaluated as R{e} = Σijk|ψSOMO(rijk)|2ΔxΔyΔz × rijk. This measure can be used to judge whether or not the metal is ionized. 3. R({e}–H): The distance between R{e} and the hydrogen atom. This measure characterizes the OH{e}HO structure, and the strength of the interaction. We have examined the effect of a set of diffuse sp-type functions on the vertical ionization energy (VIE) and on the SEM of three isomers of Li(H2O)4 (Li4b, Li4c and Li4e), which are three of the isomers discussed below. These diffuse functions are added only on the oxygen atom and their exponents are 0.017, 0.003, 0.0006 and 0.00012. As a result, VIEs increase by at most 0.01 eV and are almost converged with the 6-311++G(d,p) basis set. SEMs also increase slightly by at most 3 Å3. Because both changes are not significant at all and so not influence the following discussion, we have used the 6-311++G(d,p) basis set in the present calculation. III. OH{e}HO STRUCTURE IN WATER CLUSTER ANIONS In our studies on water cluster anions, (H2O)n– (n = 2, 3, 4 and 6), we found stable internally bound electron structures as well as
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Suehiro Iwata and Takeshi Tsurusawa
well-known anions of a dipole bound electron.11,12 Some of isomers are shown in Fig. 1. Isomers 2W-a and 3W-a are typical dipole bound anions. Because the end OH bond of the chain of a hydrogen bond network is most polarized among the OH bonds in the water chains, the excess electron in the dipole bound isomers of longer chains are trapped at the end of the chain.31–34 Isomers 2W-a and 3W-a are the first of the series. Figure 1: Some of optimized isomers of water cluster anions, (H2O)n–. The surface of the SOMO sphere, inside of which a half of the SOMO electron is contained, is drawn. The measure SEM is defined in the text. (2W-a) Dipole bound dimer anion. (2W-b) Dimer anion having a form (OH2){e}(H2O). (3W-a) Dipole bound trimer anion. (3W-b) Trimer anion having a form (OH2){e}(H2O)2. (3W-c) Trimer anion of D3h symmetry. (6W-a)–(6W-c) hexamer anions.
Electronic and Geometric Structures of Water Cluster Complexes
45
The internally bound electron is stable even in the dimer anion (2W-b in Fig. 1). Two water molecules form a D2h core, two water molecules facing each other at its HO bonds. Interestingly, no hydrogen bonds are present, and thus, if the electron is removed, two molecules are separated. In that sense, the excess electron {e} binds two water molecules. The binding energy is smaller than the dipole bound anion 2W-a, because of the lack of the hydrogen bond. The vertical detachment energy is larger than 2W-a. Isomers 3W-b, 3W-c, and 6W-a have a similar internally trapped electron. Isomers 3W-b and 6W-a can be written as (H2O){e}(H2O)2 and (H2O)3{e}(H2O)3, respectively. We found more similar isomers such as (H2O)2{e}(H2O)2. The SEM decreases substantially from 3W-b to 6W-a as shown in the figure. One of the most interesting structures is that of 3W-c, which has D3h symmetry, and again no hydrogen bonds exist. We looked for a similar water tetramer anion of D4h in vain; because the distances between water molecules are short, the hydrogen bonds are formed and the tetramer anion becomes either (H2O)2{e}(H2O)2 or (H2O){e}(H2O)3. We do not claim that these isomers of internally trapped electron are detected in the experiments, but we would like to rather emphasize the stability of OH{e}HO structure. We have noticed in the study of (H2O)n– that the optimized structure of the isomers which have a OH{e}HO structure is sensitive to the electron correlation. Therefore, to study the cluster containing a OH{e}HO structure we must use at least MP2 level of approximation. For hexamer ions Kim and his co-workers systematically searched many isomers.16 We have also found more isomers; three of them are 6W-a, -b and -c in Fig. 1. Experimentally two isomers I and II are distinguished in the photoelectron spectra. The difference of the vertical detachment energy (VDE) is 0.3 eV. Isomer 6W-b has a structure similar to that of the most stable isomers (called Y42) reported by Lee et al.16 There is, however, an important difference between 6W-b and Y42. In the latter, two water molecules, standing on the top of tetramer ring, are both single proton-acceptor water molecules. On the other hand, the corresponding two water molecules in 6W-b are double proton-acceptor molecules. As we discuss below, this difference has an essential effect in the frequency shifts of OH vibrations. In our calculations, the energy difference between Y-42 and 6W-b is merely 2.8 kJ/mol; the former is slightly more stable than 6W-b. In 6W-b an OH bond of each top water molecule mostly interacts with the excess electron, but the other OH bond of the same molecule also interacts weakly with the electron. Isomer 6W-c is the most stable among the isomers we examined (including Y-42). The structure of 6W-c is
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Suehiro Iwata and Takeshi Tsurusawa
derived from a prism isomer, which is one of the most stable neutral hexamers,35 by breaking two hydrogen bonds and flipping a water molecule, resulting the cluster of a large dipole moment. Two OH bonds of a single water molecule mostly interact with the excess electron. Among isomers 6W-b, Y-42 and 6W-c, 6W-b has the largest (0.50 eV) calculated VDE, which is close to the experimental value of isomer II (0.5 eV), and 6W-c is the smallest. The difference, however, is 0.11 eV; much smaller than 0.3 eV, a reported value for the difference of isomers II and I. Isomer 6W-c may be classified as a dipole bound isomer, but the local {e}HO interaction is strong as will be seen in the harmonic frequency shifts of OH modes below. In addition, an OH bond of the other top water molecule participates the local interaction. Similarly, in larger water cluster anions, the interaction of OH bonds with the excess electron is important in stabilizing the anion. So once Kim called the electron surrounding by water molecules “a wet electron”.15 In the following we demonstrate that the electron–HO interaction, which we start to call the electron–hydrogen bond, and the OH{e}HO structure are essential in the electronic and geometric structures of metal-water clusters. IV. ELECTRONIC AND GEOMETRIC STRUCTURE OF M(H2O)n The optimized structures for Li(H2O)n and Na(H2O)n for n = 1 to 6 are given in Figs 2–6. The SEM in our definition is the volume of the sphere in the figures. In Table 1 three measures characterizing the SOMO, the VIE, and the relative energy among isomers are summarized. The geometric structures of isomers are classified in terms of the number of water molecules (m) in the first solvation shell, and we will denote such a classified isomer as “MmW” isomer. The electronic structures of M(H2O)n are classified using SEM and R({e}–M) into three types; surface (S), semi-internal (I) and quasi-valence (V). The correlations of SEM with R({e}–M) are shown in Fig. 7, from which the classification is deduced. The definition of these types is as follows: 1. Surface (S): SEM is larger than 75 Å3. In isomers of this type, an electron is detached from the metal atom, and the ejected electron is delocalized on the surface of the cluster. 2. Semi-internal (I): SEM is smaller than or equal to 75 Å3 and R({e}–M) is longer than 2.0 Å. The electron is detached from the metal atom and captured internally by OH bonds of the water molecules. The structure OH{e}HO plays a key role in localizing the ejected electron.
Electronic and Geometric Structures of Water Cluster Complexes
47
Table 1. The distance between R{e} and the metal atom, the shortest four distances between R{e} and the hydrogen atoms, SEM, VIE and ΔEISO Type
MnW
R({e}–M)a
R({e}–H)a
SEMb
VIEc
ΔEISOd
Li1
V
M1W
0.60
3.19
34
4.34
–
Na1
V
M1W
0.53
3.59
44
4.17
–
Li2
V
M2W
0.98
2.81
65
3.75
–
Na2
V
M2W
0.90
3.33
61
3.65
–
Li3a
S
M3W
1.50
2.42,2.42,2.42,2.85
115
3.39
0.0 0.4
Li3b
S
M3W
1.69
1.76,1.96,2.11,2.17
95
3.43
Na3b
S
M3W
1.65
2.03,2.33,2.42,2.84
101
3.40
0.0
Li3c
V
M2W
1.41
2.63,2.81,3.06,3.33
40
3.78
22.9
Na3c
V
M2W
1.34
3.05,3.22,3.32,3.84
48
3.68
3.9
Li4a
S
M4W
2.13
1.74,1.78,2.29,2.47
96
3.31
0.0 0.4
Li4b
S
M4W
2.21
1.34,1.34,2.44,2.44
93
3.30
Na4b
S
M4W
2.68
1.39,1.39,2.48,2.48
83
3.36
0.0
Li4c
I
M3W
2.71
1.48,1.66,2.68,2.90
63
3.53
11.6
Na4c
I
M3W
2.94
1.48,1.60,2.77,3.02
69
3.40
6.6
Li4d
I
M3W
2.55
1.07,1.24,2.23,2.85
75
3.42
17.8
Na4d
I
M3W
2.49
1.17,2.08,2.21,3.04
63
3.55
8.1
Li4e
V
M2W
1.90
1.98,1.98,2.95,2.95
28
3.97
37.9
Na4e
V
M2W
1.92
2.12,2.12,3.18,3.18
36
3.90
12.6
Li5a
I
M4W
2.99
1.52,1.59,1.82,2.90
67
3.36
0.0
Na5a
I
M4W
3.47
1.49,1.57,1.95,3.01
65
3.37
0.0
Li5b
I
M4W
2.98
1.53,1.58,2.75,2.83
62
3.33
2.1
Li5c
I
M4W
2.51
1.62,1.92,2.01,2.53
63
3.48
2.5
Li5d
I
M3W
3.34
1.16,1.73,2.70,2.74
51
3.50
14.3
Na5d
I
M3W
3.40
1.23,1.78,2.74,2.80
48
3.51
9.2
Li5e
I
M3W
3.12
1.51,1.70,2.01,2.70
36
3.72
20.4
Na5e
I
M3W
3.18
1.61,1.72,2.00,2.98
36
3.70
15.8
Li6a
I
M5W
3.27
1.38,1.57,1.87,2.70
66
3.34
11.1
Na6a
I
M5W
3.69
1.25,1.74,1.97,2.77
61
3.44
0.0
Li6b
I
M4W
3.73
1.07,1.76,2.60,2.67
53
3.35
4.9
Na6b
I
M4W
4.05
1.02,1.88,2.53,2.75
53
3.37
2.4
HK-VIa
I
M4W
3.15
1.52,1.58,1.71,3.01
55
3.49
0.0
HM-m
V
M3W
1.38
3.59,3.59,3.59,3.96
52
3.35
2.4
a
In Å. In Å3. c In eV. d In kJ/mol. b
3. Quasi-valence (V): SEM is smaller than 55 Å3, and R({e}–M) is shorter than 2.0 Å. The SOMO electron is not yet completely detached from the metal atom. The SOMO is approximately a sp hybrid orbital, though it is more diffuse than the ordinal valence
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Suehiro Iwata and Takeshi Tsurusawa
s and p orbitals. This type of isomer has a larger VIE than those of the other types. A. M(H2O)1, M(H2O)2 and M(H2O)3 First we examine Li(H2O)1 and Li(H2O)2 complexes, which are already studied by Hashimoto and Kamimoto.10 The SOMO surfaces of Li(H2O)1 and Li(H2O)2 are shown in Fig. 2. The SOMO in both complexes is almost spherical and its center is close to the Li atom as is seen in Table 1. The SEM of Li(H2O)1 is as small as 34 Å3, and the SEM of Li(H2O)2 substantially increases up to 65 Å3. They might be classified as quasi-valence type, but because the center of SOMO is so close to the Li atom, the SOMO can be called 2s or 2s+2p hybrid valence orbital. As is seen in Fig. 2 and Table 1, the geometric structure of Na(H2O)1 and Na(H2O)2 is very similar to the corresponding Li complexes; and SOMO characteristics of Na(H2O)1 and Na(H2O)2 are, however, slightly different.
Figure 2: The optimized structures for Li(H2O)1, Na(H2O)1, Li(H2O)2 and Na(H2O)2. The metal–oxygen bond lengths and the hydrogen bond lengths are given in angstrom.
Electronic and Geometric Structures of Water Cluster Complexes
49
Three isomers are found for Li(H2O)3, and two isomers are for Na(H2O)3 (see Fig. 3). The SOMO surfaces of all of the isomers are so different from those of M(H2O)1 and M(H2O)2. Isomer Li3a has C3 symmetry, and all oxygen atoms lie nearly on a plane. Li–O bond distances in Li3a are too short to form hydrogen bonds among the water molecules in the first solvation shell. We also found a similar planar C3 structure for Na(H2O)3, which turned out to have two imaginary frequencies and collapsed to the isomer Na3b by forming a hydrogen bond between a pair of water molecules. Isomers Li3b and Na3b have a pair of hydrogen-bonded water molecules. The difference in the strength of the hydrogen bond in Li3b and Na3b results from the difference in the ionic radius of Li+ and Na+, which is seen in the metal–oxygen bond distances. Isomer Li3a, having no hydrogen bonds, is as stable as isomer Li3b. The electronic structures of Li3a, Li3b and Na3b are of typical surface type; the SEMs are as large as 115 Å3, 95 Å3 and 101 Å3, respectively. In these isomers the metal atom is ionized, and the ejected electron is distributed on the surface of the cluster. One of the interesting findings in the surface type electron is that R{e}, the center of SOMO, is closer to the metal ion than to the hydrogen atoms of water molecules, although some of OH bonds are directed toward {e}, as seen in the figure. Figure 3: The optimized structures for Li(H2O)3 and Na(H2O)3. The hydrogen bonds are shown by dotted lines, and their lengths are given in parentheses.
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Suehiro Iwata and Takeshi Tsurusawa
Isomers Li3c and Na3c are of M2W. The energy difference of isomers Li3c and Li3a is as large as 22.99 kJ/mol. On the other hand, the corresponding difference of Na3c and Na3b is less than 4 kJ/mol. These suggest that the difference between the strength of the M–O bond and the hydrogen bond between the first and second shell water is larger for M = Li than that for M = Na. The characteristics of isomers of Li3c and Na3c are smaller SEM, shorter R({e}–M) and longer R({e}–H) than those of M3a and M3b, as is shown in Table 1. The electron in SOMO is more strongly bound to the metal atom than that of the other isomers, and therefore, we classify M3c as the quasi-valence type. It might be worth emphasizing that the interaction between {e} and HO bonds determines the orientation of the second shell water molecule and one of the first shell water molecules. So the OH{e}HO structure starts to appear in all of the isomers of M(H2O)3. It should be emphasized that clusters as small as M(H2O)3 have a similarity in the structures of Li and Na clusters, in spite of the rather large difference in M–O distance. Hashimoto and Kamimoto (HK) examined isomers of Li(H2O)3 with several basis sets.10 Hashimoto and Morokuma (HM) also reported the structures of isomers of Na(H2O)3.8 Some of their isomers are similar to Li3a, Li3b and Na3b. They also found a few isomers of M2W having two hydrogen bonds. The quasi-valence type isomers Li3c and Na3c are not reported, probably because they expected that the isomers of this type are less stable than the isomers having two hydrogen bonds. B. M(H2O)4 The isomers of Li(H2O)4 and Na(H2O)4 in Fig. 4 have similar structures except for the metal–oxygen distances. An exception is Li4a; the counterpart Na4a collapses to Na4b as Na3a does to Na3b. Isomers Li4b and Na4b have C2 symmetry and have two hydrogen bonds. Because of a larger ionic radius of the Na+ ion, the Na–O bonds in Na4b are much longer and weaker than the Li–O bonds in Li4b, and thus the water molecules in Na4b can be reoriented to form stronger hydrodgen bonds. The SOMOs of three isomers are of surface type, as their SEMs indicate, although the distances R({e}–M) are substantially larger than in Li3b and Na3b. Besides, some of R({e}–H) are short, which suggests stronger interaction between OH and {e}. Two pairs of M3W isomers, M4c and M4d, are found in our study. In M4c, the water molecule in the second solvation shell is a double proton-acceptor water molecule; one of OH bonds of the molecule
Electronic and Geometric Structures of Water Cluster Complexes Figure 4:
51
The optimized structures for Li(H2O)4 and Na(H2O)4.
strongly interacts with an electron cloud {e}. In M4d, a pair of water molecules in the first shell are hydrogen-bonded. The energy difference between M4c and M4d is 6.24 kJ/mol for M = Li and 1.55 kJ/ mol for M = Na. The SOMO electron of both M3W isomers is semiinternal, as their SEMs range from 63 Å3 to 75 Å3. There are noticeably short R({e}–H)s. It should be noticed that even though M4d has
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the first shell structure of M3b, the electron distribution {e} of M4d is different from that of M3b. This implies that the second shell water molecule in M4d, forming the OH{e}HO structure, substantially reduces the electron distribution {e}. An M2W isomer, M4e, is found for both metals. Both have C2 symmetry, and a pair of water dimers coordinate to the metal atom. The isomer is less stable than the others. The SEM and R({e}–M) indicate the character distinct from the other isomers, and the SOMO is a typical quasi-valence orbital. C. M(H2O)5 and M(H2O)6 For M(H2O)5, three M4W isomers for Li and one for Na are found (Fig. 5). There is a double proton-acceptor water molecule in the second shell in Li5a, Li5b and Na5a, which share a similar electronic structure. The SOMO is of semi-internal type, and the ejected electron {e} interacts with the double proton-acceptor water molecule and with one of the first shell water molecules. The number of OH bonds strongly interacting with {e} in isomer Li5b is two, while it is three in isomer Li5a. This difference comes from the position of the hydrogen bond within the first solation shell. The energy difference of the isomers, however, is merely 2.1 kJ/mol. The attempt to locate the corresponding isomer Na5b has failed. There is a large free space in the other side of water molecules in M5a, which suggests that one more water molecule can hydrate to the metal atom; in fact isomers Li6a and Na6a are found as shown in Fig. 6. The SEMs become smaller and R({e}–M) longer than the corresponding M5a. It is, however, worth noticing that three shortest R({e}–H)s are not much changed; the structure (OH2){e}(HO) is almost common in M5a and M6a, though the latter has a M5W core. Most of the M4W form of M(H2O)n (n > 4) have the structure of M4b as an ion core, which has two strong intrashell hydrogen bonds of four-membered ring. In M5a, one of the rings is replaced with a six-membered hydrogen bond ring. If two of the four-membered rings are replaced with six-membered rings, it becomes one of the isomers found for Na(H2O)6 by Hashimoto and Morokuma.8 It is expected that a similar core structure persists both for K(H2O)n and Cs(H2O)n. Isomer Li5c is also M4W, and its first shell structure is similar to Li4a. But, the character of the SOMO is changed to semi-internal in our classification; R({e}–M) becomes longer, and the SEM is as small as 63 Å3. The change of SOMO results from stronger structure OH{e}HO; one of HO is of the proton acceptor water molecule in
Electronic and Geometric Structures of Water Cluster Complexes Figure 5:
53
The optimized structures for Li(H2O)5 and Na(H2O)5.
the second shell. The energy difference from the M4W isomer, Li5a, is only 2.51 kJ/mol, though the structure is very different. Two isomers (M5d and M5e) of M3W are examined for M(H2O)5. The SOMO of both isomers is of semi-internal type. A large
54
Suehiro Iwata and Takeshi Tsurusawa Figure 6:
The optimized structures for Li(H2O)6 and Na(H2O)6.
R({e}–M) clearly indicates the ion-pair formation in these isomers. Isomers M5d have three hydrogen bonds, and two OH bonds of the second shell molecules interact with the ejected electron {e}. On the other hand, isomers M5e have only two hydrogen bonds, but three OHs strongly interact with {e}. The SEMs are small, in particular, for isomers M5e. There are more isomers of M3W and M2W types expected, with different hydrogen-bonding networks of water molecules. There are many more isomers in M(H2O)6 than in M(H2O)5; some of them are reported by HK for M = Li10 and HM for M = Na.8 We have chosen two isomers of M5W and M4W of M(H2O)6 to examine the structural dependence of the vertical ionization energy. As already mentioned above, isomers M6a are derived from M5a by adding a water molecule at the other side of {e}. This extra water molecule lengthens R({e}–M), but the character of SOMO is not much affected, as both SEM and R({e}–H) are similar to each other in M6a and M5a. Isomers M6b are representatives of M4W; they are derived from isomers M5d of M3W by adding a water molecule to the metal ion. In Li6b, four of the oxygen atoms in the first shell are nearly tetrahedrally coordinated, while in Na6b they are distorted from the tetrahedral configuration, because of a hydrogen bond within the first shell. Even with this difference, the characteristic measures of SOMO are very similar to each other as is seen in
Electronic and Geometric Structures of Water Cluster Complexes
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Figure 7: The correlation between SEM and R({e}–M). The broken lines indicate the boundary for the criteria to classify the isomers. I, V and S stand for semiinternal, quasi-valence and surface type electrons, respectively.
Table 1. Isomer Li6a is slightly less stable (6.20 kJ/mol) than isomer Li6b, while isomer Na6a is a little more stable than isomer Na6a. The energy difference is in any case insignificant. Hashimoto and his co-workers reported several isomers for M(H2O)6 in their papers. Isomers HK-VIa and HM-m in Fig. 5 and Table 1 are their most stable isomers for Li(H2O)610 and for Na(H2O)6,8 respectively. To compare the relative stability, the structures were re-optimized with the MP2 /6-311++G(d,p) level of calculations. Isomer Li6b is a little less stable than HK-VIa. It is probably because the latter has two six-membered rings. Isomer Na6a of M4W is slightly more stable than isomer HM-m of M3W. The SOMOs of all isomers are semiinternal, except for HM-m, whose SOMO is quasi-valence in our definition, as a very short R({e}–M) indicates. Concluding the subsection, we should emphasize that the OH{e}HO structure becomes a key unit in the isomers of n ≥ 3. Also it is worth mentioning that for n ≥ 4 there are several (or many) isomers within 8 kJ/mol. The ordering of the calculated stability energy among the isomers might be sensitive to the basis set superposition correction. Experimentally it is most likely that a few of isomers co-exist in the molecular beam, as was recently found in (H2O)6–36 and Mg+(H2O)n.37
56 Suehiro Iwata and Takeshi Tsurusawa
Figure 8: The theoretical infra-red (IR) absorption spectra of representative isomers of surface type (a and b), quasi-valence type (c and d), and semi-internal type (e and f) of M(H2O)n, M = Li and Na. The standard of the shift ΔvOH is defined in the text. The structure is inserted in the spectra. The stick IR bands are assigned to the modes shown at the bottom of the figure. The black sticks are for OH modes of weak or dangling hydrogen bonds.
Electronic and Geometric Structures of Water Cluster Complexes
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D. The Frequency Shifts of the OH Stretching Modes in M(H2O)n Figures 8 and 9 show the calculated infrared spectra for some typical isomers under the harmonic approximation. The structure of the isomer is inserted in each figure. The abscissa of the figure is the shift ΔνOH, defined as:
(
)
free ,sym free ,anti ΔvνOH = vνOH – vν OH + vν OH /2 free ,sym free ,anti where νv OH and ν are the symmetric and anti-symmetric v OH harmonic frequencies of a single water molecule calculated with the same level of approximation as for the complexes. Figure 8 shows the representative spectra of three types of isomers (S, V, and I) for both Li and Na complexes; 8(a) and 8(b) for the surface (S) type, 8(c) and 8(d) for the quasi-valence (V) type, and 8(e) and 8(f) for the semi-internal (I) type. Depending on which OH is mostly vibrating in each normal mode, the sticks are shaded. At the first sight it is evident that almost no difference is found in the spectra of the Li and Na complexes, independent of the types of the isomers. In particular, the spectra of Li4b (Fig. 8(a)) and of Na4b (Fig. 8(b)), both of which are of the surface type, are almost identical. The structure has a C2 axis. A very strong infrared (IR) band at ΔνOH = –360 cm–1 is an antisymmetric mode of two OH bonds which interact with the ejected surface electron. The symmetric mode has a weak intensity and slightly smaller |ΔνOH| than the antisymmetric mode. This strong IR band around –350 cm–1 is characteristic of the surface type as is also seen in the spectrum of Li3b, shown in Fig. 9(a). When there is no symmetry in the cluster, more than one strong IR mode of HO bonds ({e}HO bonds) interacting with the electron, inherent in the OH{e}HO structure, is found in the calculated IR spectrum for the surface type isomers. The number of the strong IR modes depends on the number of the HO bonds involved in the OH{e}HO structure and on the symmetry of the cluster. Because the electron distribution in the surface type is very diffuse, the OH stretching motion induces a large change in the {e} distribution and thus the large change in the total dipole moment. Hashimoto and Morokuma have shown the spectral patterns for Na(H2O)4.7 In their calculation, because the electron correlation is not included in geometry optimization and the frequency calculations |ΔνOH| is about one half of our values, but the features of the spectral pattern are similar to those of the surface type. The shifts ΔνOH in the quasi-valence type, Li4e and Na4e, shown in Figs. 8(c) and 8(d), are –300 to –250 cm–1. The shift for the
The theoretical infra-red absorption spectra of some of the isomers of Li(H2O)n. See the caption for Fig. 8.
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Figure 9:
Suehiro Iwata and Takeshi Tsurusawa
Electronic and Geometric Structures of Water Cluster Complexes
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hydrogen-bonded OH bonds to the second shell water molecule is much larger in this type, which is in contrast with the corresponding shift in the surface type. The IR intensity for the modes in the OH{e}HO structure is weaker than in the case of the surface type, because the SOMO electron distribution is mostly bound by the metal ion, and not so much affected by the OH stretching motion. The calculated IR spectra for the semi-internal type are distinct from the other types; the IR bands of both OH, the one interacting with the electron {e}, and the one hydrogen-bonded to the water molecule, shift by as large as –600 to –300 cm–1. The typical examples are found in the spectra of Li5d and Na5d in Figs. 8(e) and 8(f). The other examples are shown in Figs. 9(b), 9(c) and 9(d). In the spectra of Li5d and Na5d, a pair of OH modes shift downward; one of them is the stretching mode of the {e}HO bond, and the other is the mode of the OH bond of the first shell water molecule which is hydrogen-bonded to the second shell water molecule. The ordering of these two modes is different in Li5d and Na5d, which results from the difference in the metal ion-oxygen distance. The strongest and most downward shifted band in Figs. 9(b) and 9(c) is typical of the {e}HO mode of the double proton-acceptor water molecule. In Fig. 9(d) a band of the similar type is found, though the intensity is not as strong as in 9(b) and (c). E. Spectral Patterns for OH Stretching Mode and Geometric Structures of M(H2O)n As seen in Figs. 8 and 9, the calculated IR spectrum reflects the geometric and electronic structures of the clusters. Therefore, to identify the isomers detected in the experiments, the vibrational spectroscopy is expected to be very informative, as it was in the previous studies of water clusters with a phenol,38 a benzene39 and halogens.17 In M(H2O)n, both ordinal hydrogen bonds and {e}HO bonds co-exist, and therefore, the spectrum might be congested. In some isomers the shifts of the OH modes of the hydrogen bonds are larger than those of the {e}HO bonds, and in the others the order is reversed. Furthermore, the IR intensity of both the {e}HO modes and the hydrogen bonded OH modes are comparable in our calculations. By examining many calculated spectra, we have found two regular spectral patterns, which reflects the relative conformations (A and B in Fig. 10) of {e} and the second shell water molecule. As shown in Fig. 10, conformation A has three strong IR bands; the one with a larger shift is the mode of the {e}HO bond and the other two are the
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hydrogen bonded OH modes. Because in this type of conformation the water molecule of the {e}HO bond is a double proton-acceptor, the terminal hydrogen atom in the {e}OH bond is more positively charged than the usual one, and therefore the {e}•••HO interaction is stronger and the shift is larger. On the other hand, in conformation B, one of the OH bonds of a single proton acceptor water molecule interacts with the electron {e}, and the interaction is weaker than in conformation A. The shift of the hydrogen-bonded OH mode is larger than that of the {e}HO mode, and the spectral pattern becomes as shown in the lower part of Fig. 10. Typical examples are seen in the spectra of Li4e and Na4e (Figs. 8(c) and 8(d)), both of which have two equivalent configurations B. Most of the clusters, however, have two non-equivalent water molecules interacting with the electron {e}. For instance, isomers Li5d and Na5d (Figs. 8(e) and 8(f)) have conformations A and B, and therefore, the spectra are the sum of these two patterns. These regularities might be helpful in future experimental studies. Figure 10: The IR spectral patterns of the model conformations in M(H2O)n.
Electronic and Geometric Structures of Water Cluster Complexes
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F. The Frequency Shifts of the OH Stretching Modes in Hexamer Anion (H2O)6– Ayotte et al.34 reported the vibrational spectra of water cluster anions (H2O)n–. With help of ab initio MO and DFT calculations, they attributed the observed spectrum of hexamer anion to that of a chain-like isomer. To assign the spectra, however, they had to use the scaling factors which depend on the vibrational modes. The characteristics of the observed spectrum is a pair of strong bands at Δv = –440 and –330 cm–1. In their assignment the pair is attributed to the hydrogen bonded OH inside of the chain. One of the difficulties in their assignment is that the photodetachment spectrum suggests the OH bond length change by 1.1% in the electron detachment process. Because in the dipole bound isomer the local interaction of the OH at the end of chain with the electron is weak, the OH bond length does not change by the electron detachment; in our calculations it is less than 0.001 Å. In Fig. 11, the calculated spectra for three hexamer anions in Fig. 1 are shown. Three of them have a pair of {e}HO modes. In 6W-a and 6W-c, there are other intense bands, which are the modes of the hydrogen bonds. On the other hand, 6W-b shows only two strong bands as experimentally observed. Both are the {e}HO modes, anti-symmetric and symmetric of HO modes of two top water molecules (see Fig. 1). The shifts are larger than –200 cm–1, but much smaller than the experimentally observed shifts. As in the experimental spectrum, there are weak bands at the lower frequency region than two strong bands, which are the modes of HO bonds between the tetramer ring and the top water molecules. Although the calculated shifts are substantially underestimated, the spectral pattern of 6W-b is the most similar to the observed one among the isomers we examined. Besides, the OH bonds which interact with the electron {e} is shortened by 0.01 Å in our calculation by the electron detachment. More extensive treatment for the electron correlation might be required to evaluate the change of HO bonds under a strong electric field created by the trapped electron {e}. G. The Correlation of the Shift ΔνOH with the Lengthening of OH Bonds in Hydrogen Bonds and in OH{e}HO Structure To scrutinize the bonding nature between the electron and OH bonds, we examined the correlation between the shift ΔνOH of the stretching frequency and the OH bond length and the correlation between ΔνOH and the distance R({e}…H).
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Figure 11: The theoretical IR absorption spectra of three isomers of water hexamer anions (6W-a)–(6W-c) (H2O)6–. The arrowed bands indicate the modes of {e}HO bonds.
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As seen in Figs. 8 and 9, the calculated downward shifts of the harmonic frequencies of OH bonds are as large as those of the hydrogen bonded OH bonds. It is well known that the OH bond lengths of water molecules are lengthened when the OH is hydrogen-bonded. As the basicity of the proton acceptor increases, the OH bond is lengthened in conjunction with the downward shift of the OH vibrational frequency. Figure 12(a) shows the correlation of the shift ΔνOH both for the hydrogen bonded OH bonds and for the {e}HO bonds with the OH bond lengths. It is clear that all plotted data points are almost indistinguishable among the hydrogen bonded OH bonds and the {e}HO bonds in the Li and Na water clusters. The plots demonstrate that the {e}HO bonds are very similar with the ordinal hydrogen bonds in its character. The similar correlation was found in the harmonic frequency shifts in pure water cluster anions, shown also in Fig. 12(b).14 The shifts in the pure water cluster anions are smaller, but if two figures (a) and (b) are overlapped, two plots are indistinguishable, which again indicates the {e}HO bonds in water cluster anions and in M(H2O)n are same in their character. For hydrogen bonds, the hydrogen bond distance R(O…H) is another measure to see the strength of the hydrogen bonds. In the OH{e}HO structure, the distance between the center of the electron distribution {e} (R{e}) and the H atom, R({e}…H), can be used in place of R(O…H). In Fig. 13 the correlation of the OH frequency shifts with the distances R(O…H) and R({e}…H) is plotted. The data for hydrogen bonds are plotted as shaded circles (HB in the legend). In the hydrogen bonds, although the distance R(O…H) converges almost at 1.7 Å, the strong correlation of the shifts with R(O…H) is evident. In the OH{e}HO structure, two linear relations (I and II) are found. As we will discuss later, these correspond to distinguishable types of the conformation of the center of {e} and {e}OH bonds. In the plots the types of the electron distribution {e} are distinguished by square marks for surface type, triangle marks for quasi-valence type, and circle marks for semi-internal type, respectively. The metal dependence is shown by filled marks for Na(H2O)n and by the open marks for Li(H2O)n, but it is indistinguishable in the plots. We can notice a few characteristics in the plots. All of the triangle marks are close to the line II. Most of the square marks are also close to the line II, but these points are more scattered than the triangle marks, and some of the square marks at small ΔνOH fall on the line I. The circle marks are found only below ΔνOH = –220 cm–1, and fall on both the lines I and II. We have overlapped the similar plots for water anions and found that the points are either on line I or II. To explore the causes of two types of linear relations in the plots, we have to analyze the geometric conformation of the
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Figure 12: The correlation of the harmonic frequency shift ΔνOH with the OH bond length. (a) For M(H2O)n, M = Li and Na. Both of OH bonds, the ordinal hydrogen bonded (HB) OH as well as the {e}HO bonds in the OH{e}HO structures, are included in the plots. The filled square and triangle marks are for the hydrogen bonded OH in the clusters, and the open square and triangle marks are for the OH bonds interacting with the electron {e}. (b) For the water cluster anions (H2O)n–. Only the {e}HO bonds in the OH{e}HO structures are shown.
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Figure 13: The correlation of the harmonic frequency shift ΔνOH with the distance R(X•••H) between the hydrogen atom and either the center of the electron {e}, R{e}, or the proton accepting oxygen atom O of the neighboring water molecule.
SOMO electron {e} and water molecules in the clusters. In Fig. 14, five types of the relative conformations of the SOMO electron {e}, and water molecules and the metal ion are shown. In the first two types A and B, the OH bonds of the second shell water molecules interact with the electron {e}. In the quasi-valence type isomers, the interacting site of OH bonds and the electron {e} has conformation B as is seen in Li4e and Na4e (Figs. 8(c) and 8(d)), and the shifts |ΔνOH| are not large. R({e}•••H) is longer than 2.0 Å and their corresponding points are on the line II. Conformation B is also found in the semi-internal isomers as in the left part of Li5d and Na5d (Figs. 8(e) and 8(f)), but the shifts are on line I. In general, the shifts of conformation B in the semi-internal type isomer are on I. The right part of Li5d and Na5d is typical of conformation A. The other examples are found in Li4c, Li5a and Li6b in Fig. 9. Their shifts |ΔνOH| are large and on line I. The water molecule interacting with the electron {e} in conformation A is the double proton acceptor molecule in the second shell. They are mostly found in the semi-internal type of {e}. In the ordinal hydrogen bonds, it is known that the double proton acceptor water molecule forms a strong hydrogen bond; the polarization of the OH bonds
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Suehiro Iwata and Takeshi Tsurusawa
Figure 14:
Five types of model geometric conformations of the electron {e} and water molecules.
of the molecule are induced by two hydrogen bonds to the oxygen atom. Similarly in the {e}HO bonds the double proton acceptor molecules strongly interact with the electron {e}; most of the points on line I for ΔνOH < –350 cm–1 correspond to this type of interaction. The largest shift is as large as –565 cm–1 in Li6b (Fig. 9(d)), where the OH bond directs linearly toward the center of the electron {e} and the distance R({e}•••H) is 1.07 Å. In conformation C, similar to the conformation A, the OH bond of the first shell molecule directs linearly toward the center of the electron {e}; the example is found in the left side of Li4c (Fig. 9(b)). Their shifts are on line I. In conformation D, both OHs in a water molecule are directed toward the electron {e}, although these are not in equal proportion. In contrary to the conformation C, the OH bonds do not direct toward the center of the electron {e}. In conformation E, both OH bonds of a molecule interact with the {e}, but none of them directs toward the center of {e}. The examples of conformation E are Li4b and Na4b in Fig. 8, and Li3b in Fig. 9(a); all of them are of the
Electronic and Geometric Structures of Water Cluster Complexes
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surface type. The shifts |ΔνOH| for the surface type clusters are at most 330 cm–1, and R({e}…H) are longer than 1.75 Å. Exceptions are for M4b isomers in Figs. 8(a) and 8(b), in which the shifts |ΔνOH| are as large as 365 cm–1 and R({e}…H) are as short as 1.34 Å. The example of conformation D is the left part of Li5a in Fig. 9(c). The data points on line II for R({e}…H) < 2.0 Å are those of conformations D and E. H. Vertical Ionization Energies (VIEs), and their Size- and MetalDependencies Table 1 summarizes the calculated VIEs of M(H2O)n, which are evaluated by taking the difference of MP2 energies of the neutral and cation clusters at the optimized geometry for the neutral cluster. Before discussing the calculations, it is worth noticing what has been known experimentally. Photoelectron spectra have not been measured for these neutral clusters because of the difficulty in sizeselection of neutral clusters. Instead, the threshold photon energy, where the ions start to be detected in the mass spectrometer, is experimentally determined. The ionization threshold energy (ITE) could be close to the VIE, only if the geometries of the initial (neutral) and final (cation) clusters were similar to each other. In this case, both should be close to the adiabatic ionization energy. In the clusters we are studying, the cation clusters M+(H2O)n might be more strongly bound than the corresponding neutral clusters. More importantly, the interaction between the electron {e} and the OH bonds influences the geometric structures of hydrated water molecules in the neutral clusters, as we have seen in Figs. 2–6. Therefore, it is expected that VIE might be slightly larger than the ITE in most cases. There is another complication; if a few isomers co-exist in the experimental beam condition, the observed ITE is determined by the isomer which has the smallest ITE. Table 1 (also the papers of HK and HM) shows that the energy difference among the isomers is small, and that the number of possible isomers increases with the size of clusters. So the direct comparison of the calculated VIE with the observed ITE is not straightforward. With these reservations, the trends in the calculated VIE are still informative in exploring the experimentally observed features in the ITE. At a glance, the VIEs in Table 1 for n ≥ 3 are almost size- and metal-independent; the values range from 3.3 to 4.0 eV. In Fig. 15(a), the correlation between SEM and VIE is shown. Refer also to Fig. 7, where the correlation between SEM and R({e}–M) is given. Distinctively the isomers of quasi-valence type (V) SOMO, M3c and
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M4e (M = Li and Na), have larger VIE, smaller SEM and shorter R({e}–M) than the others. The VIE of M4e is larger than that of M3c, which is contrary to the experimental trends in ITE. The VIE decreases almost linearly with the SEM. These isomers, except for Na3c, are less stable than the other isomers. Thus, we may be able to exclude these isomers from the candidates for the clusters detected in the experiments. In Fig. 15(a), the isomers of surface type (S) SOMO, Li3a, M3b, Li4a and M4b, are clearly distinguished from the others. They have almost same VIE; the VIEs of M(H2O)4 are slightly smaller than those of M(H2O)3. Experimental ITEs are 3.36 eV for Li(H2O)3,1 3.25–3.3 eV for Na(H2O)3,2 3.2 eV for Li(H2O)4,1 and 3.17 eV for Na(H2O)4.2 The calculated VIEs for M(H2O)3 are close to the experimental ITEs, although a slight difference in the experimental ITE of Li and Na is not reproduced in the calculations. The geometric structures of these isomers are expected not to be changed by the ionization, and the VIE should be close to the adiabatic and threshold ionization energies. The calculated VIE difference of surface type M(H2O)3 and M(H2O)4 is nearly 0.1 eV or less than that, which is slightly smaller than the experimental one. Among the isomers of surface type, isomer Na4b may be classified as an intermediate to semi-internal type, as Fig. 15 shows. Two of water molecules interacting with {e} are the proton-acceptors in the hydrogen bonds, and their hydrogen atoms become more positive. Because of stronger {e}OH interaction, the SEM is reduced. In larger clusters, the hydrogen-bond network evolves, and the surface type SOMO is not possible to exist. As Fig. 15(a) shows, the VIEs of isomers having the semi-internal (I) type SOMO range from 3.3 to 3.5 eV, independently of the metal element and the size of clusters; the exception is isomers M5e, whose VIE is 3.7 eV; the reason for this will be discussed below. Even though isomers of the (I) type generally have a restricted range of VIE, SEM and R({e}–M), the correlation among them is not so straightforward. It is because the structure of the OH{e}HO unit does play a key role in determining both VIE and SEM. To analyze the determining factors of the VIE, more careful examination of the geometric and electronic structures of the clusters is required. One of characteristics in the isomers of semi-internal type is the similarity of the structure of the corresponding isomer Li(H2O)n and Na(H2O)n. The structures around the ejected electron {e} of the corresponding pairs (Li4c, Na4c), (Li4d, Na4d), (Li5a, Na5a), (Li5d, Na5d), (Li5e, Na5e), (Li6a, Na6a) and (Li6b, Na6b) resemble each other, although the difference in the ionic radii causes the structural change around the metal atom ion and the
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Figure 15: (a) The correlation between SEM (SOMO extent measure) and VIE (vertical ionization energy) of M(H2O)n, M = Li and Na. (b) The correlation between SEM and VDE (vertical detachment energy) of water cluster anions (H2O)n–.
distance R({e}–M). Their structures have a common form of M+(H2O)m · (H2O)t · (H2O)–n–m–l where the metal atom is ionized and becomes a hydrated ion M+(H2O)m (m = 3–5) in the clusters. The water cluster (H2O)n–m–l traps an ejected electron and becomes
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Suehiro Iwata and Takeshi Tsurusawa
a water cluster anion (H2O)–n–m–l, which determines the shape of the SOMO, as are seen in the figures. The structure OH{e}HO is the essential part of the anion part. The energy required to ionize an electron is, however, governed not only by the anion part but also by the hydrated metal ion M+(H2O)m. The potential (VSOMO) on the HMI SOMO electron could conceptually be written as VSOMO = V SOMO , WC HMI + V SOMO , where V SOMO is a long range potential of the hydrated WC metal ion (HMI), and V SOMO is the short range potential of the water cluster (WC) (H2O)n–m–l. Because of these two factors, the correlation of SEM with VIE and with R({e}–M), shown in Fig. 10, looks somewhat weak. Nevertheless, the SEM and VIE of the pairs (Li5a, Na5a), (Li5d, Na5d), (Li5e, Na5e) and (Li6b, Na6b) are close to each other. The common feature among these pairs is that the pair has either long R({e}–M) or nearly equal R({e}–M). We have seen that the SEM is an appropriate measure to characterize the electronic structure of the ejected electron {e} and the OH{e}HO structure. Three factors can be identified in determining WC the OH{e}HO structure and V SOMO , and therefore its SEM. One is the strength of the bond dipole of the OH bonds which directly interact with the ejected electron. It is known that as a hydrogen bond chain becomes longer, the charge on the terminal hydrogen atom becomes more positive and consequently the bond dipole of the OH bond becomes larger. It is also known that the hydrogen atoms of the proton-acceptor water molecules are more positively charged. This is particularly true for the double proton-acceptor molecule.40 The larger bond dipoles of OH bonds make SEM smaller. The examples are seen in the SEMs of pairs of isomers; {Li5a(67 Å3), Li6b(53 Å3)}, {Na5a(65 Å3), Na6b(53 Å3)}, {Li4c(63 Å3), Li5d(51 Å3)}, and {Na4c(69 Å3), Na5d(48 Å3)}. As the cluster size of semi-internal electron type becomes large and the hydrogen bond chain becomes long, the bond dipole of OH bonds in the OH{e}HO structure become large. As a result, the SEM becomes smaller. Another factor is the number of OH bonds in the OH{e}HO structure. The SEM becomes smaller as the number of surrounding OH bonds increases. An example is the SEM of Li5e and Na5e, which have three OH bonds in the OH{e}HO structure; two of them are those of the proton-acceptor molecules. Their SEMs are as small as 36 Å3. Because of the small SEM, their VIEs are as large as 3.70 eV, and in Fig. 15(a) their points are located far from those of the other semi-internal type isomers. The relative orientation of OH bonds also plays a role. For example, when two dipoles of the opposite direction are collinear, the electrostatic potential well between the dipoles becomes the deepest. The factor may have little effect in the present cases, but it might play a role in the pure water cluster ions.
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71
In our present level of calculations and with the restricted experimental data available, we cannot identify the experimentallydetected isomers, which have nearly equal ionization threshold energy for n ≥ 4 of M(H2O)n (M = Li and Na). From the above results, we might, however, be able to deduce the working hypothesis for further studies. The ion-pair structure, M+(H2O)m · (H2O)t · (H2O)–n–m–l, is the basic unit of the clusters of n > 5; m = 3, 4 or 5. The most probable m is 4. Among the isomers we have studied, M4b, M5a, and M6b, all of which have a M4W core, explain the observed features; the convergence and the metal-independence of VIE. They are the most stable or close to the most stable in energy. The metal independence of VIE results from the ion-pair structure as the experimentalists hypothesized. The convergence of WC HMI VIE is attained by the cancellation of two factors V SOMO + V SOMO . In large, n, R({e}–M) is long, and consequently the electrostatic potenHMI tial V SOMO becomes weaker. At the same time, the hydrogen bond chain becomes longer and therefore the interaction between the ejected electron and the terminal OH bonds becomes stronger, and WC becomes larger. V SOMO In Fig. 15(b) the correlation of the vertical detachment energy of water cluster anions and their SEM is shown. The inverse relation is more clearly seen than in Fig. 15(a). Because the absence of a positive charged ion, the ionization energy is more directly related to the size of the orbital. The plot is suggestive to the structural difference of two hexamer anions, whose VDEs differ by 0.3 eV. I. Electron–Hydrogen Bond in OH{e}HO Structure and its Similarity and Difference with the Usual Hydrogen Bond We have already emphasized the similarity of the {e}•••HO interaction with the hydrogen bonds. The XHO interaction of the ion–hydrogen bonds in X–(H2O)n complexes, X = F, C1, Br, I, and Cu,17 might more closely resemble the {e}•••HO interaction than the O•••HO interaction in the ordinal hydrogen bonds. Therefore, we call the {e}•••HO interaction the “electron–hydrogen bond”. There are very important differences in the electron–hydrogen bond from the ordinal hydrogen bond and the ion-hydrogen bond. In the former, there is no nuclear center near the center of the negative charge, which attracts the OH bonds. Besides, always more than one OH bonds are attached to an electron to form the OH{e}HO structure. In fact, the electrostatic potential created corporately by two or more OH bonds of water molecules traps the electron, and in turn, the OH bonds are strongly polarized by the
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Suehiro Iwata and Takeshi Tsurusawa
negative charge and are attracted to it. The interrelation between the electron distribution {e} and OH bonds is essential to form the stable OH{e}HO structure. V. CONCLUSION We have investigated the water clusters containing a group 1 metal atom M(H2O)n (M = Li and Na) for n = 1–6 and pure water cluster anions (H2O)n– with ab initio MO methods. These isomers of M(H2O)n are classified into three types, and among these types of clusters the semi-internal electron type isomers have the ion-pair structure, M+(H2O)m · (H2O)t · (H2O)–n–m–l, in the clusters M(H2O)n, and possibly determine the features of the observed ITE. The structure of (H2O)–n–m–l part contains the OH{e}HO structure, and the structure around the ejected electron is determined by the interaction within the OH{e}HO structure, which is also found in (H2O)n–. The calculations indicate that there are a few isomers of nearly equal stabilization energy. The number of those isomers increases substantially with n. Photoelectron spectra and vibrational spectra are more informative than ionization threshold spectra for the structures of the isomers. More theoretical work is in progress.14 In the present study, we have reached a model to explain the observed convergence of ITEs at n = 4 and their metal-independence. We cannot, however, say anything about why the converged value is the VIE of bulk water. To understand it, further extensive theoretical studies are required. We also calculated the harmonic vibrational frequencies of the M(H2O)n and (H2O)n– clusters and found the strong correlation between the lengthening of OH bond length and the down-shift of OH frequency as is known in the hydrogen bonding systems. Thus, we call the {e}•••HO interaction in the clusters an electron–hydrogen bond. This bond is unique in the sense that no positive charge exists at the center of the electron distribution which binds the OH bonds. The electron itself is localized under the electrostatic field created corporately by a few OH bonds. The self-consistent type mutual action between the localization of the electron and the polarization of OH bonds is essential in this bond. The electron–hydrogen bond also plays an important role in the water cluster anions. By examining the correlation between the harmonic frequency shifts and the distance R({e}•••H), we found two types of {e}•••HO interactions. When an OH bond is enough polarized by the hydrogen bond network, the OH bond and the center of the electron R{e} line up almost colinearly, and the interaction between the
Electronic and Geometric Structures of Water Cluster Complexes
73
electron {e} and the OH bond becomes stronger. In the other types of conformations, the OH bonds direct toward R{e} slantwise. In the ion-pair complexes, M+(H2O)n–, and also in some of the isomers of water cluster anions, the electron–hydrogen bonds and the structural unit OH{e}HO determine the geometric structure of the whole cluster. There are other cases where a kind of OH{e}HO structures might be stable or quasi-stable as a resonant state. In liquids and glassy solutions, and in polymers, the hydrogen bonds and the other stronger bonds determine the backbone of the structure, in which some of the OH bonds (or the other polar XH bonds) are not hydrogen bonded and exist as dangling bonds. If a few of those dangling OH (or XH) bonds would happen to face toward each other, they could generate the electrostatic field enough to trap an electron permanently or temporally. The solvated electron is one of the examples, and the trapped electrons in γ-irradiated amorphous organic solids at 77K observed in the near IR region might be the other examples.41,42 More systematic and thorough researches on the light of electron–hydrogen bond and XH{e}HY structures are required. ACKNOWLEDGMENTS The present work was partially supported by the Grant-in-Aids for Scientific Research (No. 09304057, 11640518 and 11166270) by the Ministry of Education, Science, Sports, and Culture, Japan, and by Research and Development Applying Advanced Computational Science and Technology, Japan Science and Technology Corporation (ACT-JST). A part of calculations was carried out at the Computer Center of the Institute for Molecular Science. REFERENCES (1) (2) (3) (4)
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Suehiro Iwata and Takeshi Tsurusawa T. Kamimoto and K. Hashimoto (1996) Structures and Dynamics of Clusters (T. Kondow, K. Kaya, and A. Terasaki, eds). Universal Academy Press: Tokyo, pp. 563-572. K. Hashimoto and T. Kamitomo (1998) J. Am. Chem. Soc., 120: p. 3560. T. Tsurusawa and S. Iwata (1999) J. Phys. Chem., A. 103: p. 6134. T. Tsurusawa and S. Iwata (2000) J. Chem. Phys., 112: p. 5705. T. Tsurusawa and S. Iwata (1998) Chem. Phys. Lett., 287: p. 553. T. Tsurusawa and S. Iwata (2000) Chem. Phys. Lett., 315: p. 433. K.S. Kim, S. Lee, J. Kim, and J.Y. Lee (1997) J. Am. Chem. Soc., 119: p. 9329. S. Lee, J. Kim, S.J. Lee, and K.S. Kim (1997) Phys. Rev. Lett., 79: p. 2038. K. Fuke, K. Hashimoto, and S. Iwata (1999) Adv. Chem. Phys., 110: p. 431. J.E. Combariza and N.R. Kestner (1994) J. Chem. Phys., 100: p. 2851. S. Xantheas (1996) J. Phys. Chem., 100: p. 9703. P. Ayotte, G.H. Weddle, J. Kim, and M.A. Johnson (1998) J. Am. Chem. Soc., 120: p. 12361. O.M. Cabarcos, C.J. Weinheimer, and J.M.L.S.S. Xantheas (1999) J. Chem. Phys., 110: p. 5. C.-G. Zhan and S. Iwata (1995) Chem. Phys. Lett., 232: p. 72. T. Clark and G. Illing (1987) J. Am. Chem. Soc., 109: p. 1013. H. Tachikawa and M. Ogasawara (1990) J. Phys. Chem., 94: p. 1746. C.A. Naleway and M.E. Schwartz (1972) J. Phys. Chem., 76: p. 3905. J. Schnitker and P.J. Rossky (1987) J. Chem. Phys., 86: p. 3471. L. Turi, A. Mosyak, and P.J. Rossky (1997) J. Chem. Phys., 107: p. 1970. H. Shiraishi, K. Ishigure, and K. Morokuma (1988) J. Chem. Phys., 88: p. 4637. Gaussian 94 (Revision E.2), M.J. Frisch, G.W. Trucks, H.B. Schlegel, P.M.W. Gill, B.G. Johnson, M.A. Robb, J.R. Cheeseman, T.A. Keith, G.A. Petersson, J.A. Montgomery, K. Raghavachari, M.A. Al-Laham, V.G. Zakrzewski, J.V. Ortiz, J.B. Foresman, C.Y. Peng, P.Y. Ayala, M.W. Wong, J.L. Andres, E.S. Replogle, R. Gomperts, R.L. Martin, D.J. Fox, J.S. Binkley, D.J. Defrees, J. Baker, J.P. Stewart, M. Head-Gordon, C. Gonzalez, and J.A. Pople. Gaussian, Inc., Pittsburgh PA, 1995. Gaussian 98 (Revision A.2), M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, V.G. Zakrzewski, J.A. Montgomery, R.E. Stratmann, J.C. Burant, S. Dapprich, J.M. Millam, A.D. Daniels, K.N. Kudin, M.C. Strain, O. Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Clifford, J. Ochterski, G.A. Petersson, P.Y. Ayala, Q. Cui, K. Morokuma, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J. Cioslowski, J.V. Ortiz, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R.L. Martin, D.J. Fox, T. Keith, M.A. AlLaham, C.Y. Peng, A. Nanayakkara, C. Gonzalez, M. Challacombe, P.M.W. Gill, B.G. Johnson, W. Chen, M.W. Wong, J.L. Andres, M. Head-Gordon, E.S. Replogle, and J.A. Pople. Gaussian, Inc., Pittsburgh PA, 1998. D.M.A. Smith, J. Smets, Y. Elkadi, L. Adamowicz (1997) J. Chem. Phys., 107: p. 5788. D.M.A. Smith, J. Smets, Y. Elkadi, L. Adamowicz (1998) J. Chem. Phys., 109: p. 1238. D.M.A. Smith, J. Smets, L. Adamowicz (1999) J. Chem. Phys., 110: p. 3804.
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3 DETERMINATION OF SEQUENTIAL METAL ION–LIGAND BINDING ENERGIES BY GAS PHASE EQUILIBRIA AND THEORETICAL CALCULATIONS: APPLICATION OF RESULTS TO BIOCHEMICAL PROCESSES Michael Peschke, Arthur T. Blades and Paul Kebarle*
I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 II. Experimental Methodology and Theoretical Calculations . . . 82 A. Apparatus used for Ion-Equilibria Determinations Involving Metal Ion–Ligand Complexes Obtained from Electrospray . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 B. Determination of Ion–Ligand Equilibria . . . . . . . . . . . . . . 83 C. Sequential Ligand (n,n–1) Dissociation Equilibria: MLnz+ = MLz+ n–1 + L. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 D. Ligand Dissociation Equilibria with Mixed Ligands 2+ 2+ such as MAxB2+ = MA2+ x B, and MAxByC = MAxBy C . . . . . 85 E. Ligand Dissociation Equilibria with Mixed Ligands some of which are Negative Ions . . . . . . . . . . . . . . . . . . . . . 85 F. Ligand Exchange Equilibria . . . . . . . . . . . . . . . . . . . . . . . . 86 G. Theoretical Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Advances in Metal and Semiconductor Clusters Volume 5, pages 77–119 © 2001 Elsevier Science B.V. All Rights Reserved. ISBN: 0-444-50726-4
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III. Results and Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .87 A. Hydration of some Singly and Doubly Charged Ions . . . . .87 B. Binding Energies for Mg2+, Ca2+ and Zn2+ with Ligands L = Acetone and N-Methylacetamide in MLn2+for n = 1 to 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .91 C. Exchange Equilibria: CuA2+ 2B = CuB+ 2A: The Dominance of Histidine . . . . . . . . . . . . . . . . . . . . . . .105 D. Metalloion–Ligand Binding Energies and Biological Function of Metalloenzymes such as Carbonic Anhydrase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .108 E. Conclusions Concerning the Role of Strongly Bonding Ligands in Metalloenzymes such as Carbonic Anhydrase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .115 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .117 I. INTRODUCTION Determination of gas phase equilibria involving singly-charged ions M+ and solvent molecules like H2O (see eq. 1) or other ligands providing the sequential bond enthalpies ΔHon,n–1 and entropies ΔSon,n–1 (note, ΔHon–1.n = ΔHon,n–1) were initiated some 30 years ago.1,2 M(H2O)+n–1 + H2O = (M+(H2O)+n)* (M(H2O)*n)+
+ N2 =
(n–1,n)
(1)
M(H2O)+n
Such studies have provided a wealth of data3 on ion–solvent and ion–ligand interactions. Extensive theoretical work5,6 and experimental studies7 were also stimulated. The above studies were limited to singly charged ions M+, yet doubly charged ions M2+ are also of paramount importance in chemistry and biochemistry. The general method used for ion clusters M(H2O)+n or generally ML+n where L stands for ligand, was to generate M+ in the gas phase and expose it to ligand vapor. The formation of ML+n then proceeds spontaneously by third body dependent association reactions. The third bodies, generally supplied by inert gas molecules like N2, CH4, etc., are needed to remove the excess energy released on formation of the new M–L bond. This method has some drawbacks. (a) Not all metal ions M+ of interest are easily produced in the gas phase and the same holds true even more so for doubly charged ions. An additional problem that occurs with multiply charged ions, are side reactions which lead to charge separation such as intra electron transfer, eq. 2, or proton transfer, eq. 3. (M(L)n2+)* = ML+n–1 + L+
(2)
Determination of Sequential Metal Ion–Ligand Binding Energies
(M(H2O)n2+)* = MOH(H2O)x++ H3O+(H2O)n-x-1
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(3)
These reactions generally occur only when the precursor ion MLn2+ has excess energy which is the case for the ion–ligand adduct formed in clustering reactions like eq. 1 under conditions where the collisional quenching of the excess energy by the third gas is not extremely fast. An important example of problems created by intramolecular proton transfer is given by the work of Spears and Fehsenfeld8 who had produced Ca2+ in a flowing afterglow apparatus and were trying to hydrate it. They did observe the first hydrate Ca(H2O)2+, but the second hydration led exclusively to intracluster proton transfer: Ca(H2O)2+ + H2O = CaOH+ + H3O+
(4)
which they considered an “unusual” reaction. Multiply charged ion–ligand complexes exist in solution and in fact much of the impetus for study of ion–ligand complexes in the gas phase derives from the great importance of these species in condensed phase chemistry and biochemistry. The electrospray method developed by John Fenn and coworkers9 proved to be a method by which ions present in solution could be transferred to the gas phase.10 Realizing that electrospray would be a method which may overcome the difficulties discussed above, we were quick to use that technique11,12 for the production of ion–ligand complexes in the gas phase. Results obtained until 1997 and developments of the technique have been reviewed relatively recently.13 An extraordinary large variety of ion–ligand complexes involving ions like Li+, Na+, K+, Rb+, Cs+, Be2+, Mg2+, Ca2+, Sr2+, Ba2+, Sc2+, Cr2+, Mn2+, Fe+, Fe2+, Co2+, Co3+, Ni2+, Cu+, Cu2+, Zn2+, Ag+, etc., can be produced readily by electrospray.11–13 One simply uses solutions of metal salts dissolved in methanol or water. The desired ligand may be added to the solution or later in the gas phase. In the absence of strongly bonding ligands in the solution, the ions obtained by electrospray are always ion-solvent molecule clusters. Thus, one observes Ca(H2O)n2+ when an aqueous solution of CaCl2 in water is used. Unfortunately, all the problems are not solved with the electrospray technique. Side reactions leading to charge separation still do occur, but only below a certain minimum size of the cluster. Thus, for example, the Ca(H2O)n2+ clusters can be dissociated to lower n clusters by collision induced dissociation11 or increased temperatures, for the case of equilibrium measurements.11–14
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However, at n = 2, the loss of H2O becomes completely suppressed by the proton transfer reaction leading to CaOH+ and H3O+. Metal ions with a higher second ionization energy than IE (Ca+) = 11.9 eV experience on declustering, proton transfer sooner, i.e. at a higher n. Thus, for Be2+, whose IE (Be+) = 18.2 eV, charge separation due 2+ to proton transfer becomes dominant14 at Be(H2O)2+ 8 and Zn , + 15 whose IE (Zn ) = 18.0 eV, proton transfer begins to dominate at Zn(H2O)2+ 6 . This means that the bond enthalpies and free energies cannot be determined below n = 8 for Be(H2O)n2+ and n = 6 for Zn(H2O)n2+. On the other hand Ba2+ whose IE (Ba+) = 10 eV, is very low, can be dissociated right down to the naked ion. Ligands which do not have protic hydrogens, such as dimethylsulphoxide (DMSO) or dimethylformamide (DMF) lead to charge separation by electron transfer. The process in general begins to occur at significantly lower ligand number n, than is the case for the protic ligands like H2O and CH3OH.11 Even when charge separation does not interfere, the determination of the sequential bond energies such as ΔGon,n–1 by ion equilibria, may not be possible for doubly charged ions, because the bond energies at low n for these species can be very high and the corresponding equilibria can be observed only at very high temperatures, not accessible with the present apparatus. Fortunately ab initio theoretical calculations are now possible for many ions and ligands for ion–ligand complexes at low n and lead not only to bond energies and entropy changes of good accuracy but also provide structural information. Thus, there is a complementarity between the data obtained from equilibria which are easily determined at high n and the theoretical calculations which are best done at low n. We have adopted this approach which we believe to be best suited to the task for the present time. There have been many experimental determinations of metal ion–ligand complexes ML+n by a variety of methods, such as ion equilibria,1–4,16 ion beam,17 and FT-ICR collision induced dissociation and photodissociation methods.18 Most important other contributions have been the numerous ab initio theoretical calculations.19-23 The application of the above data has been largely aimed to increase understanding of the bonding and structure of metal ion–ligand complexes as a part of general chemistry. Studies specifically directed towards applications in biochemistry have been much less numerous. The application of gas-phase energetics involving isolated molecules to biochemistry is extremely challenging because of the very complex environment present in biocomplexes such as enzymes, which can greatly modify the magnitude of the energy changes determined in the gas phase. In particular reactions
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involving ions are subject to great modification due to stabilization of the ions by solvation due to the environment. Furthermore, the environment is not a “simple” solvent like water, but includes also environmental effects due to the protein. Thus, the protein in a metalloenzyme provides not only the amino acid functional groups that are the ligands that bond directly to the metal ion, but also a complex environment which via non-covalent interactions such as hydrogen bonding, dipole and polarizability stabilize the ion–ligand complex. Another very important difference between the previous studies1–4,16–23 and bio-metalloion complexes is the composition of the ligands. While in the previous studies, all the ligands in the metal ion–ligand complex were generally the same, bio-complexes are characterized by the presence of different ligands. In some cases all four or six ligands which are directly bonding to the metal ion can be different, for examples see structures X–XII, in Results and Discussion. This diversity of chosen ligands is not surprising. For example, in metalloenzymes, in general only one of the ligands is directly active in the reaction that is catalyzed, however the nature of the other directly bonded ligands exerts an electronic control on the bonding of the active ligand, tuning it thus to the requirements of the catalytic process. This primary tuning by the directly bonded ligands can be achieved only by “proper choice” of a given ligand complement. Thus, understanding why a given complement of directly bonding ligands was chosen by the evolutionary process, for a given metalloenzyme, represents an important challenge for the chemist interested in metal ion–ligand bonding interactions. There are significant complexities, even when all the ligands are the same, when one focuses not on the average bond energy of the ligands but on the values of the sequential bond energies. Thus, ligands which lead to very strong bonding interactions for the first few bonds, say (1,0) and (2,1), may lead to very much weaker interactions for the last directly bonding ligands, such as the (4,3) interaction for a metal like Zn2+, who generally forms a four-coordinated complex. Often the 4,3 bond for an initially strongly bonding ligand can be weaker than the 4,3 bond of an initially weakly bonding ligand. Understanding the causes for these changes represents a first step in understanding the even more complex changes when different ligands are introduced. To meet the above challenges, we have studied changes in sequential bond energies when the same ligand is introduced and changes when the ligand composition is more complex. Both, ion–ligand complexes with the same ligand and with mixed ligand composition can be obtained in the gas phase by electrospray and
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bond energies at higher n,n–1 can be determined by the ion equilibrium technique. The low (n,n–1) bond energy values can be obtained from theory. In a few limited cases, such as carbonic anhydrase, we have been able to include also the effects of the protein and aqueous environment on the energy changes and provide a dissection of the effect of the directly bonding ligands on the catalyzed reaction. II. EXPERIMENTAL METHODOLOGY AND THEORETICAL CALCULATIONS A. Apparatus used for Ion-Equilibria Determinations Involving Metal Ion–Ligand Complexes Obtained from Electrospray The ion source reaction chamber, see Fig. 1, has been described previously24 in some detail. Therefore only a brief account will be given here. The M+ or M2+ ions were produced by electrospray generally from ~10–4 mol/l solutions of MX or MX2 salts in methanol or aqueous solution. The solution was electrosprayed at a 1 μl/ min flow rate through the electrospray capillary (ESC), see Fig. 1. Some of the spray vapors containing M+(Sl)n or M2+(Sl)n ions where Sl are solvent molecules, i.e., CH3OH or H2O, are transferred to the fore chamber (FC) of the ion source via the capillary (PRC). To reduce solvent vapor intake, the entrance of the capillary (PRC) was purged with a current of source gas (SG), consisting of dry N2. The fore chamber and reaction chamber (RC) were at the same pressure, 10 torr, which was maintained by pumping via the pumping lead (PL). Ions in the plume at the exit tip of the capillary (PRC) are deflected towards the 4 mm entrance hole in the interface electrode (IN), which leads to the reaction chamber (RC). The ion deflection is achieved by applying an electric field between the electrode attached to PRC and IN. Reagent gas consisting of dry nitrogen N2 at 10 torr and the ligand vapor(s) at known partial pressures in the millitorr range flow through the lead (RG) into RC and out of RC through the hole in IN. The ions react with ligand molecules L, in the reaction chamber. Some of the ions reaching the orifice (OR) at the bottom of the reaction chamber, escape into the vacuum region which houses the triple quadrupole mass spectrometer used for ion detection. The ion intensity ratios detected with the quadrupole Q3 were used for the equilibrium determinations, see eqs. 1 to 4, Q0, Q1 and Q2 were used as ion guides (AC only). The fore and reaction chambers are housed in a copper block which was heated with cartridge heaters (not shown in Fig. 1) embedded in the copper block and the temperature of the block
Determination of Sequential Metal Ion–Ligand Binding Energies
83
and reaction chamber was determined with the thermocouple (TC). B. Determination of Ion–Ligand Equilibria Two different types of equilibria are generally determined; these are ligand dissociation and ligand exchange equilibria. These can be represented by the two general equations: MB+ = M+ + B
(ligand B, dissociation)
–ΔG° = RT ln Keq
K eq =
(5)
P M+ • P B PMB+
where PM+/PMB+ is replaced by the ion intensity ratio for the two ions MB+ + C = MC+ + B
(ligand exchange)
–ΔG° = RT ln Keq
K eq =
(6)
PMC + PB • PMB+ PC
where PMC+/PMB+ is replaced by the ion intensity ratio of the two ions. C. Sequential Ligand (n,n–1) Dissociation Equilibria: MLnz+= MLz+n–1 + L The equilibria are determined when only one reagent gas vapor, that of L whose partial pressure PL is known, is introduced into the reaction chamber RC, see Fig. 1. The reactant ions entering RC when only MX2 and pure solvent, such as H2O, was used, are generally M(H2O)n2+, when low IE(M+) such as, say Ca2+ are used (see Introduction). The M(H2O)n2+ ions are observed in the absence of a reagent gas in RC and n depends on the temperature of RC. The H2O clustering equilibria can be determined by introducing H2O vapor in RC. Other ligand L equilibria can be determined by introducing vapor of that ligand into RC. Clean MLn2+ mass spectra are observed when L bonds more strongly to M2+ than H2O. In that case a complete exchange of H2O for L occurs, which is followed by the establishment of the MLn2+ clustering equilibria. Examples of such equilibria are the results25a for 2+ Ca(Me2CO)2+ n = Ca(Me2CO) n–1 + Me2CO
(7)
2+ Ca(MAcA)2+ n = Ca(MAcA) n–1 + MAcA
(8)
and
84 Michael Peschke, Arthur T. Blades and Paul Kebarle
Figure 1: Ion-source and reaction chamber for determination of ion–molecule equilibria. Electrospray generator ESC. Pressure reducing capillary PRC transfers ions, produced by electrospray, from atmospheric pressure to 10 torr pressure of forechamber FC. Electric field imposed between electrode EL and interface plate IN, drifts ions from PRC plume into reaction chamber RC. Reagent gas RG consisting of 10 torr nitrogen N2 carrier gas and reactant gases at known 1–100 mtorr partial pressures flows into reaction chamber RC and out of RC into forechamber FC. Gases pumped out of forechamber by pumping lead PL. Ion-molecule equilibria establish in reaction chamber RC. Ions escaping through orifice OR into vacuum are detected and their intensities determined with a quadrupole mass spectrometer. Ion-source reaction chamber is machined out of a copper block CB which is heated by heating cartridges (not shown). Temperature of block is determined with thermocouple TC.
Determination of Sequential Metal Ion–Ligand Binding Energies
85
(where MAcA stands for N-methylacetamide) which are discussed in Part A of Section III. D. Ligand Dissociation Equilibria with Mixed Ligands such as 2+ MAxB2+ = MA2+ = MAxBy2+ x + B, and MAxByC y C Ligand equilibria of mixed ion complexes can be determined by obtaining from the electrospray process a suitable ion ligand complex. Addition of some strongly bonding ligand to the solution can lead to the production by electrospray of a precursor ion which has incorporated the strongly bonding ligands. An example of this type of experiment is the production of Zn(Im)32+ where Im stands for imidazole. Imidazole is the substituent in the histidine residue in proteins and serves as a model for the ligation of this residue. The fourth ligand in the Zn ligand complex in carbonic anhydrase is H2O. The bond energy for this fourth ligand can be determined by using H2O as the reagent vapor in the reaction chamber RC. The Zn(Im)32+ supplied from the electrospray reacts with H2O in RC and the equilibrium: Zn(Im)3H2O2+ = Zn(Im)32+ + H2O
(9)
leading to the bond-free energy of the H2O ligand can be determined (see Part C of Section III). E. Ligand Dissociation Equilibria with Mixed Ligands some of which are Negative Ions Negative ions are a special case of strongly bonding ligands in the gas phase. Metal ion-mixed ligand complexes can be prepared via electrospray. The ionic ligands can be the negative counterions of salts added to the solution that is used for electrospray, or the actual counterions X– of the MX2 salt used. At higher negative counterion X– concentrations, formation of the adducts MX+ ligated to additional neutral ligands, can be produced by electrospray. For example, the ion Zn(CH3CO2)Im2+ which contains the acetate anion can be produced by electrospray from a solution of Zn(CH3CO2)2 which contains also imidazole. Supplying H2O vapor to the reaction chamber RC, one can determine the equilibrium: Zn(Im)2(CH3CO2)(H2O)+ = Zn(Im)2(CH3CO2)+ + H2O (10)
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Michael Peschke, Arthur T. Blades and Paul Kebarle
The Zn(Im)2(CH3CO2)(H2O)+ complex models the Zn ligand complex in the reaction site of carboxypeptidase (see Part C of Section III). A large variety of M2+ containing complexes have been prepared25b by the above method. F. Ligand Exchange Equilibria Ligand exchange equilibria involving two ligand species, A and B, can be determined when ligand vapors of A and B are introduced in the reaction chamber. It is necessary that the affinity of the two ligands to the metal ion is not very different. Thus assuming that A bonds much more strongly than B, MA complexes will dominate and it would be necessary to use very high concentrations of B relative to A before MB complexes show up in measurable concentrations at equilibrium. Another restriction, which is present at higher third gas pressures as used in the present experiments, is the competition between ligand association-dissociation reactions and ligand exchange. The only way to restrict the ligand exchange study to low ligand n numbers is to work at sufficiently high temperatures where the high ligand number complexes are unstable. For singly charged ions for which the bonding is weaker, one can observe the equilibria at low total ligand n numbers, without having to go to inaccessibly high temperatures. An example of such a study26a are the exchange equilibria involving the Cu+ ion, for two different ligands A and B. CuA2+ 2B = CuB2+ + 2A
(11)
which could be determined at moderate temperatures (390K). While higher ligand number complexes like CuA3+, CuA2B+, etc., were also observed, their concentrations were low because Cu+ bonding to the third ligand is very much weaker than to the first two.26b A similar study involving Ag+ was also made.27 The intermediate equilibria, CuA2+ B = CuAB+ + A
(12)
are also observed simultaneously. Thus free energy change information for the half and complete exchange is obtained. For the application of such data to metalloion biocomplexes, see Part A of Section III. G. Theoretical Calculations All computations in this study were done using the Gaussian 94 suite of programs. Due to the large number of atoms involved in some of
Determination of Sequential Metal Ion–Ligand Binding Energies
87
the ion–ligand complexes and the desire to use a common computational level to facilitate comparisons, the B3LYP set of DFT functionals was chosen as the theoretical model. From previous studies in our laboratory, the 6-311++G(d,p) basis set was found to give very reliable energy values and was therefore chosen as the standard level for both optimization and frequency calculations. It contains sufficient diffuse functions and is flexible enough to give a good account of the longer ranging ion–ligand interactions. In addition, this basis set is large enough to generally reduce the basis set superposition error for the relatively large ion–ligand bond energies below the error bars inherent in the method and makes special corrections unnecessary. For Ca, the only element in this study not included in the 6-311++G(d,p) basis set, the valence triple-ζ basis set by Ahlrich supplemented with two contracted d polarization functions was used (0.43·d(1.97) + 1.0·d(0.40)). Inclusion of the polarization functions is essential, since computational results without the polarization functions can differ by more than 30 kcal/mol. III. RESULTS AND DISCUSSION A. Hydration of some Singly and Doubly Charged Ions The sequential bonding energies of ion hydrates provide important basic information and a “natural scale” to which other ion–ligand interactions can be compared. Thus, only ion–ligand interactions which are very much stronger than those with water molecules will lead to stable ion–ligand complexes in solution. Similarly, metalloion–ligand complexes inside a protein such as an enzyme, must provide sufficient stability to prevent the escape of the metal ion to the aqueous environment (such as the cytoplasm) surrounding the enzyme. The bond enthalpies for the magnesium hydrates Mg(H2O)2+ n obtained from ion–equilibria determinations28 are given in Fig. 2. The bond enthalpies for the hydrates of the isoelectronic singly charged Na+, which were determined in much earlier work from this laboratory,1 are given for comparison. Due to the much weaker bonding for the singly charged ion Na+, all ΔHon,n–1 down to n = 1 could be determined by means of ion equilibria, within an experimentally easily accessible temperature range. For the much stronger bonding Mg2+ ion, the energies for the lower hydrates were too high and could not be determined experimentally. The data in Fig. 2, given for this low range, are theoretical results of Pavlov and co-workers,23 obtained with density functional theory.
88
Michael Peschke, Arthur T. Blades and Paul Kebarle
Figure 2: Experimental ■ values, for enthalpy of dissociation of ΔHn,n–1 for hydrates of sodium1 and experimental28 ◆ and theoretical values23 Ë for hydrates of Mg2+.
The ΔHon,n–1 values are seen to decrease rapidly, particularly so for the doubly charged Mg2+ ion. The decreases are largest at low n. The decreases observed for the singly charged ions have been attributed1,22 to ligand–ligand repulsion due to the permanent and induced dipoles and to Pauli repulsion. Less efficient ion core
Determination of Sequential Metal Ion–Ligand Binding Energies
89
polarization and to a much smaller extent, charge transfer from the ligands to the core ion, have been also invoked,1,19. For doubly charged ions such as Mg2+, Ca2+, Zn2+, etc., the same factors will be involved also. Since the doubly charged ions are much smaller than the corresponding isoelectronic singly charged ions, dipole and Pauli repulsion will be larger and a somewhat increased charge transfer effect is also expected for Mg2+ and Ca2+. A much larger charge transfer effect is expected for Zn2+ for the first two ligand bonding interactions. For a theoretical energy component analysis of Zn2+, of one–ligand complexes, see Garmer & Gresh.21 The decreasing bonding due to the cumulative effect of the rapidly increasing repulsion due to dipole and Pauli repulsion and of charge transfer and less efficient core polarization, lead ultimately to transition of the ligands to an outer shell. A comparison between the sequential hydration enthalpies of Mg2+ and Ca2+ obtained from theoretical 23 and experimental determinations is provided in Fig. 3. Fortunately, there is an overlap between the theoretical results and the experimental determinations in the region between (n,n–1)= (6,5) and (8,7) which is the region where transitions to the outer shell may be expected. This overlap allows a comparison between the theoretical and experimental results. See also the hydration data for Mg2+ and Ca2+ in Tables 1 and 2. There is very good agreement for the (6,5) results. Thus, for Ca2+, ΔGo6,5 = 16.1 (exp) vs 15.7 kcal/mol (theor) and ΔHo6,5 = 25.3 (exp) vs 25.5 kcal/mol (theor). However the agreement for the higher n which correspond to the transition to the outer shell is less good, with the experimental results indicating somewhat higher endoergicities for the dissociation. The major differences occur for the entropy terms. Thus for Ca2+, ΔSo7,6 = 20.2 (exp) vs ~35 cal/degree mol (theor), which corresponds to an approximate average for the two theoretical structures,23 I and II, shown in Fig. 4. The relatively very low experimental ΔSo7,6 = 20.2 cal/degree mol value for calcium indicates that the outer shell water molecule has much more freedom than is the case for the theoretical structures I and II. Noting that I and II have almost the same free energy ΔGo7,6, 7.4 (I) vs 7.2 (II), see Table 2, it was argued28 that the transition between these two structures would be very facile and that this would lead to a high mobility of the outer water molecule resulting in a quasi-translation over the “surface” of the inner shell. Using a model for such a transition, an entropy value was obtained,28 which is very close to the experimental entropy change. Sequential hydration energies were determined28 also for Sr2+ and Ba2+. These results indicate that the transition to the outer shell
90
Michael Peschke, Arthur T. Blades and Paul Kebarle
Figure 3: Enthalpy changes ΔHon,n–1 for Mg2+ and Ca2+. Data for n = 1 to n = 7 ~ Mg; Ë Ca are theoretical results (Pavlov),23 while ■ Mg; ◆ Ca data from n = 6 to n = 14, are experimental results.28
occurs later for these ions, probably after n = 7, for Sr2+ and n = 8 or higher for Ba2+. Noting that ΔGon,n–1 and ΔHon,n–1 for Mg2+ and Ca2+ become very similar at high n, Fig. 3, one could expect that the difference between ΔGo0,n (Mg2+) and ΔGo0,n (Ca2+) at high n might correspond
Determination of Sequential Metal Ion–Ligand Binding Energies
91
Table 1. Thermochemical dataa for reaction M(H2O)n2+= M(H2O)2+ n–1 + H2O. Mg2+
Ca2+
ΔG
ΔH
ΔS
n
ΔG
ΔH
ΔS
6
16.0
24.6
29.1
6
16.1
25.3
31.1
7
12.8
20.3
25.3
7
10.9
16.9
20.2
8
10.9
18.0
23.8
8
9.6
16.1
21.9
n
9
9.5
17.0
25.1
9
8.4
15.3
23.1
10
8.1
15.7
25.5
10
7.3
14.5
24.0
11
7.0
14.3
24.3
11
6.5
13.3
22.7
12
6.2
12.9
22.3
12
5.8
13.0
24.1
13
5.6
12.3
22.5
13
5.2
12.4
24.4
14
5.1
12.1
23.7
14
4.7
11.9
24.2
(a) Data from van’t Hoff plots. ΔG° in kcal/mol at 298 K, standard state 1 atm. ΔH° in kcal/ mol, ΔS° in cal/degree mol. Estimated error: ΔG° 0.5 kcal/mol; ΔH° 1 kcal/mol; ΔS° 2 cal/degree mol. 28
to the difference between the total free energies of hydration, ΔGoh (Mg2+) – ΔGoh (Ca2+) which correspond to transfer of the naked ions from the gas phase to aqueous solution and can be evaluated via thermodynamic cycles.29 Taking the theoretical values for the (0,6) hydration and the experimental values for the (6,14) hydrations, the differences obtained were: ΔGo0,14 (Mg2+) – ΔGo0,14 (Ca2+) = –74.0 kcal/mol which is very close to ΔGoh (Mg2+) – ΔGoh (Ca2+) = –77.3 kcal/mol.29 Similarly, ΔΗo0,14 (Mg2+) – ΔΗo0,14 (Ca2+) = –81 kcal/mol, versus ΔΗoh (Mg2+) – ΔΗoh (Ca2+) = –83 kcal/mol.29 The closeness of the results indicates that an unknown ΔGoh (M2+) or ΔΗoh (M2+) could be obtained from gas phase hydration data which extend to sufficiently high n. B. Binding Energies for Mg2+, Ca2+ and Zn2+ with Ligands L = Acetone and N-Methylacetamide in ML2+ n for n = 1 to 7 The oxygen ligands acetone (Me2CO) and N-methylacetamide (MAcA) are expected to bond much more strongly than water to Mg2+, Ca2+ and Zn2+. N-methylacetamide is a good model30 for interactions of the carbonyl oxygen from the peptide backbone, while comparisons with acetone provide a useful insight on the effect of the –NHCH3 group on the bonding of the carbonyl oxygen to the metal ion. Previous equilibrium measurements31 for K+ which is isoelectronic to Ca2+ involving several ligands had provided the following ΔΗo1,0 (kcal/mol) values: H2O 17.9; Me2CO 26; dimethylformamide 31; dimethylacetamide 31; and dimethylsulfoxide 35. Similar orders
92
Table 2. Binding energies of H2O to Mg2+ and Ca2+ (from theoretical calculations by Pavlov et al.23).(a) (ΔΗo7,6)(e)
(ΔΗon,n–1)(h)
(ΔΓo7,6)(e)
Mg(H2O)52+
279.4
Mg(H2O)5(H2O)2+(b)
300.2
Mg(H2O)5(H2O)2+(c) Mg(H2O)4(H2O)22+(c)
285.9
–
236.6
–
165.4
–
307.8
21.9
248.2
11.6
199.6
34.2
299.0
306.8
20.9
246.5
9.9
202.1
36.7
299.5
307.5
21.6
246.9
10.3
203.4
38.0
Mg(H2O)62+
303.9
311.8
25.9
250.9
14.3
203.2
37.8
Mg(H2O)6(H2O)2+(c)
322.9
331.8
20.0
260.3
9.4
239.6
36.4
Mg(H2O)72+
307.8
Mg(H2O)6(H2O)22+(d)
337.2
346.7
14.9
266.6
6.3
269.9
30.3
Ca(H2O)52+
209.7
215.2
–
168.5
–
156.7
–
Ca(H2O)5(H2O)2+ (c)
228.2
234.8
19.6
177.9
9.0
190.7
34.0
Ca(H2O)5(H2O)2+ (c)
228.5
235.4
20.2
177.4
8.9
194.6
37.9
Ca(H2O)4(H2O)22+(c)
225.7
233.0
17.8
174.0
5.5
198.0
41.3
Ca(H2O)62+
234.4
240.7
25.5
184.2
15.7
189.7
33.0
Ca(H2O)6(H2O)2+ (f)
250.7
258.09
17.4
191.4
7.2
223.6
Ca(H2O)6(H2O)2+ (g)
252.0
259.7
191.6
7.4
228.4
38.7
Ca(H2O)72+
248.2
19.0
(ΔΓon,n–1)(h)
(ΔΣo7,6ΔS)(e)
(ΔSon,n–1)(h)
(a) Data quoted in Table 2 are only for n = 5 to n = 8 hydrates. A much wider set of energies is available in the original reference.23 ΔEn,0 corresponds to the energy change at 2+ T = 0 K for the reaction: M(H2O)x(H2O)2+ y = M + (x + y) H2O: where x + y = n. (b) Oxygen of outer shell molecules forms one hydrogen bond to an inner shell water molecule. (c) Oxygen of outer shell molecule forms two hydrogen bonds, one each to hydrogens of two adjacent inner shell water molecules. (d) Each outer water molecule forms two hydrogen bonds to different inner water molecules and one inner water molecule is engaged in two hydrogen bonds. (e) Pavlov et al.23 published only the ΔEo7,6 values at 0K. The ΔHo7,6, ΔGo7,6 and ΔSo7,6 at T = 298K values given in the table were obtained from evaluated corrections to ΔEo7,6 from the Gaussian 94 file, graciously provided to us by the authors.23 The vibrational frequencies were evaluated at the Hartree-Fock level.23 (f)See Structure II in text. (g)See Structure I in text. (h)Difference between given structure for n and most stable (n–1) structure.
Michael Peschke, Arthur T. Blades and Paul Kebarle*
ΔEon,0 (kcal/mol)
Complex
Determination of Sequential Metal Ion–Ligand Binding Energies
93
Figure 4: Two structures for Ca(H2O)6(H2O)2+ obtained by Pavlov et al.23 The ΔG° of formation for the two structures are almost the same. However, II has a higher ΔGo7,6 than structure I.
94
Michael Peschke, Arthur T. Blades and Paul Kebarle
with a somewhat more restricted variety of ligands were obtained32 also for Na+ which is isoelectronic with Mg2+ and with a large2 variety of ligands,26 for Cu+ which is isoelectronic with Zn2+ (see Part C of Section III). Figure 5: Bond enthalpies ΔH for Mg2+ and acetone H F, Nmethylacetamide ❍ ●, and water Ë ◆. Open symbols indicate theoretical results, full symbols experimental determinations.
Determination of Sequential Metal Ion–Ligand Binding Energies
95
Figure 6: Bond enthalpies ΔH for Ca2+ and acetone H F, Nmethylacetamide ❍ ●, and water Ë ◆. Open symbols indicate theoretical results, full symbols experimental determinations.
As was the case for the previous hydration study28 of the doubly charged ions, see Part A of this section, equilibrium determinations only for n > 5 were possible. Bond energies for n < 6 were based on theoretical calculations.25a Since only sparse data were available in
96
Michael Peschke, Arthur T. Blades and Paul Kebarle
the literature for the present ligands, the theoretical calculations were performed in this laboratory.25a Due to the greater complexity of the present ligands, the calculations could not be extended to all values of n between 1 and 6. A summary of the bond energy data obtained25a from the theoretical calculations and equilibria is given in Table 3, while Figs 5 and 6 provide plots of the sequential bonding enthalpies for H2O, Me2CO and MAcA to Mg2+ and Ca2+. The theoretical bond enthalpies ΔΗo1,0 increase in the order Ca, Mg, Zn for all three ligands, H2O, Me2CO, MAcA, see Table 4. The difference observed for Ca2+ and Mg2+ is expected simply on the Table 3. Bonding energies(a) of acetone (Me2CO) and N-methylacetamide 2+ (MAcA) to Mg2+, Ca2+ and Zn2+ for the reaction: M(L)2+ n–1 + L → M(L)n Zn L = Me2CO
ΔH°298
Mg
ΔS°298
ΔG°298
ΔH°298
Ca
ΔS°298
ΔG°298
ΔH°298
ΔS°298
ΔG°298
89.3
27.6
81.1
1,0
153.5
27.5
145.3
121.2
27.3
113.0
2,1
104.9
34.3
94.7
95.0
28.9
86.4
63.3
39.3
51.5
6,5
17.4
28.5
9.0
22.3
34.8
11.9
24.2
30.9
15.0
7,6
14.4
24.6
7.0
13.6
22.4
6.9
11.6
17.8
6.3
174.9
31.0
165.7
106.5
29.3
97.7
3,2
L = MacA 1,0 2,1
140.9
28.9
132.3
122.2
36.6
111.3
5,4
25.1
31.4
15.8
25.3
30.6
16.1
6,5
22.9
30.8
13.7
22.6
30.8
13.5
23.7
30.9
14.5
7,6
20.8
29.9
11.8
19.9
28.1
11.5
19.6
27.7
11.3
8,7
17.9
26.5
10.0
9,8
17.5
29.0
8.9
(a) All energies are given in kcal/mol and the entropies are given in cal/mol·K. The standard level for all computational values (1,0; 2,1 and 3,2 reactions) is B3LYP/6311++G(d,p).
Table 4.
Comparison of bond enthalpies for M2+L complexes(a) ΔHo1,0 (kcal/mol)
L Ca2+
Mg2+
Zn2+
H2O
56.5
81.8
Me2CO
89.3
153.589.3
121.1
MAcA
106.0
140.9
175.0
(a) Selected values from Tables 2 and 3.
103.1
Determination of Sequential Metal Ion–Ligand Binding Energies
97
basis of the smaller size of the Mg2+ ion. Bauschlicher and coworkers19b have attributed the strong bonding for Cu+ which is isoelectronic (3d10,4s0) to Zn2+, to an ability of Cu+ to reduce the metal–ligand repulsion by sd sigma hybridization. A similar effect might have been expected also for Zn2+. However, the theoretical calculations25a show that the sdσ hybridization is much less important for Zn2+ because the higher charge of Zn leads to a stronger charge transfer interaction, independent of sds hybridization. The charge transfer donor–acceptor interaction increases25a in the order H2O < Me2CO < MAcA, as could have been expected on the basis that a ligand with high polarizability is a better electron donor.33 The calculations25a indicate that the charge transfer is very much smaller for Ca2+ and Mg2+ so that the bonding to these ions is essentially purely electrostatic. The stronger bonds in Mg2+ and Ca2+ with Me2CO and MAcA, relative to water are then due to the larger dipole moments and higher polarizability of these ligands relative to water. The much stronger bonding in ZnL2+ and ZnL22+ for Me2CO and MAcA relative to water is due to stronger electrostatic interactions, but also very significantly due to charge transfer from the ligands to Zn2+ and the formation of two electron bonds. The specific two-electron bonding carries only up to ZnL22+ and therefore, the fall off of ΔΗon,n–1 with n is more rapid above n = 2 for Zn2+ relative to Mg2+ and Ca2+. For further specific differences between the isoelectronic Cu+ and Zn2+, see original work.25a Some of the effects discussed are clearly supported by the structures III–VIII, shown in Figs 7–9. Thus, the dominance of electrostatic bonding for Mg2+ and Ca2+ is evident in the structure of the complexes with acetone, structure V, which shows a linear alignment of the C–O–M bonds that corresponds to coaxial alignment of the dipole moment of acetone. With Zn2+, structure VI, due to the presence of electronic donor–acceptor interactions, the C–O–Zn bond is bent. Electron donor interactions lead to a lengthening of the C–O bond, and the greatest increase of the C–O bond is seen for MAcA and Zn, where the bond is 1.329 Å (structure VIII), which is much longer than the C–O bond in free MAcA where the bond is 1.221 Å (structure IV). For additional details see Peschke et al.25a The initially more strongly bonding Me2CO and MAcA lead to a more rapid decrease of ΔΗon,n–1 with n for Mg2+, Ca2+, Zn2+, so that at high n, such as n = 6, the bond energies for H2O, Me2CO and MAcA become essentially equal (see Table 3 and Figs 4 and 5). The more rapid decrease for Me2CO and MAcA relative to water for Mg2+ and Ca2+ is probably due to the bigger dipole–dipole and Pauli repulsion expected for these ligands, while for Zn2+ the additional effect of the already mentioned charge transfer leads to an even more rapid fall off.
98
Michael Peschke, Arthur T. Blades and Paul Kebarle Figure 7:
Calculated structures for acetone and N-methylacetamide.
Determination of Sequential Metal Ion–Ligand Binding Energies
99
Figure 8: Calculated structures for Mg(Acetone)2+ and Ca(Acetone)2+. Bond distances for Ca(Acetone)2+ are given in brackets, structure V. Calculated structure for Zn(Acetone)2+, structure VI.
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Michael Peschke, Arthur T. Blades and Paul Kebarle
Figure 9: Calculated structures for Mg(N-methylacetamide)2+ and Ca(Nmethylacetamide)2+. Bond distances for Ca(N-methylacetamide)2+ are given in brackets, structure VII. Calculated structure for Zn(N-methylacetamide)2+, structure VIII.
Determination of Sequential Metal Ion–Ligand Binding Energies
101
An equalization at higher n is also present when different metal ions are bonded to the same ligands. The bond strength order Zn > Mg > Ca observed at low n becomes greatly attenuated and even reversed at high n. Thus the ΔΗo6,5 values (kcal/mol) for acetone are: 17.4 (Zn); 22.3 (Mg) and 24.2 (Ca), see Table 3. Crowding of the inner shell due to dipole and Pauli repulsion occurs earlier for the smaller ions and is probably responsible for the observed reversal. The earlier work on the M2+ hydrates, see Part A of this section, and particularly the theoretical results by Pavlov et al.23 had shown that for Mg2+ and Ca2+, the transition to the outer shell occurs after the six coordinated complex is formed. Pavlov’s data23 also showed that for Zn2+, the transition occurs earlier, i.e., after the four coordinated complex was formed. The results for Me2CO and MAcA bonded to Mg2+ and Ca2+ can be explained if the inner shell occupation numbers for water are also assumed for these ligands. For Zn2+, the situation is less clear, particularly for acetone. One must also take into account that the transitions to the outer shell are not governed only by “crowding” in the inner shell but also by the type of bonding present in the outer shell. Strong bonding between the inner and outer shell molecules, such as H bonding, can promote earlier transitions to the outer shell. Useful insights are provided by an examination of the specific ΔH and ΔS values in the region of the transition to the outer shell for Ca2+ and the three ligands: H2O, Me2CO and MAcA. These results are detailed Table 5. The much larger drop from ΔΗo6,5 to ΔΗo7,6 observed for acetone must be related to a transition to an outer shell for the seventh ligand and the absence of H bonding for acetone in the outer shell. The ΔΗo6,5 = 23.7 is smaller than that for H2O, 25.3, and this is probably due to the larger repulsion of the MAcA in the (crowded) six shell and the more extensive charge transfer expected from MAcA. Table 5.
Enthalpy and entropy changes in inner to outer shell transition region for Ca2+ hydrates(a) ΔH° kcal/mol
ΔS° cal/degree mol
Ca(H2O)6,5
25.3
31.1
Ca(H2O)7,6
16.9
20.2
Ca(Me2CO)6,5
24.5
30.9
Ca(Me2CO)7,6
11.6
17.8
Ca(MAcA)6,5
23.7
30.9
Ca(MAcA)7,6
19.6
27.7
Ca2+
(a) Selected data from Table I.
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Michael Peschke, Arthur T. Blades and Paul Kebarle
On the other hand ΔH7,6 (MAcA) = 19.6 is larger than that for H2O, 16.9. This difference shows that a stronger hydrogen bond is formed between the inner and outer shell MAcA molecules relative to the inner-outer shell H2O molecules. Stronger H bonding for MAcA is expected because it involves a carbonyl oxygen of the outer MAcA molecule which is a better H acceptor than the oxygen of the water molecule. The N–H hydrogen of the inner MAcA involved in the hydrogen bond may be also more acidic than the hydrogen of a water molecule, thus further strengthening the H bond for the MAcA system relative to that for H2O. The low value ΔSo7,6 = 20.2 cal/degree mol for H2O was attributed to a quasi-translational motion of the outer shell molecule which can move over the inner shell H2O molecules via the structures I and II, see Part A of this section. The very low ΔSo7,6 = 17.8 cal/ degree mol for Ca and acetone can be also rationalized on the basis of a very free quasi-translation of the outer shell acetone molecule over the “surface” provided by the inner shell Ca(Me2CO)62+ complex. Due to the absence of H bonding, the seventh molecule is very weakly bonded and thus free to quasi-translate. For MAcA a rather high ΔSo7,6 = 27.7 cal/degree mol is observed, which is incompatible with a free translation. There are two important differences between Ca(MAcA)62+ (see structure IX shown in Fig. 10) and Ca(H2O)62+. The amide complex has only six protic hydrogens, furthermore the free rotation of the inner shell water molecules which is required for the conversion for structures I to II in the Ca(H2O)6(H2O)2+ water complex is expected to be only a hindered rotation in the acetamide complex. The formation of bridged analogues to structure I, will be very much less likely for the acetamide complex and therefore a facile mobility leading to a low ΔSo7,6 entropy cannot be expected. The changes between ΔHo6,5 = 23.3, ΔHo7,6 = 13.6 and ΔSo6,5 = 34.8; ΔSo7,6 = 22.4 (Table 3) for Mg2+ and acetone are similar to those for Ca2+ and acetone, although somewhat less pronounced. This indicates that the transition to an outer shell where the outer molecule is quite free occurs not only for Ca2+ and acetone but also for Mg2+ and acetone. Comparison of the (6,5) and (7,6) values of Mg2+ and MAcA with those for Ca2+ and MAcA shows that these are also similar. Therefore also for Mg2+ and MAcA a transition from inner to outer shell probably occurs with the seventh molecule. There are also similarities between the (6,5) and (7,6) values for acetone between Zn2+ and Mg2+ but they are less consistent. Thus, ΔHo6,5 = 17.4 (Zn2+) is considerably smaller than ΔH6,5 = 22.3 for Mg2+ while the ΔH7,6 = 14.4 (Zn2+) is higher than ΔH7,6 = 13.6 (Mg). Also, the entropy changes for Zn2+ ΔSo6,5 = 28.5, ΔSo7,6 = 24.6 are far less
Determination of Sequential Metal Ion–Ligand Binding Energies
103
Figure 10: Calculated structure for Ca(N-methylacetamide)62 + at the B3LYP/ LANL2DZ level.
indicative of a transition to an outer shell where there is much greater freedom than was the case for Mg2+ and particularly Ca2+. Therefore, probably, the transition to an outer shell for Zn2+ with acetone or MAcA occurs earlier such as with the fifth or the sixth molecule. Unfortunately, data for the (4,3) changes are not available to provide more solid confirmation. The theoretical results23
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Michael Peschke, Arthur T. Blades and Paul Kebarle
for Zn(H2O)n2+ showed that the transition to an outer shell occurs with the fifth molecule. However the outer shell molecules are favored by the H bonding. For acetone, in the absence of H bonding, the transition may occur later, i.e., after the fifth ligand, even though acetone is bigger. Mg2+ and particularly Ca2+ play a most important role in biological processes.34,35 Of special interest is the participation of Ca2+ and Mg2+ in muscle relaxation and contraction, where Ca2+ binding proteins, such as muscle calcium binding parvalbumin (MCBP), are involved. This group of proteins has a common Ca2+ binding motif of two helices that flank a loop of 12 contiguous residues. The 12 residues provide the six ligands that bind to Ca2+. Backbone carbonyl oxygens from these residues, as modeled by MAcA, do participate in the Ca2+ bonding, however most often only one of the oxygens34,35 comes from that source, although there are cases where two or three carbonyl oxygens participate. The carboxy group of acidic residues such as aspartic acid (asp) and glutamic acid (glu) is also involved very often as ligand and in some proteins, such as MCBP, provide as much as four of the total six ligands. A minimum of one carboxylic group is always present. Hydroxy ligands such as serine and threonine as well as water molecules provide the rest of the ligands (see Table 2 in Kretsinger35). To address the problem posed by the presence of several different ligands, we have been successful in preparing, by electrospray, Ca2+ and Mg2+ ion ligand complexes in the gas phase, containing mixed ligands.25b These complexes did include one or more carboxylic acid groups. Thus using acetic acid as a model of the aspartic or glutamic acid residue, complexes containing one or more acetic acids, as well as MAcA or acetone, and water molecules, could be prepared and some of the binding energies determined by ion equilibria. The acidic groups, when a single group was present, corresponded to deprotonated acid, i.e., the acetate, while when multiple, included only one deprotonated species, such that the charge of the complex was z = +1. Ligand bond enthalpies and free energies obtained from ion–ligand equilibria of such Ca2+ and Mg2+ complexes as well as some limited theoretical results, will be presented in a future publication.25b See also Part C of Section II. Considering the extraordinary complexity of muscle Ca2+ and Mg2+ proteins and their function,34,35 the present results25a are as yet probably totally insufficient to provide new biological insights. The presence of strong H bonding between inner and outer shell MAcA molecules, demonstrated in the present work, may have biological significance. This point still remains to be examined.
Determination of Sequential Metal Ion–Ligand Binding Energies
105
The function of a relatively simpler system, involving the Zn metalloenzyme complex in the enzyme carbonic anhydrase, could be successfully correlated with the bond energies of the directly bonded ligands. The experiments that led to this correlation and the development of the actual energy relationships are described in Parts D and E of Section III. C. Exchange Equilibria: CuA2+ + 2B = CuB2+ + 2A: The Dominance of Histidine The determination of the ligand exchange equilibria26a CuA2+ + 2B = CuB2+ + 2A
(11)
(for experimental see Part D of Section II) provided a ladder or connecting equilibria ΔGo11 which is shown in Fig. 11. Since the determination of the temperature dependence of these equilibria was deemed to be difficult,26a the entropy changes were obtained from theoretically evaluated entropies of the reactants involved.26a This allowed the evaluation of ΔSo11 and ΔHo11. The absolute values for the gas phase reactions: CuL2+ = Cu+ + 2L
(13)
shown in Table 6, were obtained by calibrating the relative scale, Fig. 11, to one absolute value, due to calculations by Bauschlicher et al.,19b for: Cu(NH3)2+ = Cu+ + 2NH3
(14)
A discussion of the general significance of the data obtained in Table 6 such as the correlation of the bond energies with predictions of the hard and soft bases principle,33 can be found in the original publication.26a Here we consider only the implications of the data for biological ligands, i.e., ligands provided by the functional groups of peptide residues in proteins. A number of the ligands in Table 6 model such residues. Thus, MeOH models serine, EtOH threonine, MeSH cysteine, MeSMe methionine, PrNH2 (propylamine) models lysine and Me-C3H3N2 (methyl-imidazole) models histidine. Combining these results with a set of results that includes the remaining amino acids, obtained by Cerda and Wesdemiotis,37 one
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Michael Peschke, Arthur T. Blades and Paul Kebarle
Figure 11: Scale of relative dissociation free energies, ΔGo2, for reactions: CuL2+= Cu+ + 2L, based on measured free energies ΔGo1 for exchange reactions: CuA+2 + 2B = CuB+2 + 2A. Temperature 393K. Values in kcal/mol. Double arrows connect CuL+2 pairs for which exchange equilibria were determined.
Determination of Sequential Metal Ion–Ligand Binding Energies
107
Table 6. Thermochemical dataa for reaction: CuL= Cu+ + 2L. ΔGo393
ΔGo298
ΔS° (cal/K mol)b
ΔH° (kcal/mol)
110.3
116.4
63.8
135.4
101.4
–
–
–
(n-Bu)3N
98.7
–
–
–
C5H5N
96.5
101.8
55.3
118.2 116.0
L Me-C3H3N2h Et-C5H5Ni
MeCON(Me)2
93.8
99.2
56.4
Pr-NH2
93.1
98.6
57.7
115.8
Me2SO
90.4
95.8
57.1
112.8
MeCONH(Me)
89.4
94.6
55.0
111.0
MeCN
85.3
90.9
59.3
108.6
NH3
82.7
88.2
57.8
(105.4)c
MeSMe
80.4
85.5
53.5
101.4
Pr2CO
78.8
–
–
–
Et2CO
76.9
81.9
53.2
97.8
Me2COd
74.2
79.3
53.2
95.2
MeCO2Med
71.1
77.7
64.2
96.3
Et2Od
71.7
77.5
60.9
95.6
MeSHd
70.9
76.0
53.6
92.0
EtOHd
64.6
70.3
60.1
88.2
i-PrBrd
62.2
66.7
47.3
80.8
MeOHd
61.1
66.6
57.9
83.8
EtBrd
57.8
62.3
47.7
76.5
H2O
53.9
59.3
56.2
76.0
EtCld
54.4
58.7
44.8
72.1
(a) See Deng and Kebarle.26 (b)Obtained from S° values of reactants which were based on vibrational and rotational constants of reactants obtained26 with HF/3-21G* basis sets of Gaussian 94. (c) Based on theoretical calculations by Bauschlicher et al.19b This value is used to obtain absolute values from ΔGo1 experimental results for all other ligands. (d)From relative scale of ΔG° values obtained by Johnes and Staley36 and calibrated to absolute scale and evaluated ΔS° changes of present work. (e) 1-Methyl imidazole. (f) 4-Et pyridine.
comes to the conclusion27 that histidine is the strongest bonding residue of all neutral peptide residues. Cu+ is isoelectronic with Zn2+ and therefore histidine can be expected to be also the most strongly bonding neutral residue for Zn2+. Indeed, theoretical calculations by Garmer and Gresh,21 performed in connection with the HSAB theory, provide exactly such a result. We consider this to be a very significant finding, because histidine is the most often occurring residue in metalloenzymes and metalloproteins, particularly so for Cu2+ and
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Michael Peschke, Arthur T. Blades and Paul Kebarle
Zn2+ metalloproteins. The observation that the most strongly bonding residue occurs also most often, needs to be explained. Such an explanation is provided in the next section. D. Metalloion–Ligand Binding Energies and Biological Function of Metalloenzymes such as Carbonic Anhydrase In the area of metalloenzymes, and particularly Zn2+ metalloenzymes such as carbonic anhydrase, impressive advances have been made in establishing the reaction mechanism of the catalyzed reaction.38 The experimental investigations involved also determinations of the crystallographic structure of carbonic anhydrase and particularly the structure of the active site.39 The power of these techniques was enormously increased by the use of site-directed mutagenesis, where specific amino acid residues, suspected to be participating in the stabilization of the transition states in the wild type of the enzyme, are replaced and the crystallographic structure and enzymatic activity of these variants is determined and compared with that of the wild type.40 Numerous purely theoretical studies of the mechanism, i.e., the structure and energy of reactants and transition states, have also been made.41 The directly bonded ligands in three important Zn2+ metalloenzymes are shown in structures X–XII, Fig. 12. The previous theoretical work41 on human carbonic anhydrase CAII was largely centered on the transition states of the catalyzed reaction. These involve the directly bonded H2O ligand, see XII, and some peptide residues, which are near the reaction site, but are not any of the three remaining directly bonding histidine (his) ligands. For alcohol dehydrogenase X and carboxypeptidase XI, again the H2O is the directly bonding ligand that participates in the catalyzed reaction while the other directly bonding ligands are “inactive”. It will be noted that his is present in all the three enzymes but in CAII there are three his, while for the other two enzymes also the cys and glu ligands participate. The his, cys and glu functional groups that interact with Zn2+, can be modeled by the compounds: imidazole, deprotonated CH3S– and C2H5CO2–. The question can be asked: Why were the specific directly bonded ligands in structures X–XII selected by the evolutionary process? In Part C of this section, the finding was made that imidazole, i.e. his, is the most strongly bonding neutral residue. The negatively charged glu and cys groups are expected also to be strongly bonding, particularly so in the low polarity environment of a protein. The strong bonding provided by these ligands must
Determination of Sequential Metal Ion–Ligand Binding Energies
109
Figure 12: Directly bonding ligands to Zn2+ in the reactive center of enzymes: alcohol dehydrogenase X, carboxypeptidase XI, and carbonic anhydrase XII. histidine (his) deprotonated glutamate (glu) and cysteine (cys).
certainly be connected with the need to achieve stability for the Zn2+ ion in the enzyme, relative to the aqueous environment of the cytoplasm outside the enzyme. On the other hand, the choice of a specific composition of the directly bonding three ligands in X–XII must be related to the specific reaction catalyzed by the given enzyme. The three “inactive” ligands determine the strength of bonding of the fourth ligand, H2O, and therefore also the energies of transition states and other reaction intermediates. On the basis of the previous results on sequential bond energies and their changes with ligands of different dipole moments, polarizability and size, see Parts A and B of this section, one can expect that the bonding of the fourth ligand will be very much weakened. Strongly bonding ligands were
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Michael Peschke, Arthur T. Blades and Paul Kebarle
seen (Parts A and B) to lead to greater weakening of the bonding for the last ligand. The presence of weak bonding for the last ligand may be expected to be favorable to the catalytic process. This means that the strongly bonding ligands fulfill two purposes: they provide stability of the Zn2+ ion in the enzyme and weaken the bond of the active ligand. The strong effect of the first three ligands on the bonding of the fourth (H2O) in tetra-coordinated Zn2+, is illustrated by the data given in Table 7. The specific choices of the strongly bonding ligands, structures X–XII, should therefore be connected with the bonding requirements at the fourth site, which are specific to the given reaction that is catalyzed. Proofs for the above premises could be provided for carbonic anhydrase.42 For the Zn2+ to be thermodynamically stable in carbonic anhydrase, the total stabilization energy provided by: (a) the directly bonding ligands; (b) the first to “second solvation shell” strong hydrogen bonding interactions of the Zn ligand complex with suitably placed residues near the ion ligand complex (see Fig. 7), and; (c) the solvation provided by the protein and the aqueous environment surrounding the protein, must be more exoergic than the total free energy of hydration of Zn2+ in liquid water:
ΔGoh (Zn2+) = –470 kcal/mol29
(15)
The values obtained42 for the terms stabilizing Zn2+ in the enzyme are given in Table 8. They add up to:
ΔGostab.Enz (Zn2+) = –477 kcal/mol42
(16)
The stabilization provided by the three imidazole ligands provides 340 kcal/mol, see Table 8, a very important contribution to the total. Furthermore, imidazole has suitable protic hydrogens whose protic character is increased by the Zn2+ and these provide a substantial part of the 55 kcal/mol due to “second shell” interactions (Table 8). The Table 7.
How choice of first three ligands determines the bond-free energy of the fourth (reactive) ligand ΔG° kcal/mol(a)
Reaction 2+
Zn(H2O)3(H2O) = Zn(H2O)32+ + H2O Zn(NH3)3(H2O)2+ = Zn(NH3)32+ + H2O Zn(Im)3(H2O)2+ = Zn(Im)32+ + H2O
34.3 (theor.) 22.5 (theor.) 12.0 (theor.) 14.0 (exp.)
Zn((Im)2CH3CO2)(H2O)+ = Zn((Im)3CH3CO2)+ + H2O (a) For origin of data see Peschke et al.
42
5.0 (exp.)
Determination of Sequential Metal Ion–Ligand Binding Energies
111
Table 8. Model for interaction of Zn2+ with ligands, protein and aqueous solution for carbonic anhydrase (CAII). Type of interaction
Free energy change (kcal/mol)(a)
2+ (1) Zn(Im)2+ 3 =Zn + 3Im
ΔG = 340
(2) Zn(Im)3H2O2+ = Zn(Im)32+ + H2O
13
(3) Non-covalent interactions, i.e., strong hydrogen bonds induced by Zn2+ charge: His94 to Gln92; His96 to Asn244, His119 to Glu117 and H2O ligand to Thr199
55
(4) Solvation by protein
34
(5) Solvation by aqueous environment
26
(6) Solvation by conical cleft in CAII Total
9 477
(a) For origin of data see Peschke et al.42
ability of his as a directly bonding ligand to provide stability of the Zn2+ in the enzyme is fully documented by these numbers. The stability of Zn2+ in the enzyme in aqueous solution has been determined experimentally by Kiefer and Fierke.40a The Zn2+ dissociation constant, KD, was determined from which the free energy for dissociation from the enzyme to the aqueous solution can be obtained.
ΔGoD (ZnEn) = –RT ln KD = 15.8 kcal/mol
(17)
This value is close to the result of 7 kcal/mol, predicted by the modeling calculations from the difference between the free energies, eq. 15 and eq. 16. The interest in the modeling result is not so much because it can predict a reasonable value for ΔGoD (ZnEn), but because it provides a dissection of the energy terms contributing to ΔGoD, see Table 8, and a verification of the very important role of the histidine ligands in the stabilization of Zn2+ in the enzyme. The importance of the specific evolutionary choice of three his ligands for carbonic anhydrase, could also be demonstrated.42 Carbonic anhydrase catalyzes reactions 18 and 19 in aqueous solution. CO2 + H2O = H2CO3
(18)
H2CO3 + H2O = H3O+ + HCO
(19)
This reaction requires catalysis, because the first step is associated with a large free energy barrier.43–45 The second step is very fast in both directions, compared to 18, and therefore the production of
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Michael Peschke, Arthur T. Blades and Paul Kebarle
Figure 13: Amino acid residues and hydrogen bonds in the active center of human carbonic anhydrase. His-96, His-94, and His-119 are the three ligands of Zn2+. The residues Asn-244, Glu-117, and Gln-92 form strong hydrogen bonds with hydrogens of the three imidazole (histidine) ligands. Four water molecules participate in a proton shuttle which transfers a proton from the water ligand to His-64.
H2CO3 or H3O+ + HCO3– in aqueous solution are functionally equivalent steps from the standpoint of the catalysis. The reaction catalyzed by carbonic anhydrase is extremely fast, with a turnover rate38,39 of k = 106 s–1. The generally accepted mechanism,38–41 involves two steps. The deprotonation of the H2O ligand (EnZnH2O)2+(aq) = (EnZnOH)+(aq) + H+(aq)
(20)
followed by the formation of the bicarbonate anion by a nucleophilic attack of the hydroxide group in (EnZnOH)+ on CO2. (EnZnOH)+(aq) + CO2(aq) (EnZnHCO3)+(aq) (EnZnH2O)2+(aq) + HCO3–(aq)
H2O ⎯⎯→ ⎯
(21)
Determination of Sequential Metal Ion–Ligand Binding Energies
113
The reactions 20 and 21 each represent an overall reaction. The individual steps and transition states thereof have been the subject of theoretical studies41 which deal explicitly also with the very important participation of protein residues near the reaction center, that facilitate the reaction. However the energy changes for all the steps adding up to the overall reaction 20 and the reaction 21 have not been determined. As mentioned before, the role of the directly bonded histidines in facilitating the reactions also has not been subject to systematic study.41 To provide such a study, the free energies for the reactions involving the Zn2+ ion ligated by four ligands L one of which is always H2O, were determined by theoretical calculations for a variety of ligands. (LxZnOH2)2+ = (LxZnOH)+ + H+
(22)
(LxZnOH)+ + CO2 + H2O = (LxZn(H2O))2+ + HCO3–
(23)
Also determined were the energies for the dehydration reaction (LxZnOH2)2+ = (LxZn)2+ + H2O
(24)
The results from these calculations, where ΔGo22 and ΔGo23 are plotted versus ΔGo24, are shown in Fig. 14. Two approximately straight lines are observed. The use of more strongly electron donating ligands like imidazole decrease the binding energy of H2O, as was already discussed (Table 7). A linear positive correlation of ΔGo23 with ΔGo24 is observed. However the deprotonation reaction (22) becomes more endoergic on use of strongly electron donating ligands, leading to a negative correlation of ΔGo22 with ΔGo24. A fast turnover mechanism would be possible only if the enzyme catalyzed reactions 22 and 23 have either a negative free energy, or if positive, then a low positive energy, lower than 10 to 15 kcal/mol. Since the gas phase model reactions show that ligands with increasing electron donor properties have opposing effects on the two reactions 22 and 23, the choice of the three ligands should be such that it leads to ΔGo22 and ΔGo23 values, both of which are close to zero. The free energy values shown in Fig. 14 are for the gas phase reactions. Both are highly endoergic for Lx = (Im)3. An inclusion of the effect of the enzyme environment for the reactions Im3ZnO22+ and Im3ZnOH+ was made42 which was analogous to the procedure illustrated in Table 8. The hydration free energies ΔGoh of the simple ionic reactants, H+, HCO3- and the
114 Michael Peschke, Arthur T. Blades and Paul Kebarle
Figure 14: (Upper plot) Free energies for the dehydroxylation reaction LxZnOH+ = LxZn2+ + OH-, plotted versus the free energies for the dehydration reaction LxZnOH22+ = LxZn2+ + H2O. A linear correlation is observed. (Lower plot) Free energies for the deprotonation + + reaction LxZnOH2+ 2 = LxZnOH +H , versus the free energies of the dehydration reaction. An inverse proportionality is observed for the deprotonation. The ligands L are identified in the figure. Data for some of the metal ions such as Mg2+ and Ca2+ are also included and are seen to fit in the plots.
Determination of Sequential Metal Ion–Ligand Binding Energies
115
neutral CO2 present in reactions 22 and 23, are available in the literature29 and were also included. With the inclusion of all these terms, reactions 22 and 23 model the enzyme mediated reactions 20, 21 in aqueous solution. These results are displayed in Fig. 15. For simplicity, the same energy terms, correcting for stabilization by the environment, were applied also to the ion ligand complexes LxZn2+ which were not (Im)3Zn2+. The results demonstrate that the best compromise that leads to both reactions 20 and 21 having ΔGo20 and ΔGo21 close to zero occurs exactly when three imidazole ligands are present. E. Conclusions Concerning the Role of Strongly Bonding Ligands in Metalloenzymes such as Carbonic Anhydrase Ligands such as histidine (imidazole) which bond very strongly to the metal ion fulfill a dual function in metalloenzymes. (a)The strong bonding provides the needed stability for the metal ion in the enzyme which prevents the ion from escaping into the strongly solvating aqueous environment outside the enzyme. The results described involving theoretical calculations of the binding energies of the directly bonded ligands in the Zn(Im)3(H2O)2+ complex and a semiquantitative inclusion of the stabilization due to the protein and aqueous environment, provide a semiquantitative breakdown of the total stabilization of Zn2+ in the enzyme, which shows that by far the most important stabilization is due to the three imidazole ligands. (b)Due to the very substantial stabilization of the ion by the polarizability and electron transfer from the three strongly bonding ligands, the bonding to the fourth ligand, H2O (or OH–) is much weakened. Such a weakening is required for the catalytic process. The generally accepted mechanism for carbonic anhydrase (CAII) involves a deprotonation reaction (20) and an HCO3– forming reaction (21). The two reactions have conflicting requirements concerning the nature of the direct bonding ligands. Reaction 21 is facilitated by strongly charge donating ligands while reaction 20 is slowed down by such ligands. To satisfy these conflicting requirements, the three primary ligands must be so chosen as to lead to free energy changes ΔGo20 and ΔGo21, which are both close to zero. The three imidazole ligands fulfill this requirement, as shown in Fig. 9. Thus, the evolutionary “choice” of the three histidine ligands in CAII appears to be the optimal choice – the choice that is just right.
116 Michael Peschke, Arthur T. Blades and Paul Kebarle
Figure 15: (Lower plot) Free energies for the reaction, En'LxZnOH22+ = En'LxZnOH+ +H+(aq). (Upper plot) Free energies for the reaction En'LxZnOH+(aq) + CO2 + H2O = En'LxZn OH22+(aq) + HCO3–(aq). The two data points, where Lx = (Im)3, correspond to reactions 20 and 21, whose energies model approximately the reactions of the CAII enzyme in aqueous solution. Free energies for other ligands are also given. The corrections for the effect of the environment for the other ligands were taken to be the same as those for 20 and 21. The plot shows that only the three imidazole ligands lead to free energies which are close to zero for both reactions.
Determination of Sequential Metal Ion–Ligand Binding Energies
117
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Dzidic, I. and Kebarle, P. (1970) J. Phys. Chem., 74: p. 1466. Kebarle, P. (1977) Annu. Rev. Phys. Chem., 28: p. 445. Keesee, R.G. and Castleman, A.W. (1986) J. Phys. Chem. Ref. Data, 15: p. 1011. Kebarle, P. (1974) Modern Aspects of Electrochemistry, (Conway, B.E. and Bockris, J.O.M. eds), Plenum Press: New York, Vol. 9, p. 1. Kraemer, W.P. and Diercksen, G.H.F. (1970) Chem. Phys. Lett., 5: p. 463. (b) Diercksen, G.H.F. and Kraemer, W.P. (1972) Theor. Chim. Acta, 387. (c) Kishenmacher, H., Popkie, H., and Clementi, E. (1973) J. Chem. Phys., 59: p. 5842. Chandrasekhar, J., Spellmeyer, D.C., and Jorgensen, W.L. (1984) J. Am. Chem. Soc., 106: p. 903. Okumura, M., Yeh, L.I., and Lee, Y.T. (1988) J. Chem. Phys., 88: p. 79. Spears, S.K. and Fehsenfeld, F.C. (1972) J. Chem. Phys., 5698. Yamashita, M. and Fenn, J.B. (1984) J. Phys. Chem., 4451. (b) Whitehouse, C.M., Dryer, R.N., Yamashita, M., and Fenn, J.B. (1985) Anal. Chem., 56: p. 675. Kebarle, P. and Tang, L. (1993) Anal. Chem., 65: p. 272A. Blades, A.T., Jayaweera, P., Ikonomou, M.G. and Kebarle, P. (1990) J. Chem. Phys., 92: p. 5900. Blades, A.T., Jayaweera, P., Ikonomou, M.G., and Kebarle, P. (1990) Mass Spectrom. Ion Processes, 101: p. 325; 102: p. 251. Klassen, J.S., Ho, Y., Blades, A.T., and Kebarle, P. (1998) Thermochemistry of Singly and Multiply Charged Ions Produced by Electrospray. In: Advances in Gas Phase Ion Chemistry, (Adams, N.G. and Babcock, L.M., eds), Vol. 3. Peschke, M., Blades, A.T., and Kebarle, P. (1999) Intern. J. Mass Spectrometry, 185/186/187: p. 685. Blades, A.T., and Kebarle, P. Determination of Hydration Equilibria of Zn(H2O)n2+ (unpublished work). Jones, R.W. and Staley, R.H. (1982) J. Am. Chem. Soc., 104: p. 2296. Halle, L.F., Armentrout, P.B., and Beauchamp, J.L. (1982) Organometallics, 1: p. 963. (b) Ervin, K.M. and Armentrout, P.B. (1985) J. Chem. Phys., 83: p. 166. (c) Aristov, N. and Armentrout, P.B. (1986) J. Am. Chem. Soc., 108: p. 1806. (d) Ervin, K., Loh, S.K., Ristov, N., and Armentrout, P.B. (1983) J. Phys. Chem., 87: p. 3593. (e) Schultz, R.H., Elkind, J.L., and Armentrout, P.B. (1988) J. Am. Chem. Soc., 110: p. 411. (f ) Armentrout, P.B. and Kickel, B.L. (1996) Gas-Phase Thermochemistry in Transition Metal Ligand Systems. In: Organometallic Ion Chemistry, (Freiser, B.S., ed.), Kluwer: Dordrecht. Burnier, R.C., Cody, R.B., and Freiser, B.S. (1982) J. Am. Chem. Soc., 109: p. 7436. (b) Cassady, C.J. and Freiser, B.S. (1984) J. Am. Chem. Soc., 106: p. 6176. (c) Ho, Y.P., Yang, Y.C., Klippenstein, S.J., and Dunbar, R.C. (1997) J. Phys. Chem. A., 101: p. 3338. Bauschlicher, C.W. Jr., Langhoff, S.R., Partridge, H., Rice, J.E., and Komorwicki, A. (1991) J. Chem. Phys., 95: p. 5142. (b) Bauschlicher, C.W. Jr., Langhoff, S.R., and Partridge, H. (1991) J. Chem. Phys., 94: p. 2068. (c) Bauschlicher, C.W. Jr., Sodupe, M., Partridge, H. (1992) J. Chem. Phys., 96: p. 4453. Glendening, E.D. and Telles, D. (1996) J. Phys. Chem., 100: p. 4790.
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(21) Garmer, D.H. and Gresh, N. (1994) J. Am. Chem. Soc., 116: p. 3556. (22) Katz, A.K., Glasker, J.P., Beebe, S.A. and Bock, C.W. (1996) J. Am. Chem. Soc., 118: p. 5752. (23) Pavlov, M., Siegbahn, P.E.M., and Sandström, M. (1998) J. Phys. Chem. A., 102, 219. (24) Blades, A.T., Klassen, J.S., and Kebarle, P. (1996) J. Am. Chem. Soc., 118: p. 12437. (25) (a) Peschke, M., Blades, A.T., and Kebarle, P. (2000) J. Am. Chem. Soc., 122: p. 10440. (b) “Binding Energies of Ion–Ligand Complexes of Metal Ions M2+ with Ligands L in Which One of the Ligands, X-, is a Negative Ion.” Peschke, M., Blades, A.T., and Kebarle, P. J. Phys. Cem. (in preparation). (26) Deng, H. and Kebarle, P. (1998) J. Am. Chem. Soc., 120: p. 2925. (b) Deng, H. and Kebarle, P. (1998) J. Phys. Chem. A., 102: p. 571. (27) Schafer, H. Horn, and R. Ahlrichs (1992) J. Chem. Phys., 97: p. 2571. (b) Basis sets were obtained from the Extensible Computational Chemistry Environment Basis Set Database, Version 1.0, as developed and distributed by the Molecular Science Computing Facility, Environmental and Molecular Sciences Laboratory which is part of the Pacific Northwest Laboratory, P.O. Box 999, Richland, Washington 99352, USA, and funded by the U.S. Department of Energy. The Pacific Northwest Laboratory is a multi-program laboratory operated by Battelle Memorial Institute for the U.S. Department of Energy under contract DE-AC06-76RLO 1830. Contact David Feller, Karen Schuchardt, or Don Jones for further information. (28) Peschke, M., Blades, A.T., and Kebarle, P. (1998) J. Phys. Chem. A., 48: p. 9978. (29) Marcus, Y. (1985) Ion Solvation, Wiley-Interscience: Chichester, Chapter 2, p. 13. (30) Roux, B. and Karplus, M. (1991) Biophys. J., 59: p. 961. (b) Roux, B. and Karplus, M. (1993) J. Am. Chem. Soc., 115: p. 3250. (31) Sunner, J. and Kebarle, P. (1984) J. Am. Chem. Soc., 106: p. 6135. (32) Klassen, J.S., Anderson, S.G., Blades, A.T., and Kebarle, P. (1996) J. Phys. Chem., 100: p. 14218. (33) Bassolo, F. and Pearson, R.G. (1967) Mechanism of Inorganic Reactions, Wiley: New York, 2nd ed., pp. 33ff. (b) Huheey, J.E. (1983) Inorganic Chemistry, Harper & Row: New York, 3rd ed., pp. 312ff. (c) Parr, R.G. and Pearson, R.G. (1983) J. Am. Chem. Soc., 105: p. 7512. (d) Pearson, R.G. (1988) Inorg. Chem., 27: p. 734. (e) Pearson, R.G. (1988) J. Am. Chem. Soc., 110, 7684. (f) Pearson, R.G. (1989) J. Org. Chem., 54: p. 1423. (g) Pearson, R.G. (1995) Inorg. Chim. Acta, 240: p. 93. (34) Stzynadka, N.C.J. and James, N.G. (1989) Ann. Rev. Biochem., 58: p. 951. (35) Kretsinger, R.H. (1976) Ann. Rev. Biochem., 916: p. 239. (36) Johnes, R.W. and Staley, R.H. (1982) J. Am. Chem. Soc., 104: p. 2296. (37) Cerda, B.A. and Wesdemiotis, C. (1995) J. Am. Chem. Soc., 117: p. 9734. (38) Silverman, D.N. and Lindskog, S. (1988) Acc. Chem. Res., 21: p. 30. (b) Coleman, J.E. (1998) Current Opinion in Chemical Biology, 2: p. 222. (39) Ericksson, A.E., James, T.A., and Liljas, A. (1988) Proteins Struct. Funct. Genet., 4: p. 274. (b) Häkansson, K., Carlsson, M., Svenson, L.A. and Liljas, A. (1992) J. Med. Biol., 227: p. 1192. (c) Xue, Y., Vidgren, J., Svensson, L.A., Liljas, A., Jonsson, B.H., and Lindskog, S. (1993) Proteins, 15: p. 80.
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(40) Kiefer, L.L. and Fierke, L.L. (1994) Biochemistry, 33: p. 15233 and references therein. (b) Kiefer, L.L., Palermo, S.A., and Fierke, C.A. (1995) J. Am. Chem. Soc., 117: p. 6831. (c) Ipolito, J.A. and Christianson, D.W. (1994) Biochemistry, 33: p. 15241. (d) Lesburg, C.A. and Christianson, D.W. (1995) J. Am. Chem. Soc., 117: p. 68348. (41) Pullman, A. (1981) Ann. N.Y. Acad. Sci., 367: p. 340. (b) Allen, L.C. (1981) Ann. N.Y. Acad. Sci., 367: p. 385. (c) Liang, J.Y. and Lipscomb, W.N. (1989) Int. J. Quant. Chem., 36: p. 299. (d) Zheng, Y.J. and Merz, K.M. (1992) J. Am. Chem. Soc., 114: p. 10498. (e) Merz, K.M. Jr and Banei, L. (1997) J. Am. Chem. Soc., 119: p. 863. (f) Zheng, Y.J. and Merz, K.H. Jr. (1992) J. Am. Chem. Soc., 114: p. 10498. (42) Peschke, M., Blades, A.T., and Kebarle, P. (2000) J. Am. Chem. Soc., 122: p. 1492. (43) Jönsson, B., Karström, G., Wennerström, H. and Roos, B. (1976) Chem. Phys. Lett., 41: p. 317. (b) Jönsson, B., Karström, G., Wennerström, H., Forsen, S., Roos, B., and Almlöf, J. (1997) J. Am. Chem. Soc., 99: p. 4628. (44) Nguyen, M.T. and Ha, T.K. (1984) J. Am. Chem. Soc., 106: p. 599. (45) Wright, C.A. and Boldyrev, A.I. (1995) J. Phys. Chem., 99: p. 12125.
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4 DOUBLY CHARGED TRANSITION METAL COMPLEXES IN THE GAS PHASE Anthony J. Stace
I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 II. The Preparation of Multiply Charged Metal Complexes . . . . 125 III. Analysis and Interpretation of Data . . . . . . . . . . . . . . . . . . . . . 130 IV. Conclusion and View of the Future . . . . . . . . . . . . . . . . . . . . . 142 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 A. INTRODUCTION For approximately 20 years cluster science has sought to “bridge the gap” between the chemical and physical characteristics of individual atoms and molecules, and the corresponding properties of their bulk materials.1,2 In a number of instances, this statement is being realized: for example, there now exists good experimental data on the gradual progression from metal atom ionization energy to work function.3,4 However, there are still some areas of bulk behaviour where much work needs to be done before cluster science makes an impact on our understanding of the detailed physics and chemistry. One such subject is the solvation of multiply charged metal ions. From the work of Kebarle and co-workers5 and Castleman and co-workers,6 there exist a comprehensive catalogue of the solvation thermodynamics of large numbers of singly charged Advances in Metal and Semiconductor Clusters Volume 5, pages 121–144 © 2001 Elsevier Science B.V. All Rights Reserved. ISBN: 0-444-50726-4
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cations and anions. This information has provided a quantitative picture of the interactions responsible for creating primary solvation shells surrounding metal ions ranging from Li+ through to Ag+ and Au+.5,6 Unfortunately, the more common oxidation states of many metals, and in particular transition metals, are frequently greater than one.7 Therefore, in comparison to the very extensive treatment afforded singly charged metal ions, some of the most important metals in chemistry and biochemistry have not been subjected to the same detailed experimental examination under their most natural conditions. The reasons for this distinction between, on the one hand, very accurate thermodynamic information on singly charged ions, and on the other, a rather vague picture regarding the co-ordination and stability of multiply charged ions, is not difficult to appreciate. The second ionization energies (IE) of many transition metals are higher than the first ionization energies of many of the solvent molecules, which surround them (see Table 1 for some typical values). That a multiply charged metal ion can be stable under such conditions acknowledges the intimate relationship which exists between the bulk solvent and the ion.8 In the gas phase, the situation is somewhat different: in a typical experiment, thermodynamic information is obtained by establishing an equilibrium between metal–solvent complexes of varying sizes:5,6 M+Ln + L ⇔ M+Ln+1,
(1)
via a sequence of steps that is initiated by the generation of metal ions, M+, in the presence of a solvent, L. Any attempt to repeat this operation for M2+ ions leads to charge transfer at the first collision; a process that is driven by the large energy difference between the IE of a single solvent molecule and the second IE of the metal. Therefore, there exists a significant technical problem, which is how to create multiply charged metal ion–solvent complexes in the gas phase without incurring charge transfer? The dominant interactions that exist between a single neutral ligand and a doubly charged metal ion are summarized in Fig. 1a, where a model due primarily to Tonkyn and Weisshaar9,10 has been adapted to suit the case of an M2+ metal ion and a single solvent or ligand molecule. The latter is attracted to the ion via a strong induced dipole interaction V(r) = –αq2/r4, where α is the polarisability of the ligand concerned, q = +2 (the charge on the ion), and r is the separation between the ligand and the ion. Also shown is a second curve which represents the purely repulsive Coulomb interaction that would result from charge transfer, and
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Table 1. Ionization energies of metal atoms and ligands discussed in the text. Metal
1st ionization energy/eV
2nd ionization energy/eV (a)
Copper
7.73
Silver
7.58
20.29 21.5
Gold
9.22
20.5
Manganese
7.65
15.03
Holmium
6.02
11.8
Ligands CO2 Pyridine (C5H5N) Acetone ({CH3}2CO)
13.8
–
9.3
–
9.7
–
Acetonitrile (CH3CN)
12.2
–
H2O
12.6
–
NH3
10.16
–
Methanol (CH3OH)
10.8
–
Ar
15.75
–
(a)
Energy required for the step M+ → M2+ + e–
this potential is given by V(r) = +q2/r. At infinite separation, potential energy differences between the two interactions are determined by the value of IE(M+) – IE(L). If this number is large, then charge transfer can be accompanied by a significant release of kinetic energy, and examples of such behaviour in small [Mg.(ROH)n]2+ clusters have been presented earlier.11,12 The high exothermicity associated with the processes described by Fig. 1a together with the data in Table 1, serve to account for why it is difficult (if not impossible in some circumstances) to prepare a stable doubly charged metal complex containing a single ligand molecule. When doubly charged complexes containing several (>3) ligands or solvent molecules are considered, the situation regarding charge transfer is significantly different from above.13 However, it is not simply a question of shifting the curves shown in Fig. 1a in order to allow for the differential solvation of M2+ and M+. Although solvation enthalpy changes may be in the order M2+ > M+, the potential energy surfaces must still cross at some point (or along a seam) because the energies of the isolated ions together with the solvent, still follow the pattern M2+ < M+. As Marcus14 has noted in an analysis of electron transfer in condensed phase transition metal complexes, the assignment of a coordinate linking the M2+ and M+ charge states is no longer as obvious as that shown in Fig. 1a. Several factors within the complex are influenced by the movement of a charge: (i) there will be small changes in ligand–metal distances because polarization interactions will be influenced by the reduction in charge density at
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Figure 1: Diagrams representing the interaction between a doubly charged metal ion and a variable number of ligands (L): (a) as isolated entities in the gas phase where a collision between the metal ion and a single molecule can lead to charge transfer (adapted from ref. 10); (b) in a cluster containing several ligands and/or in a solution of L; ΔE# represents a barrier to charge transfer; further details are given in the text (adapted from ref. 11).
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the metal site; (ii) some of the ligand molecules may re-orientate; (iii) the ligand accepting the charge will adopt a position with respect to the metal ion, which is different from the other ‘spectator’ ligands. The net result is a many-dimensional surface, which at its simplest can be represented by Fig. 1b. Here, the passage from stable [M.Ln]2+ to stable [M.Lm]+ (where m < n) is presented in the form of two intersecting potential energy curves, which contain an avoided crossing and charge transfer follows the lowest-energy adiabatic surface. Presented in this form, the surface contains an essential element, which accounts for the stability of the doubly charged complexes. Namely, there is a barrier to charge transfer (ΔE#), which in the condensed phase represents metal ion reduction and can be promoted, for example, by disproportionation.8 In the gas phase, ΔE# can be overcome by either photoexcitation15 or the collisional activation11,12 of complexes. The relative depths of the two attractive wells (and hence the magnitude of the barrier) will shift as a function of the degree of solvation. A second component to the multidimensional surface, which is not represented in Fig. 1b, is the repulsive interaction that exists between [M.Lm]+ and L+ (together with [n-m-1]L) once charge transfer has occurred: this surface should be similar to that given in Fig. 1a, but with M2+ and M+ shifted by solvation. The repulsive surface really only makes its presence felt in the gas phase, where the Coulomb interaction between two singly charged units can result in a very significant release of kinetic energy.11,12 In the condensed phase, any electrostatic repulsion will be moderated by the surrounding solvent (as determined by the dielectric constant), and kinetic energy relaxation times will be of the same order of magnitude (~10–11 s) as other equally energetic processes, such as the photo-induced cage effect.16,17 II. THE PREPARATION OF MULTIPLY CHARGED METAL COMPLEXES To date, there are two effective solutions (!) to the problem of generating gas-phase solvent complexes containing multiplycharged metal ions. By far the most frequently used technique is electrospray, where the ions of interest exist as an electrolyte in the liquid phase prior to entry into the gas phase under vacuum. Kebarle and co-workers18–20 have been very successful in using this approach to obtain data on the binding energies of water molecules in [Mg(H2O)n]2+ complexes for n > 5. Likewise, Williams et al.21,22 have used electrospray in association with FTICR (Fourier Transform Ion Cylotron Resonance) to study the unimolecular decay kinetics of doubly charged metal–water complexes, from which
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ligand binding energies have also been derived. In contrast, Posey et al.23,24 have used electrospray to study the charge transfer spectroscopy of Fe(II)-based complexes, and in particular, the spectral shifts induced by the presence of solvent molecules clustered with each complex. A completely different approach to the formation of multiply charged complexes has been developed primarily within the group at Sussex,11,12,25–35 and what follows is a brief description of the technique and a summary of some of the experiments undertaken to date. Neutral clusters of the desired metal–solvent combination are prepared first and these are then ionized by high (~100 eV) electron impact. The result is a multiply charged metal ion encapsulated within a stable solvent environment, which can be created from a very broad range of materials, the only requirement being that the solvent has sufficient vapour pressure to generate gas-phase clusters. Candidate solvents include many of the traditional inorganic ligands, such as pyridine and acetonitrile, and several new ligands which have not been utilized previously, but still have the ability to stabilize a multiply charged metal ion. In this context, CO2 has proved to be an excellent example of the latter, and has led to some speculation as to the potential ability of supercritical CO2 as a solvent for multiply charged metal ions.13 The initial preparation of neutral metal/ligand complexes relies on generating metal vapour through which solvent clusters pass in order to facilitate the attachment of a neutral metal atom via a pickup process. Numerous experiments have shown that within the pickup region the optimum partial pressure of metal vapour is of the order of 10–2 mbar. To achieve this value for a wide range of metals, use has been made of existing technology in the form of molecular beam epitaxy (MBE) ovens. Two systems have been used: (i) an oven with a capacity of 30 cm3 which has an upper temperature limit of 1750K, and is capable of generating an ion current of ~10–11 A for [Cu.(pyridine)4]2+ complexes, which is sufficient for studies of their charge transfer spectroscopy;15 (ii) a low capacity system (~10 cm3) which can reach a temperature of ~2000K, and has thus far been used to study complexes involving gold(II)31 and chromium(II).34 In addition to experimentation with ovens, considerable effort has also been taken to provide adequate pumping within the pick-up region to ensure long-term operation of the oven filament. MBE ovens are not normally designed to operate under the harsh conditions experienced in a typical cluster beam apparatus; Fig. 2 shows an arrangement that has been refined over a period of several years, and has proved capable of providing stable metal ion beams for 6–8 hours of continuous operation daily whilst maintaining a filament
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lifetime of 9–12 months. Thus far, the pick-up technique has been used to prepare complexes in association with Mg(II),11,12,25,26,32 Sr(II),28 Cu(II),27,29 Ag(II),13 Au(II),31 Mn(II),34 Cr(II),34 Pb(II),35 Ho(II) and Ho(III).30 An examination of tabulated metal vapour pressures suggests that the approach discussed here should be suitable for a significant fraction of the metals found in the periodic table. For many of the metals listed above it has been possible to attach a broad range of solvents covering approximately 20 different systems; from Ar and CO2 through to benzene, and certain bidentate ligands, such as penta 2,4 dione.26 Pick-up techniques are not new in cluster science; Scoles and coworkers36,37 have used the technique for a number of years to prepare mixed rare gas–molecule clusters for the purposes of studying their spectroscopy. Del Mistro and Stace38 have presented a molecular dynamics description of the process, where the successful Figure 2: Schematic diagram of the ‘pick-up’ apparatus developed for the purposes of studying metal ion chemistry.
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attachment of a molecule to a small argon cluster appears to require the promotion of a phase transition followed by the evaporation of argon atoms. The latter presumably acting as a heat sink. Extension of the pick-up technique to molecular clusters is not as straightforward as might have been anticipated. The generation of molecular clusters, such as (CO2)n or ({CH3}2CO)n, is a comparatively easy process, and by monitoring ion signals arising from these clusters it is observed that the intensities of clusters in the range n = 2–50 maximize under very moderate expansion conditions in a supersonic beam apparatus. However, attempts to operate the pick-up process with a molecular vapour undergoing supersonic expansion under these conditions does not work. Likewise, more severe expansion conditions using helium as the carrier gas are also ineffective. Experimentation has shown that, for any molecular solvent (L), it is necessary to generate mixed LnArm clusters for the pick-up to be effective, and there appear to be two reasons for this. First, these mixed clusters are going to be ‘colder’ than their pure molecular counterparts; clustering is an exothermic process and not all of that energy will be dissipated by collisions in the expansion. Since large molecular clusters often have high heat capacities, they do not achieve the very low temperatures, ~1K, normally associated with the supersonic cooling of isolated molecules. A typical internal temperature for a cluster may be closer to ~100K. By attaching argon atoms, we can be assured that the internal energy is close to or below the minimum binding energy, which for LnArm will be the Arm–1–Ar bond energy. A second important consideration is that following a collision between a metal (M) and LnArm, the collision complex, MLnArm, has to dissipate energy and shedding argon atoms most easily achieves this. Almost all of the experiments performed thus far using the pick-up technique have been undertaken using a mixture of 1% L in argon and backing pressures of between 30 and 60 psi behind a 200-μm diameter conical nozzle. One final, but very important component to any experiment of this type is a high-resolution mass spectrometer. Multiply charged ions appear in mass spectra at non-integer m/z positions and it is important that these are clearly resolved from adjacent, and often very much more intense, singly charged ions. Our experiments have been constructed in association with a VG ZAB-E reverse geometry, double focusing instrument, which not only allows high-resolution mass spectra to be recorded, but can also be used to record fragmentation patterns.39 A schematic diagram of the complete apparatus is shown in Fig. 3, and Fig. 4 shows a short section of a typical mass spectrum recorded for [Mn.(CO2)n]2+ complexes.40 In addition to the ions of interest there are numerous singly charged ions
Figure 3:
Schematic diagram of the complete apparatus, showing the cluster beam chamber, ‘pick-up’ section, and the mass spectrometer.
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composed of various combinations of manganese, argon and carbon dioxide, and although these can sometimes interfere with the ions of interest, they are unavoidable by-products to the mechanism by which the Mn(II) complexes are generated. Under the circumstances shown in Fig. 4, ions which can readily be identified can act as mass-markers in the assignment of multiply charged complexes. Such a procedure is frequently necessary because complexes have been observed to lose H and H2,11,12 and it is important in any structural interpretation of the data to be certain that parent and not fragment ion intensities are being examined. Other groups that have used electrospray to generate multiply charged metal-ligand complexes,18–24 have recorded mass spectra on instruments ranging from quadrupole mass spectrometers to Fourier transform ion cyclotron resonance machines. Mass spectra recorded using electrospray do not appear to be affected by the presence of by-products in the same way that the pick-up method suffers.18–20,23,24 III. ANALYSIS AND INTERPRETATION OF DATA With reference to Fig. 1, it can be seen that collision-based ion–molecule clustering techniques may fail with multiply charged metal ions because as the two species approach, they encounter a surface crossing (Fig. 1a) which can promote charge transfer. However, using the pick-up approach, multiply charged complexes are prepared already sitting within the potential well; whether or not charge transfer then occurs depends upon the position of the crossing, which in turn is influenced by the well depth and the degree of ion solvation.26 Very few multiply charged metal ions can be stabilized with just a single ligand, which suggests that for these complexes, the surface crossing is located close to the equilibrium Mn+–L bond distance.26 As the number of ligands increases, the well depth increases, and the position of the crossing moves to larger internuclear distances.26 An interesting exception to the observation of single ligand instability is the series CuAr2+, AgAr2+ and AuAr2+, all of which are stable even though the second IE of each metal is at least 5 eV higher than that of the first IE of argon.33 Although no quantitative explanation of these observation is available as yet, one possibility being explored is that direct ionization of the neutral complex places the resultant ion in a metastable state, which would be inaccessible via an M2+–Ar collision. Similar doubly charged states have been seen for heteroatomic rare gas dimers.41 To date, most of the experiments undertaken on [M.Ln]2+ complexes using the technique outlined above, have been of a semiquantitative nature. The two principal measurements being: (i) the
Figure 4: Mass spectrum recorded following the attachment of manganese atoms to carbon dioxide clusters and ionization using 100 eV electrons.
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minimum number of ligands required to stabilize a given M2+ ion; and (ii) the metal–ligand combination with the maximum intensity. To supplement these measurements, experiments have also been undertaken on the collision-induced fragmentation patterns of sizeselected ions. The minimum number of ligands necessary to stabilize a particular [M.Ln]2+ combination is significant in relation to Fig. 1, in that it is a measure of the degree of interaction between the central ion and individual solvent molecules. As noted above, there are some circumstances where the interaction is such that quite unexpected “ligands” will stabilize multiply charged metal ions, i.e. argon in CuAr2+. In most instances, however, it is found that two or three molecules are required to yield a stable [M.Ln]2+ complex. The ion–ligand combinations that have the highest intensities are, we believed, linked to the optimum co-ordination numbers of the metal ions concerned. The rationale is that the technique used to generate the ions leaves them with a significant level of internal excitation, and that subsequent fragmentation leads to the preferential appearance of stable structures. In the absence of any internal considerations, such as those which may lead to the appearance of stable structures, the intensity profile adopted by a cluster ion series, [M.Ln]2+, is influenced by two factors. First, there is an instability created by the probability of charge transfer in the smaller clusters, which means that ion intensities drop markedly at low values of n, and in most cases, disappear completely for n ≤ 2. The second factor is the decline in ion intensity as n increases that is normally associated with the size distribution of any series of clusters. The latter typically exhibits an exponential decay as a function of n; however, the exact profile adopted by any distribution can be influenced by experimental parameters, such as nozzle pressure and temperature. Although the finer details of any ion intensity distribution do not normally retain any memory of their neutral state, the overall shape of an intensity distribution can be moderated by changes in those initial conditions associated with the expansion process. This is particularly true of this type of experiment, where it is necessary to generate neutral clusters of the form LmArn. Very often the expansion pressures required to produce these species are quite different from those appropriate for intense beams of pure Lm clusters, and the subsequent ion intensities reflect those differences. During the time that elapses between the formation and observation (~10–4 s) of ions, the internal energy deposited by the ionization/reorganization steps will drive two processes. First, those ions with an internal energy above the charge transfer threshold will eventually curve cross and undergo Coulomb explosion, which will
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deplete the population of smaller [M.Ln]2+ complexes. Secondly, large cluster ions will undergo sequential unimolecular decay steps until their internal energy drops below the binding energy of the next ligand to be lost. In this way, stable structures will make their presence known in a mass spectrum by an increase in intensity at the expense of larger less stable complexes.39 Such decay processes have been identified as being responsible for the evolution of “magic numbers” in the mass spectra of rare gas cluster ions.39 Therefore, by analogy we believe that [M.Ln]2+ complexes with the highest intensities also represent the most stable structures. Table 2 lists some examples of stable combinations taken from experiments on a range of ligands in association with several different transition metal ions. In most instances, the optimum co-ordination number is four, which in the case of Cu(II) and Ag(II) probably corresponds to a square planar configuration (see below),7 and for Mn(II) (assuming the complex is high-spin) a tetrahedral geometry.7 However, there are some interesting exceptions. The data for [Cu.(H2O)n]2+ and [Cu.(NH3)n]2+ show maxima at n = 8, which is quite different from the traditional bulk solvation unit for these Cu(II) complexes where n is normally taken to be six.7 A very satisfying interpretation of the cluster result has been presented by Bérces et al.42 who used density functional theory (dft) to calculate optimum structures for [Cu.(H2O)n]2+ and [Cu.(NH3)n]2+ complexes for n = 3–8. The results show that, in both cases, the first four ligands form a planar tetragonal primary hydration shell coordinated directly to the central Cu2+ ion. However, beyond n = 4 additional ligands, which could occupy the two vacant axial sites, in fact prefer to form a secondary solvation shell in a 4+4 arrangement. The secondary shell molecules form double acceptor bonds with adjacent water molecules in the primary shell, and because the latter are highly polarized, the resultant hydrogen bonds are unusually strong.42 For [Cu.(H2O)6]2+ the calculated difference in energy between an octahedral primary shell and a 4+2 configuration is 71 kJ mol–1, and for [Cu.(H2O)8]2+ the energy difference between a 6+2 and a 4+4 configuration is 23 kJ mol–1. The relative stabilities of the corresponding [Cu.(NH3)n]2+ complexes are lower because of differences in strength of the hydrogen bonds. What is particularly interesting about the latter results, is that each ammonia molecule in the outer solvation shell appears to form two acceptor bonds even though NH3 has only one lone pair of electrons. Further experiments both by ourselves and Lisy et al.43 point to hydrogen bonding having a very pronounced influence on the solvent structure surrounding both singly and doubly charged metal ions. Support for these observations is to be found in recent calculations.33
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Table 2. Number of ligands (n) in each doubly charged complex, [M.Ln]2+, with the highest intensity. Metal Ligand
Manganese (a)
Copper
Silver
CO2
4
4
4
Pyridine (C5H5N)
4
4
(b)
Acetone ({CH3}2CO)
4
5
4 (6)(c)
Acetonitrile (CH3CN)
4
4
4 (6)(c)
H2O
8
(d)
5–11
NH3
8
(d)
(b)
8(a)
(d)
4
Methanol (CH3OH)
(a) Taken from ref. 40. (b)No data available. (c) Number in brackets denotes the presence of a secondary maximum in the ion intensity profile. (d)No evidence of a stable doubly charged complex.
In aprotic solvents, the coordination of multiply charged ions appears to be largely influenced by a combination of the electronic configuration of the metal and ligand size. Table 2 lists a selection of examples taken from data recorded using clusters composed of aprotic solvents in association with the metal ions Mn2+, Cu2+, and Ag2+, and Figs 5 and 6 show ion intensity profiles recorded for the three metals in association with acetone, and for silver in association with acetonitrile. Although these experiments are capable of generating [M.Ln]2+ complexes containing large numbers of ligands, unlike the hydrogen bonded examples, the relative intensities decline very rapidly beyond n = 4 in the case of Cu2+ and Ag2+, and beyond n = 6 in the case of Mn2+. The situation for Cu(II) reflects behaviour expected of a d9 electron configuration where Jahn-Teller distortion results from a degenerate electronic ground state. The response from a regular octahedron is to enhance ligand co-ordination in the xy plane and to displace those ligands lying in the z direction. The resultant differences in binding energy between equatorial and axial sites reflects the fact that the unpaired electron occupies the antibonding dx2–y2 orbital. The DFT calculations on [Cu.(H2O)n]2+ and [Cu.(NH3)n]2+ complexes show bonding to axial sites to be very unfavourable in comparison to the formation of hydrogen bonds in a secondary solvation shell.42 In both cases, the central, primary solvation core is a square-planar [Cu.L4]2+ unit. Extending this observation to the many aprotic solvents investigated for Cu2+, the consistent appearance of the [Cu.L4]2+ unit as the metal/ligand combination with maximum ion intensity, would suggest the presence of numerous square-planar configurations. The
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results would further suggest that bonding to axial sites is sufficiently unfavourable as to suppress any evidence of [Cu.L6]2+ complexes being of even secondary significance in terms of stability. The situation for Ag2+ is slightly different from that observed for Cu2+. There are very few stable condensed phase silver(II) complexes,7 and of those that have been observed, the majority have nitrogen as the coordinating atom, e.g. [Ag.(pyridine)4]2+; there are no condensed phase silver(II) complexes where the sole coordinating atom is oxygen. From Table 1 it can be seen that silver has the highest second ionization energy of the transition metals; therefore the silver(II) oxidation state is going to be the most difficult to stabilize, which also accounts for the fact that in the condensed phase silver(II) complexes are powerful oxidising agents. As seen in Table 2, it is possible to prepare stable Ag2+ complexes in the gas phase and in several instances, the coordinating atom is oxygen; however there is an interesting trend which reflects a difference between nitrogen and oxygen in terms of their respective abilities to stabilize the ion. Complexes with the latter require five ligands to stabilize the doubly charged metal ion, and Fig. 6 shows the situation for [Ag.({CH3}2CO)n]2+; in contrast, when coordinated with a nitrogen-containing molecule, maximum stability is achieved with four ligands, for example, [Ag.(CH3CN)n]2+ as shown in Fig. 6. Gold(II) complexes follow the pattern seen for copper(II)40, an observation which is consistent with these two metals having similar second ionization energies. There are several reasons why we believe the appearance of particularly intense (stable!) [Cu.L4]2+ and [Ag.L4]2+ ions is not just an artefact of the experiment, i.e. arising possibly from a competition between unimolecular and charge transfer fragmentation. First, there are numerous examples of where [Cu.(L)4]2+ ions are not the most intense,40 and for these, e.g. [Cu.(H2O)8]2+, a logical explanation can be provided.42 Secondly, observations on the formation of stable complexes between aprotic solvents and holmium ions in the form of Ho2+ and Ho3+, show six-fold co-ordination as the most intense (stable) combination.30 Finally, data recorded for Mn2+ (Table 2 and Fig. 5) provide evidence of both [Mn.L4]2+ and [Mn.L6]2+ as intense (stable) ions.40 Recent experiments involving Mn2+ have proved to be particularly interesting. The metal ion has a d5 electron configuration, which means that no preferential orientation of ligands should be expected because high-spin complexes have nothing to gain in terms of ligand-field stabilization.7 Although chemical reactivity has not previously been discussed, of the metal ions examined Mn2+ might be expected to be the least reactive. By
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Figure 5: Relative intensities recorded for [Cu.({CH3}2CO)n]2+ ions and [Mn.({CH3}2CO)n]2+ ions plotted as a function of n. The data for Cu(II) represent weighted averages of the 63Cu and 65Cu isotopes.
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Figure 6: Relative intensities recorded for [Ag.({CH3}2CO)n]2+ ions and [Ag.(CH3CN)n]2+ ions plotted as a function of n. The data represent weighted averages of the 107Ag and 109Ag isotopes.
analogy with iso-electronic Cr+ in the ground state,44,45 the barriers to reaction for the 6S state of Mn2+ should be high because all pathways are spin-forbidden. Contrary to these comments, complexes between primary alcohols and Mn2+ exhibit very
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specific four-fold co-ordination, and the smaller members of each series display evidence of quite extensive reactivity.33 Both these observations have been attributed to the formation of complexes with Mn(II) in an intermediate spin state ( 4G), which would yield a square-planar 4-coordinate configuration and would also allow the metal ion to undergo spin-allowed reactivity. Density functional calculations on [Mn.(CH3OH)n]2+ complexes appear to support the proposal that alcohol ligands may stabilize spin states other than the 6S atomic state of Mn2+.33 In addition to recording intensity patterns, experiments have also been undertaken on the collision-induced dissociation (CID) patterns of size-selected ions. Such experiments can confirm that an ion is indeed doubly charged, but they can also support conclusions regarding stable structures, and reveal evidence of chemical reactivity. Fragmentation patterns are monitored using the MIKES technique (Mass-analyser Ion Kinetic Energy Spectra).46 On a reversegeometry double focusing mass spectrometer, the magnetic field can be held constant as it transmits an ion with a particular m/z value, and the electrostatic analyser (ESA) is then scanned in order to identify fragment ions through changes in kinetic energy. Fig. 7 shows a typical MIKE scan recorded for [Cu.({CH3}2CO)4]2+ following collisional activation where the background pressure in the collision cell located in the second field-free region (see Fig. 3) has been increased to ~10–6 mbar. In addition to a peak arising from the loss of one neutral ligand, it is also possible to identify the presence of a feature due to the charge transfer step: [Cu.({CH3}2CO)4]2+ → [Cu.({CH3}2CO)2]+ + {CH3}2CO+ + {CH3}2CO For the process M12+ → M2+ + M3+, where the mass of the metalcontaining product is such that M2+/M12+ > 1, the identification of charge transfer reactions is readily achieved by sweeping the ESA to transmit ions with kinetic energies between (eV') and 2(eV'),48 where V' is the acceleration voltage on the ion source, which for these experiments is 5 kV. In this region of the scan, there is no interference from other non-charge transfer processes. In contrast, scanning between (eV') and zero can lead to congested spectra due to an overlap of unimolecular and charge transfer products. Figure 7 is an example of a complete scan between 2(eV') and zero. There is just a single feature due to unimolecular decay where [Cu.({CH3}2CO)4]2+ is seen to lose neutral {CH3}2CO, which can occur without charge transfer since [Cu.({CH3}2CO)3]2+ is observed in the mass spectrum as a stable ion. The two accompanying charge
Figure 7: MIKE spectrum recorded following the collision-induced dissociation of [Cu.({CH3}2CO)4]2+ within the collision cell marked in Fig. 3. Reaction products are identified by changes in kinetic energy using the electrostatic analyzer. The prominent charge transfer products are labeled, and the label (–1) is used to denote the loss of a neutral acetone molecule without charge transfer. Doubly Charged Transition Metal Complexes in the Gas Phase 139
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transfer processes involve the loss of either {CH3}2CO+ + neutral {CH3}2CO or {CH3}2CO+ + 2{CH3}2CO. It is interesting to note that there is almost no signal corresponding to the loss of just {CH3}2CO+ from [Cu.({CH3}2CO)4]2+, but that a very significant fraction of the charge transfer product is contained within the step which leads to the loss an ion plus a neutral molecule. We believe the reason for this observation to be the underlying stability of the singly charged Cu+.({CH3}2CO)2 fragment, since Cu(I) complexes tend to be linear.7 A similar pattern of behaviour was observed following the collisional activation of [Au.(pyridine)n]2+ complexes.31 A further distinguishing feature of the latter reactions is the width of each peak, which reflects the kinetic energy released as a result of charge transfer followed by Coulomb explosion. As the two positive charges separate, some fraction of the accompanying repulsive energy is transferred into kinetic energy of the fragments. For charges initially spaced 2 Å apart this energy could be up to ~7 eV in the centre-of-mass frame, but as with the reaction of neutrals on a repulsive potential energy surface, energy can also be partitioned into internal degrees of freedom of the fragments. There appears to be no obvious relationship between the release of Coulomb repulsion as kinetic energy and the structure (complexity) of a ligand. Figure 8 shows a MIKE scan of the complex [Mn.({CH3}2CO)4]2+ which was recorded under similar conditions to those used in Fig. 7. Features due to the loss of one and two neutral acetone molecules are present, as is an extensive range of charge transfer products, some of which have been identified. Also apparent in the scan are peaks due to decomposition of the acetone molecule. In particular, it would appear that charge transfer can be accompanied by the reaction: [Mn.({CH3}2CO)4]2+ → H3CMn+{CH3}2CO + CH3CO+ + 2{CH3}2CO In this respect, the fragmentation data support the conclusion that some fraction of the Coulomb repulsion appears as internal energy in the charge transfer products. Although the charge has been assigned to the CH3CO+ fragment, there is no evidence from the results to confirm this, and it is quite possible that it is {CH3}2CO+ that emerges from the charge transfer process. However, the loss of CH3 is frequently observed from {CH3}2CO+ and the reaction is known to have a low activation energy. The probability of charge transfer is strongly influenced by the number of ligands attached to the metal ion, and very few complexes with more than six ligands exhibit such behaviour. There
Figure 8: MIKE spectrum recorded following the collision-induced dissociation of [Mn.({CH3}2CO)4]2+ within the collision cell marked in Fig. 3. Reaction products are identified by changes in kinetic energy using the electrostatic analyzer. The prominent charge transfer and reaction products are labeled, and the labels (–1) and (–2) are used to denote the loss of neutral acetone molecules without charge transfer. Doubly Charged Transition Metal Complexes in the Gas Phase 141
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could be a number of reasons for this observation: (i) the magnitude of the barrier to charge transfer (Fig. 1b) increases with the number of ligands, and the energy deposited by a collision may not be sufficient to surmount a barrier imposed by six or more ligands; (ii) charge transfer may require the loss of several ligands in order to reduce or eliminate the barrier, and again the energy required for this initial step will increase with the number of ligands; (iii) finally, in a large complex, the charge once transferred could move back onto the metal ion. Even with a steeply repulsive potential, the time scale for electron transfer (~10–16) will still be more rapid than any nuclear motion. It is anticipated that laser experiments will contribute to a better understanding of the charge transfer mechanism, since unlike a collision, a photon can deliver a fixed amount of energy to a specific site, e.g. the π* orbital of a ligand or an excited electronic state of the metal ion.15 IV. CONCLUSION AND VIEW OF THE FUTURE Although these experiments are still very much in their infancy, it is clear from these preliminary studies that a wide range of quite fundamental questions that can be addressed from an examination of size-selected [M.Ln]2+ complexes. Electronic spectra traditionally recorded in the condensed phase can be interrogated at a level where contributions from individual ligands can be analysed. In this context, it may be possible to ‘switch-on’ the Jahn-Teller effect by studying the spectroscopy of Cu(II) complexes as a function of size. Currently, we have been successful in promoting both the reduction and oxidation47 of copper complexes by collisions with a background gas. Future experiments will search for analogous photoinduced charge transfer processes;15 in the case of Fe(II) complexes, Posey and co-workers23,24 have already made significant progress in this direction. One very fundamental question, which these experiments should reveal, is what makes a good solvent or ligand in terms of the ability of a molecule or molecules to stabilize a multiply charged metal ion. In this respect, the complexes we cannot prepare, for example [Pb.(H2O)n]2+ and [Ho.(CH3OH)n]2+ may give as much information as those we can. ACKNOWLEDGMENTS The authors would like to thank EPSRC for generous support for this research program in terms of instrumentation and personnel. The author would also like to thank the following for their contribution to the success of the project: Nick Walker, Rossana Wright,
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Steve Firth, Perdita Barran, David Kirkwood, Hazel Cox, and Ljiljana Puskar. REFERENCES (1) (2) (3) (4)
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Harberland, H. (ed.) (1994) Clusters of Atoms and Molecules. Springer Series in Chemical Physics, Springer-Verlag: Berlin, Vol. 52. Harberland, H. (ed.) (1994) Clusters of Atoms and Molecules II. Springer Series in Chemical Physics, Springer-Verlag: Berlin, Vol. 56. Rademann, K., Kaiser, U., Even, U. and Hensel, F. (1987) Phys. Rev. Lett., 59: p. 2319. Pastor, G.M. and Bennemann, K.H. (1994) In: Clusters of Atoms and Molecules. (Harberland, H., ed.) Springer Series in Chemical Physics, Springer-Verlag: Berlin, Vol. 52, pp. 86–113. Kebarle, P. (1977) Annu. Rev. Phys. Chem., 28: p. 445, and references therein. Keesee, R.G. and Castleman, A.W., Jr. (1986) J. Phys. Chem. Ref. Data, 15: p. 1011, and references therein. Cotton, F.A. and Wilkinson, G.W. (1988) In: Advanced Inorganic Chemistry, Wiley: London. Burgess, J. (1978) Metal Ions in Solution. John Wiley & Sons: New York. Tonkyn, R. and Weisshaar, J.C. (1986) J. Am. Chem. Soc., 108: p. 7128. Weisshaar, J.C. (1993) Acc. Chem. Res., 26: p. 213. Woodward, C.A., Dobson, M.P., and Stace, A.J. (1996) J. Phys. Chem., 100: p. 5605. Woodward, C.A., Dobson, M.P., and Stace, A.J. (1997) J. Phys. Chem., 101: p. 2279. Walker, N. R. , Wright, R. R., and Stace, A. J. (1999) J. Am. Chem. Soc., 121: p. 4837. Marcus, R.A. (1964) Annu. Rev. Phys. Chem., 15: p. 155. Puskar, L., Barran, P.E., Wright, R.R., Kirkwood, D.A., and Stace, A.J. (2000) J. Chem. Phys., 112: p. 7751. Ray, D., Levinger, N.E., Papanikolas, J.M., and Lineberger, W.C. (1989) J. Chem. Phys., 91: p. 6533. Murrell, J.N., Stace, A.J., and Dammel, R. (1978) J. Chem. Soc., Faraday Trans., 74: p. 1532. Blades, A.T., Jayaweera, P., Ikonomou, M.G., and Kebarle, P. (1990) J. Chem. Phys., 92: p. 5900. Blades, A.T., Jayaweera, P., Ikonomou, M.G., and Kebarle, P. (1990) Int. J. Mass Spectrom. Ion Processes, 101, 325; 102: p. 251. Peschke, M., Blades, A.T., and Kebarle, P. (1998) J. Phys. Chem., 102: p. 9978. Rodriguez-Cruz, S.E., Jockusch, R.A., and Williams, E.R. (1999) J. Am. Chem. Soc., 121: p. 1986. Rodriguez-Cruz, S.E., Jockusch, R.A., and Williams, E.R. (1999) J. Am. Chem. Soc., 121: p. 8898. Spence, T.G., Burns, T.D., Guckenberger, G.B., and Posey, L.A. (1997) J. Phys. Chem., 101: p. 1081. Spence, T.G., Burns, T.D., Posey, L.A. (1998) J. Phys. Chem., 102: p. 7779.
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(25) Dobson, M.P., Stace, A.J. (1996) J. Chem. Soc. Chem. Commun., p. 1533. (26) Walker, N.R., Dobson, M.P., Wright, R.R., Barran, P.E., Murrell, J.N., and Stace, A.J. (2000) J. Am. Chem. Soc., 122, 11138. (27) Stace, A.J., Walker, N.R., and Firth, S. (1997) J. Am. Chem. Soc., 119, 10239. (28) Dobson, M.P. and Stace, A.J. (1997) Int. J. Mass Spectrom. Ion Processes, 165/ 166: p. 5. (29) Walker, N.R., Firth, S., and Stace, A.J. (1998) Chem. Phys. Lett., 292: p. 125. (30) Woodward, C.A., Walker, N.R., Wright, R.R., and Stace, A.J. (1999) Int. J. Mass Spectrom., 188: p. 113. (31) Walker, N.R., Wright, R.R., Barran, P.E., and Stace, A.J. (1999) Organometallics, 18: p. 3569. (32) Barran, P.E., Walker, N.R., and Stace, A.J. (2000) J. Chem. Phys., 112, 6173 (33) Walker, N.R., Wright, R.R., Cox, H., and Stace, A.J. In preparation. (34) Puskar, L., Barran, P.E., and Stace, A.J. Unpublished results. (35) Barran, P.E., Puskar, L., and Stace, A.J. In preparation. (36) Levandier, D.J., Goyal, S., McCombie, J., Pate, B., and Scoles, G. (1990) J. Chem. Soc. Faraday Trans., 86: p. 2361. (37) Gu, X.J., Levandier, D.J., Zhang, B., Scoles, G., and Zhuang, D. (1990) J. Chem. Phys., 93: p. 4898. (38) Del Mistro, G. and Stace, A.J. (1992) Chem. Phys. Lett., 196: p. 67. (39) Lethbridge, P.G. and Stace, A.J. (1988) J. Chem. Phys., 89: p. 4062. (40) Walker, N.R. (1999) Gas-phase Studies of Multiply-charged Transition Metal Complexes. D. Phil. thesis, University of Sussex. (41) Echt, O. and Märk, T.D. (1994) In: Clusters of Atoms and Molecules II. Harberland, H. (ed.) Springer Series in Chemical Physics, Springer-Verlag: Berlin, Vol. 56., pp 183–220. (42) Bérces, A., Nukada, T., Margl, P., and Ziegler, T. (1999) J. Phys. Chem., 103: p. 9693. (43) Lisy, J.M. (1997) Int. Rev. Phys. Chem., 16: p. 267. (44) Armentrout, P.B. (1991) Science, 251: p. 175. (45) Fisher, E.R. and Armentrout, P.B. (1992) J. Am. Chem. Soc., 114: p. 2049. (46) Cooks, R.G., Beynon, J.H., Caprioli, R.M., and Lester, G.R. Metastable Ions, Elsevier: Amsterdam, 1973. (47) Wright, R.R. and Stace, A.J. Unpublished results.
5 MICROSOLVATION OF COORDINATED DIVALENT TRANSITION-METAL IONS: ESTABLISHING A SPECTROSCOPIC CONNECTION WITH THE CONDENSED PHASE Lynmarie A. Posey
I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 II. Experimental Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 A. Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 B. Selective Cluster Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . 150 C. Characterization of Cluster Temperature Using Metastable Decomposition. . . . . . . . . . . . . . . . . . . . . . . . . 156 III. Ligand-Field Excitation of [CuII(bpy)(serine – H)]+• . . . . . . . 160 IV. Metal-to-Ligand Charge Transfer in Iron(II)Polypyridine Complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 A. The Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 B. Charge Transfer in the Cluster Limit: Sequential Solvation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 C. Quantifying the Connection with the Condensed Phase. 170 V. Metalloporphyrin Q-Band Excitation. . . . . . . . . . . . . . . . . . . . 175 VI. Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 Advances in Metal and Semiconductor Clusters Volume 5, pages 145–185 © 2001 Elsevier Science B.V. All Rights Reserved. ISBN: 0-444-50726-4
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Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .181 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .182 I. INTRODUCTION Gas-phase clusters have shown promise as tools for elucidating the molecular-scale interactions between ions and solvent that influence electronic structure and reactivity in bulk solution. They offer the significant advantage of control over the local environment surrounding an ion, which is unattainable in the condensed phase. Furthermore, gas-phase clusters eliminate bulk solvent effects and remove the influence of counterions. For transitionmetal ions, the difficulty in establishing a connection between the properties of gas-phase clusters and condensed-phase behavior is directly related to the propensity of these ions to exist in oxidation states higher than +1 in the condensed phase.1 Obviously, for clusters to serve as microscopic models for transition-metal ions and coordination complexes in solution, the same formal oxidation state or at least overall charge must be maintained on the metal ion. The major obstacle to applying cluster methodology to problems involving transition-metal ions and ionic coordination complexes has been finding an ionization/volatilization technique that preserves the oxidation states found in the condensed phase. Perusal of the mass spectrometric literature for transition-metal ions and coordination complexes prior to 1990 reveals only a limited number of instances where ionic species containing transition-metal ions with charges greater than +1 were observed.2–8 The problems encountered in generating gas-phase species containing a single transition-metal ion and coordinated neutral ligands or electrostatically bound neutral solvent molecules are twofold. First, the limited volatility of transition metals, their salts, and ionic coordination complexes hampers the production of gas-phase species. Secondly, the second ionization energies (IEs) of transition-metal ions9 exceed the first IEs of most neutral molecules.10 Consequently, a doubly charged transition-metal ion interacting with a single neutral solvent molecule or ligand will ionize the neutral species to form two ions with a charge of +1; these mutually repulsive ions cannot remain associated in the absence of solvent. The alternate approach of attempting to remove a second electron from a singly charged transition-metal ion already clustered with a neutral molecule has the same net result. Ionization removes the electron from the species with the lowest IE, the neutral molecule, to form two positively charged ions.
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The breakthrough in gaining gas-phase access to the chemically and biologically relevant +2 and +3 oxidation states of transitionmetal ions occurred in 1990 when the groups of Kebarle11,12 and Chait13 reported that electrospray ionization (ESI) transfers these species to the gas-phase without reduction. Kebarle and co-workers observed clusters formed by doubly charged alkaline earths and transition metals11,12,14 as well as triply charged transition metals and lanthanides12,15 with a variety of organic solvents and water. They also determined the sequential free energies of hydration for several doubly charged metal ions by second-shell water from equilibrium cluster distributions. Their collision-induced dissociation (CID) experiments probed the minimum number of solvent molecules necessary to stabilize multiply charged transition-metal ions. Meanwhile, Chait and co-workers13 demonstrated that ESI transferred the ionic coordination complex tris-2,2′-bipyridylruthenium(II), [Ru(bpy)3]2+, to the gas phase as the doubly charged ion; they also observed formation of clusters with the acetonitrile electrospray solvent. Subsequently, Bojesen and co-workers16 reported ESI mass spectra of several mixed-valence transition-metal complexes. Prior to the work described in this chapter, electrospray ionization17,18 had been widely applied in analytical mass spectrometry (MS) of biological macromolecules with the primary goals of mass determination and structural determination using tandem MS methods. The objectives in our work were quite different, namely spectroscopic investigation of the impact of the local solvent environment on the electronic structure of multiply charged transitionmetal ions and coordination complexes. Furthermore, while this work took advantage of the propensity of ESI to produce multiply charged ions, it also exploited the tendency of ESI to produce clusters with the electrospray solvent. Cluster formation is largely viewed as a nuisance in analytical applications. Previous spectroscopic studies19–27 involving transition-metal ions clustered with neutral atoms and molecules were limited to the singly charged species. Electrospray ionization appeared to offer gas-phase access to the higher oxidation states of transition-metal ions, but it was first necessary to show that ESI could generate sufficient quantities of the targeted ionic species for spectroscopic investigation using laser photodissociation mass spectrometry. Next, spectroscopic characterization of the electronic structure of the resulting gas-phase ions was required to show that they were truly analogs of solution species. The experimental approach and instrumentation developed to study gas-phase clusters prepared by ESI are detailed in Section II. The temperature of species generated by
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ESI and its impact on the cluster spectroscopy arose as a secondary experimental issue during the course of this work. Section II also discusses application of the evaporative ensemble model28,29 to extract cluster temperatures from measured metastable decay fractions. Three different spectroscopic approaches exist for probing the interactions of transition-metal ions isolated in gas-phase clusters with their ligands and/or solvent; this chapter provides examples of each approach. The transitions between the d-orbitals of a transition-metal ion, whose degeneracy is removed by the presence of the ligands, offer the most direct spectroscopic probes of the influence of ligands on the electronic structure of transition-metal ions. However, the weakness of ligand-field transitions presents an experimental challenge. Section III presents the results of ligand-field excitation of the gas-phase complex [CuII(bpy)(serine – H)]+•, where bpy = bipyridine; this study demonstrated that ligand-field transitions could be detected using laser photodissociation mass spectrometry, despite the low intensity ion beam produced by ESI. Charge-transfer (CT) transitions within a coordination complex reveal the modulating effect of surrounding solvent molecules on the interactions between the transition-metal ion and coordinated ligands. Section IV describes our investigation of the influence of sequential solvation on the energetics of photoinitiated metal-toligand charge transfer (MLCT) in the coordination complex bis(2,2′:6′,2″-terpyridine)iron(II), [Fe(terpy)2]2+. Finally, the ligand’s electronic absorption spectrum offers a complementary perspective on the interaction of the metal ion with its local environment. Excitation of the Q-bands of the metalloporphyrin nickel(II)-5,10,15,20-tetrakis(N-methyl-4-pyridyl)porphine, [Ni(TMPyP)]4+, clustered with a single dimethyl sulfoxide (DMSO) molecule described in Section V illustrates this approach. II. EXPERIMENTAL APPROACH The goal of the studies described in this chapter was measurement of the electronic absorption spectra of transition-metal ions and coordination complexes transferred to the gas phase by ESI. The intensity of the cluster-ion beam generated by ESI,30 like other cluster-ion production methods, precluded direct measurement of the attenuation of the laser beam exciting electronic transitions in the clusters. Consequently, we resorted to using laser photodissociation mass spectrometry to overcome this obstacle. This technique offered the sensitivity of single-ion detection, and it had already seen widespread application in spectroscopic studies of metal ions
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clustered with neutral species.19–24,31–39 This strategy for measuring electronic absorption spectra required careful selection of target systems because absorption would only be detected if accompanied by a change in mass. The electronic excitation energy deposited in the chromophore had to either directly photodissociate the chromophore or undergo efficient conversion to vibrational energy within the cluster to trigger dissociation of at least one of the weakly bound cluster constituents. The numerous low-lying electronic states of many first-row transition-metal ions, which facilitate radiationless relaxation of excited electronic states, made them ideal candidates for such an approach. A. Instrumentation A tandem mass spectrometer was designed to optimize the overlap between the low intensity continuous wave (cw) ion beam produced by ESI and the tunable laser beam used to probe it. A detailed description of this instrument, shown schematically in Fig. 1, has been provided in previous publications.30,40,41 The cluster-ion beam generated by ESI was accelerated and focused before travelling through the Wien filter (Colutron Research, Model 600B),42,43 which performed the primary mass selection by deflecting all ions in the vertical plane except those with the selected mass-to-charge (m/z) ratio. After exiting the Wien filter, the ions were deflected 90° by a simple electrostatic turning quadrupole44 to merge with the tunable output of a cw Figure 1: Tandem mass spectrometer with an electrospray ionization source configured for laser photodissociation spectroscopy measurements. Argon Ion-pumped Coherent 899-01 Ti:Dye Laser
Electrospray Ionization Source
Acceleration & Steering Optics
Wien Filter
Turning Quadrupole
Microchannel Plates
1 atm
Horizontal Focusing Optics Deceleration Optics
Quadrupole Ion Guide Quadrupole Mass Filter Conversion Dynode & Channeltron
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dye/Ti:sapphire laser (Coherent 899-01, typical linewidth < 2 GHz) pumped by an argon ion laser. A slit lens45 located at the exit of the turning quadrupole provided focusing in the horizontal plane to compensate for dispersion introduced by the turning quadrupole. The aperture for primary mass selection was located after the horizontal focusing optics. The mass-selected ion beam and laser beam copropagated for roughly 1 m as they passed through the deceleration/ focusing lens stack (Colutron Research, Model 400) and quadrupole ion guide (0.95 cm diameter, 80.0 cm length rods) powered by a commercial radiofrequency supply (Extrel QCRF1, 100 W, 1.2 MHz). Upon exiting the ion guide, the ions entered the quadrupole mass filter (Extrel EXM-340 system, 300 W, 0.88 MHz, 1.59 cm diameter rods, m/z range 1-1400), which resolved photoproduct ions from mass-selected parent ions. Ions were detected using an off-axis conversion dynode in combination with an ion-counting Channeltron detector (Galileo Electro-Optics 4870). The signal from the Channeltron was amplified (Stanford Research Systems SR440) and registered by a photon counter (Stanford Research Systems SR400). Photodissociation mass spectra were collected by monitoring the ion-beam signal for 10-ms intervals while the laser beam was chopped at 30 Hz. The data collected were sorted based on the laser state to obtain laser-on–laser-off difference spectra showing depletion of the mass-selected parent ion and production of photoproduct daughter ions. Measurement of either depletion of the parent ion or production of daughter ions as the laser wavelength was scanned yielded photodissociation action spectra. This phasesensitive detection approach permitted photoproduct ions to be easily distinguished from ions formed by metastable decomposition or collision-induced dissociation (see below). B. Selective Cluster Synthesis As mentioned in the Introduction, the key to producing clusters containing divalent transition-metal ions was the application of ESI. An expanded view of the ESI source configuration used for most of the work described herein is provided by Fig. 2. A Vestec E200 ESI source46 was modified following the design reported by Chait and co-workers47 by replacing the conical nozzle in the original source with a heated metal capillary. This configuration offered the major advantage over the original Vestec design of moving the electrospray needle to an exterior location, allowing the spray to be monitored visually to ensure the stability required for spectroscopic applications.
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Figure 2: Electrospray ionization source configured for selective cluster synthesis using a solvent-saturated nitrogen purge. Skimmer #1 Electrospray Region (1 atm)
Heated Metal Capillary 1 × 10-5 Torr
2 Torr N2/Solvent Vapor Purge 0.2 Torr
The ions produced by ESI were sampled into the mass spectrometer by a 20-cm long metal capillary (1.5 mm o.d., 0.76 mm i.d.). The ions then passed through two skimmers with apertures of 0.6 and 1.0 mm before entering the mass spectrometer vacuum chamber (1 × 10–5 Torr with the ESI source operating). The metal capillary and two skimmers defined two regions of differential pumping in the ESI source, which had operating pressures of 2 and 0.2 Torr. The first of these two relatively high-pressure zones in the source played an important role in the cluster synthesis technique described below. The pressure in the second region was still high enough to prevent full acceleration of the ions until after they passed through the second skimmer and entered the “collision-free” confines of the mass spectrometer. Consequently, the potential difference with respect to the second skimmer defined the kinetic energy of the ions throughout the mass spectrometer.48 Clusters consisting of the ionic analytes and the electrospray solvent arise from incomplete desolvation49–51 in the ESI process. In analytical applications, these clusters are typically removed by countercurrent flow of dry N2 gas17,52 or thermal desolvation.46,47 The ESI source used in this work was designed to thermally desolvate the ions by heating the high pressure regions of the source. In practice, only the metal capillary connecting the electrospray ionization region at 1 atm to the first stage of differential pumping was heated in order to preserve clusters formed by ESI. Heating the metal capillary to 30–40°C prevented solvent from freezing and slowed the deposition of nonvolatile analytes within it. Unfortunately, depending exclusively upon the ESI process for cluster formation had the inherent limitation that clusters could only be produced
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with solvents which were suitable as electrospray solvents. Solvents having high surface tension, such as dimethyl sulfoxide and dimethylformamide, were ruled out because the potential differences required to initiate ESI exceeded the onset for corona discharge between the electrospray needle and counter electrode.53 We discovered an alternate method54 for generating clusters while trying to determine the origin of clusters containing a single water molecule in the mass spectrum of [Fe(bpy)3](ClO4)2 electrosprayed from methanol (Fig. 3). These clusters had incorporated water from the air surrounding the electrospray needle, which could be removed by purging the region around the needle with dry N2 (Fig. 2). Subsequently, we found that saturating the N2 purge with methanol vapor enhanced the stability of the [Fe(bpy)3•(CH3OH)n]2+ cluster distribution. However, all the clusters with methanol disappeared when the purge was turned off. The conditions under which the signal intensity was optimized with the purge present removed all of the clusters formed directly by ESI. This observation prompted us to introduce other polar solvent vapors to the N2 purge, which resulted Figure 3: Electrospray ionization mass spectrum of 1.5 × 10–4 M [Fe(bpy)3](ClO4)2 in methanol. The mass spectrum shows an evenly spaced distribution of methanolbased clusters, [Fe(bpy)3•(CH3OH)n]2+ up to n = 6, at which point interloper peaks (*) corresponding to [Fe(bpy)3•(CH3OH)n•(H2O)1]2+, n ≥ 6, appear.
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in formation of clusters exclusively with the solvent in the purge rather than the electrospray solvent (Fig. 4). This approach enhanced the versatility of ESI as a source of gas-phase clusters by making it possible to generate clusters with solvents that were unsuitable as electrospray solvents. Mixed solvent clusters with methanol were only observed when methanol was present in the purge under
Figure 4: Mass spectrum of a 1.5 × 10–4 M solution of [Fe(bpy)3](ClO4)2 in methanol electrosprayed in the presence of a gentle solvent-saturated N2 purge to the region surrounding the electrospray needle. This approach selectively formed clusters with the purge solvent indicated to the left of each mass spectrum. Mixed clusters with methanol were only observed when methanol was present in the purge. In the mass spectrum collected with a mixed methanol + acetone purge, the clusters [Fe(bpy)3•(methanol)n]2+ and [Fe(bpy)3•(acetone)m]2+ are identified by the symbols † and ∇, respectively; the unlabeled peaks correspond to [Fe(bpy)3•(methanol)n(acetone)m]2+ clusters. Spectra are normalized to the peak intensity of the [Fe(bpy)3]2+ ion at m/z = 262. (From Spence, T.G., Burns, T.D., and Posey, L.A. (1997) J. Phys. Chem. A., 101: p. 139.)
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the conditions that optimized cluster formation with the purge solvent. The experimental parameter that played a key role in the selective formation of clusters with the purge solvent was the potential difference between the heated metal capillary and skimmer #1, ΔV, as illustrated by the mass spectra in Fig. 5. The capillary, which samples the electrospray and ambient air into the mass spectrometer, and skimmer #1 defined the first stage of differential pumping in the ESI source. The pressure in this stage of the source was approximately 2 Torr. At a low potential difference of 150 V without the purge (Fig. 5a), the resulting mass spectrum exhibited a progression of [Fe(bpy)3•(CH3OH)n]2+ clusters produced directly by the ESI process. Increasing the potential difference between the capillary and first skimmer from 150 V to 500 V removed all of the methanol clusters, and only the unsolvated [Fe(bpy)3]2+ complex remained (Fig. 5b). Introduction Figure 5: Cluster mass spectra shown as a function of the potential difference (ΔV) between the heated metal capillary and skimmer #1 (Fig. 2) and the purge solvent. The mass spectra are normalized with respect to sampling time, and the total ion signal is given to the right of each spectrum. (From Spence, T.G., Burns, T.D., and Posey, L.A. J. Phys. Chem. A., 101: p. 139.)
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of the purge saturated with the vapor of a solvent, such as ethanol (Fig. 5c) or acetone (Fig. 5e), while maintaining the high potential difference (ΔV = 500 V) generated clusters exclusively with the solvent present in the purge. With ethanol as the purge solvent, clusters containing methanol, both pure and mixed with ethanol, were only observed when the potential difference was reduced (Fig. 5d). When acetone vapor was introduced to the N2 purge, [Fe(bpy)3]2+ formed clusters exclusively with acetone independent of ΔV (Figs 5e and 5f). The selective formation of clusters with the purge solvent when a large potential difference (500 V) was applied across the 2-Torr region of the ESI source was consistent with complete collisional desolvation of the [Fe(bpy)3]2+ ions carrying methanol from the ESI process followed by resolvation with the purge solvent under the mild expansion conditions30,54 at skimmer #1. The mixed cluster distribution observed at an intermediate potential difference of 250 V with ethanol as the purge solvent (Fig. 5d) could also be rationalized by this stepwise desolvation/resolvation mechanism. The kinetic energy imparted by a potential difference of 250 V was insufficient to completely desolvate the [Fe(bpy)3•(CH3OH)n]2+ clusters. As a result, the mass spectrum included residual clusters with methanol from ESI, mixed clusters formed by association of ethanol with the partially desolvated [Fe(bpy)3•(CH3OH)n]2+ clusters, and clusters with ethanol arising from resolvation of the bare [Fe(bpy)3]2+ ion. A second mechanism was clearly operative in the case of acetone because clusters formed exclusively with acetone even under conditions where collisional desolvation was incomplete. In a related study, Cheng et al.55 found that ESI of aqueous solutions of metal salts in the presence of organic solvent vapor evaporated from a beaker placed near the electrospray needle produced either pure clusters with the organic solvent or mixed aqueous/organic clusters. They rationalized their observations based on the relative binding affinities of the organic solvents and water and proposed a solventdisplacement mechanism for cluster formation. Solvents with higher binding affinities than water irreversibly displaced it from the cluster to produce pure clusters with the organic solvent, while solvents with binding affinities comparable to water reversibility exchanged with it to yield mixed clusters. In this work, such a solvent displacement mechanism appeared to govern cluster formation with acetone at low potential differences. Since ion-dipole interactions were expected to dominate the binding of acetone and methanol to [Fe(bpy)3]2+, acetone fit the criterion of having a stronger binding affinity than the electrospray solvent because of its significantly larger dipole moment (2.88 D vs. 1.70 D for methanol).56
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C. Characterization of Cluster Temperature Using Metastable Decomposition The techniques commonly used to generate gas-phase ionic clusters effectively separate ion production from cluster formation. For example, electron-impact ionization of a supersonic expansion57,58 and laser vaporization59,60 generate plasmas initially; clusters form subsequently through condensation of neutral species about the ions as the entrained species and carrier gas expand into the vacuum. The free-jet expansion following ion formation ensures significant cooling. With both of these techniques for cluster-ion production, rotational temperatures below 30K59–64 are common. Lisy and co-workers31 use ion “pick-up” by pre-existing clusters downstream from the expansion to produce ionic clusters. The groups of Scoles65,66 and Stace67,68 practice another variation of the “pick-up” method in which pre-existing clusters incorporate a neutral species downstream from the expansion prior to ionization by electron impact. These “pick-up” methods yield higher cluster temperatures31 than either ionization of a free-jet expansion or laser vaporization because there is no opportunity for cooling to remove the energy released by ion association or ionization. The features common to all of these methods are the formation of clusters as a gas expands into a vacuum and separation of cluster formation from ionization. In contrast, direct production of ionic clusters by ESI occurs at atmospheric pressure and combines volatilization, ionization, and cluster formation. The resulting clusters experience numerous collisions as they travel first from the ESI region (1 atm) through the metal capillary to the first stage of differential pumping and then through the two stages of differential pumping at pressures of 2 Torr and 0.2 Torr. In addition, the potentials applied to the electrospray needle, metal capillary, and two skimmers create drift fields across the three high-pressure zones that partially accelerate the ions relative to the neutral background gas. As discussed above, the “drift” potential between the capillary and skimmer #1 can be employed to collisionally desolvate ions. Meanwhile, Knudsen number69 calculations indicate mild expansion conditions for our ESI source configuration.30 The opposing effects of collisional heating as the ions move from the electrospray needle into the mass spectrometer and cooling under mild expansion conditions raised questions about the internal energies of the ions exiting the ESI source and the impact of temperature on the photodissociation action spectra recorded for these clusters. Metastable decomposition (Fig. 6) occurring
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Figure 6: Mass spectrum produced by the metastable decomposition of [Fe(bpy)3•(CH3OH)3]2+ during the approximately 150-μs transit time between the primary mass selector and secondary mass analyzer. (From Spence, T.G., Burns, T.D., Guckenberger, G.B., V, and Posey, L.A. (1997) J. Phys. Chem. A., 101: p. 1081.)
[Fe(bpy)3•(CH3OH)n]2+ 1
2
3
Ion Intensity
n = 0
240
260
280
300
320
340
360
Mass/Charge
during the ~150-μs flight of mass-selected ions from the primary mass selector to secondary mass analyzer provided a means to estimating the temperature of the clusters. A number of groups31,33,70–72 had previously applied the evaporative ensemble model28,29 developed by Klots to relate metastable decay fractions to cluster temperatures and sequential binding energies. We followed this approach, which is outlined below, to estimate temperatures for [Fe(bpy)3]2+•(CH3OH)n clusters formed directly by ESI. This work represented the first effort to characterize the temperatures of ions produced by ESI. The evaporative ensemble model is based upon the assumption that a fraction of the clusters produced lose neutral solvent molecules sequentially before and after primary mass selection, kn +1 kn kn – 1 • S n +1]2+ ⎯⎯ ⎯→[M • S n ]2+ ⎯⎯→ [M • S n – 1]2+ ⎯⎯ ⎯→ ... (1)
where M = [Fe(bpy)3]2+ and S = CH3OH. The function
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Pn (E n , t1 ) =
kn +1 [exp(–k n t 1 ) – exp(–k n +1t1 )] k n +1 – k n
(2)
describes the distribution of internal energies in the cluster ensemble at the time of primary mass selection, t1. Between primary mass selection and secondary mass analysis at t2 , the distribution of internal energies evolves to Pn–1(En–1,t2) = Pn(En, t1)[1 – exp(–knt2)]
(3)
through metastable decomposition as illustrated by Fig. 7. The shaded high-energy portion of the internal energy distribution function at t1, Pn(En, t1) (solid line) becomes the new internal energy distribution function Pn–1(En–1, t2) (dashed line) through metastable loss of one neutral solvent molecule by the time of mass analysis, t2. Figure 7: Illustration of the evolution of cluster internal energy distributions resulting from metastable decomposition in the evaporative ensemble model.28
P(E, t)
Pn(En, t1)
Pn-1(En-1, t2)
0.0
0.5
1.0
1.5
2.0
Eint(eV)
2.5
3.0
3.5
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The shift in the maximum of the shaded region to Pn–1(En–1, t2) corresponds to the binding energy of the nth solvent molecule. The fraction of clusters that lose a single solvent molecule between mass selection and mass analysis is given by R n –1 =
ò Pn –1 (E n – 1 , t 2 ) dE ò Pn (E n , t1 ) dE
(4)
Sequential binding energies and cluster internal energies were determined from the observed metastable decay fractions30 using RRK rate constants31,33,70,71 æ E – Vn kn (E n ) = A çç n è En
ö ÷÷ ø
L (n )– 1
(5)
with L(n) = 6n + 13, while varying the ratio of solvent binding energies Vn+1 and Vn until agreement was reached between the observed and calculated metastable decay fractions. For [Fe(bpy)3]2+•(CH3OH)n clusters, the average internal energies calculated from the evaporative ensemble energy distribution ∞
E n = ò 0 E n Pn (E n ,t1 )dE n
(6)
ranged from 0.691 eV for n = 2 to 1.00 eV for n = 6. In the context of the non-Boltzmann energy distribution of the evaporative ensemble, a cluster temperature is determined by partitioning the average internal energy evenly between the active modes31 Tn = E n /k B L(n )
(7)
Temperatures ranging from 321K for n = 2 to 239K for n = 6 result. While these temperatures may seem remarkably low considering the large potential differences and relatively high pressures in the ESI source, closer examination of the conditions suggests that these results are not unreasonable. The highest electric field in the ESI source is found between the needle and metal capillary (3000 V/ 0.003 m = 1 × 106 V/m); however, the ambient pressure is 1 atm in this region. If the background gas molecules are treated as stationary targets, the accelerated ions travel on the order of 3 nm under the influence of the drift field between collisions and are only accelerated by a potential difference of 3 mV. Furthermore, many of the ions in the electrospray region are incorporated in large droplets or clusters. Energy deposited in these droplets or clusters
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through collisions is distributed over a large number of internal degrees of freedom. Evaporating solvent can also carry away some of the collision energy; the weak ion-solvent and solvent-solvent bonds limit the extent of heating. The highest energy collisions actually occur in the first stage of differential pumping, where electric fields range from 6 × 104 V/m to 2 × 105 V/m. Electric fields at the low end of this range preserve clusters generated by ESI, while electric fields at the upper end of this range provide adequate collision energies to completely desolvate the analyte ions. It is difficult to estimate the actual collision energies in the first stage of differential pumping because the gas density in the region traversed by the ions is certainly higher than the background pressure of 2 Torr. Finally, the ions experience mild expansion conditions as they pass through skimmer #1, which results in some cooling. The net result is that cluster ions generated by ESI have temperatures comparable to the solution from which they originated.
III. LIGAND-FIELD EXCITATION OF [CuII(BPY)SERINE – H)]+• Arguably, ligand-field transitions provide the most direct probe of the influence of the local environment on a transition-metal ion. The difficulty in probing ligand-field transitions in the cluster environment arises from the weakness of these transitions combined with the low concentrations of gas-phase cluster ions. The d-d transitions are Laporte-forbidden in centrosymmetric ligand fields, and in tetrahedral ligand fields they are only partially allowed through d-p mixing.73 We selected the complex [CuII(bpy) (serine – H)]+• to explore the possibility of probing ligand-field transitions in divalent transition-metal ions isolated in the gasphase. This complex belongs to a family of coordination complexes consisting of a rigid aromatic bidentate ligand and a deprotonated amino-acid ligand that have been studied in solution as models for hydrophobic and aromatic interactions relevant in biological systems.74,75 The d9 CuII ion is anticipated to have a square-planar coordination geometry by analogy to similar complexes.76 The [CuII(bpy)(serine – H)]+• complex was an appealing target for application of laser photodissociation to detect absorption indirectly because the gas-phase ion was known to undergo collisionally activated dissociation (CAD) at collision energies (Elab = 5 eV, Ecom = 0.55 eV)77 that were well below the photon energies required to excite the ligand-field transition (λmax = 614 nm, ε = 58 L mol–1 cm–1, in 50/50 (v/v) aqueous methanol). In multiple, low-energy collisions with Ar, [CuII(bpy)(serine – H)]+• dissociated through three major paths to form four ionic products as shown in the reaction
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scheme proposed by Ture±ek and co-workers77 (Fig. 8). The major decomposition path responsible for 49% of the CAD products yielded 2 and 3 through sequential loss of formaldehyde from the serine α-side chain followed by loss of the remainder of the deprotonated serine. The branching percentages for 2 and 3 were 8% and 41%, respectively. Transfer of the serine hydroxyl group to the CuII ion followed by elimination of the remainder of the serine to yield 4 accounted for 43% of the observed CAD products. A decarboxylation-dehydration reaction produced 5 as a minor product (7%). Excitation of [CuII(bpy)(serine – H)]+• at 575 nm (2.16 eV) yielded the photoproduct-ion mass spectrum shown in Fig. 9. Notably, only three of the four products observed for low-energy, multiple-collision CAD appeared in this mass spectrum. The branching fractions for the photodissociation channels are shown above the proposed product-ion structures in Fig. 8. The decarboxylation-dehydration channel, which yielded 5 in CAD, was absent with photoexcitation even though the photon energy exceeded the energy of each of the low-energy collisions by nearly a factor of 4. Metastable decomposition and single collisions at higher energies (5.7–8.6 eV) also accessed the decarboxylation-dehydration decay channel.78 With ligand-field excitation, migration of the serine hydroxyl group to the CuII ion followed by loss of the rest of the serine moiety to produce [CuII(bpy)(OH)]+• accounted for 54% of the product yield. The remaining photoproducts formed in the sequential dissociation pathway initiated by loss of –H2CO with branching percentages of 12% and 34% for 2 and 3, respectively. As in the CAD experiments with multiple low-energy collisions,77 the bulk of the product ions generated by this decomposition pathway totally eliminated the deprotonated serine ligand. Interestingly, under single-collision conditions where the collision energies were 2–3 times higher than the energy of the absorbed photon, only 41% of the product generated by this pathway made it to 3 as opposed to 74% with photoexcitation.78 These experiments were motivated, in part, by the desire to test the feasibility of using laser photodissociation mass spectrometry to study weak ligand-field transitions in ions generated by ESI. Excitation at 575 nm with a laser fluence of 1.2 × 102 W cm–2 (0.55 W, 0.75 mm beam diameter) photodissociated 0.8% of the mass-selected [CuII(bpy)(serine – H)]+• ions. Comparison of the measured photoproduct yield with the number of ions expected to absorb based on the molar absorptivity of [CuII(bpy) +• in 50/50 (v/v) aqueous methanol solution (serine – H)] (ε = 49.5 L mol–1 cm–1 at 575 nm) provided an upper limit on the efficiency of photodissociation. Assuming 100% overlap between
O
O
N
-H2CO
HO
O
N
N H2
N H2
N
N
-CO2 , -H2O
-H2CCHNH2CO2
0.54
0.00
N
N Cu N
4 (m/z = 236,238)
H
N H
N Cu
2 (m/z = 293,295)
1 (m/z = 323,325)
HO
-•OC(OH)CHNH2
N Cu
Cu
HO
0.34
Cu N
5 (m/z = 261,263)
3 (m/z = 219,221)
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0.12
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Figure 8: Reaction scheme proposed by Ture±ek and co-workers77 for collisionally activated dissociation of [CuII(bpy)(serine – H)]+• with the photoproduct branching ratios measured for 575-nm excitation reported above each structure. (Adapted from Gatlin, C.L., Ture±ek, F., and Vaisar, T. (1995) J. Mass Spectrom., 30: p. 1617.)
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Figure 9: Laser-on–laser-off difference mass spectrum showing photoproduct ions generated by ligand-field excitation of [CuII(bpy)(serine – H)]+• at 575 nm. The labels correspond to the numbered structures in Fig. 8. (From Spence, T.G., Trotter, B.T., and Posey, L.A. (1998) Int. J. Mass Spectrom. Ion Processes, 177: p. 187.)
Laser-on – Laser-off
Ion Intensity
3
4
2
2
5
200
220
240
260
280
300
320
m/z the ion and laser beams in the laser interaction region, 1.0% of the [CuII(bpy)(serine – H)]+• ions were expected to photodissociate, giving a quantum yield of at least 0.8 for this process. The [CuII(bpy)(serine – H)]+• complex efficiently converted electronic excitation energy to vibrational motion along three of the four dissociative reaction coordinates. This study faced the added complication of significant background signal for the four ionic product channels, which arose predominantly from metastable decomposition with a smaller contribution from collisional dissociation.78 Nevertheless, it was possible to detect ligand-field excitation of ≤ 1% of the mass-selected [CuII(bpy)(serine – H)]+• ions by monitoring photoproduct ions. IV. METAL-TO-LIGAND CHARGE TRANSFER IN IRON(II)-POLYPYRIDINE COMPLEXES A. The Problem The inorganic photochemistry literature contains numerous references to “specific solvent effects,” spatially directed interactions between a charge-transfer (CT) chromophore and solvent attributed to hydrogen bonding79–81 or Lewis acid-base bonding.82–84
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However, there is remarkably little direct evidence for specific molecular-scale interactions between CT chromophores and neighboring solvent molecules. These effects are typically inferred from the failure of dielectric continuum models to describe the solvent dependence of the energy of the optical CT transition, Eop. The strongest evidence for specific molecular interactions between CT chromophores and solvent in the condensed phase comes from a series of optical85–88 and complementary electrochemical studies89,90 of metal-to-ligand charge transfer (MLCT) and metalto-metal charge transfer (MMCT) carried out in mixtures of acetonitrile and dimethyl sulfoxide (DMSO). At mole fractions as low as 0.1 DMSO, Eop deviated significantly from the linear dependence anticipated if the composition of the first solvent shell reflected the bulk solvent composition. Hupp and co-workers85,86 attributed the deviation to preferential solvation of the coordination complexes under study by DMSO and concluded that first-shell solvent provided the bulk of the solvent reorganization energy. Gas-phase cluster studies have the potential to directly address the contributions of individual solvent molecules to the solvent reorganization energy, resolving first-shell interactions from those of the bulk. The theory developed to describe photoinitiated CT in the condensed phase91 partitions the energy of the associated optical transition, Eop, into contributions from the zero-point energy difference between the ground and CT-excited states, ΔEo; inner-sphere reorganization of the chromophore, Ein; and outer-sphere or solvent reorganization, Eout as follows: Eop = ΔEo + Ein + Eout
(8)
Experimentally, Eop corresponds to the maximum of the CT absorption band. In the condensed phase, Eop is typically measured as a function of solvent, and the resulting data are plotted as a function of the optical and/or static dielectric constants of the medium derived from dielectric continuum theory.92–96 In principle, the y-intercept yields ΔEo + Ein; however, Hupp and coworkers97 have shown that this approach significantly overestimated Ein for MMCT in [(NH3)5RuIII–4,4′-bpy–RuII(NH3)5]5+. The presence of counterions, which can significantly impact Eop through ion pairing,98 presents an added complication to studying CT in solution. At first glance, agreement with the predictions of dielectric continuum theory might suggest the absence of specific directed interactions between the CT chromophore and neighboring
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solvent molecules. Such agreement, at the very least, might be interpreted as indicating that directed molecular interactions are weak compared to the interaction of the CT chromophore with solvent molecules behaving as a polarizable dielectric. However, in order to see deviation from the predictions of a dielectric continuum model when examining the solvent dependence of Eop, one or more of the solvents in question must exhibit significantly different interactions with the CT chromophore. Consequently, no detailed information on the interactions between solvent and solute at the molecular level can be extracted from the condensed phase studies in the absence of deviation from the dielectric continuum model. In contrast, gas-phase clusters make it possible to distinguish the influence of first-shell solvent molecules from more distant solvent molecules by discarding most of the bulk solvent. In the gas-phase cluster limit, ΔEo + Ein , becomes the energy of the CT transition in the absence of solvent. The solvent reorganization energy, Eout, can then be easily tuned by sequential addition of solvent molecules to determine the contributions of the nth solvent molecule ΔEout,n = Eop,n – Eop,n–1, where Eop,n and Eop,n–1 are the energies of the optical CT transition for clusters containing n and n – 1 neutral solvent molecules, respectively. The system targeted for our MLCT studies was the low-spin bis(2,2′:6′,2″-terpyridine)iron(II) complex, [Fe(terpy)2]2+, clustered with dimethyl sulfoxide (DMSO). This complex, like the other Fe(II)-polypyridines and the widely studied Ru(II)-polypyridines,99 absorbs visible light to transfer an electron from one of the metal d t2g -orbitals to a π*-orbital localized on one of the ligands. The energy levels of [Fe(terpy)2]2+ involved in MLCT absorption and subsequent relaxation are illustrated schematically in Fig. 10. The presence of low-lying ligand-field electronic states in [Fe(terpy)2]2+ distinguishes it from the weakly fluorescent Ru(II)-polypyridine complexes and facilitates rapid nonradiative relaxation before emission can occur.99,100 This nonradiative decay process is initiated by intersystem crossing ( τ 1MLCT1 < 1 ps) to the 5T2 state 101 and is followed by relaxation back to the 1A1 ground state. McCusker et al.101 have proposed that interaction with the solvent mediates relaxation from the 5T2 state (τ = 2.54 ± 0.13 ns in water at 298K). The absence of measurable radiative decay pathways in [Fe(terpy)2]2+ made it ideally suited to using photodissociation to detect absorption. The chromophore converted the energy from excitation of the 1MLCT1 ← 1A1 transition to vibrational excitation of the cluster, which led to evaporation of DMSO solvent molecules,
1MLCT
erpy)(terpy-)]2+ [Fe(terpy)2]
2+
Bis(2,2':6',2"-terpyridine)iron(II)
1T
Eop = Ein + Eout + ΔEo
2
T1
3
T2
Lynmarie A. Posey
1
166
Figure 10: Schematic representation of the low-lying electronic energy levels of [Fe(terpy)2]2+ based on the work of McCusker et al.101 The designations for the ligand-field states are based on the symmetry of the ligand field rather than the overall symmetry of the complex.
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[FeII(terpy)2•(DMSO)n]2++ hν → [FeIII(terpy–)(terpy)•(DMSO)n]2+*
(9)
[FeIII(terpy–)(terpy)•(DMSO)n]2+*→ [FeII(terpy)2•(DMSO)m]2+ + (n–m)DMSO
(10)
B. Charge Transfer in the Cluster Limit: Sequential Solvation Action spectra were collected by measuring photodepletion of massselected [Fe(terpy)2•(DMSO)n]2+ clusters, n = 1–11, to monitor the evolution of the MLCT absorption band with the addition of solvent. Fig. 11 shows representative action spectra for the clusters containing one and eight DMSO molecules and the absorption spectrum of [Fe(terpy)2](PF6)2 in bulk DMSO. These spectra exhibited a net red shift in the MLCT band with the addition of DMSO molecules, which was consistent with the ground-state dipole moment of zero and creation of an excited-state dipole moment Figure 11: Photodepletion action spectra of [Fe(terpy)2•(DMSO)n]2+ clusters, n = 1 and 8, resulting from excitation of the 1MLCT1 ← 1A1 transition shown with the absorption spectrum of 3 × 10–5 M [Fe(terpy)2](PF6)2 in DMSO at 20°C. The maxima of the three spectra are normalized to facilitate comparison. (From Spence, T.G., Trotter, B.T., and Posey, L.A. (1998) J. Phys. Chem. A., 102: p. 7779.)
n=8
n=1
Relative Intensity
[Fe(terpy)2•(DMSO)n]2+
Solution Spectrum
1.5
1.6
1.7
1.8 E, 104 cm-1
1.9
2.0
2.1
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with the transfer of an electron from the metal center to one of the 2,2′:6′,2″-terpyridine ligands. The long-range ion-dipole interaction between [Fe(terpy)2]2+ and the solvent remained unchanged in the transition from the ground to excited state. Closer examination of the effects of sequential solvation revealed that the interaction between the coordination complex and firstshell DMSO molecules was more complicated than a simple stepwise shift to lower energy with the addition of each solvent molecule. The maximum of the action spectrum for each [Fe(terpy)2•(DMSO)n]2+ cluster (n = 1–11) was determined from a nonlinear least-squares fit41 of the spectrum to a log-normal lineshape,102 The maxima, which correspond to Eop, are plotted as a function of cluster size in Fig. 12. The red shift toward the bulk limit did not begin immediately with the addition of DMSO solvent molecules; the MLCT band initially shifted to higher energy as the second and third DMSO molecules were added. The MLCT band maxima were the same within experimental error for n = 1, 4, 5. At n = 6, the anticipated shift to the red began in earnest and continued at approximately the same rate with the addition of each Figure 12: Maxima from the photodepletion action spectra of [Fe(terpy)2•(DMSO)n]2+ clusters, n = 1–11, corresponding to the lowest energy MLCT absorption band of [Fe(terpy)2]2+, plotted as a function of the number of DMSO molecules, n. (From Spence, T.G., Trotter, B.T., and Posey, L.A. (1998) J. Phys. Chem. A., 102: p. 7779.)
1.88
Band Maximum, 10 4 cm -1
[Fe(terpy)2 •(DMSO)n ] 2+ 1.86
1.84
1.82 Solution Band Maximum 1.80
1.78 0
2
4
6 Cluster size, n
8
10
12
Microsolvation of Coordinated Divalent Transition-Metal Ions
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subsequent DMSO until the ninth DMSO was added. The reorganization energies for the sixth through eighth DMSO were –87 ± 31 cm–1, –119 ± 30 cm–1, and –108 ± 30 cm–1, respectively. These values were comparable to the solvent reorganization energies of 125–150 cm–1 per DMSO estimated from MMCT studies in mixed acetonitrile/DMSO solutions by Blackbourn and Hupp.86 Addition of the ninth DMSO shifted Eop for MLCT to higher energy. For n = 9, the energy of the MLCT transition was intermediate between that for n = 8 and n = 10. With the addition of the tenth and eleventh DMSO, the shift to the red resumed, albeit at an apparently slower rate. The analysis of the metastable decomposition of [Fe(bpy)3•(CH3OH)n]2+ clusters using the evaporative ensemble model described in Part C of Section II showed a decrease in cluster temperature with increasing size. Consequently, temperature was ruled out as the origin of shift in the MLCT band with the addition of solvent. The first question that arose in examining these data was why did the first five solvent molecules have so little effect on the energy of the MLCT transition? Clearly, the solvation of the ground and excited states by these first five DMSO molecules was roughly equal. In contrast, the onset of the MLCT bands for [Fe(bpy)3•(CH3OH)n]2+ clusters, n = 1–6, shifted smoothly to lower energy with addition of solvent. Space-filling models of [Fe(terpy)2]2+ and the analogous [Fe(bpy)3]2+ complex generated using MacroModel103 with crystallographic coordinates104,105 as input revealed striking differences between these two iron(II)-polypyridines. The three bipyridine ligands shrouded the FeII ion, while the two terpyridyl ligands left the FeII ion partially exposed to solvent. Molecular mechanics simulations with an MM2* force field and Monte Carlo energy minimization103 showed that at least four DMSO molecules fit easily in the pockets created by the terpyridine ligands. The DMSO molecules in the pockets could interact with +2 charge, which was primarily localized on the metal center in the ground state. With excitation of the MLCT transition, these solvent molecules transiently experienced the increased positive charge on the metal ion and at least a partial negative charge on one of the ligands. The absence of a significant shift in the energy of the MLCT transition as DMSO molecules filled the pockets indicated that the interactions of these DMSO molecules with the ground and excited state charge distributions in [Fe(terpy)2]2+ were offsetting. Solvent molecules at longer range experienced the same net charge whether [Fe(terpy)2]2+ was in its ground or excited state; in other words, the ion–dipole interaction in the ground and excited states were the same. The additional interaction that stabilized the MLCT
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excited state relative to the ground state was the dipole-dipole interaction between the solvent and excited-state dipole moment of [Fe(terpy)2]2+. This picture of four or five DMSO solvent molecules nestled in the pockets created by the planar terpyridine ligands was consistent with the metastable decay fractions measured for [Fe(terpy)2•(DMSO)2]2 clusters (Fig. 13a). The metastable decay fractions for loss of the first DMSO, Rn–1, were below 0.10 for n = 1, 2, and 3. The value of Rn–1 rose to 0.14 for n = 4 before dropping back below 0.10 for n = 5. In going from n = 3 to n = 4, the shift of the MLCT band with addition of DMSO changed from blue to red. This pattern of even-odd alternation in the values of Rn–1 continued for n = 6 and 7 until Rn–1 reached a plateau of 0.375 ± 0.14 for n = 8–10. In contrast, the metastable decay fractions were significantly higher (Fig. 13b) for [Fe(bpy)3(DMSO)n]2+, where the bipyridyl ligands encapsulated the metal ion. The values of Rn–1 ranged from 0.11 to 0.15 for n = 1–3 before rising sharply to 0.35 and 0.60 for n = 4 and n = 5, respectively. For n = 6, Rn–1 returned to 0.13. For larger [Fe(bpy)3(DMSO)n]2+ clusters (n = 7–10), the metastable decay fraction ranged from 0.36 to 0.64. Overall, the metastable decay fractions for [Fe(terpy)2(DMSO)n]2+ clusters were significantly lower than those for [Fe(bpy)3•(DMSO)n]2+ clusters, indicating a stronger binding interaction of DMSO with [Fe(terpy)2]2+. C. Quantifying the Connection with the Condensed Phase If clusters are to play a role in deciphering the details of interactions at the molecular level which contribute to bulk observables, it is essential as a starting point to establish that the species isolated in gas-phase clusters are the same as those found in bulk solution. The presence of the intact MLCT absorption band in [Fe(terpy)2•(solvent)n]2+ and [Fe(bpy)3•(solvent)n]2+ clusters provided convincing qualitative evidence that the ions transferred to the gas phase by ESI were indeed analogs of solution species.30,40,41,106 The next step was to quantify the relationship between the energy of the MLCT transition for [Fe(terpy)2]2+ in clusters and solution. In solution, the interactions with solvent that influence the energy of the CT transition are typically modeled using dielectric continuum theory, and the related experiments involve measurement of the solvent dependence of the CT absorption band. Meyer and co-workers107 have used Kirkwood’s equation108 for the mutual electrostatic interaction between an ion and a polar solvent to predict the solvent reorganization associated with photoinitiated
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Figure 13: Metastable decay fractions, Rn–i (i = 1, 2) measured for a) [Fe(terpy)2•(DMSO)n]2+ and b) [Fe(bpy)3•(DMSO)n]2+ clusters.
MLCT in [M(bpy)3]2+, where M = Fe, Ru. The new interaction created between an Fe(II)-polypyridine, such as [Fe(bpy)3]2+ or [Fe(terpy)2]2+, and a polar solvent with preparation of the MLCT excited state is a dipole-dipole interaction. From Kirkwood’s equation, the energy of this interaction or the solvent reorganization is given by
E out =
μes2 æç 1 – Dop ö÷ b 3 çè 2Dop + 1 ÷ø
(11)
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where μ– es is the excited-state dipole moment, b is the effective radius assuming a roughly spherical ion, and Dop is the optical dielectric constant of the bulk solvent. The quantity (1 – Dop)/(2D op + 1) reflects the number density of polarizable electrons and their polarizability in a dense isotropic medium.109 This description neglects the details of the solvent’s molecular structure and treats it simply as a dielectric continuum. Combining this expression for the solvent reorganization energy with equation (8) yields the following expression for the maximum of the MLCT absorption band in [Fe(terpy)2]2+:
E op = ΔE o + E in +
μes2 æç 1– Dop ö÷ b 3 çè 2Dop + 1 ÷ø
(12)
which predicts a linear dependence of Eop on (1 – Dop)/(2D op + 1) with a slope of μ– 2es/b3 and y-intercept of ΔEo + Ein. The data plotted in Fig. 14 showed the predicted linear behavior for the solvents acetone, acetonitrile, N,N-dimethylformamide, dimethyl sulfoxide, methanol, and pyridazine with a slope of 3.687 × 103 cm–1 and y-intercept of 1.876 × 104 cm–1. The effective radius of Figure 14: Band maximum for MLCT absorption by [Fe(terpy)2]2+ in bulk solution, Eop, plotted as a function of (1 – Dop)/(2 Dop + 1) for six polar organic solvents.
1.81
6
Slope = 3.69 × 103 cm-1 Intercept = 1.876 × 104 cm-1 R = 0.993
5 4
4
Band Maximum, 10 cm
-1
1.82
3 1.80
2
1. Pyridazine 2. Dimethyl Sulfoxide 3. Dimethylformamide 4. Acetone 5. Acetonitrile 6. Methanol
1 1.79
1.78 -0.24
-0.23
-0.22
-0.21
-0.20
-0.19
(1 - Dop)/(2 Dop + 1)
-0.18
-0.17
-0.16
Microsolvation of Coordinated Divalent Transition-Metal Ions
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5.25 Å estimated from a space-filling model generated with crystallographic coordinates yielded an excited-state dipole moment of 10.3 D for [Fe(terpy)2]2+. Interestingly, this standard approach to examining solvent reorganization in the condensed phase suggested that there was nothing special about the interaction between the solvent and CT chromophore. However, the gas-phase cluster studies have provided evidence for specific ion-solvent interactions involving the first four or five DMSO molecules that were missed by the condensed-phase approach because all of the solvents studied had similar directed interactions with the CT chromophore. The quantitative connection between the cluster data and Eop in solution was established using Jortner’s Cluster Size Equation (CSE) approach.110,111 This method develops the cluster-size dependence of a property by taking the property’s bulk value and subtracting a correction factor, C(n), for the solvent volume excluded from the cluster. For MLCT the corresponding CSE is Eop (n) = Eop (∞) – C(n)
(13)
where Eop(∞) is the energy of the MLCT transition in bulk solution and the correction factor
C(n ) =
μes2 æç 1– Dop ö÷ Rc3 çè 2Dop + 1 ÷ø
(14)
is based upon the expression for the solvent reorganization energy given in equation 11. Equations 11 and 13 differ only by replacement of b from equation 11 with the cluster radius Rc in equation 13. From the expression for the cluster volume including [Fe(terpy)2]2+, Rc can be written as a function of cluster size, n
æ b3 ö Rc3 = nR o3 + b 3 = R o3 çç n + 3 ÷÷ = R o3(n + 5.28) Ro ø è
(15)
where Ro = 3.014 Å is the effective radius of a DMSO molecule determined from its density. The predictions of the CSE
Eop (n ) = E op ( ∞) –
æ 1– Dop ö μ es2 ç ÷ 3 R o ( n + 5.28) çè 2 Dop + 1 ÷ø
(16)
are shown in Fig. 15 with the measured values of Eop for [Fe(terpy)2•(DMSO)n]2+ clusters (n = 1–11). The values measured
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Figure 15: Metal-to-ligand charge-transfer band maxima for [Fe(terpy)2•(DMSO)n]2+ clusters (● ) and the cluster size equation (CSE) from equation 15 plotted as a function of cluster size, n. 1.90
1.90 CSE Solution Limit
1.88
1.86
1.86
1.84
1.84
1.82
1.82
1.80
1.80
Band Maximum, 104 cm-1
Eop(n), 104 cm-1
1.88
1.78
1.78 0
5
10
15
20
Cluster Size, n
for the smallest clusters deviated by as much as 2.7 × 102 cm–1 from the CSE developed from a dielectric continuum model, which was not surprising since the model neglected the details of molecular structure. However, the experimentally determined MLCT band maxima agreed nearly quantitatively with the predictions of the CSE with addition of the tenth and eleventh DMSO molecule. This corresponded to the size range where the slope of the experimental data changed, which would be consistent with closing of a solvent shell. The hydration number for [Fe(bpy)3]2+ was estimated at n = 9–11 from viscosity and density measurements.112 The observation of quantitative agreement between the data for clusters containing as few as ten or eleven solvent molecules and the predictions of a dielectric continuum model strongly suggests that for the purposes of modeling solution behavior, ionic coordination complexes in solution can be viewed as clusters containing the firstshell solvent embedded in a dielectric continuum. Addition of the first 11 DMSO molecules brought the energy of the MLCT transition to within 305 ± 30 cm–1 of the bulk limit. Unfortunately, no data were available on Eop for the unsolvated [Fe(terpy)2]2+ ion because excitation of the MLCT band did not dissociate either of the tridentate terpyridine ligands from the complex. Nevertheless, Eop for [Fe(terpy)2]2+ could be estimated
Microsolvation of Coordinated Divalent Transition-Metal Ions
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from the cluster data. Extrapolation of the cluster data to n = 0 suggested that Eop for the unsolvated ion could be as low as 1.860 × 104 cm–1. The y-intercept of Eop plotted as a function of (1 – Dop)/(2Dop + 1) for a variety of solvents (Fig. 14) was 1.876 × 104 cm–1, which corresponded to ΔEo + Ein in the dielectric continuum treatment of MLCT. Note that the y-intercept predicted by dielectric continuum theory tends to overestimate the contribution of Ein.97 Assuming that Eop for the gas-phase [Fe(terpy)2]2+ ion fell between 1.860 × 104 cm–1 and 1.876 × 104 cm–1, the first 11 DMSO molecules contributed 54–63% of the bulk solvent reorganization energy. The CSE equation predicted that the next 11 DMSO molecules would only provide an additional 13–17% of Eout. The magnitude of the experimentally determined solvent reorganization energy was consistent with the results of computational efforts to predict the energies of CT transitions for solvated coordination complexes. The computational efforts to investigate the effects of solvation on MLCT have focused on [Ru(NH3)5L]2+, L = pyridine (pyr) or pyrazine, in water. Zerner and co-workers113 have used intermediate neglect of differential overlap (INDO) at the configuration interaction (CI) level of theory to calculate the energy of the MLCT transition in [Ru(NH3)5(pyr)]2+ with 5, 10, or 15 associated water molecules. They found that 10 water molecules provided 75% of the shift from the energy calculated for the gasphase complex and the actual energy of the transition in solution. With 15 water molecules, 94% of the shift was recovered. Zeng, Hush, and Reimers114 followed a different approach by combining Monte Carlo simulations to determine ground-state solvent configurations with ab initio SCF (self consistent field) and INDO methods to calculate the MLCT energies for the gas-phase [Ru(NH3)5L]2+ complex. From these calculations, they concluded that only solvent within 5 Å of the MLCT chromophore made a significant contribution to the energy of the transition. V. METALLOPORPHYRIN Q-BAND EXCITATION A third approach to probing the interactions between a transitionmetal ion and its local environment involves excitation of coordinated ligands. Free-base porphyrins and metalloporphyrins exhibit two sets of strong π → π* transitions in the visible and near ultraviolet. The Q-bands are found between 500 and 600 nm (ε = 1–2 × 104 M–1 cm–1), while the Soret (B) bands occur between 380 and 420 nm (ε = 2–4 × 105 M–1 cm–1).115 Upon coordination of metal ions to free-base porphyrins, the number of Q bands decreases from four to two with the concomitant increase in
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symmetry from D2h to D4h. The energy of metalloporphyrin Q bands depends strongly on the electronic structure of the coordinated metal ion. Coordination of first-row transition-metal ions having no partially filled d-orbitals, such as ScIII, TiIV, and ZnII, weakly perturbs the π-system of the porphyrin ring with little impact on the porphyrin absorption and emission spectra. These metalloporphyrins are designated as regular, and their absorption and emission spectra are said to be normal. In contrast, the partially filled d-orbitals of first-row transition-metal ions, including CrIII, MnIII,IV, FeII, CoII,III, NiII, and CuII, significantly affect the absorption and emission spectra of the porphyrin ring through strong mixing with the porphyrin π-orbitals or through introduction of additional low-energy transitions. The resulting metalloporphyrins are classified as irregular. The influence of metal-ion coordination on the energies of the Q bands leads to further classification of the irregular metalloporphyrins.115 Hypso metalloporphyrins exhibit Q bands that are blueshifted relative to the corresponding normal spectra of regular metalloporphyrins. Strong mixing between d-orbitals of the transition-metal ions FeII (low spin), NiII, CoII,III, and CuII and the lowest unfilled porphyrin π*-orbital shifts the Q bands to higher energy and also makes the absorption spectra of these hypso metalloporphyrins sensitive to the molecules coordinated to the metal above and below the porphyrin ring. Transition-metal ions, such as MnIII,IV, CrIII, FeII (high spin), and FeIII, form hyper irregular metalloporphyrins, which are characterized by red-shifted Q bands and additional absorption features typically of CT character. The emission properties of hypso and hyper irregular metalloporphyrins also differ significantly from the regular porphyrins. Several of the first-row transition-metal ions, FeII,III, CoII,III, MnIII, and NiII, quench porphyrin fluorescence almost completely (Φf < 10–4)115 because of the presence of low energy d-d transitions.116 These radiationless, irregular porphyrins are ideal candidates for investigation using laser photodissociation mass spectrometry. We have performed a preliminary survey of the impact of complexation of a single axial dimethyl sulfoxide molecule on the electronic absorption spectrum of nickel(II)-5,10,15,20-tetrakis(Nmethyl-4-pyridyl)porphine, [Ni(TMPyP)]4+, a radiationless, hypso irregular metalloporphyrin (Fig. 16). This water-soluble porphyrin117 was selected for this work because of the singly charged N-methyl-4-pyridyl groups in the four meso ring positions. Coordination of a divalent transition-metal ion with a porphyrin displaces two acidic protons to form a metalloporphyrin with the same overall charge as the free-base porphyrin. Van Berkel and co-workers118 had
Microsolvation of Coordinated Divalent Transition-Metal Ions Figure 16:
177
Structure of the metalloporphyrin nickel(II)-5,10,15,20-tetrakis (N-methyl-4-pyridyl)porphine, [Ni(TMPyP)]4+.
previously shown that protonation, sodiation or charge-transfer ionization was required to produce gas-phase ions in ESI of the neutral metalloporphyrins formed by a divalent transition-metal ion and a neutral free-base porphyrin. In contrast, trivalent transitionmetal ions, such as MnIII, FeIII, CrIII, coordinated with the neutral porphyrin octaethylporphyrin form a singly charged ion in solution, and this species was the dominant ion in the ESI mass spectrum.118 Electrospray ionization of 1.5 × 10–4 M [Ni(TMPyP)]Cl4 in methanol with a DMSO purge produced the rich mass spectrum shown in Fig. 17, which included the parent ion [Ni(TMPyP)]4+ and [Ni(TMPyP)•(DMSO)n]4+ clusters (n = 1, 2). Cluster formation was attributed to coordination of DMSO molecules above and below the porphyrin ring. Two types of triply charged ions were also produced. The first type was a reduced [Ni(TMPyP)]3+ ion with a propensity to
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Figure 17:
Electrospray ionization mass spectrum of 1.5 × 10–4 M [Ni(TMPyP)]Cl4 in methanol obtained with a DMSO-saturated nitrogen purge.
[NiIITMPyP(DMSO)n]4+ 1
2
Ion Intensity
n=0
[NiIITMPyP-m(CH3)]3+ m=10
[NiIITMPyP(Cl)]3+
×10
150
200
m/z
250
300
lose methyl groups, presumably from the meso N-methyl-4-pyridyl groups. Collision-induced dissociation of [Ni(TMPyP)]4+ produced the same ions,119 which pointed to collisions with background gas in the high-pressure zones of the ESI source as the origin of these ions. The second type of triply charged ion, [Ni(TMPyP)Cl]3+, contained one of the chloride counterions from the [Ni(TMPyP)]Cl4 salt used to prepare the solution electrosprayed. In ESI of chloride and p-tosylate salts of the free-base porphyrin TMPyP, only the p-tosylate ion associated with TMPyP4+ to form a gas-phase ion pair, [(TMPyP)(p-tosylate)]3+.119 Association of the chloride ion only with the metallated porphyrin was consistent with coordination of the chloride ion by NiII as an axial ligand. Photodissociation of the mass-selected [Ni(TMPyP)•(DMSO)]4+ cluster yielded [Ni(TMPyP)]4+ as the only photoproduct [Ni(TMPyP)•(DMSO)]4++hν→[Ni(TMPyP)]4+ +DMSO (17) Since no metastable decomposition was observed for [Ni(TMPyP)•(DMSO)]4+, photodepletion of the cluster was most conveniently determined by measuring the appearance of the [Ni(TMPyP)]4+ photoproduct. Fig. 18 shows the photodepletion action spectrum of [Ni(TMPyP)•(DMSO)]4+ with the absorption
Microsolvation of Coordinated Divalent Transition-Metal Ions
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Figure 18: Wavelength-dependent photodepletion of the [Ni(TMPyP)•(DMSO)]4+ cluster normalized to 1 W laser power and the absorption spectrum of 1.5 × 10–5 M [Ni(TMPyP)]Cl4 in DMSO solution in the region of the Q(0,0) and Q(1,0) bands. 0.25
24 [NiIITMPyP]Cl4 in DMSO Solution
20
[NiIITMPyP]4+•DMSO Cluster
0.20
Depletion %%Depletion
0.15 12 0.10 8 0.05
4
0 16000
Absorbance Absorbance
16
17000
18000
19000
0.00 20000
E, cm-1
E, cm-1
spectrum of 1.5 × 10–5 M [Ni(TMPyP)]Cl4 in DMSO. The Q(0,0) and Q(1,0) bands were clearly present in the cluster’s photodepletion action spectrum. Since these data were collected at 2.5-nm intervals rather than with continuous scanning of the laser, the data density was lower than in spectra shown previously. A qualitative comparison of the cluster spectrum and the solution spectrum pointed to narrower features in the cluster spectrum. The maximum of the Q(0,0) band occurred at 17671 ± 36 cm–1 in the [Ni(TMPyP)•(DMSO)]4+ cluster. The NiII ion forms hypso metalloporphyrins whose absorption spectra are blue-shifted relative to the corresponding regular metalloporphyrins because of strong mixing between the filled metal dπ-orbitals (dxy + dxz, dxy – dxz) and unfilled porphyrin eg (π*)-orbital.115,120 This mixing has been described as metal dπ → porphyrin eg(π*) backbonding.115,116 The Q(0,0) band shifted a mere 67 ± 40 cm–1 in going from the cluster with one axial DMSO to bulk solvation of [Ni(TMPyP)]4+, which permitted coordination of a second axial DMSO ligand. This result demonstrated the important role played by the axially coordinated solvent in determining the energy of the Q(0,0) band. The bulk solvent itself had a minor impact on the π → π* transition giving rise to the Q(0,0) band. The blue shift in going from the [Ni(TMPyP)•(DMSO)]4+
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cluster to [Ni(TMPyP)]4+ in bulk solution was consistent with the axially coordinated DMSO molecules behaving as σ-donors. There were insufficient data beyond the maximum in the cluster’s Q(1,0) band to definitively determine the band maximum, although it did appear to be lower in energy than the corresponding band in bulk solution. Clearly, more data are required before a more detailed comparison between the solution and gas-phase spectra can be made; however, these results have illustrated application of a ligand’s spectrum as another tool for probing the interactions between transition-metal ions and their environment. This study also provided additional evidence for the ability of ESI to take solution species and transfer them to the gas phase without significant alteration of their electronic structure. VI. CONCLUDING REMARKS Clearly, the key to establishing a connection between the properties of transition-metal ions isolated in gas-phase clusters and their solution counterparts is access to the same oxidation states. This chapter has described the application of electrospray ionization coupled with laser photodissociation mass spectrometry to achieve this goal. While mass spectrometry confirmed that ESI preserved the overall charge state of the ionic coordination complexes transferred from solution to the gas phase, laser excitation of ligand-field, chargetransfer, and ligand-based electronic transitions detected via photodissociation demonstrated conclusively that the resulting gas-phase ions have an electronic structure analogous to their solution counterparts. The experimental techniques and spectroscopic studies presented in this chapter provide a foundation for future efforts that exploit the control offered by gas-phase clusters and the complementary perspectives offered by ligand-field, charge-transfer, and ligand-based electronic transitions to investigate the molecularlevel interactions between transition-metal ions and their environment. ACKNOWLEDGMENTS This research was performed at Vanderbilt University with support from the National Science Foundation under grants CHE9616606/ CHE9996170 and Research Corporation through a Cottrell Scholar Award. The author gratefully acknowledges the contributions of Thomas G. Spence, Thomas D. Burns, G. Brody Guckenberger, V, Brett T. Trotter, and Zsuzsanna Hargitai, to the development of the
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instrumentation required to perform these studies and their efforts in executing the experiments. ABBREVIATIONS b bpy CAD CI CID CSE CT cw Dop DMSO ε Δ Eo Ecom Ein Elab Eop Eout ESI IE INDO μes MLCT MMCT MS m/z Φ pyr Rc Rn–i SCF τ terpy TMPyP ΔV
Effective ion radius 2,2′-Bipyridine Collisionally activated dissociation Configuration interaction Collision-induced dissociation Cluster size equation Charge transfer Continuous wave Optical dielectric constant Dimethyl sulfoxide Molar absorptivity Zero-point energy difference between ground and charge-transfer excited states Center-of-mass collision energy Inner-sphere reorganization energy Laboratory kinetic energy Energy of optical charge-transfer transition Outer-sphere or solvent reorganization energy Electrospray ionization Ionization energy Intermediate neglect of differential overlap Excited-state dipole moment Metal-to-ligand charge transfer Metal-to-metal charge transfer Mass spectrometry Mass-to-charge ratio Quantum yield Pyridine Cluster radius Metastable decay fraction for sequential loss of i solvent molecule(s) from a cluster containing n solvent molecules Self-consistent field Excited-state lifetime 2,2′,2″-Terpyridine 5,10,15,20-Tetrakis(N-methyl-4-pyridyl)porphine Potential difference between the capillary and skimmer #1 in the ESI source
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6 ZERO ELECTRON KINETIC ENERGY PHOTOELECTRON SPECTRA OF METAL CLUSTERS AND COMPLEXES Dong-Sheng Yang
I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 II. Experimental and Computational Methods . . . . . . . . . . . . . . 190 A. Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 B. Computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 III. Small Bare Metal Clusters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 A. Vanadium Dimer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 B. Vanadium Trimer and Tertramer . . . . . . . . . . . . . . . . . . . 197 C. Yttrium Dimer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 IV. Metal Cluster Oxides, Carbides, and Nitrides . . . . . . . . . . . . . 201 A. Triniobium and Trizirconium Monoxides . . . . . . . . . . . . 201 B. Triniobium and Triyttrium Dicarbides . . . . . . . . . . . . . . . 203 C. Triniobium Dinitride . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 D. Pentaniobium Dicarbide and Dinitride . . . . . . . . . . . . . . 209 V. Ammonia and Ether Complexes of Metal Atoms . . . . . . . . . . 212 A. Ammonia Complexes of Aluminum, Indium, and Vanadium Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 B. Dimethyl Ether Complexes of Zirconium and Yttrium . . 216 VI. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 Keywords: ZEKE spectroscopy, metal cluster, metal-ligand complex Advances in Metal and Semiconductor Clusters Volume 5, pages 187–225 © 2001 Elsevier Science B.V. All Rights Reserved. ISBN: 0-444-50726-4
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I. INTRODUCTION In molecular photoelectron spectroscopy (PES), a photon provides the energy to eject an electron from an electronic bound state. By applying an energy conservation relationship, the ionization potential (IP) is the energy difference of the incident photon (hν) and the kinetic energy of the emitted electrons (Ekin) , that is IP = hν – Ekin. The IP values correspond to the energy differences of the ground state of the molecule and the various states of the cation. Based on this relationship, two general approaches can be used to probe the cationic states of a molecule (or the neutral states of a negative ion). One is to measure the photoelectron signals as a function of electron kinetic energies at a given photon wavelength. This approach is sometime referred as conventional PES. It is relatively simple to implement experimentally and does not require a tunable light source. Thus, the method has been widely used since the inception of the photoelectron technique in the 1960s,1 and most of the photoelectron experiments on metal-containing molecules were reported with this method over the past four decades.2–9 While there is no fundamental limitation to the spectral resolution of PES, the practical resolution is limited by the difficulties in separating electrons with small differences of kinetic energies. Typical resolution in the study of the metal compounds is in the range of 20–30 meV (160–240 cm–1),2–7 although it can be improved to 5–10 meV (40–80 cm–1) with a combination of a laser light source and a hemispherical analyzer.8,9 In the second approach, photoelectrons with a given kinetic energy are detected as a function of the incident photon wavelength. If electrons with zero (or near zero) kinetic energies are measured, the technique is called zero electron kinetic energy (ZEKE) photoelectron spectroscopy.10 In contrast to the conventional PES, ZEKE spectroscopy can offer spectral resolution approaching the linewidth of the incident photon.10 A resolution of 1.5 cm–1 has been obtained in the spectra of a small metal cluster.11 There have been several excellent reviews and a recent book on ZEKE.10,12–15 The reader is referred to these for further details. Briefly, the ZEKE technique can be implemented in two ways. One is that ZEKE electrons are produced directly via threshold photoionization of neutral molecules or photodetachment of negative ions. The ZEKE electrons are then collected by a small pulsed electric field that is delayed from the ionization time to discriminate against kinetic electrons. This approach has been used to study metalcontaining anions, such as Au2–,16 Ag2–,16,17 Au6–,18 FeC2–,19 and FeCO–20 and has proved rather difficult to implement experimentally. The other approach is to generate ZEKE electrons via pulsed field
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ionization (PFI) of photoexcited Rydberg molecular states. In this approach, the photon energy falls just short of the IP and an electron is excited to a Rydberg state. While low-lying Rydberg states (with low principle quantum number n) readily interact with the molecular core and rapidly decay through raditionaless transitions, such as predissociation or autoionization, the higher Rydberg states (n > 150) have lifetime on the order of microseconds (μs) or longer and can be selectively ionized with a pulsed electric field. The long lifetime of the high-lying Rydberg states are attributed to the complicated Stark mixing of the Rydberg states due to stray electric fields present in the excitation volume and inhomogeneous electric fields formed by nearby prompt ions. Because these high-lying Rydberg states lie typically 5 to 10 cm–1 below the ionization threshold, the electrons produced by the electric field ionization carry near zero kinetic energies and are also called ZEKE electrons. This approach is now known as ZEKE-PFI or PFI-ZEKE or simply as ZEKE. Because of the long lifetime of the Rydberg states, a time delay can be placed between the photoexcitation and field ionization to discriminate against prompt electrons produced by direct photoionization. Thus, as photon wavelength is scanned through the manifold of the Rydberg states, ZEKE electrons are produced a few cm–1 below each ionic state. With a slight constant energy offset determined by the electric field strength, the ZEKE-PFI spectrum reveals the (ro)vibronic levels in the corresponding ionic states, which is similar to the ZEKE spectrum from direct threshold photoionization. In fact, ZEKE-PFI has now become the most widespread experimental realization of ZEKE spectroscopy. Furthermore, one distinguishes between one-photon and two-photon ZEKE-PFI. In the one-photon experiments, the optical excitation links the ground electronic state (or thermally populated low-lying excited states) of the neutral molecule to an electronic state (usually the ground electronic state) of the cation. One-photon ZEKE-PFI is particularly useful for the species for which there is no known electronic transitions, such as in most metal clusters and complexes. In the two-photon experiments, a known electronic transition of the neutral species is normally used to select specific quantum states prior to accessing the high-lying Rydberg levels. Obviously, resonant two-photon ZEKE-PFI can only be applied to the species for which electronic transitions are known. ZEKE-PFI spectroscopy has emerged as a most promising means to provide quantum state-specific information and to probe the structure of metal clusters and complexes in the gas phase. First, high spectral resolution can be achieved without knowledge of the intermediate states of a molecule. This is a major advantage because the problems arising from dense vibronic manifolds will be avoided.
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Also, because the ground electronic states of the neutral and the cation will be the most well understood and most easily calculable electronic states of any metal cluster or complex, the comparison of experimental data with theoretical predictions will be facilitated. Second, the IPs of many metal clusters and complexes are in a spectral region easily accessible by frequency-doubled tunable dye lasers, making the application of the technique fairly routine. Third, some vibrational normal modes of polyatomic metal-containing molecules are small enough to be populated at the room temperature, making it possible to measure the vibrational frequencies of neutral species, in addition to those of the corresponding ions. Using ZEKE-PFI, we have studied small bare metal clusters,11,21,22 metal cluster oxides,23,24 carbides,25–27 nitrides,27,28 as well as ammonia29–31 and ether32,33 complexes of metal atoms. We have been able to obtain rotationally resolved spectra and measure the bond length of an open d-subshell cationic dimer and to obtain vibrationally resolved spectra and determine electronic and geometric structures of some larger species. We use one-photon and two-photon excitation schemes prior to field ionization, depending on the availability of the information about the intermediate states of the species. The rotationally resolved ZEKE-PFI spectra of vanadium dimer are obtained through twophoton excitation, while the vibrationally resolved spectra of the other systems are obtained through single-photon excitation. The assignment of the carrier of the single-photon ZEKE electrons is aided by the velocity slippage present in the seeded molecular beam and by the correlation with the ionization threshold of the molecule.21 The interpretation of the vibrationally resolved spectra and the determination of the molecular geometries are facilitated by density functional theory (DFT) and ab initio calculations and spectral simulations based on the Franck-Condon (FC) principle. The combination of the ZEKE-PFI spectra and theoretical calculations has allowed us to obtain reliable structures for some of the complex metal species. In this chapter, I will attempt to provide an overview of our ZEKE-PFI work. Spectral analyses for the metal ammonia and ether complexes are only preliminary at this writing but are included for completeness. For the reader’s reference, I will also point out the ZEKE-PFI work carried out by other research groups. II. EXPERIMENTAL AND COMPUTATIONAL METHODS A. Experiment Fig. 1 shows the schematic diagram of the instrument used in our laboratory. It consists of two vacuum chambers. The first chamber
Figure 1: Schematic of the molecular beam ZEKE-PFI photoelectron spectrometer system. DP, diffusion pump; TP, turbomolecular pump; TOF, time-of-flight tube; MCP, microchannel plate detector.
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houses a Smalley-type cluster source34 pumped by an Edwards 2200 l/s oil diffusion pump. The second chamber houses the ZEKE-PFI spectrometer pumped by two Seiko Seiki 400 l/s turbomolecular pumps. A gate valve separates the two chambers. The cluster source consists of a piezoelectric pulsed valve to deliver intense gas pulses,35 a motor driven mechanism to rotate and translate a metal rod to ensure each laser pulse vaporizes a fresh surface of the metal target; a clustering tube to help maximize the production of the species of interest; a skimmer to collimate the molecular beam; and a pair of scavenging electrodes to remove the residual ionic species which survive the expansion process from entering the second chamber. The clustering tube can be cooled down to 77K or heated up to 700K. The ZEKE-PFI spectrometer consists of a two-stage extraction assembly, a 34 cm long flight tube, and a dual microchannel plate detector (Galileo). The extraction elements, which have cylindrical symmetry, are extended up along the sides of the flight tube to prevent field penetration from the dc voltage applied to the detector. The entire spectrometer is housed in a cylindrical, double-walled, μ-metal shield, to isolate the spectrometer from the earth’s magnetic field. The spectrometer can also, equally well, be operated as a two-field, space-focused, Wiley-McLaren 36 time-of-flight mass spectrometer by supplying appropriate voltages. Bare metal clusters were produced by laser vaporization (355 or 532 nm) of a metal rod (> 99%) in the presence of a pulse of helium gas from the piezoelectric pulsed valve. A trace amount of an appropriate reactant (e.g., ethylene, nitrogen, oxygen, ammonia, and dimethyl ether) was doped in helium gas to produce metal cluster compounds and metal atom complexes. The resulting clusters passed down a clustering tube (2 mm inner diameter, 2 cm length) and were supersonically expanded into the first vacuum chamber. The clustering tube was maintained at room temperature or cooled by liquid nitrogen. The supersonic jet was collimated (2 mm diameter) ~ 5 cm downstream from the exit end of the clustering tube. After passing the deflection electrodes, the neutral molecular beam entered the second chamber. The ZEKE-PFI measurements on all molecules were taken via a single-photon excitation, except for vanadium dimer for which a resonant two-photon scheme was employed. Prior to the singlephoton ZEKE-PFI experiments on a molecule, photoionization efficient (PIE) curves were recorded to locate the approximate IP of the molecule. Then, with the laser energy set above the IP, experimental conditions, such as the timing and the fluence of
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both the vaporization and ionization lasers, the backing pressure of the helium gas, and the reactant concentration, were carefully optimized to maximize the ratio of the mass peak of the molecule of interest in the time-of-flight mass spectrum to that of all other peaks. This step was crucial for identifying the carrier of the ZEKE electrons. With the optimized experimental conditions, the molecule was excited to high-lying Rydberg states by a single-photon excitation. After a suitable delay, the high-lying Rydberg states were field ionized by a voltage pulse from a Stanford DG535 digital delay generator applied to the repeller plate. Typically, a field of 1 V cm–1 was applied for 100 ns after a delay of ~3 μs. A DC field of 0.08 V cm–1 was used to reject electrons from prompt photoionization. The ZEKE electron signals, capacitively decoupled from the microchannel plate detector anode, were amplified by a Stanford SR445 300 MHz preamplifier and averaged by a Stanford SR250 gated integrator. The averaged output was fed to a computer, which also controlled the scanning of the dye lasers. The experimental repetition rate was 10 Hz, and 30 samples were typically accumulated at each data point. B. Computation DFT methods were used to calculate minimum energy structures and harmonic vibrational frequencies of the neutral and cationic clusters. Three computational codes, deMon-KS,37 Gaussian,38 and Amsterdam Density Functional (ADF),39 were used in some cases, such as triniobium dicarbide and dinitride, to test the sensitivity of the results to the choices of functional, basis set, and implementation. It has been found that these computational codes all yield similarly general features for the geometries and vibrational frequencies. Thus, only the representative results are presented. The computational details for the individual cluster were described previously.23,25,26,28 For the ammonia and ether complexes of metal atoms, DFT and ab initio methods were employed. FC factors were calculated assuming that the neutral and ionic potentials are both harmonic. Normal coordinates for the neutral and ion are linear combinations of Cartesian displacements of the atoms from the neutral or ionic equilibrium geometry. The normal coordinates of the neutral and ion differ because the equilibrium geometries are different and the linear combinations of the atomic displacements are different. Normal coordinates for the neutral and ion are denoted by q and q', respectively, and are defined in terms of the Cartesian displacements of the atoms by:
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q' = (L') T d ,
(1)
q = (L) T d.
(2)
and
The L and L' matrices are determined by diagonalizing massweighted Cartesian force constant matrices for the neutral and ion. The two sets of normal coordinates are related,40 q' = Sq + Q,
(3)
S = (L') T L,
(4)
Q = (L') T D
(5)
where
and
D being the vector of the differences of the mass-weighted Cartesian coordinates at equilibrium for the neutral and ion. The fact that S is not an identity matrix, because the normal coordinates of the ion are rotated with respect to those of the neutral, was first pointed out by Duschinsky.41 Assuming that the potentials of the neutral and ion are adequately described by an harmonic approximation makes it possible to calculate the FC overlaps in closed form (without setting S = 1 or neglecting differences between the neutral and ion frequencies) using recursion relations given by Doktorov et al.42 In the case of Nb3O, using the L matrices computed from DFT we find an S matrix that is very close to the identity and a Q vector whose components are substantial. In such a case, a good approximation to the FC structure of a cold spectrum is obtained for a transition by using displacement parameters expressed in terms of the final state (cation).43,44 In this case, the intensity of transitions between two vibrational states is due to the displacement of the two electronic surfaces. Bi the displacement of the ith normal coordinate determines the intensity of the ith totally symmetric mode, Bi = (ωi/h)1/2 Q i
(6)
Here Qi is a component of the vector Q defined above. This treatment reduces the FC integral to the product of one-dimensional integrals.
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Spectral broadening was simulated by giving each line a Lorenztian lineshape with the FWHM (full width at half maximum) of the experimental spectra. III. SMALL BARE METAL CLUSTERS A. Vanadium Dimer Langridge-Smith et al. first studied the neutral V2 molecule in the gas phase using resonant two-photon ionization (R2PI) spectroscopy and reported a rotationally resolved band system with the origin near 700 nm.45 The band system was assigned to the A 3Πu ← X 3Σg– transition. Also using R2PI, Spain et al. obtained an additional band system in the infrared spectral region.46,47 By recording two-photon PIE curves, James et al. observed two ionization thresholds and attributed them to the two spin-orbit components of the cation ground state X 4Σg–.48,49 We measured ZEKE-PFI spectra of V2 using two-photon excitation through the 700 nm A 3Πu ← X 3Σg– system. The spectra have a FWHM of 1.5 cm–1, which is sufficient to resolve the rotational levels of the ground state of the vanadium dimer cation. Figure 2 presents typical ZEKE-PFI spectra obtained by prior excitation of transitions – – in the A 3Π1u ← X Σ0g (0,0) and A 3Π2u ← X 3Σ1g (0,0) bands.11 There are striking differences between the ZEKE-PFI spectra recorded through the 3Π1u and 3Π2u components. First, The spectra through the 3Π1u component show only transitions to the 4Σ–1/2g level (Fig. 2 (a) and (b)), while the spectra through the 3Π2u component show transitions to both the 4Σ–1/2g and 4Σ–3/2g levels (Fig. 2 (c) and (d)). This observation is consistent with the ΔΣ = ±1/2 selection rule of photoionization of a diatomic molecule derived by Xie and Zare50 and confirms the 4Σg– symmetry of the cation ground state suggested by previous studies.48,49 The second major difference is that when probing from the 3Π1u component, only two J+ values are accessed, while probing from the 3Π2u component, a wide range of J+ values are observed. Detailed analysis of the rotational spectra is based on the Xie and Zare selection rules50 and the rotational Hamiltonian matrix for a 4Σ– state in a Hund case (a).51 The analysis of the rotationally resolved spectra allows us to determine the bond length, r0 = 1.7347 Å, of the X 4Σg– state of V2+. The experimental bond length of V2+ is in a remarkable agreement with the DFT value, 1.741 Å.49 The bond length of V2+ is shorter than that of V2, 1.77 Å,45 providing an evidence for the fact that V2+( D00 = 3.140 eV) is more strongly bound than V2 (D00 = 2.753 eV).48,49 Other spectroscopic parameters from the ZEKE-PFI spectra are adiabatic IP,
ZEKE-PFI spectra of V2 recorded with the excitation laser tuned to the lines Q(1) (a) and R(7) (b) in the A 3Π1u ← X 3Σ0g (0,0); to Q(2) (c) and R(6) (d) in the A 3Π2u ← X 3Σ1g (0,0) band. From reference 11.
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51271.14 cm–1; electronic term value, 51282.20 cm–1; second-order spin-orbit splitting parameter, 5.248 cm–1; rotational constant, 0.21993 cm–1; and spin-rotation constant 0.0097 cm–1. B. Vanadium Trimer and Tertramer Cox et al. measured the IPs of V3 (44300 ± 400 cm–1) and V4 (45400 ± 400 cm–1) from the PIE spectra.52 Our single-photon ZEKE-PFI measurements greatly improve the IP values of the two clusters, which are 44342 ± 3 cm–1 for V3 and 45644 ± 3 cm–1 for V4.21 The ZEKE-PFI spectrum of V3 displays some fine structure in addition to the strong 0–0 band (Fig. 3). One of these bands is located at 172 cm–1 to the blue of the band origin. By comparing the observed energy spacing and theoretical vibrational frequency, this band may be attributed to the transition from the ground electronic state of V3 to the first excited level of a totally symmetric vibration mode of the ground electronic state of V3+, although an alternative explanation involving low-lying (spin-orbit) excited electronic state may also be considered. For V4, there is no additional band appearing in the ZEKE-PFI spectrum, other than the 0–0 transition. Grönbeck and Rosén53 and Wu and Ray54 recently calculated geometries and IPs of small vanadium clusters using DFT methods. Grönbeck and Rosén found that the lowest energy geometry of both V4 and V4+ was planar and that the adiabatic IP of the cluster was 44400 cm–1, close to our experimental value, 44342 cm–1. In contrast, Wu and Ray found that the lowest energy isomer of V4 and V4+ was a tetrahedron and that the adiabatic IP of V4 was 41100 cm–1. Although they did not report the detailed structural parameters for V4 and V4+, Grönbeck and Rosén and Wu and Ray did show that the adiabatic and vertical IPs of V4 were almost identical, implying the geometries of the neutral and ion are very similar. Thus, the similar geometries between V4 and V4+ may be the reason for the lack of vibrational progressions in the ZEKE-PFI spectra, although the autoionization of the excited vibrational levels of V4+ may also be possible. The 0–0 bands in the V3 and V4 spectra have a FWHM of 8 cm–1, which is five times that of V2 spectrum.11 This line broadening is attributed to rotational band envelopes that cannot be resolved with the resolution, 1.5 cm–1, of our spectrometer. Similar rotational envelopes have also been observed for the other metal clusters.23–28 C. Yttrium Dimer Knickelbein determined the IP of Y2 to be 40000 ± 400 cm–1 from the PIE spectrum.55 Simard performed R2PI measurements in the
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Figure 3: ZEKE-PFI spectrum of V3, together with DFT results for the vibrational frequencies of the cation. From reference 21.
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10000–20000 cm–1 region, but failed to record any signal.56 Knight et al. failed to obtain an electron spin resonance (ESR) spectrum of Y2, whereas the same experimental conditions gave a spectrum for Sc2.57 Based on the ESR experiments, Knight et al. suggested that Sc2 has a 5Σu– ground state, while the ground state of Y2 might be 1Σ or 3Δ, but not 5Σ.58 However, Walch and Bauschlicher59 and Dai and Balasubramanian60 found using high level ab initio methods that the lowest energy state of Y2 was 5Σu–, rather than 1Σg+. Dai and Balasubramanian also calculated the IPs for the ionization processes of Y2+(4Σg–) ← Y2 (5Σu–) and Y2+(2Πu) ← Y2 (1Σg+), which are 36980 cm–1 for the quartet ← quintet transition and 35080 cm–1 for the doublet ← singlet process.61 Our ZEKE-PFI measurements were to establish the ground states of Y2+ and Y2. A representative ZEKE-PFI spectrum is presented in Fig. 4.22 The spectrum shows two strong bands at 40129 and 40326 cm–1 and a number of weak ones. Each of the two strong bands consists of a doublet separated by 4 cm–1. The doublet structure is clearly shown from the expansion of the first strong band, band A, in Fig. 4. The whole profile of the doublet spans about 22 cm–1. Based on the previous experiments in which rotational temperatures of 25–30 K were observed, and on the DFT calculations from which the rotational constants of Y2 were predicted to be on the order of 0.05 cm–1, the rotational envelope of a single vibronic band should span no more than 12 cm–1. Thus, the doublet is considered to be due to two overlapping vibronic transitions, each consisting of unresolved rotational structures. In the spectral analysis, the ZEKE-PFI spectrum is assumed to originate from only one of the two possible ionization processes: Y2+(4Σg–) ← Y2 (5Σu–) or Y2+(2Πu) ← Y2 (1Σg+). If the spectrum were assigned to the Y2+(2Πu) ← Y2 (1Σg+) transition, the doublet structure of the two strong bands at 40129 and 40326 cm–1, as well as the weak feature at 39946 cm–1, would be left unexplained. Also, the spectral intensity profile would be in a very poor agreement with the calculated FC factors. Thus, the Y2+(2Πu) ← Y2 (1Σg+) transition could not be responsible for the observed spectrum. On the other hand, the assignment presented in Fig. 4 explains every experimental feature both in terms of the energy positions and intensity distributions and agrees with the theoretical predictions. These facts strongly suggest that the Y2+(4Σg–) ← Y2 (5Σu–) transition is responsible for the observed ZEKE-PFI spectrum. Based on this spectral assignment, both the 5Σu– (Y2) and 4Σg– (Y2+) states suffer from extensive second-order spin-orbit interactions. The splitting is 210 cm–1 between the 4Σ–3/2,g (Ω = 3/2) and 4Σ–1/2,g (Ω = 1/2) components, 64 cm–1 between 5Σ–2,u (Ω = 2) and 5Σ–1,u (Ω = 1), and 4 cm–1 between 5 – Σ 1,u (Ω = 1) and 5Σ–0,u (Ω = 0). The IP of Y2+(4Σ–1/2,g) ← Y2 (5Σ–0,u) is
ZEKE-PFI spectrum of Y2, together with the spectral assignment. The first band, band A, is expanded to show the doublet structure. From reference 22.
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determined to be 40131 cm–1. The vibrational frequencies are measured as 197 cm–1 for the X 4Σg– state of Y2+ and 185 cm–1 for the X 5 – Σu state of Y2. In addition to the clusters discussed above, the ZEKE-PFI spectra of aluminum and silver dimers have also been reported.62,63 IV. METAL CLUSTER OXIDES, CARBIDES, AND NITRIDES A. Triniobium and Trizirconium Monoxides The ZEKE-PFI spectrum of Nb3O at 300 K is shown in Fig. 5(a).23 This spectrum together with the one recorded at 100K (not shown) yields the following preliminary spectroscopic and structural information for the cluster. First, the cluster ion has a totally symmetric vibration mode of 312 cm–1. This mode is most likely a symmetric vibration of the niobium atoms because a symmetric Nb–O vibration would have a much higher frequency.64 Second, the vibrational modes of the neutral that are associated with the hot bands should have frequencies smaller than 500 cm–1, an estimate based on the thermal populations at 300 K. Third, the geometries of the neutral and the cation are rather similar because only a short progression appears in the spectrum. To assign the spectrum in detail and to determine the geometries of the cluster, DFT calculations and spectral simulations were carried out. Two minimum energy structures were obtained from many trial geometries. The most stable structure for both Nb3O and Nb3O+ has planar C2v symmetry (see the insertion in Fig. 5(b)). The oxygen atom is bound with equal bond lengths to two Nb atoms. Two distinct Nb–Nb bond distances are present in the cluster with the Nb–Nb bond bridged by oxygen being longer than the other two. The ground electronic symmetry of the C2v structure is 2B1 for the neutral and 1A1 for the ion. A second stable structure is calculated to be three-dimensional with the oxygen bound to three Nb atoms (see the insertion in Fig. 5(c)). This structure lies 1.03 eV higher in energy than the planar one for both the neutral and ion, implying that the IPs are similar for the three- and two-dimensional structures. The geometric symmetry of the three-dimensional structure is Cs for the neutral and C3v for the cation. The reduced symmetry of the neutral structure is largely due to Jahn-Teller distortions. Spectral simulations were carried out by calculating multidimensional FC factors using the geometries, harmonic vibrational frequencies, and normal mode coordinates obtained for Nb3O and Nb3O+ from the DFT calculations. Figure 5 compares the
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Figure 5: Experimental (a) and simulated (b, c) ZEKE-PFI spectra of Nb3O at 300 K. The simulation (b) was performed with the planar structure and vibrational frequencies from the DFT calculations. The simulation (c) was calculated using the three-dimensional structure and vibrational frequencies from the DFT calculations. From reference 23.
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simulations with the experimental spectrum. The theoretical transition energies are plotted relative to the position of the 000 band of the experimental spectrum. A remarkable agreement exists between the experiment and theory for the planar structure. However, the experimental spectrum is very different from the simulation of the three-dimensional structure. Thus, the comparison indicates that Nb3O and Nb3O+ have the planar C2v structure, rather than the three-dimensional one. The good agreement between the experiment and the simulation of the planar structure makes the spectral assignment trivial. The main progression consisting of the bands 0, 1, and 2 in Fig. 5(a) is due to the transitions from the vibrationless level of the ground state of the neutral to vibrational levels of the symmetric niobium bending in the cation. The frequency of this vibration is 312 cm–1. The hot band, band a, is the transition from the first vibrational level of the symmetric niobium bending mode in the neutral to the vibrationless level of the ground state of the ion. The neutral bending mode has a frequency of 320 cm–1. On the high frequency side of the main progression (bands 0', 0", and 1') are the sequence bands due to the asymmetric niobium–niobium stretching. The frequency of this mode is not determinable from the sequence structure but the frequency difference in the ion and neutral is measured as 23 cm–1. On the low frequency side of the main progression (bands b and c) are the sequence bands associated with the out-of-plane deformation of the cluster. This mode is 11 cm–1 smaller in the ion than in the neutral. The general feature of the ZEKE-PFI spectrum of Zr3O (not shown) is similar to that of Nb3O.24 The frequency of the symmetric zirconium bending vibration is measured as 272 cm–1, 40 cm–1 less than that of Nb3O. The IP of Zr3O is 41838 cm–1, 2740 cm–1 lower than that of Nb3O. Two DFT methods (B3P86/LANL2DZ and ADF) predict the similar conformation of this complex to that of Nb3O, e.g., a planar C2v symmetry. Both DFT methods identify 4B1 as the ground state of the ion, with the 2A2 state being about 0.3 eV above. For the neutral species, B3P86/LANL2DZ predicts the 5A2 state to be 0.04 eV below the 3A2 state, while the ADF predicts the quintet to lie 0.09 eV above the triplet. The comparison of the simulations and the experimental spectrum indicates either of the 4B1←5A2 or the 4 B1←3A2 transitions may be responsible for the observed ZEKE-PFI spectrum, but not the 2A2 ← 3A2 transition. B. Triniobium and Triyttrium Dicarbides ZEKE-PFI spectra of the metal trimer carbides show much richer structure than those of the oxides discussed above.25,26 Figure 6(a)
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Dong-Sheng Yang Figure 6: ZEKE-PFI spectra of Nb312C2 (a), Nb313C2 (b), and Y312C2 (c). From references 25 and 26.
presents the spectrum of Nb312C2 at the room temperature.25 The spectrum consists of a strong vibrational progression (an) and six weak ones (bn, cn, dn, en, fn, and gn). All seven progressions have the same energy interval of 258 cm–1. Six of the seven progressions can be grouped into three pairs, an and bn, cn and dn, and fn and gn, with
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the same energy separation of 20 cm–1. The separation of dn and en is 13 cm–1. The fn progression is 339 cm–1 from the main progression an. The an progression has a FWHM of 7 cm–1, which decreases to 5 cm–1 at 100 K, due to the narrowing of rotational envelope. The intensities of most of the small bands depend on the cluster source conditions. Figure 6(b) presents the spectrum of Nb313C2, which has the same energy spacing and intensity profile as that of Nb312C2, but shifts to the red by ~3 cm–1. From these two spectra, we conclude that the geometries of the neutral and ion are rather different because relatively long progressions appear in the spectra. The observed transitions are associated with the vibrations of the niobium atoms because the energy interval of the progressions is independent of the carbon isotopes. One of the normal modes of the niobium symmetric vibrations has a frequency of 258 cm–1 in the ion. The DFT calculations predict that triniobium dicarbide has two stable geometries: trigonal bipyramid and doubly bridged structures. The energy differences of the two structures are calculated to be less than a few hundredths of eV, implying that the two theoretical structures are indistinguishable in terms of their energies. The trigonal bipyramid structure has a D3h geometry and a 1A1' ground electronic state. Adding an electron to Nb3C2+ populates a degenerate orbital (e"), leading to a Jahn-Teller distorted neutral structure with a lower symmetry, C2v or Cs, depending on the computational methods. The electronic state of Nb3C2 is 2A1 (C2v) or 2A' (Cs). For the doubly bridged structure, both Nb3C2 and Nb3C2+ have a C2v symmetry. The ground state of the doubly bridged structure is 1A1 for the ion and 2A1 for the neutral. Like niobium trimer monoxide, niobium trimer dicarbide also prefers the state with low electron spin multiplicity. Figure 7 compares the simulations from both the trigonal bipyramid and doubly bridged structures with the experimental spectrum.25 The comparison indicates that the cluster has the trigonal bipyramid structure, rather than the doubly bridged one. The overall good agreement between the simulation from the trigonal bipyramid structure makes detailed spectral assignments possible. These assignments are summarized below. The main progression an is due to the transitions from the ground state of the neutral to the vibrational levels of the degenerate e' mode in the ion. The e' mode is identified as the symmetric bending of the niobium atoms with a frequency of 258 cm–1. Because of the low symmetry of the neutral cluster, the degenerate e' mode splits into two non-degenerate modes, a1 and b2 in C2v or a' and a" in Cs symmetry. In the rigid molecular limit, this symmetry
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Figure 7: Experimental (a) and simulated (b,c) ZEKE-PFI spectra of Nb312C2. The simulation (b) was performed with the trigonal bipyramid structure and vibrational frequencies from the DFT calculations. The simulation (c) was calculated using the doubly bridged structure and vibrational frequencies from the DFT calculations From reference 25.
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transformation would have a one-to-one correspondence. That is, only transitions from the neutral ground state to the vibrational levels involving an arbitrary number of quanta of one component of the e' and an even number of quanta of the other component of the e' mode are allowed. However, our calculations indicate a rotation of the normal coordinates of the e' mode of the ion with respect to the corresponding modes of the neutral. This rotation results in the e' mode being a 30–50% mixture of the neutral a1 with b2, or a' with a". The bn, cn, and dn progressions are associated with the transitions, respectively, from the first excited level of the a1 (or a'), b2 (or a"), and a1+b2 (or a'+a") modes to the vibrational levels of the e' mode in the ion. The frequencies are measured as 238 cm–1 for the a1 (or a') mode and 83 cm–1 for the b2 (or a") mode. The remaining progressions, en, fn, and gn, are the combination bands due to the transitions involving the bending and stretching modes of the niobium atoms. The frequency of the symmetric stretching is 326 cm–1 in the neutral and 339 cm–1 in the ion. The ZEKE-PFI spectrum of Y3C2, as shown in Fig. 6(c), has a similar structure with that of Nb3C2, although the IP and vibrational frequencies of Y3C2 are much lower.26 The IP of Y3C2 is measured to be 34065 cm–1. The yttrium symmetric stretching mode has a frequency of 228 cm–1 in the ion. Two yttrium bending modes have the frequencies of 82 and 24 cm–1 in the neutral and a degenerate frequency of 86 cm–1 in the ion. Unlike Nb3C2 the excitation of the yttrium stretching mode in the neutral was not observed in the spectrum of Y3C2, although the yttrium mode should be thermally populated at the room temperature. The DFT geometry optimizations find only a stable trigonal bipyramid structure for the triyttrium dicarbide. The trigonal bipyramid geometry has either a C2v or a D3h symmetry, depending on the electron spin multiplicity. For the neutral cluster, electronic states with multiplicities of 2 and 4 are calculated to be the most stable. The doublet gives a C2v geometry with a 2B1 ground state, while the quartet gives a D3h geometry with a degenerate 4E' state. The 2B1 state is 0.3 eV lower in energy than the 4E'state. The removal of an electron from the neutral states forms ionic states with possible multiplicities of 1, 3, and 5. These ionic states are calculated to be 1A1', 3B1, and 5A2, with the singlet state being the lowest in energy and the highest in geometric symmetry (D3h). From the calculated electronic states of the neutral and ion, There are four electronically allowed ionization processes: 1A1' ← 2B1, 3B1 ← 2 B1, 3B1 ← 4E', and 5A2 ← 4E'. However, the comparisons between the experimental and simulated spectra indicate that the most likely process is 1A1' ← 2B1.
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C. Triniobium Dinitride Figure 8(a) presents the spectrum of Nb3N2.28 The spectrum is characterized by a short progression with the energy interval of 257 cm–1 and small bands on the blue side of the main progression, which are 17 cm–1 apart. The spectral intensity profile appears much different from that of Nb3C2, but rather similar to that of Nb3O. The energy spacing, 257 cm–1, of the progression is close to that of the main progression in the spectrum of Nb3C2. These observations indicate Figure 8: Experimental (a) and simulated (b) ZEKE-PFI spectra of Nb3N2. The simulation was calculated using the doubly bridged geometry and vibrational frequencies from the DFT calculations. From reference 28.
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that the structure of triniobium dinitride does not change significantly upon ionization, as in the case of triniobium monoxide, and one of the niobium vibrations has a frequency close to that of triniobium dicarbide. Unlike triniobium dicarbide for which trigonal bipyramid and doubly bridged structures are stable, triniobium dinitride is calculated to adopt only the doubly bridged geometry (see the insertion in Fig. 8(b)). For this doubly bridged structure, both Nb3N2 and Nb3N2+ have a C2v symmetry with a 2B1 ground state for the neutral and a 1A1 ground state for the ion. The simulation from the 1A1 ← 2B1 transition is shown in Fig. 8(b). The comparison of the experiment and theory indicates that the 257 cm–1 progression is due to the symmetric bending of the niobium atoms in Nb3N2+. The small bands on the blue side of the main progression are sequence bands associated with the symmetric bending vibrations of the niobium atoms. The asymmetric bending mode is 17 cm–1 smaller in the neutral than in the ion. D. Pentaniobium Dicarbide and Dinitride ZEKE-PFI spectra of Nb5C2 and Nb5N2 are shown in Fig. 9.27 Each spectrum consists of several bands. The band separation is 9 cm–1 in the case of Nb5C2 and 13 cm–1 in the case of Nb5N2. The first band with the lowest energy is attributed to the 0–0 transition with the transition energies of 37104 cm–1 for Nb5C2 and 37563 cm–1 for Nb5N2. Other bands are assigned to the transitions from the excited vibrational levels of the neutral clusters to the ground electronic states of the ions because the band intensities depend on the cluster source temperatures. The lack of the vibrational progressions may indicate similar geometries between the neutral and ionic clusters or the autoionization of the excited vibrational levels of the ionic clusters. However, there have not been high level theoretical calculations reported on the structures of these two clusters. Table 1 summarizes IPs and vibrational frequencies of the metal clusters discussed above. The IPs of the ligated clusters are lower than that of the bare metal clusters. The IP reduction upon the carbon coordination is very similar for the clusters of the same sizes. For example, the IPs of both triniobium and triyttrium dicarbides are about 6200 cm–1 (or 0.8 eV) lower than those of the corresponding bare clusters.55,65 However, the IP reduction upon the oxygen coordination is quite different for different metals. For instance, the IP of Nb3O is about 2300 cm–1 lower than that of Nb3, while the IP of Zr3O is only about 300 cm–1 less than that of Zr3.66
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Dong-Sheng Yang
Figure 9:
ZEKE-PFI spectra of Nb5C2 (a) and Nb5N2 (b). From reference 27.
The lower IPs of the ligated clusters than those of the corresponding bare ones imply that the metal–ligand bonds are stronger in the ion than in the neutral clusters, on the bases of the thermodynamic cycle, D0 (Mn+ – L) –D0 (Mn – L) = IP (Mn) – IP (MnL), where L = 2C, 2N or O. This is also evident from the higher metal–ligand stretching frequencies in the ionic clusters, as predicted by the theory. To help understand the ionization effect on the metal–ligand bonding in these clusters, we performed Mulliken population analysis for some of the clusters and found that in addition to the covalent contributions, the metal–ligand bonding has
Zero Electron Kinetic Energy Photoelectron Spectra Table 1. Cluster
211
–1
IPs (cm ) and vibrational frequencies (cm–1) of metal clusters(a) δ+ (Mn)(b)
IP
νs+(M–M)(b)
(c)
δ (Mn)(b) (d)
νs (M–M)(b) (d)
Reference
Nb3
46858
Nb3O
44578
312 (326)
(386)
320 (322)
(366)
23
Nb3C2
40639
258 (278)
339 (385)
237 (250)
327 (378)
25
Nb3N2
43902
257 (277)
(395)
(261)
(391)
Nb5
43950(c)
65
Nb5C2
37104
27
Nb5N2
37563
Y2
40129
Y3
40325(c)
Y3C2
34065
Zr3
42105(c)
Zr3O
41838
V2
51271
11
V3
44342
21
V4
45644
Ag2
61745
134
63
Al2
48304
178
62
227
335
65, 69
28
27 197 (202)
185 (183)
22 55
86 (87) (239)
228 (245) 272 (288)
82 (92)
(232)
177(d)
258(d)
26 66
(236)
(281)
24
21
(a) Except where noted, values are from the PFI-ZEKE measurements. The uncertainty of the measurements is typically ~3 cm–1, except for V2 for which the uncertainty is ~ 0.5 cm–1. The values in parentheses are from the DFT calculations and are averaged if results are available from more than one computational codes. (b) δ+ (Mn) and νs+ (M–M) are the symmetric metal bending and stretching in the cation ground state. δ (Mn) and νs (M–M) are the symmetric metal bending and stretching in the neutral ground state. (c) From photoionization efficiency measurements with the uncertainty of ± 400 cm–1. (d) From resonant Raman spectroscopic measurements in argon matrix.
considerable ionic character due to the combination of the electropositive metals and electronegative ligands. For example, the calculated orbital overlaps between the yttrium and carbon atoms are the same in Y3C2 and Y3C2+, indicating that the covalent contributions to the Y–C bonds are similar in the neutral and ion. In contrast, the net charges on the yttrium atom increase from an average of 0.46 to 0.77, while the negative charges on the carbon atoms, –0.66, remain unchanged. Thus, the stronger Mn+–L bonds are largely due to the enhancement of electrostatic attractions in the ionic clusters. Examination of the metal vibrational frequencies in Table 1 shows that the niobium vibrations have the highest frequencies and that the yttrium vibrations have the lowest. Because the atomic masses of Nb, Zr, and Y are very similar, the higher frequencies mean stronger metal–metal bonds. Thus, the strengths of the metal–metal bonding
212
Dong-Sheng Yang
may be arranged in the order of Nb–Nb > Zr–Zr > Y–Y in these ligated clusters. Different bonding strengths among these metals have also been found for metal dimers and trimers. For example, the bond dissociation energies of Nb2, Zr2, and Y2 have been measured as 5.48, 3.05, and 1.62 eV, respectively.48,67,68 The M–M stretching frequency of Nb3 has been measured as 335 cm–1, while that of Zr3 as 258 cm–1 from the resonant Raman spectra in argon matrix.69,70 Morse has discussed the causes for the bonding differences in the metal dimers.71 The main reason for the weak Y–Y bonding is the strong s-electron repulsion between the 4d15s2 ground states of the yttrium atoms. To form chemical bonds, at least one of the 4d15s2 yttrium atoms must be promoted to a configuration, such as 4d25s1, to reduce the Pauli repulsion between the filled-s orbitals. The energy for promoting the s-electron is 1.36 eV from the 4d15s2 to 4d25s1 configuration. For zirconium, the promotion energy for the s-electron is 0.59 eV, while for niobium no promotion is necessary since the ground state configuration is 4d45s1. Thus, the bonding difference in these metal clusters is largely due to the difference in the promotion energies required to prepare the metal atoms into appropriate electron configurations. The M–M bonds in the ligated metal cluster ions are slightly stronger than those in the corresponding neutrals. This is indicated by the frequencies of the M–M stretching vibrations (Table 1). For example, for triniobium dicarbide the Nb–Nb stretching frequency is 327 cm–1 in Nb3C2 and 339 cm–1 in Nb3C2+. For the other clusters, although experimental frequencies are not available for comparisons, the theoretical calculations show a similar increase of the M–M stretching frequencies upon ionization. V. AMMONIA AND ETHER COMPLEXES OF METAL ATOMS A. Ammonia Complexes of Aluminum, Indium, and Vanadium Atoms Several ab initio calculations have been reported on the ground states of the aluminum–ammonia complex and its cation.72–75 All of the calculations predicted that the ground state of AlNH3 has a slightly distorted molecular structure from C3v symmetry. The distortion has been understood as a result of JahnTeller distortion of the degenerate 2E state. The ground state of the ion complex AlNH3+ has been calculated to be 1A1 with C3v symmetry. The energy barrier between the addition complex AlNH3 and the insertion complex HAlNH2 has been calculated to be in the 23–34 kcal/mol range. The reaction of the Al atom with NH3 has been
Zero Electron Kinetic Energy Photoelectron Spectra
213
studied with EPR and FTIR in argon matrices76,77 and laser photoionization in the gas phase.78,79 Although the EPR and FTIR studies failed to detect the existence of the addition complex in argon matrices, PIE and R2PI measurements showed the formation of AlNH3 and AlND3 in the gas-phase. There have been fewer previous studies on the indium– and vanadium–ammonia complexes. For InNH3, the only study was the single-photon PIE measurements.80 For VNH3, the reported experimental work involved collisioninduced dissociation measurements of the bond dissociation energy of VNH3+.81,82 Theoretically, there were a modified configurationpair functional (MCPF) calculation on the VNH3+ ground state83 and a semiempirical calculation on both VNH3 and VNH3+.84 Figure 10(a) shows the ZEKE-PFI spectrum (FWHM = 8 cm–1) of AlNH3 in the region of 39400–41400 cm–1.29 The spectrum mainly consists of two relatively short progressions, a and b, with the same energy interval of ~ 330 cm–1. The progression b is 58 cm–1 to the red of the corresponding bands of the progression a. Assuming that AlNH3 has a C3v symmetry, two electronic states of the complex, 2A1 and 2E, may be derived from the interactions between the ground state Al 2P (3p1 ) and the ground state NH3 (1A1). In the 2A1 state, both of the Al pz electron and lone-pair of nitrogen are on the molecular axis, while the Al px(y) electron is off-axis in the 2E state. The stronger repulsion between the metal pz electron and the nitrogen lone-pair makes the 2A1 state less stable than the 2E state. Thus, the electronic ground state is expected to be 2E, as predicted by ab initio calculations, which may be split into the 2E1/2 and 2E3/2 levels by spin-orbit interactions. Thus, the two progressions (a, b) can be considered to be the transitions from the two spin-orbit levels (progression a from the 2E1/2 and the progression b from the 2 E3/2 state). The spin-orbit splitting of the atomic Al in the 2P (3p1) state is 112 cm–1.85 This splitting is expected to be reduced by forming a complex because of the recoupling of the angular momentum in a molecular framework. The reduction is estimated by a factor of 1/3 in a strong field approximation (Hund’s case a).86 Thus, the expected splitting in a Al complex is 75 cm–1, which is very close to the observed values in the Al-rare gas complexes (80 cm–1 in AlAr and 78 cm–1 in AlKr).87 The spin-orbit splitting of 58 cm–1 in AlNH3 is somewhat smaller than the expected value, 75 cm–1. Because spin-orbit constants depend on the effective charges on atoms, that is, a positive charge causes a contraction of the atomic orbitals and an increase in the spin-orbit constants, while a negative charge has an opposite effect on the spin-orbit splitting,86 the smaller than the expected splitting observed in AlNH3 may indicate that Al carries a negative charge upon the NH3 coordination.
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Dong-Sheng Yang
Figure 10: ZEKE-PFI spectra of AlNH3 (a) and InNH3 (b). From references 29 and 30.
Indeed, our ab initio calculations on AlNH3 predict that the charge on Al is –0.29. It should also be stressed that the 58 cm–1 spacing is too small to be a vibrational frequency based on the theoretical calculations.
Zero Electron Kinetic Energy Photoelectron Spectra
215
The 330 cm–1 interval of the progressions a and b is assigned to the aluminum–ammonia stretching vibration in AlNH3+. The measured frequency (ω3+ = 339 cm–1 and ω3+x3+ = 3.1 cm–1) is in an excellent agreement with the theoretical value (331 cm–1). In addition to the progressions a and b, there are a number of smaller bands in the spectrum. The band at 227 cm–1 to the red of the band origin (39,746 cm–1) of the progression a can be assigned to the hot band 310 as the ν3 progression, c, can be identified (except for the 311 band). The calculated frequency, 222 cm–1, for the neutral mode (ν3) well reproduces the observed value. The bands at 40243 and 40303 cm–1 (marked with “*” in Fig. 10(a)) may be assigned to the aluminum–ammonia bending vibration in the ionic complex, 601, because the energy interval, 557 cm–1, from their band origins are very close to the theoretical frequency, 558 cm–1, of the bending mode. These bands with Δν6 = +1 can be observed through the JahnTeller interaction in the neutral ground state. The bands at 40573 and 40631 cm–1 (marked with “+” in Fig. 10(a)) may be assigned to the combination bands of the intermolecular stretching and bending modes, 301601. However, the much stronger intensity of the combination band 301601 than the fundamental 601 band is anomalous, and the assignment for these bands is tentative. An alternative assignment of these bands is to the symmetric HNH bending mode 201. However, the ab initio calculations predict a vibrational frequency of 1347 cm–1 for the bending mode, which is much higher than the observed energy spacing of 885 cm–1. The ZEKE-PFI spectrum of InNH3 (Fig. 10(b)) is much simpler than that of AlNH3.30 This is expected because the spin-orbit splitting of the atomic indium is so large (2P3/2 – 2P1/2 = 2212.56 cm–1)85 such that the corresponding 2E3/2 level in the complex is not thermally populated under our experimental conditions. The IP of InNH3 is measured to be 39689 cm–1, which is very similar to the IP of AlNH3, 39746 cm–1. The indium–ammonia stretching frequency is measured to be 234 cm–1 (ω3+) in the ion and 141 cm–1 (ν3) in the neutral complex. These experimental frequencies again match well with the calculated values (233 cm–1 for In+–NH3 and 153 cm–1 for In–NH3). The spectrum of VNH3 displays very little vibronic activity, as shown in Fig. 11.31 By comparison with the theoretical calculations, the band at 44,429 cm–1 may be attributed to the V+–NH3 stretching (ν3+) with a fundamental frequency of 413 cm–1 and the band at 44,585 cm–1 to the V+–NH3 bending (ν6+) with a fundamental frequency of 570 cm–1. The small bands on the both sides of the strongest band (the 0–0 band at 44,015 cm–1) may be attributed to the partially resolved rotational structure.
216
Dong-Sheng Yang Figure 11: ZEKE-PFI spectrum of VNH3. From reference 31.
B. Dimethyl Ether Complexes of Zirconium and Yttrium Atoms Metal-ether complexes have been extensively studied in solution because of the fundamental importance to molecular recognition and potential applications in chemical separations.88 Studies in the gas phase have also been reported with the motivation to probe the intrinsic reactivity of ethers with various metal atoms.89,90 It has been found that reaction products are largely determined by the nature of the metal centers. For example, alkali metal ions generally form stable association complexes with ethers,89 whereas transition metal ions tend to form a variety of products arising from the dissociation of insertion complexes.90 There has been no previously spectroscopic evidence for the formation of stable transition metal-ether association complexes. However, our ZEKE measurements show that the stable adducts are formed between the transition metal atoms (e.g., Zr, Y) and dimethyl ether in the molecular beams. Figure 12(a) presents the ZEKE-PFI spectrum of zirconium-dimethyl ether complex.32 Three vibrational intervals can be identified from the spectrum, which are 254, 450, and 856 cm–1.
Zero Electron Kinetic Energy Photoelectron Spectra
217
Figure 12: Experimental (a) and simulated ZEKE-PFI spectra of ZrO(CH3)2 (b) and (CH3)ZrO(CH3) (c). The simulations were performed with the molecular structures and vibrational frequencies from the DFT calculations. From reference 32.
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Dong-Sheng Yang
The short progressions indicate a small change in the geometry of the complex upon ionization. By comparing with the frequencies of the free dimethy ether,91 the 450 and 856 cm–1 progressions can be assigned to the COC symmetric bending and the CO symmetric stretching modes. The 254 cm–1 interval does not match any of the symmetric modes of the ligand, it is assigned to the ZrO symmetric stretching in the ion complex. The same mode has the frequency of 214 cm–1 in the neutral complex. The identification of the COC bending mode and the low frequency of the ZrO stretching mode indicate that the carrier of the ZEKE-PFI spectrum is an adduct, in which Zr atom binds to oxygen without disrupting any of the CO bonds. The IP of the complex is measured to be 42591 cm–1. The association complex probed in the ZEKE-PFI experiment is also supported by the spectral simulations. The theoretical spectra are presented in Fig. 12(b) and (c), which are calculated from the 4 B1← 3B1 transition of the addition complex (Fig. 12(b)) and the 2 A’ ← 3A" transition of the insertion complex, in which Zr atom is inserted between the oxygen and carbon atoms (Fig. 12(c)). The comparison of the theory and experiment, although not perfect, clearly shows that the carrier of the ZEKE spectrum is the simple adduct, rather than the insertion structure. Although the insertion complex is calculated to be 3.44 eV lower in energy than the adduct, the formation of the insertion complex has a barrier of 0.6 eV, whereas the formation of the adduct is a barrierless process. Replacing zirconium with yttrium, the ZEKE-PFI spectrum shows a stronger vibronic activity (Fig. 13(a)),33 implying a larger geometric change of the yttrium-dimethyl ether complex upon ionization. The ionization energy of the complex is measured to be 37997 cm–1. The IP reduction upon the ether ligation is slightly larger than that in the case of zirconium. As in the spectrum of zirconium complex, three vibrational modes can be identified, which are Y+O stretching (260 cm–1), COC bending (451 cm–1), and CO stretching (830 cm–1). In addition, the frequency of the Y+OC symmetric bending is measured to be 122 cm–1. We have also obtained the ZEKE-PFI spectrum of the 1:2 yttrium-dimethyl ether complex, Y[O(CH 3)2]2, as shown in Fig. 13(b).33 In contrast to the 1:1 complex, the spectrum of the 1:2 complex is much simpler, which only shows the yttrium-ether stretching (201 cm–1) and the CO stretching (864 cm–1) in the ionic complex. The IP of the di-ligand complex is measured to be 29932 cm–1, 8065 cm–1 lower than the IP of the corresponding mono-ligand complex.
Figure 13:
PFI-ZEKE spectra of YO(CH3)2 (a) and Y[O(CH3)2]2 (b). νYO+ (symmetric stretch of Y+–O, νCO+ (symmetric stretch of C–O), and νCOC+ (symmetric bending of C–O–C) are the vibrational modes in the ionic complexes. From references 33.
Zero Electron Kinetic Energy Photoelectron Spectra 219
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Dong-Sheng Yang
Table 2 summarizes the IPs and metal-ligand vibrational frequencies of the complexes discussed above, along with the IPs of the metal atoms.92 As shown in Table 2, the IPs of the metal atoms are dramatically decreased upon the coordination of ammonia or dimethyl ether. The IP reduction also correlates with the increase of the metal–ligand vibrational frequencies upon Table 2.
IPs (cm–1) and metal–ligand stretching frequencies (cm–1) of metal complexes
Complex/atom
IP(a)
νs+(M+–L)(b)
νs (M–L)(b)
Reference
Y
50144
YO(CH3)2
37997
260
33
YO(CD3)2
37971
231
33
Y[O(CH3)2]2
29932
201
33
Y[O(CD3)2]2
29875
182
Zr
53505
ZrO(CH3)2
42591
V
54412
VNH3
44015
In
46670
92
33 92
254
214
32 92
414(c)
31 92
InNH3
39689
Al
48278
AlNH3
39746
339
227
29
AlH2O
41018
328
172
94
AlH2D
40994
316
Na
41449
234
141
30 92
94 92
NaNH3
34435
305
215
93
NaND3
34368
286
196
93
NaH2O
35323
300
207
93
NaH2D
35249
296
206
Mg
61671
MgCH3
53265
Zn
75768
ZnCH3
58661
Cd
72538
CdCH3
57105
VO
58383
YO
49304
AlAr
47423
93 92
516
95 92
482
445
422
356
95 92 96 97 98
67
39
99
(a) The IP uncertainty for the complexes is typically ~5 cm–1, except for YO for which the uncertainty is 0.03 cm–1. (b) νs+(M+–L) and νs (M–L) are the metal–ligand stretching frequencies in the ion and neutral ground states, respectively. (c) Tentative assignment.
Zero Electron Kinetic Energy Photoelectron Spectra
221
ionization. These observations indicate that the metal–ligand bonds are stronger in the ion than in the neutral complexes, presumably due to the additional charge-dipole interactions in the ionic species. Other metal–ligand molecules studied with ZEKEPFI include NaNH3 and NaH2O,93 AlH2O,94 MCH3 (M = Mg, Zn, and Cd),95, 96 MO (M = V and Y),97,98 and AlAr.99 Their IPs and vibrational frequencies are also included in Table 2. VI. SUMMARY ZEKE-PFI spectroscopy has been successfully applied to small metal clusters and metal–ligand complexes. The technique offers the capability to resolve vibrational structures in general and rotational structures in special cases. Geometries and ground electronic states of the neutral and ionic clusters can be determined by combining the ZEKE-PFI technique with DFT or ab initio and FC factor calculations. This synergic approach is rather important because currently it is still difficult, not to say impossible, to establish reliable structures of isolated metal clusters and complexes by either experimental or theoretical technique alone. ACKNOWLEDGMENTS The author thanks his current co-workers at the University of Kentucky and former colleagues at the National Research Council of Canada (NRC Canada) whose names appear on the papers quoted herein. He is especially indebted to Dr. P.A. Hackett, who gave a great support to the cluster project at NRC Canada. The author also thanks the Donors of The Petroleum Research Fund, administrated by the American Chemical Society, for the partial support of the work on the metal–ligand complexes. REFERENCES (1) (2) (3) (4) (5) (6) (7)
Turner, D.W., Baker, C., Baker, A.D., and Brundle, C.R. (1970) Molecular Photoelectron Spectroscopy, Wiley: New York. Cowley, A.H. (1979) Prog. Inorg. Chem., 26: p. 46. Green, J.C. (1981) Struct. Bonding (Berlin), 43: p. 37. Oskam, A. (1987) In: Spectroscopy of Inorganic Based Materials, (Clark, J.H. and Hester, R.E., eds), Wiley, p. 429. Lichtenberger, D.L. and Kellogg, G.E. (1987) Acc. Chem. Res., 20: p. 379. Bancroft, G.M. and Hu, Y.F. (1999) In: Inorganic Electronic Structure and Spectroscopy, (Solomon, E.I. and Lever, A.B.P., eds), Wiley, Vol. 1, p. 443. Wang, L.S. and Wu, H. (1998) In: Advances in Metal and Semiconductor Clusters. IV. Cluster Materials, (Duncan, M.A., ed.), JAI Press: Greenwich, CT, p. 299.
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Dong-Sheng Yang Ervin, K.M. and Lineberger, W.C. (1992) In: Photoelectron Spectroscopy of Negative Ions, (Adams, N.G. and Babcock, L.M., eds), JAI Press: Greenwich, CT, Vol. 1, p 121. Green, S.M.E., Alex, S., Fleischer, N.L., Millam, E.L., Marcy, T.P. and Leopold, D.G. (2001), J. Chem. Phys., 114: p. 2653. Müller-Dethlefs, K. and Schlag, E.W. (1991) Ann. Rev. Phys. Chem., 42: p. 109. Yang, D.S., James, A.M., Rayner, D.M. and Hackett, P.A. (1995) J. Chem. Phys., 102: p. 3129. Müller-Dethlefs, K., Dopfer, O., and Wright, T.G. (1994) Chem. Rev., 94: p. 1845. Müller-Dethlefs, K., Schlag, E.W., Grant, E.R., Wang, K., and McKoy, B.V. (1995) In: Advances in Chemical Physics, Vol. XC, (Prigogine, I., Rice, S.A., eds), Wiley, p. 1. Müller-Dethlefs, K. and Schlag, E.W. (1998) Angew. Chem. Int. Ed., 37: p. 1346. Schlag, E.W. (1998) ZEKE Spectroscopy, Cambridge University Press: Cambridge. Gantefor, G.F., Cox, D.M., and Kaldor, A. (1990) J. Chem. Phys., 93: p. 8395. Gantefor, G.F., Cox, D.M., and Kaldor, A. (1991) Z. Phys. D. Atoms, Molecules and Clusters, 19: p. 59. Gantefor, G.F., Cox, D.M., and Kaldor, A. (1992) J. Chem. Phys., 96: p. 4102. Drechsler, G., Bäβmann, C., Boesl, U., and Schlag, E.W. (1995) J. Mol. Struct., 348: p. 337. Drechsler, G., Boesl, U., Bäβmann, C., and Schlag, E.W. (1997) J. Chem. Phys., 107: p. 2284. Yang, D.S., James, A.M., Rayner, D.M., and Hackett, P.A. (1994) Chem. Phys. Letters, 231: p. 177. Yang, D.S., Simard, B., Hackett, P.A., Bérces, A., and Zgierski, M.Z. (1996) Int. J. Mass Spectrom. Ion Proc., 159, 65. Yang, D. S., Zgierski, M. Z., Rayner, D. M., Hackett, P. A., Martinez, A., Salahub, D.R., Roy, P.N., and Carrington Jr., T. (1995) J. Chem. Phys., 103: p. 5335. Yang, D.S., Zgierski, M.Z., and Hackett, P.A. to be published. Yang, D.S., Zgierski, M.Z., Bérces, A., Hackett, P.A., Roy, P.N., Martinez, A., Carrington Jr., T., Salahub, D.R., Fournier, R., Pang, T., and Chen, C. (1996) J. Chem. Phys., 105: p. 10663. Yang, D.S., Zgierski, M.Z., and Hackett, P.A. (1998) J. Chem. Phys. 108: p. 3591. Yang, D.S. and Hackett, P.A. (2000) J. Electron Spectrosc. Relat. Phenom., 106: p. 153. Yang, D.S., Zgierski, M.Z., Bérces, A., Hackett, P.A., Martinez, A., and Salahub, D.R. (1997) Chem. Phys. Letters, 227: p. 71. Yang, D.S. and Miyawaki, J. (1999) Chem. Phys. Letters, 313: p. 514. Rothschopf, G.K., Li, S.G., Perkins, J.S., and Yang, D.S. (2000) J. Phys. Chem A, 104: p. 8178. Rothschopf, G.K. and Yang, D.S. to be published. Yang, D.S., Zgierski, M.Z., and Hackett, P.A. to be published. Yang, D.S. and Rothschopf, G.K. to be published.
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(34) Dietz, T.G., Duncan, M.A., Powers, D.E., and Smalley, R.E. (1981) J. Chem. Phys., 74: p. 6511. (35) Proch, D. and Trickl, T. (1989) Rev. Sci. Instrum., 60: p. 713. (36) Wiley, W.C. and McLaren, I.H. (1955) Rev. Sci. Instrum., 26: p. 1150. (37) St-Amant, A. and Salahub, D.R. (1990) Chem. Phys. Letters, 169: p. 387; Salahub, D.R., Fournier, R., Mlynarski, P., Papai, I., St-Amant, A., Ushio, J. (1991) In: Density Functional Methods in Chemistry, (Labanowski, J. and Andzelm, J., eds); Springer, Berlin; St-Amant, A. (1992) Ph.D. Thesis, University of Montreal. (38) Frisch, M.J., Trucks, G.W., Schlegel, H.B., Gill, P.M.W., Johnson, B.G., Wong, M.W., Foresman, J.B., Robb, M.A., Head-Gordon, M., Replogle, E.S., Gomperts, R., Andres, J.L., Raghavachari, K., Binkley, J.S., Stewart, J.J.P., and Pople, J.A. (1993) Gaussian 94/DFT, Revision G.4. Gaussian, Inc., Pittsburgh PA. (39) Baerends, E.J., Ellis, D.E., and Ros, P. (1973) Chem. Phys., 2: p. 41; Ravenek, W. (1987) In: Algorithms and Applications on Vector and Parallel Computers, (te Riele, H.J.J., Dekker, Th. J., van de Vorst, H.A., eds), Elsevier: Amsterdam. (40) Sharp, T.E. and Rosenstock, H.M. (1964) J. Chem. Phys., 41: p. 3452. (41) Duschinsky, F. (1937) Acta Physicochim URSS, 7: p. 551. (42) Doktorov, E.V., Malkin, I.A., and Man’ko, V.I. (1977) J. Mol. Spectrosc., 64: p. 302 and 56: p. 1. (43) Zgierski, M.Z. (1986) Chem. Phys., 108: p. 61. (44) Zgierski, M.Z. and Zerbetto, F. (1993) J. Chem. Phys., 99: p. 3721. (45) Langridge-Smith, P.R.R., Morse, M.D., Hansen, G.P., Smalley, R.E., and Merer, A.J. (1984) J. Chem. Phys., 80: p. 593. (46) Spain, E.M., Behm, J.M., and Morse, M.D. (1992) J. Chem. Phys., 96: p. 2512. (47) Spain, E.M., Behm, J.M., and Morse, M.D. (1992) J. Chem. Phys., 96: p. 2479. (48) James, A.J., Kowalczyk, P., Langlois, E., Campbell, M.D., Ogawa A., and Simard, B. (1994) J. Chem. Phys., 101: p. 4485. (49) Simard, B., James, A.M., Kowalczyk, P., Fournier, R., and Hackett, P.A. (1994) Proc SPIE, p. 376. (50) Xie, J. and Zare, R.N. (1990) J. Chem. Phys., 93: p. 3033. (51) Féménias, J.L., Cheval, G., Merer, A.J., and Sassenberg, U. (1987) J. Mol. Spectrosc., 124: p. 348. (52) Cox, D.M., Whetten, R.L., Zakin, M.R., Trevor, D.J., Reichmann, K.C., and Kaldor, A. (1986) In: Optical Science and Engineering Series 6, Advances in Laser Science, (Stwalley, W.C. and Lapp, M., eds), American Institute of Physics: New York, Vol. 1, p. 527. (53) Grönbeck, H. and Rosén A. (1997) J. Chem. Phys., 107: p. 10620. (54) Wu, X. and Ray, A.K. (1999) J. Chem. Phys., 110: p. 2437. (55) Knickelbein, M. (1995) J. Chem. Phys., 102: p. 1. (56) Personal communications. (57) Knight Jr., L.B., Van Zee, R.J., and Weltner Jr., W. (1983) Chem. Phys. Letters, 94: p. 296. (58) Knight Jr., L.B., Woodward, R.W., Van Zee, R.J., and Weltner Jr., W. (1983) J. Chem. Phys., 79: p. 5820. (59) Walch, S.P. and Bauschlicher Jr., C.W. (1985) In: Comparison of Ab Initio Quantum Chemistry with Experiment for Small Molecules – The State of the Art, (Bartlett, R.J., ed.), Reidel: Dordrecht, p. 17.
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Dong-Sheng Yang Dai, D. and Balasubramanian, K. (1993) J. Chem. Phys., 98: p. 7098. Dai, D. and Balasubramanian, K. (1995) Chem. Phys. Letters, 238: p. 203. Harrington, J.E. and Weisshaar, J.C. (1990) J. Chem. Phys., 93: p. 854. Németh, G.I., Ungar, H., Yeretzian, C., Selzle, H.L., and Schlag, E.W. (1994) Chem. Phys. Letters, 228: p. 1. Dyke, J.M., Ellis, A.M., Feher, M., Morris, A., Paul, A.J., and Stevens J.C. H. (1987) J. Chem. Soc. Faraday Trans. 2, 83: p. 1555. Knickelbein, M. B., Yang, S.H. (1990) J. Chem. Phys., 93: p. 5760. Yang, D.S. unpublished result. Arrington, C.A., Blume, T., Morse, M.D., Doverstål, M., and Sassenberg, U. (1994) J. Phys. Chem., 98: p. 1398. Verhaegen, G., Smoes, S., Drowart, J. (1964) J. Chem. Phys., 40: p. 239. Haouari, H., Wang, H., Craig, R., Lombardi, J.R., and Lindsay, D.M. (1995) J. Chem. Phys., 103: p. 9527. Wang, H., Craig, R., Haouari, H., Liu, Y., Lombardi, J.R., and Lindsay, D.M. (1996) J. Chem. Phys., 105: p. 5355. Morse, M.D. (1998) In: Advances in Metal and Semiconductor Clusters, (Duncan, M.A., ed.), JAI Press: Greenwich, CT, Vol. 1, p. 299. Sakai, S. (1992) J. Phys. Chem., 96: p. 8369. Davy, R.D. and Jaffrey, K.L. (1994) J. Phys. Chem., 98: p. 8930. Stöckight, D. (1996) Chem. Phys. Letters, 250: p. 387. Fängström, T., Lunell, S., Kasai, P.H., and Eriksson, L.A. (1998) J. Phys. Chem. A., 102: p. 1005. Howard, J.A., Joly, H.A., Edwards, P.P., Singer, R.J., and Logan, D.E. (1992) J. Am. Chem. Soc., 114: p. 474. Lanzisera, D.V. and Andrews, L. (1997) J. Phys. Chem. A., 101: p. 5082. Di Palma, T.M., Latini, A., Satta, M., Varvesi, M., and Giardini, A. (1998) Chem. Phys. Letters, 284: p. 184. Jakubek, J. and Simard, B. (2000) J. Chem. Phys., 112: p. 1733. Di Palma, T.M., Latini, A., Satta, M., Varvesi, M., and Giardini-Guidoni, A. (1998) Eur. Phys. J. D., 4: p. 225. Walter, D. and Armentrout, P.B. (1998) J. Am. Chem. Soc., 120: p. 3176. Marinelli, P.J. and Squires, R.R. (1989) J. Am. Chem. Soc., 111: p. 4101. Langhoff, S.R., Bauschlicher, Jr., C.W., Partridge, H., and Sodupe, M. (1991) J. Phys. Chem., 95: p. 10677. Tsipis, A.C. (1998) J. Chem. Soc. Faraday Trans., 94: p. 11. Moore, C.E. (1971) Atomic Energy Levels, Natl. Stand. Ref. Data Ser. No. 35, Natl. Bur. Stand.: Washington, DC. Lefebvre-Brion, H. and Field, R.W. (1986) Perturbations in the Spectra of Diatomic Molecules, Academic Press: Orlando, FL. Challender, C.L., Mitchell, S.A., and Hackett, P.A. (1989) J. Chem. Phys., 90, 5252. Izatt, R.M., Pawlak, K., Bradshaw, J.S., and Bruening, R.L. (1991) Chem. Rev., 91: p. 1721. More, M.B., Ray, D., and Armentrout, P.B. (1997) J. Phys. Chem., 101: p. 831; Wu, H.F., and Brodbelt, J.S. (1994) J. Am. Chem. Soc., 116: p. 6418; Chu, I.H., Zhang, H., and Dearden, D.V. (1993) J. Am. Chem. Soc., 115: p. 5736.
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(90) Alvarez, E.J., Wu, H.F., Liou, C.C., and Brodbelt, J. (1996) J. Am. Chem. Soc., 118: p. 9131; Zagorevkii, D.V., Holmes, J.L., Watson, C.H., and Eyler, J.R. (1997) Eur. Mass Spectrom., 3: p. 27; Huang, S.K. and Allison, J. (1983) Organometallics, 2: p. 883; Burnier, R.C., Byrd, G.D., and Freiser, B.S. (1981) J. Am. Chem. Soc., 103: p. 4360. (91) Sverdlov, L.M., Kovner, M.A., and Krainov, E.P. (1974) Vibrational Spectra of Polyatomic Molecules, Wiley: New York, p. 477. (92) Lide, D.R. and Frederikse, H.P.R. (eds) (1997) CRC Handbook of Chemistry and Physics, 78th edn, CRC Press: New York. (93) Rodham, D.A. and Blake, G.A. (1997) Chem. Phys. Letters, 264: p. 522. (94) Agreiter, J.K., Knight, A.M. and Duncan, M.A. (1999) Chem. Phys. Letters, 313: p. 162. (95) Barckholtz, T.A., Powers, D.E., Miller, T.A. and Bursten, B.E. (1999) J. Am. Chem. Soc., 121: p. 2576. (96) Panov, S.I., Powers, D.E. and Miller, T.A. (1998) J. Chem. Phys., 108: p. 1335. (97) Harrington, J. and Weisshaar, J.C. (1992) J. Chem. Phys., 97: p. 2809. (98) Linton, C., Simard, B., Loock, H.P., Wallin, S., Rothschopf, G.K., Gunion, R.F., Morse, M.D., and Armentrout, P.B. (1999) J. Chem. Phys., 111: p. 5017. (99) Willey, K.F., Yeh, C.S., and Duncan, M.A. (1993) Chem. Phys. Letters, 211: p. 156.
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7 STABILITY, STRUCTURE AND OPTICAL PROPERTIES OF METAL ION-DOPED NOBLE GAS CLUSTERS Michalis Velegrakis
I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 II. Apparatus and Experimental Methods . . . . . . . . . . . . . . . . . . 229 III. Mass spectroscopy: Stability and structure of clusters. . . . . . . 232 A. Dopants with Spherical orbitals . . . . . . . . . . . . . . . . . . . . . 232 B. Geometrical Model of Hard Spheres and Cluster Growth Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 C. Molecular Dynamics Simulations. . . . . . . . . . . . . . . . . . . . 241 D. Dopants with Non-Spherical Orbitals . . . . . . . . . . . . . . . . 247 IV. Photofragmentation spectroscopy: Optical Properties of Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 A. Photofragmentation and Photoabsorption. . . . . . . . . . . . 251 B. The Sr+Ar Complex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 C. The Sr+Ar2 Complex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 D. Sr+Arn Clusters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 V. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
Advances in Metal and Semiconductor Clusters Volume 5, pages 227–265 © 2001 Elsevier Science B.V. All Rights Reserved. ISBN: 0-444-50726-4
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I.
INTRODUCTION
The physical and chemical properties of small atomic and molecular clusters have been the object of intensive experimental and theoretical investigations in the last twenty years.1–5 It is well established that cluster properties are strongly dependent on the cluster size (number of constituent atoms). Therefore, clusters represent the intermediate regime between isolated molecules and bulk matter. Small ionic clusters constitute prototypes for studying elementary interactions between ions and atoms or molecules and can model a variety of physical and chemical processes such as electronic energy transfer, laser media, metal–ligand interactions, solvation effects and metal–insulator transitions. The rapid progress in experimental molecular beam techniques, in combination with lasers in recent years, allowed production of clusters for almost every element in the periodic table as well as mixed clusters. These systems are relatively easy to produce using modern cluster ion sources. The size distribution of the produced clusters is analyzed with mass-spectroscopic techniques. In particular, time-of-flight (TOF) mass spectrometry6 is a relatively simple and effective method which can be used to obtain reliable information concerning cluster stability. The intensity distribution of the detected clusters often exhibits local irregularities that are attributed to the particular stability of the corresponding clusters, whose sizes correlate to so-called “magic” numbers. The stability and the structure of the clusters arises from the nature of the interatomic interactions in the cluster. In van der Waals clusters, the valence electrons are localized on the constituent atoms, which are held together by short-range electrostatic forces. The atoms in the cluster can be considered as close-packed spheres and the structure of these clusters is determined mainly by geometrical factors. Clusters from noble gas atoms are the most simple systems in this category and their structural and stability properties can be inferred from hard-sphere packing models or by the application of isotropic pair potentials, as the pioneering works of Mackay,7 and Hoare and Pal8 have shown. After the experimental discovery of the magic numbers in Xen clusters by Echt et al.9 a large number of studies, experimental as well as theoretical, have appeared in the literature.10–13 Noble gas clusters doped with an atomic14–19 or a molecular20–22 positive ion are another more interesting type of cluster. Particularly, the mixed clusters of the form MXn (M = metal ion, X = noble gas atom) are of great interest since, depending on the type of the metal ion, the binding can range from van der Waals interactions to
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covalent bonds. The ability to produce such free clusters offers the opportunity to perform studies that address their stability and their structure and hence to investigate the nature of the prevailing forces. Furthermore, the composition of these mixed systems can be changed in a systematic way in order to examine the changes in the cluster properties (such as the structure) as the metal ion changes. Metal atoms embedded in noble gas clusters serve as chromophores allowing the application of electronic spectroscopy for the investigation of the optical properties of these complexes. New spectroscopic methods, such as the photofragmentation spectroscopy of mass selected cluster ions,23–31 have been applied recently in several studies concerning the binding in the diatomic M–X complexes.30,32,33 In contrast, very few studies have been performed for the larger MXn systems.34–36 From these experimental data information about the potential energy surfaces (PES) and the fragmentation dynamics of an electronically excited cluster can be obtained and related to the observed spectral shifts as function of the cluster size This chapter focuses on recent work done on metal ion-doped noble gas clusters in our laboratory. I present two different sets of data, which concern the structural and optical properties of clusters. In Section II, I give a brief description of the experimental methods used. In Section III, I present mass spectroscopic studies of several MXn clusters and discuss, in terms of the observed magic numbers, the applicability of theoretical models in predicting the stability and the structure of these systems. In Section IV, I present the results of photofragmentation spectroscopy on mass selected Sr+Arn (n = 1–8) clusters. These clusters can be considered as a case system where the PES and the fragmentation dynamics can be investigated, to provide insight into the optical properties of clusters. Finally, in Section V a summary of the presented results is given. II.
APPARATUS AND EXPERIMENTAL METHODS
The experimental apparatus constructed for the cluster studies is shown in Fig. 1. The production of the ionic complexes and their analysis with reflectron time of flight (TOF) techniques takes place in three successive, differentially pumped vacuum chambers. The cluster ion source is located in the first chamber. As previously37,38 described, it is a laser vaporization source without any plasma confining elements. A rotating rod of the target material (high purity metal) is placed just in front of the nozzle orifice and irradiated by the focused light of a homebuilt Q-switched Nd:YAG laser (λ = 1064 nm, Epulse = 10–80 mJ, 12.5 Hz repetition rate). The created plasma is
230 Michalis Velegrakis
Figure 1: Schematic view of the molecular beam apparatus used to produce, analyze and perform photofragmentation spectroscopy on metal ion-doped noble gas clusters. The several TOF components and the configuration of the employed lasers are indicated.
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mixed with a noble gas pulse produced by a homebuilt piezoelectric pulsed nozzle (d = 0.8mm, tpulse = 200 μs) operating at room temperature and with a backing pressure of ~5 bar. Due to association reactions in a region of high collision frequency between the noble gas atoms and the metal ions contained in the plasma, cluster growth is achieved. The clusters drift with thermal velocity (~600 m/s in the case of argon as carrier gas) through the skimmer (d = 4 mm) into the second chamber which houses the acceleration unit, a two-field Wiley-McLaren6 device. As soon as the main part of the ion packet has passed the first grid, an acceleration voltage of +2 kV is applied, initiating the TOF. Mass spectra can be recorded after the ions have passed the collimator and are measured with two micro-channel plate (MCP) detectors using two different operation modes, the linear and the reflecting. In the first case the MCP can be inserted externally (through a vacuum translator) perpendicular to the spectrometer axis, while in the latter case a second MCP is placed off-axis in order to measure the backwards reflected ions from the reflecting assembly. In both cases, the MCP output is directly connected to a computer controlled digital storage oscilloscope, where the TOF mass spectra are acquired and stored shot by shot. Two einzel lenses and four alignment plates are used to guide the ion beam over the total drift length of about 2.5 m. The TOF spectra that will be discussed are obtained by averaging several hundred single shot spectra. The mass selection is performed by a two-plate pulsed capacitor placed at the spatial focus (~1 m) of the Wiley-McLaren unit. In order to obtain the fragmentation spectrum of one selected mass, an excimer-pumped pulsed-dye laser (in collinear arrangement with the ion beam) fires when the ions under investigation are located in the mass gate. The photofragments are separated in the TOF spectrum from the parent masses as, due to the conservation of energy, the fragments have lower kinetic energy, penetrate less deeply into the reflectron, and arrive earlier at the MCP detector. This collinear ion-laser beam arrangement introduces a Doppler shift, which is of the order of 1 cm–1, but as this is comparable to the bandwidth of the used laser no further care has to be taken. By monitoring the ratio of fragments per parents, and taking into account the power of the dissociation laser measured with a pyroelectric detector, wavelength dependent photofragmentation spectra can be recorded by scanning the frequency of the dye laser. Data acquisition is obtained by feeding the ion signal and the pyroelectric detector output into the computer controlled digital oscilloscope. The same computer also controls the frequency setting of the dye laser, while coupled delay generators are used to synchronize the timing of the experiment.
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MASS SPECTROSCOPY: STABILITY AND STRUCTURE OF CLUSTERS Formation Mechanism of the Clusters
The cluster source employed in these experimental studies is of the “open type” i.e. it does not contain confining elements such as mixing chambers or reaction tubes and allows the free adiabatic coexpansion of the plasma/noble gas mixture. This mixing takes place very close to the nozzle orifice, which is in an early stage of the adiabatic expansion, and therefore it is expected that the produced clusters undergo a sufficient number of collisions to cool down. Under these circumstances it is likely that clusters are formed mainly by successive growth of smaller species through association reactions rather than by fragmentation of larger ones (unimolecular dissociation). With this method both neutral clusters and ionic ones are produced. We study the cationic clusters produced directly from the source avoiding the use of postionization techniques. Thus, it is expected that these ionic clusters are sufficiently relaxed and the measured size distributions reflect the stability of these species. These assumptions are supported by the fact that the measured cluster velocity at 200 μs after the firing of the ablation laser is ~600 m/sec in the case of Ar carrier, which is the isentropic velocity limit of the Ar molecular beam. This indicates a quite complete thermalization of the cluster beam. A.
Dopants with Spherical Orbitals
Mass Spectra, Stability and Magic Numbers In Figs 2, 3, and 4 we present TOF mass spectra of several noble gas clusters doped with different metal cations. All the systems are of the type M+Xn and the most intense peaks, that we characterize as magic size clusters, are labeled by the total number, N = n+1, of atoms in the cluster. The spectra are reproducible over a large period of years and source conditions, and are also not dependent on the wavelength of the employed laser. Special stable clusters are defined as those clusters whose corresponding peaks exhibit an enhanced intensity in the recorded mass spectra. We characterize a cluster as magic by using two criteria i) the peak that corresponds to the particular cluster size must differ by at least 10% from the neighboring ones, and ii) this behavior has to be independent of the source conditions (inlet pressure, laser fluence, ablation point distance from the nozzle etc.).
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Figure 2: The TOF spectra of Ca+Krn, Ca+Xen, Sr+Krn and Sr+Xen clusters. The most stable clusters are indicated by the total number of atoms N = n+1.
The common feature in the mass spectra of Fig. 2 for Ca+Krn, Ca+Xen, Sr+Krn and Sr+Xen is the extra stability for clusters with sizes N = n + 1 = 7,13,19,23,26,29,…,55,71, ..,147. Exactly the same stability pattern is observed for a number of similar systems In+Arn, In+Krn, Al+Arn, Al+Krn (Ref. 39), Mg+Arn (Refs 40 and 41), K+Arn and K+Krn (Ref. 41). This pattern resembles the familiar magic number sequence for the pure noble gas clusters.9,10,11 The cluster systems Al+Xen (Ref. 39), Mg+Xen (Ref. 41) and Na+Krn (Ref. 39) displayed in Fig. 3 exhibit another stability pattern which consists of the magic numbers N = 9,11,17,21,24, 26,27,30,34,55,71,147. The magic numbers N = 55,71,147 are identical to those of the noble gas clusters and those of Fig. 2. The same behavior is exhibited by the systems In+Xen , K+Xen, and Na+Arn presented in Refs. 39 and 41. In Fig. 4 we display the mass spectra of Ca+Arn clusters. This system shows the magic numbers N = 7,9,13,15,19,21,23,25, 28,31,35,55,71. Here, the numbers N = 13,19,23,55,71 resemble the magic numbers of the noble gas clusters, while the set N = 15,21,25,28,31 has not been observed in any other system.
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Michalis Velegrakis Figure 3: The TOF spectra of Al+Xen,39 Mg+Xen,41 and Na+Krn.39
Figure 4: The TOF spectrum of Ca+Arn.
Properties of Metal Ion–Doped Noble Gas Clusters
B.
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Geometrical Model of Hard Spheres and Cluster Growth Sequences
The appearance of magic number patterns, observed in mass-spectroscopic studies on Xen clusters by Echt et al.9 and on Arn clusters by Harris et al.,11 can be explained by the adaptation of icosahedral sphere-packing. These results are also confirmed by electron diffraction studies by Farges et al.42 on Arn clusters. The atoms in these systems arrange themselves in shells around a central atom. When the total number of atoms is n = 13,55, 147…, shell closing occurs, giving rise to very stable clusters, which have icosahedral geometry (Mackay-icosahedra).7 Stable clusters also are observed for n = 19,23,26,29,32,.. where in this case subshells are filled and the cluster geometry is characterized as polyicosahedral.43 The completion of shells and subshells takes place in a particular sequence (growth sequence), such that every additional atom occupies the position that offers the maximum number of neighbors (contacts). This is a direct consequence of the electron localization on the individual atomic orbitals. As a result, atoms can be treated as hard spheres, thereby allowing the application of geometrical models for determining the cluster structure. The magic number sequences appearing in the mass spectra are the fingerprints of the cluster structure. Some metal ion-doped noble gas clusters M+Xn (see Fig. 2 and the related systems mentioned in the previous paragraph) exhibit magic number series (at total number of atoms N = n+1) identical to the pure noble gas clusters, therefore, these mixed systems may have icosahedral geometries. For this to be the case, the geometrical size of the metal ion should be comparable to the noble gas atom and therefore the metal ion replaces one noble gas atom without distorting the icosahedral structure. Since mass spectra for a large number of mixed clusters of the type M+Xn (M = metal atom, X = noble gas atom) with different compositions are now available (Figs 3 and 4 and Refs. 39, 40, and 41) it is very interesting to apply to this variety of systems the hard sphere-packing model presented in our previous paper39 to explain magic numbers sequences for several metal doped noble gas clusters. The most stable clusters expected for hard sphere packing are those which have closed shells of atoms around a central atom. For clusters of the type MXn we can assume that the metal ion M is confined in the center of the cluster and is surrounded by the n noble gas atoms X. In order to obtain high symmetry and dense packing (the requirements for high stability), the most obvious way
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to arrange the noble gas atoms around the metal ion is represented by the polyhedra indicated in Fig. 5. These polyhedra (whose vertices represent the atoms of a cluster) can be formed by joining two identical regular polygons, each being made from k = n/2 = 2,3,4,5,6 atoms, and one being twisted by an angle of π/k with respect to the other one (Fig. 5, middle row). The first six polyhedra formed in this way are the tetrahedron (n = 4), the octahedron (n = 6), the square antiprism (n = 8), the pentagonal antiprism (n = 10), and the hexagonal antiprism (n=12). From the above polyhedra, only the tetrahedron and the octahedron are closed shell structures. For the square antiprism, pentagonal antiprism, and the hexagonal antiprism two additional atoms are needed to acquire the closed shell structures, the capped square antiprism (CSA) (n = 10), the icosahedron (n = 12) and the capped hexagonal antiprism (CHA) (n = 12) respectively (see Fig. 5, bottom row). It should be also mentioned, that only the tetrahedron, the octahedron and the icosahedron are regular polyhedra. We expect that the polyhedra of Fig. 5 represent stable cluster structures only if the size of the central atom fits into the cavity dimensions. By applying simple geometrical considerations this condition is fulfilled when the radius RM of the central atom and the radius RX of the noble gas atoms have the following relation: 1⁄2
ì π 2π 2π ü R∗ = R M ⁄ R X ≤ í 2 + cos æ --- ö – cos æ ------ö ⁄ 1 – cos æ ------ö ý èkø è kø è kø î þ
–1
(1)
where, k = n/2 represents the number of atoms per ring. This formula gives the maximum radii ratio, for each symmetry, in order to keep the exterior atoms in contact with each other. Thus we obtain the maximum R*-values displayed in the first row of Fig 5. for k = 2 to 6. That is, for 1.17 ≥ R* > 0.902 CHA-packing is preferred, for 0.902 ≥ R* > 0.645 icosahedral-packing, for 0.645 ≥ R* > 0.414 CSA-packing, etc. The geometrical structure of a cluster of the kind MXn can be very well represented by the polyhedra of Fig. 5, where a central atom M is surrounded by 4, 6, 10, 12, 14 noble gas atoms, which constitute a completely filled first solvation shell. Since these high symmetry polyhedra consist exclusively from triangular faces, the total number of atoms Nm in a cluster with m filled shells and having the symmetries shown in Fig. 5, is given by: Nm =Nm–1 + V + F3 m(m–2)/2
for
m > 2,
(2)
where V is the number of vertices, and F3 is the number of triangular faces. For all the polyhedra N1 = 1, while N2 = 15 for CHA,
Figure 5: Picture explaining the geometrical model of sphere packing for clusters of the type MXn. According to the radii ratio R* = RM/RX different high symmetry polyhedra with a central M atom and n atoms at the vertices can be formed. These are obtained from two twisted polygons each of them is made from k = n/2 atoms (middle row). The square antiprism, the pentagonal antiprism and the hexagonal antiprism need two additional capping atoms to form closed shell structures (bottom row).
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N2 = 13 for the icosahedron and N2 = 11 for CSA. Thus, for the case of the CHA, shells are filled at N = 15,65,175,.. atoms, for the icosahedron the successive icosahedral shells are filled at N = 13, 55, 147, 309…, atoms, whereas, for the CSA we get N = 11, 45, 119, 249..,. Similar formulas for a variety of polyhedra are given by Martin et al.44 The above simple consideration explains very well the stability of some clusters that represent closed shells, as this is the case of the icosahedral ones (N = 13,55,147..,). Harris et al.11 however, have been able to develop a cluster growth model for Arn clusters using the closed icosahedral second shell with N = 13 atoms where they placed additional atoms at adjacent triangular faces (face-packing, FP). Every time a pentagonal ring is formed, the next atom is placed on the enclosed vertex-site forming a pentagonal pyramid. The geometrical structures resulting from this procedure correspond to 6-atom pentagonal caps on the 13-atom icosahedron, and can be considered as the closing of subshells with pentagonal symmetry. This operation maximizes the number of the bonds and for the case of FP this occurs at N = 19,23,26,29 and 32. The procedure to obtain the magic number sequence for icosahedral clusters can now be generalized also for the other symmetries mentioned above. A relatively simple way to deduce similar growth sequences for the other polyhedra of Fig. 5 can be performed with the help of Schlegel diagrams. Such a diagram shows schematically all the elements (faces, edges and vertices) of a three dimensional polyhedron in two dimensions. In Fig. 6 (middle row) we show the Schlegel diagrams for the CHA, the icosahedron and the CSA. The numbers at the triangular faces of the Schlegel diagrams represent the successively added atoms. At the same time, one can count the number of the neighboring atoms which are present before the atoms are added, i.e. the number of newly formed bonds. In Fig. 6 (bottom row) we display these numbers as a function of the corresponding cluster size for each symmetry. Assuming that the contribution of every new added atom to the total binding energy of the cluster is proportional to the number of nearest neighbor bonds, these neighbor-interaction energies should then correspond to the binding energy differences of the clusters. The cases for which the number of newly formed bonds is maximized coincide with the magic numbers in the cluster stability.11 Inspecting these plots we observe that several maxima occur at N = 19,23,26,29,32, for the case of icosahedron, N = 17,21,24,27,30 and 32–35 for the case of CSA and N = 21,25,28, 31,.. for the case of CHA. In Fig. 7 we plot the geometries of the stable clusters predicted from the above hard sphere model for the icosahedral clusters and those based on the CSA packing.
Figure 6: (Top): the tree polyhedra CSA, ICOS, CHA that represent the second shell of stable MXn clusters with sizes N = n + 1 = 15, 13 and 11 respectively. (Middle): the Schlegel diagrams for the CHA, ICOS and CSA structures. The numbers at the triangular faces and vertices (circles) indicate the sequence of the added atoms in order to maximize the number of bonds. (Bottom): The number of bonds formed as the size N of the clusters grows from N –1 and by following the above sequences.
Properties of Metal Ion–Doped Noble Gas Clusters 239
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Figure 7: The geometries of stable clusters obtained from the sphere packing model with the use of Schlegel diagrams of Fig. 6. The numbers correspond to the cluster sizes that constitute growth sequences based on an icosahedral core with 13 atoms (top) or on a CSA core with 11 atoms (bottom).
Michalis Velegrakis
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The icosahedral magic number series coincide very well with those observed for the clusters displayed in Fig. 2. The magic numbers of the clusters in Fig. 3 for N ≤ 30 are identical to those predicted from the model for the CSA packing, whereas the large ones are again icosahedral. Here we do not observe closing of the third shell at N = 45. In the case of Ca+Arn (Fig. 4) the numbers N = 13,19,23,55,71 resemble the icosahedral magic numbers, while the set N = 15,21,25,28,31 seems to coincide with the series predicted from the hard sphere model for CHA packing. The appearance of two different magic number series could be due to the coexistence of two different structural trends in the clusters. According to these observed magic number sequences we can give the limits of the size ratio R* for each system. Thus for the systems in Fig. 2 it should be 1.175 ≥ R* ≥0.902, for the systems in Fig. 3 0.902≥ R* ≥0.645, and for the system Ca+Arn, R* ≥1.175. C.
Molecular Dynamics Simulations
In Ref. 41 we have performed molecular dynamics simulations to investigate the stability and the geometrical structures of metal doped noble gas clusters. The main goal of this computational study was, in addition to verifying the results of the hard sphere model, to simulate at least qualitatively the experimental spectra, thus shedding light onto what happens to the stability and structure of electrostatic clusters as the type of dopant changes. These changes affect the size (radius) of the metal ion relative to the noble gas atoms, and the interaction energy between the ion and the noble gas atoms. Interaction Potentials and Computational Methods For the description of the interactions that exist between all the atoms constituting a cluster of the type M+Xn we make two main assumptions. First, we assume that the charge is localized on the metal ion M+ and ignore charge transfer effects. Second, we assume that only two body terms are dominant in the interactions between the constituent atoms in the cluster, so that the total potential energy is simply the sum of all pair potentials. The first assumption is justified by the fact that the ionization potential of the metal atom is much lower than that of the noble gas atoms and thus no significant charge transfer is expected. The second one is based on the spherical character of the electronic configuration (s-orbital) of metal atom and the noble gas atoms, which is consistent with an
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isotropic potential. Hence we model the total potential energy E (N) of a cluster M+Xn as: N–1
N
N
E ( N ) = å V 1i ( R 1i ) + å i=2
å Vij ( Rij )
(3)
i = 2 j = i+1
We label the metal atom as 1 and thus V1i and R1i represent the metal ion–noble gas potential and distance respectively. Similarly, Vij and Rij represent the same quantities for the noble gas/noble gas interaction. For all pair interactions we use the simple two-parameter (ε,σ) Lennard-Jonnes (LJ) potential 12
6
V ( R ) = 4ε [ ( σ ⁄ R ) – ( σ ⁄ R ) ] ,
(4)
where ε and 21/6σ represent the well depth and the equilibrium distance, respectively. Throughout the calculations for the MXn systems, we use reduced energies ε* and distances σ*, where ε* = εM–X/εX–X and σ* = RM–X/RX–X. The reduced distance σ* is related to the size ratio R* of the hard sphere model (Equation 1) via σ* = (R* + 1)/2, so that direct comparisons are possible. Certainly the LJ (12,6) potential does not describe correctly the ion–atom interaction where the attractive part varies as –1/R 4 (charge-induced dipole interaction). We take this into account by using the value ε* = 10, which is relevant for most of the systems considered (see Ref. 41). (This ion–noble gas LJ-potential describes an effective pair potential for the intercluster interaction.) For this reason we perform calculations for M+Xn clusters for N = 3–31 total number of atoms with ε* = 10 and for a series of σ*-values ranging between 0.6 and 1.1. We calculate the minimum energy structures of the clusters by applying molecular dynamics quenching techniques. For a particular MXn cluster we start from an initial configuration and integrate Newton’s equations of motion with a fourth-order Runge-Kutta algorithm. The kinetic energy is removed from the system either every 100 integration steps or if the kinetic energy has achieved a maximum value. The resulting structures refer to the zero Kelvin configurations. For each cluster size, several runs are performed starting from different initial configurations. These structures are simple cubic (SC), face-centered cubic (FCC), base-centered cubic (BCC), icosahedral, CHA, CSA, octahedral or just randomly distributed N atoms. Another procedure starts with the relaxed cluster with size N–1 and using this as seed, a search for the highest coordination site of the cluster is employed, adding an atom at that site and then relaxing the N-atomic cluster. Furthermore, for
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clusters with sizes N > 15, we employ additionally the BFGS variable metric minimization method45,46 to check the minimal energy structures found by the molecular dynamics calculations or to find lower energy structures. Thus, we expect that the cluster structures we find are those with the minimum total energy. Of course there is no guarantee that we obtain the global minimum of the multidimensional potential energy surface, but starting from a range of initial configurations and employing two different minimization methods, it is likely that the system does not get trapped in a local minimum. As the main scope of the simulations performed here is mainly to detect trends in the structures of small mixed clusters as a function of the relative size σ*, we did not apply other minimization techniques.47,48 Cluster Stability and Minimum Energy Structures For the cluster sizes N = 3 and 4, which are trivial geometrical cases (an equilateral triangle and a distorted tetrahedron respectively), the total energy is independent of the σ*-values and it is simply given by E(N) = (N – 1)(ε* + 1). For the larger clusters, the lowest energies per noble gas atom [E(N)/(N – 1)] calculated for ε* = 10 are plotted as a function of the cluster size N in Fig. 8 for several σ*. The minima appearing in Fig. 8 for each value of σ* correspond to Figure 8: The lowest energy per noble gas atom for the MXn clusters calculated with molecular dynamics for several values of the relative size σ* and at ε* = 10 (see text).
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shell closures at a particular cluster size N = n + 1. Thus, the number n of noble gas atoms needed to close the second shell varies from n = 4 at σ* = 0.7 to n = 18 at σ* = 1.1. To obtain the relative stability of clusters (magic numbers) we use the second difference of the total energy,
Δ2E(N) = E(N + 1) + E(N – 1) – 2 E(N),
(5)
where positive Δ2E values correspond to relatively stable clusters. In addition, we analyze the geometry of the resulting structures, and we find that in all cases the metal ion resides in the interior of the cluster. Furthermore, according to the symmetry of the local environment of the metal ion, i.e. the geometry of the surrounding noble gas atoms, we classify the cluster structures found into three main topologies (see Fig. 9): i) the icosahedral (ICOS), where the ion lies between two twisted pentagonal rings formed from noble gas atoms (coordination number 12), ii) the capped square antiprism (CSA), where the ion is surrounded by two twisted squares (coordination number 10) and iii) a mixture of both, labeled as ICOS-CSA, where the ion lies between a pentagonal and a square ring (coordination number 11). Hence, all clusters with N≥13 can be considered as including either a 13-atomic icosahedral core, or a 12-atomic ICOS-CSA-core, or finally an 11-atomic CSA-core. Figure 10 displays in the form of bar graphs the Δ2E(N) values calculated for the different σ*-values between 0.73 to 0.9. To give also the structural information in this stability diagram, we use three different shadings. The black bars correspond to icosahedral symmetry, the white bars represent symmetries based on CSA, while Figure 9: The three main topologies ICOS, ICOS-CSA and CSA, that constitute the cluster core used to characterize the lowest energy structures resulting from the molecular dynamics simulations.
Figure 10: Bar graphs representing the second difference Δ2E(N) Equation 5) of the total binding energies E(N) calculated for ε* = 10 and for several values of σ* ranging from 0.9 to 0.73.41 The different shadings refer to different geometries. Black bars represent icosahedral clusters, white bars represent clusters with structures based on CSA, and the shaded bars denote the clusters that have mixed ICOS-CSA geometry.
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the shaded bars represent the mixed ICOS-CSA symmetries. The stable clusters resulting from these calculations can be grouped in three categories. For σ* = 0.83–0.9 stable clusters exist at sizes N = 11,13,19,23,26,29 and are characterized as icosahedral; for σ* = 0.73–0.77 stable clusters exist at N = 7,9,11,17,21,27,30 and are based on a CSA core, and for σ*=0.8 the sizes N = 9,10,11,17,18,23,26,29 exhibit enhanced stability while their geometry has a mixed ICOSCSA character. There is an exception for N = 7 and σ*< 0.77 where the structure is octahedral. This is also predicted by the hard sphere model, where for small values of σ*, octahedral symmetry is expected. The geometric structures of the magic number clusters (Δ2E ≥ 0.2) for two typical cases σ* = 0.9 and σ* = 0.73 are identical to those of Fig. 7 (as predicted by the hard sphere model), and there is also a very good correspondence with the experimental results for the cluster systems of Fig. 2 and Fig. 3 respectively. We summarize the stability and structural results from the above calculations for ε* = 10 in form of a “phase diagram” in Fig. 11. This diagram shows the magic numbers expected as a function of a given Figure 11: “Phase” diagram showing the magic numbers and the geometries expected for clusters of the type M+Xn calculated with ε* = 10.41 The dotted line at σ* = 0.82264 is the maximum size ratio for CSA geometry as predicted from the hard sphere model.
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σ* and simultaneously the structure of these magic number clusters. It is effectively a contour plot of Fig. 10 for Δ2E ≥ 0.2, and is obtained by interpolating points in σ*-dimension for a given cluster size N. The shadings of the bars have the same meaning as in Fig. 10. Thus, if some effective σ* is known for a mixed system, one can use Fig. 11 to predict which cluster sizes will be stable and also what type of symmetry these clusters will exhibit. D.
Dopants with Non-Spherical Orbitals
In Fig. 12 we display TOF mass spectra of Argon clusters doped with the transition metal ions: Ag+, Ni+ and Ti+ . The case of Ag+Arn shows Figure 12: The TOF spectra of Ag+Arn, Ni+Arn,49 and Ti+Arn.58
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stable clusters at sizes N = n + 1 = 7,9,11,17,21,30. For the Ni+Arn clusters a pronounced peak at N = 5 is observed followed by a relatively stable one at N = 7. Similar stability pattern is observed for Pt+Arn (Ref. 49), V+Arn (Ref. 50), and Nb+Arn (Ref. 51). Finally, for Ti+Arn clusters a very pronounced peak at N = 7 dominates the spectrum. This behaviour is also observed for Co+Arn (Refs 16, 50) and Rh+Arn (Ref. 51) clusters. The electronic configuration (dk) of the transition metal atoms results in a non-spherical character in the interaction between transition metal ions and noble gas atoms. Therefore the situation is in this case substantially different from the ions with spherical orbitals treated in the previous paragraphs. The structural properties of this type of cluster cannot be modeled by using hard sphere models or calculations based on pair additive potentials. Asher et al.,52 using a many-body potential energy surface minimized with a simulated annealing procedure, have shown that the calculation depends very critically on which terms of the potential multipole expansions are used. Despite this, a simple approach, which gives some insight into the structural properties of clusters of this kind, can be adapted from the ligand field theory53 (LFT). The transition atom is an open-shell element and by building a cluster the noble gas atoms are forced to occupy certain sites depending on the occupation of the d-orbitals. This approach has also been used by Bondybey and co-workers51 to explain the saturation observed in the coordination of Rh+Arn and Nb+Arn complexes. In Fig. 13 we give a schematic explanation of this model by considering the splitting and the morphology of the dk orbitals under the influence of a weak octahedral or square planar ligand field. Displayed are the cases of coinage metals Cu+, Ag+ and Au+ (k = 10), of Ni+ and Pt+ (k = 9), of Co+ and Rh+ (k = 8), of Nb+ and V+ (k = 4) and of Ti+ for the electronic configuration 3d3 (k = 3). In the case of d10 metal ions the d-orbitals are fully occupied and therefore all five d-components ( d x 2 − y 2 , d z 2 , d xy , d xz , d yz ) are equally populated in a weak ligand field. The ion exposes a spherical electron density to the noble gas ligands (see bottom of Fig. 13). For d9 and also for d4 metal ions the d x 2 − y 2 orbital is half filled (for d9) or totally empty (for d4) and therefore the metal ion will expose to the Ar ligands four sites of lower electron density in the x–y plane, allowing the Ar atoms to experience lower repulsion and therefore approach closer to the central ion. This results in a strong interaction for only four Ar atoms, and thus, a special stable square planar M+Ar4 complex. For the case of d8 and d3 metal ions both orbitals, d x 2 − y 2 and d z 2 are either half filed (for d8) or totally empty
Figure 13: The splitting and the morphology (electron density) of the dk (k = 3,4,8,9,10) orbitals in a weak octahedral or square planar field for some transition metal ions according to ligand field theory. The arrows represent electrons while the circles represent holes. The empty or half filled orbitals of the metal (M) result in sites with reduced electron density and therefore attract preferentially ligands (X) to these positions. For transition metals with k = 4,9 a square planar MX4 complex is expected to be stable, whereas for metals with k = 3,8 a stable octahedral MX6 complex is expected.
Properties of Metal Ion–Doped Noble Gas Clusters 249
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(for d3). Thus, the metal ion now exposes six sites of reduced electron density – four in the x–y plane and two along the z-axis. This morphology allows six noble gas ligands to approach closer to the metal ion resulting in a perfect octahedral M+Ar6 complex. For checking the validity of this simple model we have to compare the expected stability with the observed stability of the cluster systems where experimental results are available. Thus, for the coinage metal ion Ag+ (3d10), the spherical character of the occupied d-orbital results in a rich stability pattern similar to those observed in spherical metal ions of Fig. 3 and in particular for the cases where the radius ratio R* is 0.414< R* ≤ 0.645. Taking the ionic radius of Ag+ from Ref. 54 as 1.3 Å we obtain for the system Ag+Ar R* ≈ 0.68, which is close to the CSA packing limit. The metal ions Ni+ (3d9), Pt+(5d9), V+(3d4), and Nb+(4d4) bind preferentially with four argon atoms to give a very stable M+Ar4 complex. One can apply the LF-model to predict the structure of some small M+Arn complexes. Thus, M+Ar3 is expected to be a Tshaped structure and M+Ar5 is expected to have the geometry of a tetragonal pyramid. The stability and the structure of Ni+Ar4 and also the structures of the other small clusters have been recently verified with calculations based on the density functional theory (DFT) for the case of Ni+Arn (Ref. 49). Furthermore, the DFT results for Ni+Arn have shown that at n = 6 a stable cluster also exists as a result of bonding saturation. The stable Ni+Ar6 cluster has the geometry of a distorted (elongated) octahedron, and this is a Jahn-Teller distortion.53 According to the LF-model the strong peak observed at MAr6 for M = Co+ (3d8), Rh+(4d8) corresponds to a perfect octahedral cluster due to the half filled d x 2 − y 2 and d z 2 orbitals. Interesting is the case of Ti+Arn clusters, because it fits into this category if one assumes that the electronic configuration of Ti+ in an octahedral Ti+Ar6 cluster is 3d3. The ground state of the free Ti+ is 3d24s1 but there is a low-lying excited state 3d3 separated by only 0.11 eV from the ground state.55 Low-lying electronic states are characteristic for transition metal ions, which have a dk–1s1 type ground electronic state. These states are nearly degenerate. Furthermore, in the complexes of these ions with atomic or molecular ligands, mixing of these states is expected and therefore the application of simple LFT-arguments in predicting the structure and the stability of these clusters is not straightforward. As Partridge et al.56,57 have shown in the case of Ti+-noble gas diatomic complexes, the mixing of two lower electronic states becomes more pronounced as one goes from He to Ar. In Ref. 58 we use DFT to calculate the binding energy of small Ti+Arn clusters and we find that the electronic configuration 3d3 for
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the Ti+ in the Ti+Ar6 cluster results in a lower total energy than the 3d24s1 configuration. Therefore, we think that at least for n = 6 the Ti+ has a 3d3 electronic configuration and thus the LF-model of Fig. 13 explains quite well the observed high stability of an octahedral Ti+Ar6 complex. IV.
PHOTOFRAGMENTATION SPECTROSCOPY: OPTICAL PROPERTIES OF CLUSTERS A.
Photofragmentation and Photoabsorption
The photofragmentation spectroscopy of mass selected ions is a very powerful method to obtain detailed information about the potential energy surfaces, the dynamics and the optical properties of a complex. The laser wavelength dependence of the fragment signal in a photofragmentation process results in the photofragmentation spectrum of a particular complex. The so-obtained photofragmentation spectra can be unambiguously attributed to the selected ionic species and, in the case of cluster ions, the examination of these spectra as a function of the cluster size provides a unique way to investigate possible solvation effects in clusters. In general the absorption of light by a polyatomic complex results in a deposition of energy into the system. Assuming that each absorbed photon leads to at least one evaporation event in the time window of the measurement (~10 μsec) then, the photofragmentation cross section is equal to or constitutes a lower limit for the photoabsorption cross section. Thus, the photofragmentation data are evaluated according to the Beer’s law: D = 1– A + A⋅exp[–(σ1+σ2+...)Φ – α]
(6)
with D = IP / (IP + IF1 + IF2 +...). IP , IF1 , IF2, ..., are the integrated peak intensities of the parent ion and the several fragments respectively, σ1, σ2, ..., are the partial photofragmentation cross sections, α represents the decay due to collisions of the mass selected parent with the reflectron grids and/or the background gas, Φ is the laser fluence (photons/cm2). Finally, A is a geometrical factor that represents the overlap between the laser beam and the ion beam. For each dissociation-laser frequency, the mass spectrum has been recorded with the laser on and off to account for the fragmentation that is not due to the laser interaction. Assuming perfect overlapping (A = 1) the total photofragmentation cross section is:
σtot = σ1+σ2+ ... = – ( lnDon – lnDoff )/Φ .
(7)
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In the case of diatomic complexes where only one fragment channel is observed Equation 7 is reduced to: ( I F ) on – ( IF ) off 1 - ⋅ ---- ⋅ 1 σ = --------------------------------( I p )off Φ
B.
(8)
The Sr+Ar Complex
The diatomic complexes constitute the most elementary cluster that can be studied by photofragmentation spectroscopy. The basic understanding of binding in such small complexes is of major importance, since many features of the clusters and the condensed phase evolve from the properties of the diatomic systems. For metal ion–noble gas diatomic complexes many photofragmentation experimental results are published.30,32,33 In particular, the electronic states of alkaline earth ions–noble gas van der Waals complexes have attracted considerable interest for both experimental and theoretical studies in the last years. The molecular electronic states under investigation for these complexes are those correlating with the strong n2P ←n2S (n = 2–6) dipole transitions. In Fig. 14 we show the photofragmentation spectrum of Sr+Ar (Ref. 37) recorded in the laser frequency region 22320 to 23903 cm–1. Figure 14: The photofragmentation spectrum of the Sr+Ar complex.37 The horizontal axis corresponds to the dissociation laser frequency, while the vertical axis represents the intensity ratio of the ionic fragments (Sr+) to the parent (Sr+Ar), normalized by the dye intensity (see Equation 8). Two exited state vibrational progressions are indicated. The small intermediate peaks correspond to hot band excitation.
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The vertical axis corresponds to the intensity of the observed Sr+ fragment. The spectrum consists of two vibrational progressions. The Sr+ ion has a 5S1/2 ground state configuration and two 5P1/2 and 5P3/2 excited states due to spin-orbit splitting. The transition energies from the ground state are 23715.2 cm–1 and 24516.6 cm–1 (Ref. 55), respectively. Furthermore, two 4D5/2,3/2 states lie in-between at about 14500 cm–1. The potential curves of the molecular system are illustrated schematically in Fig. 15. The ground state for the Sr+Ar molecule is denoted as X2Σ1/2 and the two spin-orbit excited states as A2Π1/2 and A2Π3/2. These states correlate to the atomic (Sr+) states 52S1/2, 52P1/2 and 52P3/2 respectively. Furthermore, an almost repulsive B2Σ1/2 state also correlates to the atomic 52P3/2 level. Figure 15: Schematic diagram of the potential energy curves of the Sr+Ar complex.37 On the right side of the figure the asymptotic Sr+ atomic levels are indicated. The arrow displays the laser frequency which causes transitions from the ground (X2Σ1/2) to the excited (A2Π1/2,3/2) states.
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The two vibrational progressions observed in the photofragmentation spectrum of Fig. 14 are attributed to dipole transitions from the X2Σ1/2(v´´= 0) ground state to the excited A2Π3/2(v´) and A2Π3/2(v´) states. The small peaks are assigned to hot bands, i.e. transitions originating from the first vibrationaly excited level (v´´=1) of the ground state. The absolute vibrational numbering is obtained by performing isotope-resolved measurements.37 These allow, with the use of BirgeSponer plots,59 the determination of the vibrational frequencies ωe and the anharmonicities ωeχe. The dissociation energies D0 of the involved molecular states have been obtained by two different procedures, namely the Morse-potential approach59 and the Le RoyBernstein60 analysis. Although the present experiments (without the rotational structure resolved) do not yield directly any information concerning the absolute binding distance Re, the differences ΔRe between the ground and the excited states have been determined from Franck-Condon calculations using Morse potentials. Details of the application of these methods in the evaluation of the spectra can be found in Refs. 32,37,61. The potential parameters so obtained are given in Table 1. Xantheas et al.62 using ab initio methods have calculated the potential curves and the spectroscopic constants of the Sr+Ar complex. The theoretical results for the ground state and for the excited Π state are in good agreement with the experimental ones. Since the observed vibrational progressions correspond to bound-bound transitions, three possible mechanisms can be considered to be the origin of the photofragmentation. Dissociation from an excited A2Π state can proceed via curve crossing to the lower lying molecular Σ,Π, and Δ states (correlating to the atomic 4D levels), or radiative transitions to lower states, or finally Table 1: Spectroscopic constants determined from the vibrational analysis37 of the photofragmentation spectrum (Fig. 14) of the Sr+Ar complex. Energies are in cm–1 and bond lengths are in Å. X2Σ1/2
A2Π1/2 22214 ±5
22746 ±5
49.5
120.8 ± 0.5
122 ± 0.5
0.75
1.67 ± 0.04
1.6 ± 0.04
803 ±244
2303 ±232
2575 ±256
ν00 ωe ωeχe D0
A2Π3/2
2439 ±173
(a)
Δ Re
0.5 ± 0.05
(a) Represents the average dissociation energy over both Π states. 2
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via the absorption of another photon and subsequent dissociation via the repulsive B2Σ 1/2 state. The case of curve crossing seems unlikely for two reasons: (i) photofragmentation has been observed previously in similar experiments for Mg+Ar (Ref. 63) where no intermediate levels between the X2Σ and A2Π states are present, and (ii)in both progressions we observe a smooth development of the line intensities, whereas for the case of curve crossing an anomalous intensity distribution would be expected.59 Thus, there remain two possibilities for photofragmentation, namely: the radiative bound-free decay, and the two (or more) photon absorption. In every case, the fragmentation pattern that is observed here corresponds to the A2Π ← X2Σ absorption spectrum of Sr+Ar since the first laser photon probes the excited A2Π states. The photofragmentation cross section for this complex is estimated (see Equation 8) to be ~10–17 cm2. C.
The Sr+Ar2 Complex
Although a large number of studies of diatomic metal ion noble gas complexes exist, very little has been published for larger species, even for the triatomic ones.34 In Fig. 16 we present the photofragmentation spectrum of the Sr+Ar2 complex35 in the laser frequency range of 21000–27000 cm–1. In this case we observe two different ionic product channels, Sr+ and Sr+Ar. The partial cross sections of these fragments are plotted in Fig. 16a, while in Fig. 16b the total absorption signal (the sum of the two partial signals) is shown (open circles). The spectrum is characterized by two broad absorption bands at 22000 and 24000 cm–1 respectively, while a third band starts at 26000 cm–1 and extents beyond 27000 cm–1. The regions of the absorption maxima have also been recorded with a step of ~1 cm–1 but no vibrational structure could be observed. Interesting in this spectrum is the selective production of the Sr+Ar fragment that appears only in the energy region around 24000 cm–1. In order to explain the spectral maxima that occur in the spectrum of Fig. 16b and to obtain insight into the dynamics of the photofragmentation (Fig. 16a), theoretical studies for this complex are necessary. Obviously, the Sr+Ar2 complex is a large system for any accurate ab initio treatment. Therefore, we choose to use approximate theoretical methods in order to obtain potential energy surfaces for the ground and excited electronic states.
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Figure 16: The photofragmentation spectrum of the Sr+Ar2 complex.35 (a) The partial cross sections of the observed two different ionic fragments Sr+ and Sr+Ar are shown. (b) The experimental total fragmentation cross section (open circles) is compared with the calculated spectrum (solid line).
For metal atoms in an excited P-state and interacting with noble gas atoms, Baylis64 has introduced a simple model for calculating the potential energy of the system. This model treats the metal atom as a one-electron system, assuming an effective potential for the core electrons, while the interactions of the single electron with the noble gas atoms are described by first-order perturbation theory. Balling and Wright65 have first applied the model for describing the interactions of alkali atoms in noble gas matrices. A similar approach has been used by Roncero et al.66 for the calculations of the excitation spectra of the HgArn clusters. Further application of the Baylis model was performed by Boatz and Fajardo67 in studies of the optical absorption of sodium atoms in Ar clusters. The same procedure was applied by Lawrence and Apkarian68 to study the
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interaction of a hole in the p orbitals of iodine in crystalline Kr and Xe, and by Alexander et al.69 for studies of the structure and the excitation spectrum of BAr2. We have recently used this model to explore the potential energy surfaces of Sr+Arn (n = 2–8) clusters.36 Details of the calculation were presented in our previous publications35,36 and can also be found in Refs. 65,67,68,69. The main result of the model is that the potential energy surfaces of metal doped noble gas clusters of the type MXn are characterized by the three eigenvalues obtained by solving a 3 × 3 secular determinant and can be expressed in terms of M–X diatomic pair interactions. In the particular case of a triatomic complex MX2 the energies of the three excited states can be written as functions of both M–X bond lengths R1 and R2 and the angle γ between them: 1 V 1 ( R 1 ,R 2 ) = [ E 0 ( R1 ) + E 0 ( R 2 ) ] – --- [ E2 ( R1 ) + E 2 ( R2 ) ] 5 1 V 2 ,3 ( R1 ,R 2 ,γ ) = [ E0 ( R1 ) + E 0 ( R2 ) ] + ------ [ E 2 ( R 1 ) + E2 ( R 2 ) ] 10 1⁄2 3 2 2 ± ------- [ 3 ( E 2 ( R1 ) + E 2 ( R 2 ) ) – 2E 2 ( R 1 )E2 ( R2 ) ( 1 + 2A ) ] 10
(9a) (9b,c)
where 1 E 0 ( R i ) = --- [ V Σ ( R ι ) + V Π ( Rι ) ] , 3 5 E 2 ( R i ) = --- [ V Σ ( R ι ) – V Π ( R ι ) ] , 3
i = 1,2
(10)
and A = 1 – 3 cos 2 γ . The terms VΣ(R) and VΠ(R) in Equation 10 denotes the adiabatic potential curves of the excited B2Σ and A2Π states of the diatomic complex. The complete potential energy surfaces are obtained from Equation 9 by adding the noble gas X–X ground electronic state potential VX–X (r), where r is the X–X distance. The potential energy surface for the ground state of MX2 has the pairwise form: V g ( R 1 ,R 2 ,r ) = V M – X ( R 1 ) + V M – X ( R 2 ) + V X – X ( r )
(11)
where VM–X denotes the metal–noble gas ground state potential. The absorption spectrum of the Sr+Ar2 system is calculated using the classical Franck-Condon method36 and the potential parameters of the diatomic Sr+Ar complex discussed in the previous paragraph. For the excited B2Σ state, where experimental results are not available, we used the ab initio parameters of Ref. 35. Spin-orbit splitting is neglected. We assume that the transition electric dipole moment
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is independent of the cluster coordinates and that the density of states in the excited electronic states is constant. Under conditions of constant temperature we run trajectories on the ground electronic state of the system by integrating the Nosé-Hoover equations of motion.35 At several time steps the energy difference between the ground state and the three excited states is computed. The distributions of these vertical energy differences are then plotted as functions of the total energy. The solid line in Fig. 16b represents such a calculation for a temperature of 30K. The agreement with the experimental spectrum (open circles) is quite good. The ground state geometry of Sr+Ar2 has a C2v symmetry with RSr+–Ar = 3.63 Å and γ=62º. In Fig. 17 we plot the potential energy of the system calculated from Equations 9 and 10 in this symmetry as a function of the distance R of Sr+ to the middle of Ar–Ar bond Figure 17: Potential energy curves calculated for the Sr+–Ar2 complex in a C2v symmetry.35 R is the distance of Sr+ from the middle of the Ar–Ar bond r fixed at 3.76 Å. The total absorption spectrum of Fig. 16b is also shown in the energy axis. The arrows represent laser excitations from the ground electronic-vibrational state.
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(r = 3.76 Å). The three excited states are labeled as 2B2, 2B1, and 2A1 and correspond to the three possible orientations of the Sr+ p-orbital relative to Ar–Ar bond. The experimental excitation spectrum of Fig. 16b is also shown in a vertical position. The correspondence of the three observed peaks in the total absorption is obvious, so that one can conclude that in this kind of complex the electronic excitation is due solely to the excitation of the metal ion chromophore. This relatively simple picture explains the observed absorption frequencies and also the mechanism of the photofragmentation via the 2B2 and 2 A1 excited states (see the arrows in Fig. 17). The repulsive state 2A1 leads to direct fragmentation while the bound state 2B2, which has a shorter equilibrium distance than the ground state, leads partially to fragmentation via decay to the repulsive part of the ground state. The bound 2B1 state has a similar bond length as the ground state and therefore the representation of Fig. 17 is unable to explain the fragmentation via this excited state. Therefore, it is necessary to examine this case and additionally the origin of the different appearance of the Sr+ and Sr+Ar photofragments of Fig. 16a. To this end we show in Fig. 18 contours of the PES for the Sr+Ar2 obtained from Equations 9 and 10 by fixing the angle γ at 62º. The vertical photoexcitation procedure is schematically represented with the gray arrows that start from the Franck-Condon region of the ground state Vg and end at the three different excited states V1, V2 and V3. The Vg → V1 transition is a bound–bound one but, as mentioned above the different equilibrium distances of the ground and the excited state lead to fragmentation via de-excitation to the repulsive part of the ground PES. As the energy available is higher now than the binding energy of the ground state, fragmentation to Sr+ + Ar + Ar occurs (both coordinates R1 and R2 increase, see Fig. 18). The Vg→V3 excitation is a bound-free transition and leads directly to the fragmentation channel Sr+ + Ar + Ar. The transition Vg→V2 leads to a saddle point in the V2 PES and thus the wave packet can be localized in two equivalent exit channels: R1≈3.5 Å, R2 → ∞ or R2≈3.5 Å, R1 → ∞, both channels yield Sr+Ar + Ar. The diatomic fragment Sr+Ar is of course in the excited state and decays to the ground state 2Σ yielding Sr+ and Ar, or ground state Sr+Ar. These considerations explain quite well, at least qualitatively, the appearance of the two products in Fig. 16a. D. Sr+Arn Clusters In Fig. 19 we show the photofragmentation spectra of Sr+Arn (n = 2–8) clusters36 in the laser frequency range 21000–27000 cm–1. The
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Figure 18: Potential energy surfaces (contour plots) for the Sr+–Ar2 complex35 obtained from Equations 9 and 10 with γ = 62º. The energy is measured in wavenumbers with respect to the free atomic species in the same state. The arrows indicate the vertical laser transitions from the ground state Vg to the three excited states V1, V2 and V3.
open circles are the experimental results and the solid lines are the calculations for T = 30K and using the model described in the previous paragraph (including spin-orbit splitting). The experimental intensities correspond to the sum over all appearing fragments (total photofragmentation) and are normalized to unity. We have also measured Sr+Arn spectra for n = 9–15 in the energy range 22000–25000 cm–1. The spectra are very similar to that of Sr+Ar8. The general feature of the spectra in the measured energy range is that two absorption bands are observed, whereas a third one starts to appear at higher energies. The first peak for Sr+Ar3, Sr+Ar4 and Sr+Ar5 is placed at ~22500 cm–1 and is blue-shifted relative to the first one of Sr+Ar2. Similarly, the first peak for Sr +Ar6–8 is placed at ~23600 cm –1 and is blue-shifted about 1500 cm –1 from that of Sr+Ar2. The second peak for n = 4–8 is placed between 25000 and 25500 cm –1 and is
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Figure 19: The total photofragmentation spectra of the Sr+Arn, n = 2–8, clusters.35 The open circles correspond to experimental measurements while the solid lines represent the calculated absorption spectra at a simulation temperature of 30K, common for all clusters. In the right part of the figure the minimum energy structure and the symmetry group of each cluster are displayed.
red-shifted in comparison to the Sr+Ar2 second peak (at ~24000 cm–1). An exception is for n = 3 where the second peak shows a red shift of 400 cm–1. Another feature observed in the spectra is that in the cases of Sr+Ar3 and Sr+Ar6 the bands come close to one another and are also narrower than the bands of the other complexes. The calculated spectra36 show (as in the case of Sr+Ar2
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in Fig. 16b) the three characteristic bands that correspond to the three eigenstates originated from the p-orbital of Sr+, which also follow all the trends described above. It should be mentioned that the calculations are performed at a common temperature (30K) for all clusters. Using individual simulation temperatures for each particular cluster size the calculation fits much better to the individual systems, but as our aim is to explain the general trends of the spectra we limit our consideration to these general behaviors. Since we have to consider vertical transitions in the absorption spectra the geometry of the ground state of a cluster is projected to the excited state in the framework of the Born-Openheimer approximation. In Fig. 19 (right column) we show the minimum energy structures of the ground state Sr+Arn clusters for n = 2–8. Inspecting these geometries and the corresponding symmetry group we realize that Sr+Ar3 and Sr+Ar6 are special cases because they have C3v and C5v symmetries respectively and these point groups have double energy degeneracy70 (V1 = V2). This degeneracy is removed when the spin-orbit coupling is included in the calculations. Therefore the first and the second band in the absorption spectra are closer than in the other complexes. A detailed discussion of these effects and of the calculations can be found in Ref. 36. V. SUMMARY The structural and optical properties of metal-ion-doped noble gas clusters MXn have been studied using TOF mass spectroscopy and photofragmentation spectroscopy respectively. We have systematically changed the composition of the clusters, and in terms of the observed magic numbers in the mass spectra, and with the help of a hard sphere-packing model and molecular dynamics simulations, insight is given into the stability and geometrical structures of these complexes. For systems with spherical orbitals the observed structural transitions in the clusters, as the radius ratio of metal ion to noble gas atom is changed, is consistent with the picture of a central metal ion surrounded by n noble gas atoms. The same picture seems to be valid for metals with non-spherical orbitals (transition metals) but here the cluster geometry is determined from the morphology of the d-orbitals. The optical activity of mass selected Sr+Arn, n = 1–9 clusters in the frequency region 21000–27000 cm–1 is investigated with photofragmentation spectroscopy. The potential parameters obtained from the diatomic Sr+Ar complex have been utilized in a theoretical
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approach in order to understand and to reproduce the spectra and the fragmentation dynamics of the larger clusters. The observed spectral shifts as a function of the cluster size can be explained in terms of vertical transitions from the electronic ground state geometries to the excited PES. ACKNOWLEDGMENTS This work was supported by the Ultraviolet Laser Facility operating at FORTH. I thank my students Christian Lüder, Dimitris Prekas and Antonis Sfounis for their substantial contribution to the experiments presented here. I would also like to thank KarlHeinz Meiwes-Broer for stimulating discussions and Stavros Farantos, Sotiris Xantheas, George Fanourgakis and George Froudakis for our fruitful collaboration and for the many helpful discussions. REFERENCES (1)
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Jena, P., Khanna, S.N., and Rao, B.K., (eds) (1992) Physics and Chemistry of Finite Systems: From Clusters to Crystals, NATO ASI Ser. Vol. I, II, Kluwer Academic Publishers. Haberland, H. (ed.) (1995) Clusters of Atoms and Molecules, Vol. I, II, Springer Verlag, Berlin Heidelberg. Duncan, M.A. (ed.) (1993) Advances in Metal and Semiconductor Clusters, Vol. 1, Spectroscopy and Dynamics, JAI Press, Greenwich. Duncan, M.A. (ed.) (1994) Advances in Metal and Semiconductor Clusters, Vol. 2, Cluster Reactions, JAI Press, Greenwich. Duncan, M.A. (ed.) (1995) Advances in Metal and Semiconductor Clusters, Vol. 3, Spectroscopy and Structure, JAI Press, Greenwich. Wiley, W.C. and McLaren, I.H. (1955) Rev. Scien. Instr., 26: p. 1150. Mackay, A.L. (1962) Acta Crystallogr., 15: p. 916. Hoare, M.R. and Pal, P. (1971) Adv. Phys., 20: p. 161. Echt, O., Sattler, K., and Recknagel, E. (1981) Phys. Rev. Lett., 47: p. 1121. Ding, A. and Hesslich, J. (1983) Chem. Phys. Lett., 94: p. 54. Harris, I.A., Kidwell, R.S., and Northby, J.A. (1984) Phys. Rev. Lett., 53: p. 2390. Northby, J.A. (1987) J. Chem. Phys., 87: p. 6166. Doye, J.P.K., Wales, D.J., and Berry, R.S. (1995) J. Chem. Phys., 103: p. 4234. Stace, A.J. (1985) Chem. Phys. Lett., 113: p. 355. E. Holub-Krappe, G. Ganteför, G. Bröker, and A. Ding (1988) Z. Phys. D., 10: p. 319. Lessen, D.E. and Brucat, P.J. (1988) Chem. Phys. Lett., 149: p. 10. R.L. Whetten, K.E. Schriver, J.L. Persson, and M.Y. Hahn (1990) J. Chem. Soc. Faraday Trans., 86: p. 2375. G. Ganteför, H.R. Siekmann, H.O. Lutz, and K.H. Meiwes-Broer (1990) Chem. Phys. Lett., 165: p. 293.
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(19) S. Bililign, C.S. Feigerle, J.C. Miller, and M. Velegrakis (1998) J. Chem. Phys., 108: p. 6312. (20) G. Vaidyanathan, M.T. Coolbaugh, W.R. Peifer, and J.F. Garvey (1991) J. Phys. Chem., 95: p. 4193. (21) S.R. Desai, C.S. Feigerle, and J.C. Miller (1992) J. Chem. Phys., 97: p. 1793. (22) J.F. Winkel, C.A. Woodward, A.B. Jones, and A.J. Stace (1995) J. Chem. Phys., 103: p. 5177. (23) Levinger, N.E., Ray, D., Alexander, M.L., and Lineberger, W.C. (1988) J. Chem. Phys., 89: p. 5654. (24) Cornett, D.S., Peschke, M., Laihing, K., Cheng, P.Y., Willey, K.F., and Duncan, M.A. (1992) Rev. Scient. Instrum., 63: p. 2177. (25) Donnelly, S.G., Schmuttenmaer, C.A., Qian, J., and Farrar, J.M. (1993) J. Chem. Soc. Faraday Trans., 89: p. 1457. (26) Duncan, M.A. (1994) Inter. Rev. Phys. Chem., 13: p. 231, and references therein. (27) Chen, Z.Y., Cogley, C.D., Hendricks, J.H., May, B.D., and Castleman, Jr., A.W. (1988) J. Chem. Phys., 88: p. 6200. (28) Misaizu, F., Sanekata, M., Tsukamoto, K., Fuke, K., and Iwata, S. (1992) J. Phys. Chem., 96: p. 8259. (29) Donnelly, S.G. and Farrar, J.M. (1993) J. Chem. Phys., 98: p. 5450. (30) Lessen, D.E., Asher, R.L., and Brucat, P.J. (1993) In: Advances in Metal and Semiconductor Clusters, Vol. 1, (M.A. Duncan, ed.), JAI Press, Greenwich. (31) Kleiber, P.D. and Chen, J. (1998) Intern. Rev. Phys. Chem., 17: p. 1. (32) Prekas, D., Feng, B.-H. and Velegrakis, M. (1998) J. Chem. Phys., 108: p. 2712. (33) Duncan, M.A. (1997) Annu. Rev. Phys. Chem., 48: p. 69. (34) Yeh, C.S., Pilgrim, J. S., Willey, K.F., Robbins, D.L., Duncan, M.A., and (1994) Intern. Rev. Phys. Chem., 13: p. 231. (35) Fanourgakis, G.S., Farantos, S.C., Lüder, Ch., Velegrakis, M., and Xantheas, S.S. (1999) PCCP, 1: p. 977. (36) Fanourgakis, G.S., Farantos, S.C., Lüder, Ch., Velegrakis, M., and Xantheas, S.S. (1998) J. Chem. Phys., 109: p. 108. (37) Lüder, Ch. and Velegrakis, M. (1996) J. Chem. Phys., 105: p. 2167. (38) Lüder, Ch., Georgiou, E., and Velegrakis, M. (1996) Int. J. Mass Spec. Ion Proc., 153: p. 129. (39) Lüder, Ch., Prekas, D., and Velegrakis, M. (1997) Laser Chem., 17: p. 109. (40) Velegrakis M. and Lüder, Ch. (1994) Chem. Phys. Lett., 223: p. 139. (41) Prekas, D., Lüder, Ch., and Velegrakis, M. (1998) J. Chem. Phys., 108: p. 4450. (42) Farges, J., deFeraudy, M.F., Raoult, B., and Torchet, G. (1983) J. Chem. Phys., 78: p. 5067. (43) Farges, J., deFeraudy, M.F., Raoult, B., and Torchet, G. (1985) Surf. Sci., 156: p. 370. (44) Martin, T.P., Bergmann, T., Göhlich, H., and Lange, T. (1991) J. Phys. Chem., 95: p. 6421. (45) Press, W.H., Flannery, B.P., Teukolsky, S.A., and Vetterling, W.T. (1992) Numerical Recipes, 2nd edition, Cambridge Univ. Press, New York. (46) Papadakis, J., Fanourgakis, G.S., Farantos, S.C., and Founargiotakis, M. (1997) J. Comp. Chem., 18: p. 1011. (47) Fanourgakis, G.S. and Farantos, S.C. (1996) J. Phys. Chem., 100: p. 3900.
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(48) Chaudhury, P. and Bhattacharyya, S.P. (1999) Chem. Phys., 241: p. 313. (49) Velegrakis, M., Froudakis, G.E., and Farantos, S.C. (1998) J. Chem. Phys., 109: p. 4687. (50) Lessen, D.E. and Brucat, P.J. (1989) Chem. Phys. Lett., 91: p. 4522. (51) Beyer, M., Berg, C., Albert, G., Achatz, U., and Bondybey, V.E. (1997) Chem. Phys. Lett., 280: p. 459. (52) Asher, R.L, Micha, D.A., and Brucat, P.J. (1992) J. Chem. Phys., 96: p. 7683. (53) Huheey, J.E. (1983) Inorganic Chemistry, 3rd edn. Harper International SI Edition, Cambridge. (54) Butterfield, C. and Carlson, E.H. (1972) J. Chem. Phys., 56: p. 4907. (55) Radzig, A.A. and Smirnov, B.M. (1985) Reference Data on Atoms, Molecules and Ions Springer Verlag, Berlin, Heidelberg. (56) Partridge, H., Bauschlicher Jr., C.W. and Langhoff, S.R. (1992) J. Phys. Chem., 96: p. 5350. (57) Partridge, H. and Bauschlicher Jr., C.W. (1994) J. Phys. Chem., 98: p. 2301. (58) Velegrakis, M., Froudakis, G.E. and Farantos, S.C. (1999) Chem. Phys. Lett., 302: p. 595. (59) Herzberg, G. (1950), “Spectra of Diatomic Molecules”, Van Nostrand Reinhold Company Inc. (60) LeRoy, R.J. and Bernstein, R.B. (1970) J. Chem. Phys., 52: p. 3869. (61) Lüder, Ch., Prekas, D., Vourliotaki, A. and Velegrakis, M. (1997) Chem. Phys. Lett., 267: p. 149. (62) Xantheas, S.S., Fanourgakis, G.S., Farantos, S.C., and Velegrakis, M. (1998) J. Chem. Phys., 108: p. 46. (63) Pilgrim, J.S., Yeh, C.S., Berry, K.R., and Duncan, M.A. (1994) J. Chem. Phys., 100: p. 7945. (64) Baylis, W.E. (1977) J. Phys. B, 10: p. L477. (65) Balling, L.C. and Wright, J.J. (1983) J. Chem. Phys., 79: p. 2941. (66) Roncero, O., Beswick, J.A., Halbestadt, N., and Soep, B. (1990) In: Dynamics of Polyatomic van der Waals Complexes, (Halberstadt, N. and Janda, K., eds), NATO ASI ser B, Plenum: New York, Vol. 227, p. 471. (67) Boatz, J.A. and Fajardo, M.E. (1994) J. Chem. Phys., 101: p. 3472. (68) Lawrence, W.G. and Apkarian, V.A. (1994) J. Chem. Phys., 101: p. 1820. (69) Alexander, M.H., Walton, A.R., Yang, M., Yang, X., Hwang, E., and Dagdigian, P.J. (1997) J. Chem. Phys., 106: p. 6320. (70) Cotton, F.A. (1967) Chemical Applications of Group Theory, 6th edition, Interscience Publishers, NY, London, Sydney.
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8 PHOTODISSOCIATION SPECTROSCOPY AS A PROBE OF MOLECULAR DYNAMICS: METAL ION–ETHYLENE INTERACTIONS Paul D. Kleiber
I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 II. Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 III. Photodissociation Spectroscopy of Light Metal Ion–Ethylene Complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 A. Electronic Structure Calculations . . . . . . . . . . . . . . . . . . . 272 B. Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278 IV. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 A. Nonadiabatic 1B2(A´)–1A1(A´) Dissociation Dynamics . . 283 B. Vibrational Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286 C. Direct Charge-Transfer Dissociation . . . . . . . . . . . . . . . . . 291 V. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293 I.
INTRODUCTION
Excited state interactions play a central role in many important physical and chemical processes. Excited state dynamics are generally complicated and often involve multiple electronic potential energy surfaces. Nonadiabatic interactions can dominate the Advances in Metal and Semiconductor Clusters Volume 5, pages 267–294 © 2001 Elsevier Science B.V. All Rights Reserved. ISBN: 0-444-50726-4
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branching in these multichannel collisions. Nonreactive quenching through electronic-to-translational, -rotational, or -vibrational energy transfer competes with chemical reaction and it is not easy to predict a priori which process will dominate. Theoretical modeling can be difficult because of the multiplicity of surfaces and channels and the importance of nonadiabatic interactions. Detailed studies of the excited state dynamics in relatively simple chemical systems are crucial for developing both an intuitive understanding of the important physical and chemical processes, and for testing nonadiabatic theoretical dynamics models. One approach to the study of excited state interactions and dynamics involves the photodissociation of a weakly bound, molecular precursor complex, that serves to mimic a bimolecular “halfcollision”.1,2 The structure of the stable precursor can often be determined through a combination of bound state spectroscopy and electronic structure calculation. Following absorption, the subsequent half-collision begins from a well-defined geometry and electronic symmetry (orbital alignment), and with a restricted range of collision energies and relative angular momenta. Spectral measurement of the photodissociative product yield, translational energy partitioning, and photofragment vector anisotropy give information about the bonding and structure of the complex, intermediate state lifetime, the dominant reactive and nonreactive quenching pathways, and the dynamical effects that determine competitive branching into the product channels.2 Such experiments can give unique and valuable insight into the molecular orbital interactions, stereochemical effects, nuclear motion dynamics, and electronic nonadiabatic interactions that couple adiabatic Born-Oppenheimer potential energy surfaces. We have used photodissociation spectroscopy to probe the interactions of light metal ions with H2, and small alkane and alkene hydrocarbons.2–8 Metal ion–hydrocarbon interactions have been studied in the gas phase for many years.9–14 It is often found that subtle changes in metal ion electronic structure can dramatically alter the chemical branching.2,9–14 Molecular orbital interactions play a prominent role in determining the chemical dynamics, and the photodissociation “half-collision” method is an especially effective tool for probing these interactions since it allows for state selective preparation in a complex with a well defined geometry.1,2 A review of our work on the spectroscopy of weakly bound alkaline earth metal ion complexes with H2 and CH4 has been recently published.2 Here we focus the discussion on more recent experimental and theoretical studies of light metal ion–ethylene interactions. The work explores the influence of metal ion valence electronic
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structure, molecular orbital interactions, and energetic and steric effects on the spectroscopy and bonding of metal ion–ethylene πbonded complexes, and on the dynamics of C–C bond activation processes. Our studies of metal ion –H2, –CH4, and –C2H4 dynamics suggest that there are important similarities in the orbital interactions and dynamical factors that control the activation of H–H and C–H σ–bonds, and C–C π–bonds, despite the greater complexity and reduced symmetry of the metal-hydrocarbon systems.2 While our work is primarily focused on excited state interactions and quenching dynamics, it is important to note that the photodissociation spectroscopy approach will often give quantitative information about metal–ligand bonding and ground state equilibrium structures.2–8,15–17 Studies of excited state processes can also give valuable insight into ground state chemistry. It is well established that many organometallic reactions involve at least two electronic surfaces of different multiplicity, coupled by spin-orbit interaction.11 Often chemical reactions on the adiabatic ground state surface pass over an activation barrier that arises from avoided crossing with an excited state surface. Nonadiabatic funneling from the excited state, through the avoided crossing, allows direct access to the critical barrier regions of the ground state surface. Finally, we note that most important organometallic photochemistry occurs in the bulk phase, or heterogeneously on the surface of bulk materials. Bulk phase spectroscopy is complicated by the presence of overlapping bands and nonadiabatic coupling of the electronic states. Photochemical processes in the bulk often involve several steps, some of which occur on ultrafast time scales. Generally, the chemical products can be identified only after escape from the bulk cage surrounding the chromophore, and cage effects can then have a dramatic influence on the observed quantum yields and photochemical branching ratios. This can make it hard to discern the primary intramolecular dynamics. Nonadiabatic interactions in the bulk can also have a profound effect on the chemical branching by modifying potential barriers or inducing couplings between electronic surfaces, thus opening new pathways for reaction or energy disposal. The study of isolated metal ion–hydrocarbon complexes in the gas phase allows a direct measure of the quantum yield for competing reactive and nonreactive quenching processes in the primary photochemical step and in the absence of bulk caging interactions.15–18 II.
METHODOLOGY
Experimental aspects of our photodissociation spectroscopy approach have been recently reviewed and only a brief outline of
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the method will be given here.2 The apparatus consists of a laser vaporization supersonic molecular beam cluster source, coupled to an angular reflectron time-of-flight mass spectrometer (RTOFMS).19 Mass-selected cluster ions are probed spectroscopically with a tunable UV/vis pulsed laser system in the region of the reflectron. The fragment ions are mass analyzed in the second leg of the RTOFMS and detected with a multichannel plate detector in a standard tandem time-of-flight arrangement. Signals are collected with a gated integrator, digital storage scope, or multichannel scalar, depending on the signal level. In favorable cases, the center of mass kinetic energy release in the dissociation is substantial and may allow a measure of the fragment ion translational energy distribution function by a direct inversion of the observed fragment flight time profile.2 This energy partitioning can give information about the lifetime of the excited intermediate and the dissociation mechanism. Metal ions are generated by laser ablation of a solid metal rod using the second harmonic of a pulsed Nd:YAG laser. The PGV is typically operated at a backing pressure of ~20–60 psi, seeded with a 1–10% mix of sample gas in a He carrier gas. In many cases we have found empirically that the addition of trace amounts of impurity gas (e.g. H2O or CO2) aid in the formation of weakly bound clusters. The additional impurities generally cause no mass confusion in this tandem time-of-flight arrangement. The sample rod is connected to a drive mechanism allowing for simultaneous rotation and translation of the rod to keep the metal sample surface fresh. Weakly bound clusters are formed in the supersonic expansion of the metal vapor plasma with a seeded carrier gas flow. The gas expansion passes through a conical skimmer into the differentially pumped extraction chamber. Cluster ions are pulse extracted at right angles and accelerated into the third differentially pumped chamber, the flight tube of the RTOFMS. A Nd:YAG pumped tunable pulsed dye laser, with nonlinear frequency mixing capabilities, is time delayed to excite the “target” parent ion in the region of the reflectron. Parent and daughter fragment ions are reaccelerated in the reflectron and focused to an off-axis 40mm microchannel plate detector (MCP). A digital oscilloscope is used to monitor the mass spectrum, and is interfaced to a laboratory personal computer for further data analysis. When signals are large, gated integrators are used to measure the integrated signal in the parent and in each daughter ion packet. For small signals, a multichannel scaler is used for single ion counting. The mass-resolved product action spectra are then determined by measuring the integrated daughter ion signal as a function of
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photolysis laser wavelength, normalized by the parent ion signal and probe laser intensity. Quantitative information about the energy partitioning, derived from an analysis of the photofragment flight time profile, can allow detailed insight into the dissociation dynamics.2 Essentially, the observed daughter ion flight-time profile is related to a one-dimensional projection of the speed distribution function, convoluted with an anisotropy function and an instrument profile. For measurements taken at the magic angle polarization, the photofragment anisotropy effect vanishes and the speed distribution function can be extracted by deconvoluting the instrument profile. By varying the laser polarization, the photofragment anisotropy parameter can also be determined. In-house ab initio electronic structure calculations based in the Gaussian ’94 or GAMESS platforms also support the experimental work.2–8 Ground state geometry optimization calculations are typically carried out at the HF and MP2 levels for a series of basis sets to test for convergence. Equilibrium bond energies may then be evaluated in a higher level calculation. Excited state calculations include: vertical excitation energies that can be used as an aid in assigning the experimental spectra; excited state optimization and vibrational frequency calculations that give information about excited state bonding and structure; and potential energy surface scans that give insight into the dissociation dynamics and important regions of nonadiabatic coupling. In most instances, CIS level excited state calculations are sufficient for a qualitative (or even semiquantitative) analysis of the data. However, in some cases configuration interaction or dynamical correlations are important, and more time consuming MP2/ MCSCF calculations are necessary to reliably interpret the molecular dynamics. III.
PHOTODISSOCIATION SPECTROSCOPY OF LIGHT METAL ION–ETHYLENE COMPLEXES
The importance of π-bonded metal ion-hydrocarbon complexes in inorganic and organometallic chemisty has been recognized since the pioneering work of Mulliken.20 We report here on our recent studies of the photodissociation spectroscopy of Mg+–, Al+– and Ca+–C2H4,6–8 that are among of the simplest examples of such π-bonded complexes. The discussion will focus on the low energy metal centered excited states of the complex. Variations in metal ion electronic valence and character across this group lead to distinctly different excited state interactions. Comparison of the spectroscopy gives valuable insight into the influence of metal ion valence structure, molecular orbital
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interactions, and energetic and steric effects on the bonding and chemical dynamics of these metal ion–alkene complexes. A.
Electronic Structure Calculations Ground State Interactions
We have carried out a series of ab initio electronic structure calculations of the M+(C2H4) complexes (M = Mg, Al, Ca) using the Gaussian ’94 and GAMESS platforms. The computational details are discussed in References 6–8. Here we have repeated some of the calculations to ensure consistency in comparing results for different complexes. The new results show only very slight differences with the previous work, indicating that the calculations are essentially converged. Mg+(3s) and Ca+(4s) ground states are both open-shell doublet character while Al+(3s2) is closed shell singlet character. Despite these differences, the ground state bonding and structure is predominantly electrostatic and remarkably similar in each complex. In each case we find a weakly bound A1 ground state equilibrium structure with the metal ion lying atop the C=C bond of ethylene in C2V π-bonding geometry. The ethylene moiety shows a slight out-of-plane distortion, and the calculated C=C bond length (RC–C = 1.34 Å) is close to the experimental bond length for isolated ethylene (1.337 Å), consistent with the weakly-bound nature of the complex. Equilibrium structures are compared in Table 1. Note, that the electrostatic binding decreases and the bond length increases as the size of the metal ion increases from Mg to Al to Ca. Our results for the ground state binding energies and equilibrium structures of Mg+(C2H4) and Al+(C2H4) are in very good agreement with earlier, more extensive calculations by other groups.21,22 Excited State Interactions Mg+(C2H4) Excited state calculations for Mg+(C2H4) at the CIS level show five spin doublet excited states accessible in the visible and near UV6 (Fig. 1). In agreement with the earlier work of Sodupe and Bauschlicher,21 we identify three of these excited states with predominantly Mg+(3p 2P) parentage as 12B2 , 12B1, and 22A1. In the attractive states of 3pπ (2B1,2) symmetry the Mg+ ‘p’-orbital is aligned either parallel to the C=C bond (2B2), or perpendicular to the C–Mg–C plane (2B1). These symmetries reduce the electron density on axis and expose the metal ion core enhancing
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Table 1: Structural parameters for low-lying electronic states of M+(C2H4) (M = Mg, Al, Ca). Metal Mg1
Al
1
State
De(eV)
R(M-X)(Å)
R(C-C)(Å)
3s(12A1)
0.77 (0.75)3
2.60
1.34
2
3p(1 B2)
2.97
2.10
1.46
3p(12B1)
1.74 (1.8)3
2.39
1.34
3s2(11A1)
0.57 (0.37)3
2.83
1.34
3s 3p(1 B2)
2.29
1.96
1.44
3s23p(11B1)
0.28
2.48
1.34
1
2
2
Ca2
4s(1 A1)
0.51
3.01
1.33
3d(12B2)
1.12
2.43
1.39
4p(22B2)
1.14
2.84
1.33
4p(22B1)
0.87
2.93
1.33
1. Ground state calculations at the QCISD(T)//MP2/6-311++G(2d,2p) level. Excited state calculations at the CIS//MP2/6-311++G(2d,2p) level. 2. Ground state calculations at the QCISD(T)//MP2level. Excited state calculations at the CIS//MP2 level. In both ground and excited state calculations the basis set used was 6-311++G(3df,3pd) but with the Ca ‘d’ orbital splittings modified as described in Ref. 8. 3. Experimental bond dissociation energies are given in parentheses.
electrostatic attraction. The result is that both excited 2B1 and 2B2 states are attractive at long range. The third state, 3pσ(22A1), is essentially repulsive in the Mg+–C2H4 coordinate. This is expected since the Mg+ ‘3s3p’ hybridized orbital in this symmetry lies in the C–Mg–C plane and directed toward C=C bond, resulting in a long range electrostatic repulsion. Two additional excited states are identified in the near UV energy range as 22B2 and 32A1. The moderately attractive 22B2 state is an ethylene-centered excited state (correlated to the a3B1u state of C2H4 in D2h planar symmetry), mixed with charge-transfer character. The repulsive 32A1 state is nominally a metal–ligand charge transfer (CT) state arising from the Mg(3s)–C2H4+ parent. However, this state is also strongly coupled to the nearby 22A1 state. Thus, these nominal correlations are not rigorous; the electronically excited states all show evidence for mixing with nearby states of the same symmetry. Diabatic rigid body potential energy scans along the RMg–X dissociation coordinate are shown in Fig. 1 for Mg+(C2H4). Except for the RMg–X distance, all the other geometric parameters have been fixed at their ground state equilibrium values. Note that the binding is much stronger in 12B2 than in 12B1. The electronic orbital alignment in B2 symmetry is favorable for chemical interaction and 12B2 is characterized by formation of a strong, short range covalent bond.
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Figure 1: Ab initio potential energy curves for the doublet states of Mg+(C2H4) along the RMg–X dissociation coordinate. Adapted from Ref. 6.
On the other hand, 12B1 is more weakly bound at longer range by predominantly electrostatic forces. Chemical bonding interactions in the 12B2 state lead to a significant stretch in the C–C bond of the ethylene moiety for Mg+(C2H4), and the short range potential well apparent in the rigid body scan of Fig. 1 is not the true minimum energy configuration for this state. We have carried out additional CIS calculations to find equilibrium structures for the excited states (Table 1). The calculated minimum energy geometry for 12B2 shows an obvious trend toward Mg+ insertion into the C=C bond with a contraction of the Mg+–C2H4 distance from 2.60 Å to 2.10 Å, accompanied by an appreciable stretch in the C=C bond from 1.34 to 1.46 Å. The alignment of the Mg+ ‘py’-orbital in the 12B2 state of the complex affords the opportunity for good molecular orbital overlap with the π*-antibonding LUMO of C2H4. This allows for efficient transfer of electron density, weakening and stretching the C–C bond. In addition, there is some π back donation into the Mg+ 3pσorbital leading to the formation of a Mg–C–C covalent bond with a dissociation energy of De′(12B2) = 2.97 eV.
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In contrast, the molecular orbital symmetry of 12B1 is unfavorable for strong interaction with the π*-LUMO of the ethylene ligand. As a result the excited 12B1 state is more weakly bound. The excited state dissociation energy is De′(12B1) = 1.74 eV with an equilibrium bond distance of RCa–X(12B1) = 2.39 Å; the ethylene moiety remains relatively undistorted in this state (Table 1). Al+(C2H4) The electronic structure of Al+(C2H4) is much simpler (Fig. 2). The Al+(3s3p 1P1) metal centered excited states lie at much higher energy and only the metal–ligand charge-transfer (CT) states are dipole accessible in the visible and near UV spectral regions.7 The three lowest electronically excited states (11B2, 11B1, and 21A1) all have appreciable CT character in the region of Franck-Condon excitation from the ground state equilibrium, and correlate to the Al (3s23p) + C2H4+ asymptote at long range. Energy differences in the CT states result from the differing alignments of the neutral Al(3s23p) ‘p’-orbital with respect to the C–C bond of the ethylene ion. Consequently, the dominant interaction involves a single valence metal atom p-orbital and the overall structure of these low-lying CT states is similar to the metal-centered excited states in Mg+(C2H4). Thus, the Al–C2H4+ 3pπ(11B1) CT state shows a weak binding, with a dissociation energy of De′(11B1) = 0.28 eV and an Al–C2H4 equilbrium bond length of RAl–X(11B 1) = 2.48 Å. This structure is similar to that found in Mg+(C2H4) although the 1B1 state binding is much weaker. This is due in part to the different nature of the electrostatic interaction in the two clusters: in the Mg-case the charge is well-localized on the metal ion and interacts with the more diffuse and polarizable neutral hydrocarbon; in contrast in the Al-case, the excited state electrostatic interaction between C2H4+ (with a more diffuse charge distribution) and the neutral ground state Al neutral is much weaker. Again, the low-lying Al(3s23p)–C2H4+ 3pπ (11B2) state shows evidence for a strong chemical interaction leading to a deep well at shorter Al–C2H4 distances. In this state the neutral Al ground state ‘p’-orbital lies parallel to the C–C bond and mixes with the antibonding π*-LUMO of the ethylene ion. This orbital overlap facilitates the net transfer of one electron from the C–C π-bonding orbital to the Al–C σ-bond in an insertion process analogous to that in Mg+(C2H4). The Al–C2H4 equilibrium bond length shortens significantly to Re(11B2) = 1.96 Å, with a concomitant stretch in the
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Figure 2: Ab initio potential energy curves for the singlet states of Al+(C2H4) along the RAl–X dissociation coordinate. Adapted from Ref. 7.
C–C bond to RC–C(12B2) = 1.44 Å; the dissociation energy is this state is found to be De′(11B2) = 2.29 eV. Interestingly, the nominally “repulsive” 3pσ(11A1) state in + Al (C2H4) shows an avoided crossing with a higher lying state leading to a very strong short range covalent bond, characterized by the net transfer of two electrons from the C–C π-bonding orbitals into the Al–C σ-bond. While this strong binding region is not Franck-Condon accessible from the ground state equilibrium geometry, it does appear to play an important role in the CT dissociation dynamics.7 Ca+(C2H4) The excited state structure of Ca+(C2H4) is more complicated due to the presence of the low-lying Ca+(3d) orbitals. CIS level calculations of the low-lying excited states of Ca+(C2H4) show that there are eight
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metal-centered doublet excited states of the complex in the visible and near UV, five that correlate with Ca+(3d) (12B2, 22A2, 12A2, 12B1, & 32A1), and three that correlate to Ca+(4p) (22B2, 22B1, & 42A1)8 (Fig. 3). Again, the long range character and energy ordering are determined by the relative alignment of the metal ion 3d- and 4porbitals with respect to the C=C bond of ethylene. As in Mg+(C2H4) there are two additional states of note at slightly higher energies: a weakly bound ethylene centered excited state (32B2), and a repulsive CT state (52A1). Figure 3 shows a set of rigid body potential energy curves as a function of Ca+–(C2H4) intermolecular separation, and where the ethylene moiety is held rigidly fixed in its ground state equilibrium geometry. Several points are noteworthy. With the exception of 12B2 all of the Ca+(3d) based molecular states are weakly bound at larger Figure 3: Ab initio potential energy curves for the doublet states of Ca+(C2H4) along the RCa–X dissociation coordinate. Adapted from Ref. 8.
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intermolecular bond distances than in the ground state. This binding may be somewhat surprising for the 3dσ(32A1) state: in C2v symmetry the Ca+(3dσ) orbital is directed along the Ca+–ethylene intermolecular axis, and the state was expected to be essentially repulsive (as for the higher lying 4pσ(42A1) state). Weak binding results from long range ion-multipole electrostatic attraction and the smaller size of the 3dσ atomic orbital allows for closer metal–ethylene approach before repulsive exchange interactions become important. In addition, there is some s-dσ hybridization from a mixing of the 3dσ- and 4sσ-orbitals that lowers the electronic repulsion for this state. The lowest lying excited state 12B2 does, however, show a relatively strong bonding interaction as found in both Mg+(3p)– and Al+(3p)–C2H4 complexes.5,6 In those cases the interactions involved the low-lying atomic p-orbitals rather than the d-orbital as is the case here. However, analysis of the Ca+(C2H4) molecular orbitals shows that there is appreciable mixing of p-orbital character in the eigenfunction near the 11B2 state minimum. Chemical interaction in this symmetry is facilitated by favorable molecular orbital overlap between the Ca+(3dyz and 4py) orbitals and the π*-antibonding LUMO of ethylene. It is interesting that the insertion interaction is not nearly as pronounced in this state as in the previous examples. The 12B2 state equilibrium is found with dissociation energy of De′(11B2) = 1.12 eV, an intermolecular bond length of RCa–X(12B2) = 2.43 Å, and a more moderate stretch in the C–C bond to RC–C(12B2) = 1.39 Å. It is also interesting to note that the higher lying 4pπ(22B1 and 2 2 B2) states of the complex are very similar in binding and shape. We have carried out a geometry optimization for the 4pπ states at the CIS level. The Ca+–C2H4 equilibrium bond distance remains fairly large, RCa–X= 2.84 Å (2.93 Å) for 22B2 (22B1), and the ethylene moiety remains close to its free equilibrium geometry in both states. The binding energies are also predicted to be similar (De′(22B2) = 1.14 eV and De′(22B1) = 0.87 eV). This is in sharp contrast to results for the analogous Mg+(C2H4) and Al+(C2H4) complexes discussed previously where chemical bonding interactions involving the 3py-orbitals are much more important and the 3py(B2) states are much more strongly bound than the analogous 3px(B1) states. B.
Experimental Results Mg+(C2H4)
We observe five distinct absorption bands in the visible and UV photodissociaiton of MgC2H4+ (Fig. 4).6 The photofragment Mg+ is
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Figure 4: Mg+(C2H4) photodissociation action spectrum for Mg+ (solid curve) and C2H4+ (dashed curve). Adapted from Ref. 6.
observed in all spectral regions, while C2H4+ is observed only at higher energies, hν > 37,000 cm–1. Band assignments are based in part on ab initio electronic structure calculations for this complex as discussed above. Three of the bands, 12B2← 12A1, 12B1← 12A1, and 22A1 ← 12A1, are assigned as transitions correlated to the metal-centered Mg+(3p ← 3s) resonance excitation, with the different symmetry states corresponding to the three distinct alignments of the Mg+ ‘p’-orbital with respect to the C=C bond in ethylene. One of the remaining two bands is assigned as a predominantly ligand-centered transition (22B2 ← 12A1), correlated to a forbidden excitation (a3B1u ← X 1Ag) in isolated C2H4, with mixed charge transfer character. This band becomes allowed in the complex owing to angular momentum mixing with the open shell Mg+(3s) ground state. The shortest wavelength band (32A1← 12A1) is primarily due to the metal-ethylene CT process. The CT band is
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comparable in intensity to the metal-centered excitation bands, owing in part to strong mixing with the nearby metal centered 22A1 state. Observed band positions are in good agreement with the ab initio predicted vertical transition energies giving support to the assignment.6 Except for 12B1 ← 12A1 all the observed bands are apparently structureless. The 12B1 ← 12A1 excitation spectrum exhibits a strong clear progression in the Mg+–C2H4 intermolecular stretch built on the electronic state origin; this is consistent with a slight shortening of the Mg+–ethylene bond in the 12B1 state. Analysis of the vibrational spectrum also shows evidence for very weak activity in the ethylene intramolecular modes, with only the CH2–CH2 wagging motion observed. The vibrational assignment will be discussed below. Al+(C2H4) The photodissociation absorption spectrum for Al+(C2H4) exhibits three distinct absorption bands7 (Fig. 5). Al+ is the major dissociation product throughout the molecular bands, while the charge transfer product is observed only for higher energies, hν > 40,000 cm–1. Based on the ab initio results the observed radiative bands in Al+(C2H4) are all assigned to the photoinduced Al–C2H4 CT process.7 We assign the lowest energy continuum band to 11B2 ← 11A1, the intermediate structured band to 11B1 ← 11A1, and the incomplete continuum band at highest energies to the 21A1 ← 11A1 transition. The observed band positions agree well with the ab initio predicted vertical excitation energies.7 As expected from ab initio calculations, the Al+(3s2(1S0)–3s3p(1P1)) metal centered bands lie well to the blue of the spectral region probed here. Furthermore, the ethylenecentered absorption band observed in Mg+(C2H4) is not apparent in the Al+-based complex. This is also due to the differences in metal ion valence electronic structure: Mg+(3s) is open-shell and enhances the (nominally) spin-forbidden transition in ethylene through angular momentum coupling, while Al+(3s2) is closedshell and the spin angular momentum selection rules are not relaxed. The spectrum exhibits overlapping vibrational progressions, including activation of the low frequency Al+–C2H4 intermolecular modes, and also unusually strong activity in the higher frequency intramolecular ethylene modes, the HCH bend and the C–C stretch as discussed below.
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Figure 5: Al+(C2H4) photodissociation action spectrum for Al+ (upper curve) and C2H4+ (lower curve). Adapted from Ref. 7.
Ca+(C2H4) Ca+ is the only product observed in the visible spectral region.8 Molecular absorption bands are observed peaking in the red (~680nm and ~740nm) and in the blue/green (~540nm and ~470nm) regions (Fig. 6). The red bands are broad with no obvious resolved vibrational peaks. In contrast, the green and blue bands each show pronounced resonance structure and a prominent vibrational progression. We identify the observed bands with metalcentered transitions to excited states of the complex correlating with the Ca+(3d) and Ca+(4p) asymptotes for the red and blue/ green bands, respectively. The lowest energy red band near 13,500 cm–1 in the upper panel of Fig. 6 is assigned as 12B2 ← 12A1. As for the analogous 1B2 ← 1A1 transitions in Mg+– and Al+–ethylene, the band is broad and structureless. A second red band at slightly higher energies is similarly void of any resolved vibrational structure. This lack of structure is somewhat surprising since most of the Ca+(3d)-based molecular states are electrostatically bound with Re only slightly larger than the ground state (Fig 3). Franck-Condon excitation should access the band origin, and activate the Ca+–C2H4 intermolecular stretch.
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Figure 6: Upper panel: Photodissociation action spectrum for the 3d ← 4s red bands of Ca+(C2H4); Lower panel: Photodissociation action spectrum for the 4p ← 4s blue/green bands of Ca+(C2H4). Adapted from Ref. 8.
(Indeed, previous work by the Duncan research group on the analogous Ca+-acetylene complex shows this expected behavior with clear vibrational resonance structure in the 32A1 and 12B1 ← 12A1 absorption bands of Ca+(C2H2)). However, the CIS calculations place the 22A1, 32A1 and 12B1 excited states of Ca+(C2H4) all at nearly the same energy and the absorption bands are predicted to overlap. We assign the second broad band observed near 14,700 cm–1 to the overlapping transitions 22A1, 32A1, and 12B1 ← 12A1, and speculate that the band structure is unresolved due to this overlap. The energy splitting between the two red bands is close to the theoretical value, and this predicted energy splitting is likely to be more reliable than absolute band energy predictions. The blue/green bands shown in the lower panel of Fig. 6 can be clearly identified with excitation of the Ca+(4pπ) states of the complex. We assign the green band to the transition 22B2 ← 12A1,
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and the blue band to 22B1 ← 12A1. This band assignment is in good agreement with the CIS calculations. Each band shows a strong progression of the Ca+–C2H4 intermolecular stretch. Analysis of the vibrational spectrum also shows evidence for weak activity in at least two intramolecular ethylene modes, the CH2–CH2 wag and the HCH bend (see below). We should also note that recent experiments by the Duncan research group in the analogous Ca+–acetylene complex found a somewhat similar absorption band structure in the green and in the blue.23 They assigned the green band to the 22B1 state of Ca+(C2H2) and assigned the higher energy band in the blue to a combination band involving one quantum of the acetylene C–H stretch. The assignment was verified by isotope substitution. The differences in the spectral assignment are intriguing (given the similarity in the complexes) and suggest remarkably different excited state interactions between Ca+–ethylene and Ca+–acetylene. In particular, in Ca+–acetylene, the 4pπ(2B2) state must be much more strongly interacting since it is not directly observed with any significant FranckCondon factor.23 In addition, appreciable excitation of the C–H stretch in the acetylene case is surprising, and suggests more significant distortion of the acetylene ligand in the excited state of the complex than is apparent in Ca+–ethylene. IV. A.
DISCUSSION
Nonadiabatic 1B2(A´)–1A1(A´) Dissociation Dynamics
In each of the metal ion–ethylene clusters we have studied (M = Mg, Al, Ca), the absorption spectrum for the lowest energy 1B2 ← 1A1 band is a continuum. This result is perhaps surprising since the 1B2 state in every case is strongly bound. However, this observation is consistent with a large geometry change and fast predissociation from 1B2. In each case excited state dissociation channels are not energetically accessible, and dissociation must involve a nonadiabatic transition to the ground state surface. Such a nonadiabatic pathway is suggested by the ab initio results. Despite differences in metal ion valence structure, excited state character, and orbital size, the lowest lying excited state of B2 symmetry shows a similar chemical bonding interaction in each cluster. In each case, ab initio calculations find 1B2 equilibrium structures that show a pronounced shortening of the M–C2H4 bond and a concomitant increase in the C–C bond length. (Table 1) Furthermore, in each case we have been able to identify a region of inner wall conical intersection or narrowly avoided surface crossing between the 1B2 excited and 1A1 ground
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state surfaces in C2v symmetry.6–8 The alignment of the M+ ‘py’orbital in the 1B2 state of the complex affords the opportunity for good molecular orbital overlap with the π*-antibonding LUMO of C2H4.6,7 An analogous molecular orbital interaction involving the 3dyz orbital is also possible in Ca+–ethylene.8 These interactions promote efficient transfer of electron density, weakening and stretching the C–C bond. Because of the relatively large size of the M+ orbitals, the overlap is enhanced by the C–C bond stretch. This bond stretch mechanism predicts a strong electronic orbital alignment selectivity for the quenching favoring B2 alignment as observed. In the distorted insertion complex, the ground state (1A1) surface is highly repulsive, and crosses the excited (1B2) surface in a C2v symmetry-allowed crossing seam. For slightly off axis geometries (CS symmetry) the 1B2 and 1A1 surfaces are both A´ character and will show an avoided crossing, leading to a conical intersection. In higher dimensionality (as the internal coordinates of the reagents vary) the conical intersection becomes a crossing seam in the potential energy hypersurfaces. This seam opens a path for efficient quenching to the ground state surface. Equivalently, the in-plane wag vibrational motion (of b2 symmetry) in the B2 excited state can couple this state to the 1A1 ground state [B2 ⊗ B2 = A1]. The bond-stretch quenching mechanism involving a nonadiabatic transition through a region of conical intersection in near C2v geometry, is known to be important in the activation of H–H σbonds by p-state metal atoms.24–26 Significant experimental and theoretical effort has led to a clear understanding of the quenching dynamics in neutral metal atom-H2 systems. For example, the nonreactive E–V quenching process24,25 Na*(3p) + H2 → Na(3s) + H2(v´´)
(1)
and the reactive quenching process26 Mg*(3s3p) + H2 → MgH(v´´, J´´) + H
(2)
have both been studied in detail. The theoretical work includes extensive ab initio potential surface calculations of the surface crossing region, and molecular dynamics calculations.24–26 In addition, our earlier work on the photodissociation spectroscopy of Mg+(D2) has shown results similar to those presented here for Mg+(C2H4) and Al+(C2H4);2,3 the Mg+(3sσ → 3pπ) absorption spectrum consists of a weak, broad, red-shifted continuum band underlying a second band showing clear rovibronic structure. The
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continuum band is assigned to the transition 12B2 ← 12A1, and analysis of the rovibrational spectrum characterizes the structured band as 12B1 ← 12A1. The experimental results are consistent with ab initio work by Bauschlicher that show the 12B1 state to be weakly electrostatically bound, while the 12B2 state is characteristic of a strongly bound insertion complex.27 Of course, one crucial difference is that reactive quenching channel (to MgD+ + D products) dominates the photodissociation of Mg+(D2). For the M+–ethylene systems, the C=C bond is too strong to break and nonreactive E–V quenching dominates the dissociation. A somewhat analogous dynamical mechanism has also been used to explain the reactive quenching of both neutral Mg*(3s3p) and ionic Mg+*(3p) by CH4.2,4,28–33 The latter reaction has also been studied by photodissociation spectroscopy in our lab.4 For Mg+(CH4), the broad continuum Mg+(3sσ → 3pπ) absorption spectrum is consistent with a large geometry change on excitation and fast dissociation. We observe both nonreactive (Mg+), and reactive fragmentation products (MgH+ and MgCH3+). As in the analogous neutral Mg reaction, C–H bond attack follows on the attractive “Πlike” (2E) surfaces. The dominant reaction product is the methyl fragment, MgCH3+, showing that insertive geometries control the ion–molecule reaction. Measurements of the nonreactive (Mg+) product translational energy release show that Mg+ kicks impulsively off the highly extended H–CH3 bond, so that (even when the insertion reaction does not occur) the nascent CH4 product is left highly vibrationally and rotationally excited.4 The work was supported by ab initio electronic structure calculations of the ground and low-lying excited state potential energy surfaces.2,4,33 Absorption is assigned to the metal-centered transition (12E ← 12A1) in C3v geometry, followed by a geometrical relaxation of the complex to states of 2B1 and 2B2 symmetry in η 2 coordination. Ab initio calculations find a region of avoided surface crossing between the lowest two surfaces of A′ symmetry allowing a path for nonadiabatic relaxation to the ground state surface through a highly stretched H–Mg+–CH3 insertive transition state. Calculations show the transition state is evenly centered with the Mg+–H and the Mg+–C distances close to their equilibrium values in isolated MgH+ and MgCH3+, respectively. This close approach allows the C–H bond to be highly stretched and favors reaction to MgCH3+ as observed.2,4,33 The close approach in the Mg+–CH4 complex may be facilitated by the lack of Mg+(s)–CH(σ ) repulsion, and possibility for efficient donation of electron density from the occupied CH σ-bonding orbital into the unoccupied σ–orbital of the metal ion.
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The experimental and theoretical ab initio results reviewed here have shown that the bond stretch quenching mechanism is also important for M+–alkene π-bonded systems involving the activation of C=C bonds. While there are obvious similarities in the discussion, it is important to recognize fundamental and important dynamical differences for these various M+–ethylene clusters. In the photodissociation of Mg+(C2H4), the 12B2 photoexcitation is Mg+-centered, to states of predominantly Mg+(3py) character. The subsequent dissociation of the complex through an insertive bond stretch process can be considered as the half-collision analog to the electronic-to-vibrational energy transfer process: Mg+(3p) + C2H4 → Mg+(3s) + C2H4(v´´)
(3)
The photodissociation of Ca+(C2H4) through the 11B2 is similar but can also involve molecular orbital interactions with the low lying atomic 3dyz orbitals.8 In Al+(C2H4) the 11B2 absorption is more appropriately characterized as a photoinduced CT process in the supramolecule, and subsequent chemistry involves attack by the Al(3s23py) neutral ground state atom on the C–C bond of C2H4+.7 In a sense this process represents the half-collision analog of the ground state ion-molecule charge transfer reaction: Al(3s23py) + C2H4+ → Al+(3s2) + C2H4(v´´)
(4)
Our results suggest that the ground state CT reaction will proceed on the 11B2 surface through an inner wall surface crossing in C2v approach geometry and leave the ethylene neutral product with significant vibrational energy in the C–C stretch mode. This work suggests that hard chemistry involving C–C bond breaking may follow charge transfer excitation and compete with direct CT dissociation in some cases. B.
Vibrational Analysis
We now turn to a discussion of the structured vibrational bands shown in Figs 4–6. These include the (1B1 ← 1A1) bands for Mg+(C2H4) and Al+(C2H4), and the (2B2 and 2B1 ← 1A1) bands for Ca+(C2H4). For the 1B1 state of both Mg+(C2H4) and Al+(C2H4), the molecular orbital symmetry is unfavorable for chemical interaction. In addition, in Cs geometry the B1 surfaces are of A″ character and direct coupling to the A′ ground state surface is symmetry forbidden. Consistent with this, the 1B1 ← 1A1 band in both
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Mg+(C2H4) and Al+(C2H4) shows pronounced vibrational structure indicative of a long-lived complex. The 3pπ(1B1 and 1B2) states of Mg+(C2H4) and Al+(C2H4) show very different bonding character due to differing molecular orbital symmetries.6,7 In contrast, the 4pπ(22B1 and 22B2) states of Ca+(C2H4) are very similar in binding and shape.8 Both states are relatively weakly bound. Differences between the Ca+–ethylene and the Mg+– or Al+–ethylene interactions are due to an avoided crossing repulsion from the lower-lying 3d(12B1 and 12B2) states in the Ca+–case, and to the larger orbital size of the Ca+(4p) orbital which limits the effective molecular orbital overlap with the π*-antibonding LUMO of ethylene. The excited 1B1 states for both the Mg+– and Al+–ethylene complexes, and the 2B2 and 2B1 states of Ca+–ethylene, are all relatively weakly bound by predominantly electrostatic forces. In the spectroscopy of each of these states we access the band origin region showing that the metal–ethylene bond length in the excited states is similar to that of the ground state. The prominent low frequency progression observed in each band is assigned to the M+–C2H4 intermolecular stretch. In addition, there is clear evidence in all of these systems for the activation of higher frequency intramolecular ethylene vibrational modes. Expanded views of the vibrational structure can be found in the original references.6–8 Results are summarized in Table 2. Mg+(C2H4) The strongest progression in the 12B1 ← 12A1 band of Mg+(C2H4) is assigned to the (v2) Mg+–C2H4 intermolecular stretch mode (a1 Table 2: Observed vibrational mode frequencies (in cm–1) for the electrostatically bound excited states of M+(C2H4) (M = Mg, Al, Ca). Theoretical values are given in parentheses. Vibrational mode
Mg(12B1)
Al(11B1)
Ca(22B2)
Ca(22B1)
M–C2H4 stretch (a1)
329 (314)
230 (190)
237 (220)
227 (199)
M–C2H4 bend
439 (385)
328 (415)
CH2–CH2 wag (a1)
1024 (1196)
987 (1150)
H–C–H bend (a1)
1264 (1399)
C–C stretch (a1)
1521 (1706)
1320 (1470)
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symmetry) in the upper state, with frequency ω2 = 329 cm–1.6 This compares well with the ab initio predicted value of 314 cm–1. Activity of this intermolecular stretch is consistent with the expected slight shortening of the Mg+–C2H4 bond distance in the excited state. Another weaker and shorter progression is assigned to the combination band 20v301, where ν3 corresponds to the Mg+–C2H4 intermolecular out-of-plane wag of b1 character with a mode frequency of ω3 = 439 cm–1. The ab intio value is 385 cm–1. An additional higher energy mode is also present in the spectrum and must be associated with an intramolecular vibration of ethylene. It is assigned as a progression built on the CH2–CH2 symmetric wag (a1), with a fundamental frequency of ω(CH2–CH2) = 1024 cm–1. This can be compared with the ab initio value of 1196 cm–1. The weak excitation of the ethylene intramolecular modes is expected owing to the fact that the radiative transition is metal-centered and the ethylene ligand serves as a weakly bound spectator. Al+(C2H4) The 11B1 ← 11A1 band of Al+(C2H4) in Fig. 5 shows more complex vibrational mode structure with several overlapping progressions.7 The observation of vibrational resonance structure is unusual in CT transitions and is a result of the chemical interactions between the open shell Al(3s23p) and C2H4+ species in the CT state. Within the first Franck-Condon vibrational group, there is an obvious progression corresponding to a low frequency intermolecular vibration, assigned to the v2 Al–C2H4 intermolecular stretch with a fundamental mode frequency of ω2 = 225 cm–1. This compares favorably with the theoretical value of 190 cm–1 from ab initio calculation. This progression is clearly repeated in the higher energy vibrational groups, which correspond to excitation of intramolecular ethylene vibrational modes. Closer scrutiny of the first band group shows a weaker two-member progression with similar ν2 mode spacing, assigned to the combination band 20v301 of the ν3 Al–C2H4 intermolecular out-of-plane wag mode with b1-symmetry, ω3 = 328 cm–1. This is to be compared with the ab initio value of 415 cm–1. The second and third vibrational groups of Fig. 5 are clearly associated with activation of intramolecular vibrational modes of the ethylene ion in the CT state. Spectral analysis suggests there are at least two intramolecular modes active with a1 symmetry with frequencies 1264 cm–1 and 1521 cm–1. These modes are assigned to the the symmetric H–C–H bend (predicted at 1399 cm–1) and the C=C stretch (predicted at 1706 cm–1), respectively.
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Ca+(C2H4) We observe vibronic structure in two electronic bands of Ca+(C2H4), assigned to the transitions 22B2/22B1 ← 12A1 as seen in the lower panel of Fig. 6.8 Good Franck-Condon factors for each of the observed 0←0 transitions show that the equilibrium bond distances in the excited states are similar. This is consistent with calculations showing the 22B2 and 22B1 excited states to be similarly bound at relatively long range. To the high energy side of the 22B2 ← 12A1 band origin we identify an obvious vibrational progression assigned to the Ca+–C2H4 intermolecular ν2 a1-stretch. A Birge-Sponer plot of the vibrational spacings gives ω2(22B2) = (237) cm–1, while the ab initio predicted value is ω2(22B2) = 220 cm–1. Closer scrutiny of the vibronic spectrum reveals two additional progressions assigned to combination modes built on the a1-symmetry CH2–CH2 wag (with ω(CH2–CH2) = 987 cm–1) and the HCH-bend modes of ethylene (with ω(HCH) = 1320 cm–1). Ab initio calculations predict the corresponding frequencies in the 22B2 state of the complex to be 1150 cm–1 and 1470 cm–1, respectively. A small resonance peak is observed slightly to the red of the strong origin band and is assigned to a hot band in the Ca+–C2H4 intermolecular vibrational stretch of a1–symmetry giving a ground state stretch frequency of ω2(12A1) = 145 cm–1, in good agreeement with the ab initio calculations that predict a ground state stretch frequency of 144 cm–1. The data also appear to show a progression of weak hot band features but we suspect that this progression is overlapped by other progressions built on an intermolecular bending mode. Because the resonances are not resolved we cannot determine the bend frequency. A second strong absorption band is observed above the 22B1 state origin band. A Birge-Sponer analysis gives ω2(22B1) = 227 cm–1. The fundamental frequency is very close to that for the lower energy 22B2 state. The close similarity in vibrational mode frequency is expected based on the similar shapes of the weakly bound 22B1 and 22B2 states and is consistent with ab initio predictions. The experimental mode frequency (227 cm–1) can be compared to the CIS predicted value (199 cm–1) in 22B1. It is useful to compare these observations of Ca+(C2H4) with previous work on Ca+(CH4).4 The 4pπ excited states of Ca+(CH4) were found (in both the spectroscopic experimental work and by ab initio calculation) to be very weakly interacting. In fact the absorption spectrum was dominated by spin-orbit doubling (with the excited states of 2E1/2 and 2E3/2 character). In contrast, in
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Ca+(C2H4), the spin-orbit coupling is largely quenched and exchange interactions dominate the excited state splitting. This is consistent with the expectation that steric hindrance effects that limit close approach and molecular orbital overlap should be much less important in the Ca+ interaction with the open planar ethylene molecule than for the interaction with the more compact and closed CH4 molecule. Discussion Assignment of the intramolecular vibrational modes in all of these M+–ethylene complexes are based on comparison with the ab initio calculated frequencies and symmetry considerations. Within the Born-Oppenheimer approximation, in a B1 electronic state only single quantum vibrational excitation in b1 symmetry, and one or more quanta in a1-symmetry modes are allowed. Moreover, the vibrational activity should also reflect the geometrical differences for the upper and lower states, in this case, a slight a shortening of M+–C2H4 bond, and a slight out-of-plane distortion of the hydrogen atoms on ethylene and lengthening of the C–C bond. In considering the values of Table 2, it is interesting to note that the well-known “90% rule” that says SCF level vibrational frequencies are typically too high and should be scaled down by ~90% in comparison with experimental data does appear to hold reasonably well for the high frequency intramolecular ethylene vibrational modes. However, the rule does not apply to the low frequency intermolecular vibrational modes which are well-predicted at the SCF level. Comparison of the intermolecular stretch (ν2) frequencies in the Mg+–, Al+–, and Ca+–ethylene complexes shows that the electrostatic binding in the excited Mg+–complex is significantly stronger than in the Al+– and Ca+– complexes, as expected due to its much smaller size, and as predicted by ab initio calculations. It is very interesting, however, despite the weak bonding in the Al(3s23p)–C2H4+ (11B1) state, this spectral band shows a very much stronger activation (including multiple quanta) in the intramolecular ethylene vibrational modes than the corresponding transitions in Mg +(C2H4) and Ca+(C2H4). This is due to the fact that the Franck-Condon charge transfer process in Al+(C2H4) results in an ethylene ion ligand that is appreciably distorted from its equilibrium geometry. The equilibrium structure of C2H4+ shows a slight lengthening and twist in the C=C bond. In the metal-centered transitions of Mg+(C2H4) and Ca+(C2H4) the ethylene neutral ligand is much less affected.
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Direct Charge Transfer Dissociation
Direct CT photodissociation to C2H4+ product is observed at the shortest wavelengths for both Al+(C2H4) and Mg+(C2H4).6,7 In each case dissociation occurs through a repulsive A1 state of the complex and is accompanied by significant energy release. The C2H4+ product flight time profile shows appreciable anisotropy and broadening due to the energy release into relative translation. We have previously shown that these flight time profiles can be directly inverted to yield the translational energy release distribution function.2 Using the measured energy release (KE), an estimate for the bond dissociation energy can be obtained from the energy cycle, D0″ = hν – (IP(C2H4)–IP(M)) – KE.
(5)
This analysis leads to experimental values D0″(Mg+–C2H4) = 0.8 eV and D0″(Al+–C2H4) = 0.4 eV, in fairly good agreement with the ab initio predictions (De″(Mg+–C2H4) = 0.77 eV and De″(Al+–C2H4) = 0.57 eV, respectively).6,7,21,22 These experimental results confirm the weaker binding in the closed shell Al+–ethylene complex. Similar measurements should be possible in the CT photodissociation of Ca+(C2H4), but have not been completed as of this writing. For Mg+(C2H4) we can combine the experimental bond energy with the spectroscopic value for ν00 in 12B1 to find the dissociation energy in the excited state by D0´(12B1) = [E(Mg+(3p)) – E(Mg+(3s))] + D0´´ – ν00
(6)
The experimental value is also in very good agreement with the ab initio result (De´(12B1) = 1.74 eV). A corresponding analysis for Al+(C2H4) is problematic since the excited 11B1 state is known to have a significant barrier to dissociation. Interestingly, in each case the direct CT dissociation channel is the minor channel, approaching a branching of 50% only at the highest energies probed. This suggests that reverse charge transfer, followed by a nonadiabatic quenching to the metal ion ground state dissociation channel competes effectively with the CT dissociation. This process represents the bimolecular analog of internal conversion. Understanding the details of this competing nonadiabatic quenching process will require a more thorough investigation of the excited state potential energy surfaces.
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V.
SUMMARY
Metal ion–hydrocarbon interactions are of vital importance in many areas of chemistry and physics and photodissociation spectroscopy experiments, in concert with ab initio electronic structure calculations, can give detailed and quantitative information about these essential interactions. In some examples bound-quasibound state spectroscopy can be effectively used to characterize the structure of the metal ion–hydrocarbon bimolecular complex. The intermolecular vibrational modes are usually active and dominate the vibronic spectrum, giving a quantitative measure of the metal–ligand bonding interactions. We have also seen that photoexcitation of the metal-centered absorption bands of the complex can activate the intramolecular modes of the hydrocarbon ligand. In some cases, this may give information about how the internal structure of the hydrocarbon is altered in the complex. Even in cases where detailed vibronic structure is not observed, photoinduced charge transfer dissociation coupled with kinetic energy spectroscopy of the products, can give quantitative metal ion–ligand bond energies. The photodissociation of the weakly bound precursor complex also serves to mimic a bimolecular half-collision and can give important insight into the chemical dynamics. In each of the metal ion–ethylene clusters discussed here, the lowest energy transition is assigned as 1B2 ← 1A1 band and consists of a weak continuum, indicative of a large geometry change and fast predissociation from the upper state. This observation is consistent with ab initio results that show a pathway for nonadiabatic dissociation through a 1B2–1A1 surface crossing facilitated by a stretch in the C–C bond of ethylene. The dissociation follows through a π-bond stretch insertion mechanism, enhanced in B2 orbital symmetry by the good overlap of the metal atom valence orbital with the π*-antibonding orbitals of the ethylene ligand. Nonadiabatic interactions are of great importance in chemical dynamics, often controlling the competitive branching between accessible channels in organometallic photochemistry. Photodissociation half-collision studies in small bimolecular complexes systems can serve as model systems for developing and enhancing our chemical intuition, and as test cases for evaluating ab initio structure calculations and theoretical molecular dynamics models. The photodissociation spectroscopy of weakly bound bimolecular complexes has proven to be an invaluable tool for probing and elucidating metal ion–hydrocarbon chemistry, and we look forward to even more dramatic progress in the coming years.
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ACKNOWLEDGMENTS This research was supported by the National Science Foundation and by the donors to the Petroleum Research Fund of the American Chemical Society. Electronic structure calculations were carried out with support from NPACI through the San Diego Supercomputer Center. Finally, I would like to gratefully acknowledge the considerable efforts of my collaborators in this research: J. Chen, T.H. Wong, D.A. Olsgaard, J. Holmes, K.H. Yang, Y.C. Cheng, and K. Montgomery. Without their contributions this work would not have been possible. REFERENCES (1)
(2) (3) (4) (5) (6)
(7) (8) (9) (10) (11) (12) (13) (14)
(15)
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Jouvet, C., Duval, M.C., Soep, B., Breckenridge, W.H., Whitham, C., and Visiticot, J.P. (1989) J. Chem. Soc. Faraday Trans. II., 85: p. 1133, and references therein. Kleiber, P.D. and Chen, J. (1998) Int’l Rev. Phys. Chem. B, 17: p. 1. Ding, L.N., Young, M.A., Kleiber, P.D., Stwalley, W.C., and Lyyra, A.M. (1993) J. Phys. Chem., 97: p. 2181. Cheng, Y.C., Chen, J., Ding, L.N., Kleiber, P.D., and Liu, D.K. (1996) J. Chem. Phys., 104: p. 6452. Chen, J., Cheng, Y.C., and Kleiber, P.D. (1997) J. Chem. Phys., 106: p. 3884. Chen, J., Wong, T.H., and Kleiber, P.D. (1997) Chem. Phys. Lett., 279: p., 185; Chen, J., Wong, T.H., Montgomery, K., Cheng, Y.C., and Kleiber, P.D. (1998) J. Chem. Phys., 108: p. 2285. Chen, J., Wong, T.H. Cheng, Y.C., and Kleiber, P.D. (1999) J. Chem. Phys., 110: p. 11798. Holmes, J., Kleiber, P.D., Olsgaard, D.A., and Yang, K-H. (2000) J. Chem. Phys., 112: p. 6583. Eller, K. and Schwarz, H. (1991) Chem. Rev., 91: p. 1121, and references therein. Freiser, B.S. (1994) Acct. Chem. Res., 27: p. 353; Freiser, B.S. (1996) J. Mass Spec., 31: p. 703. Shaik, S., Danovich, D., Fiedler, A., Schroder, D., and Schwarz, H. (1995) Helv. Chim. Acta, 78: p. 1393. Weisshaar, J.C. (1993) Acc. Chem. Res., 26: p. 213; Weisshaar, J.C. (1992) Adv. Chem. Phys., 82: p. 213. Armentrout, P.B. (1995) Accts. Chem. Res., 28: p. 430; Armentrout, P.B. and Baer, T. (1996) J. Phys. Chem., 100: p. 12866. van Koppen, P.A.M., Bowers, M.T., Haynes, C.L., and Armentrout, P.B. (1998) J. Am. Chem. Soc., 120: p. 5704; Gidden, J., van Koppen, P.A.M., and Bowers, M.T. (1997) J. Am. Chem. Soc., 119: p. 3935. Pilgrim, J.S., Yeh, C.S., Willey, K.F., Robbins, D.L., and Duncan, M.A. (1994) Int. Rev. Phys. Chem., 13: p. 231, Duncan, M.A. (1997) Ann. Rev. Phys. Chem., 48: p. 69. Farrar, J.M. (1993) In: Cluster Ions, (Ng, C.Y., Baer, T., and Powis, I., eds), Wiley, New York, p. 243.
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(17) Lessen, D.E., Asher, R.L., and Brucat, P.J. (1993) In: Advances in Metal and Semiconductor Clusters, Vol. I, (Duncan, M.A., ed.) JAI Press, Greenwich, CT, p. 267. (18) Spence, T.G., Trotter, B.T., and Posey, L.A. (1998) J. Phys. Chem. A., 102: p. 6101. (19) Cornett, D.S., Peschke, M., Laihing, K., Cheng, P.Y., Willey, K.F., and Duncan, M.A. (1992) Rev. Sci. Instrum., 63: p. 2177. (20) Mulliken, R.S. (1952) J. Am. Chem. Soc., 64: p. 811. (21) Sodupe M. and Bauschlicher, Jr., C.W. (1994) Chem. Phys. Lett., 185: p. 163. (22) Stoeckigt, D., Schwarz, J., and Schwarz, H. (1996) J. Phys. Chem., 100: p. 8786. (23) France, M.R., Pullins, S.H., and Duncan, M.A. (1998) J. Chem. Phys., 109: p. 8842. (24) Hertel, I.V. (1982) Adv. Chem. Phys., 50, 475; Hertel, I.V. (1982) “Progress in Electronic-to-Vibrational Energy Transfer. In: Dynamics of the Excited State, (Lawley, K.P., ed.) Wiley, New York, p. 475; Botschwina, P., Meyer, W., Hertl, I.V., and Reiland, W. (1981) J. Chem. Phys. B, 75: p. 5438. (25) Truhlar, D.G., Duff, J.W., Blais, N.C., Tully, J.C., and Garrett, B.C. (1982) J. Chem. Phys., 77: p. 764, Halvick, P., and Truhlar, D.G. (1992) J. Chem. Phys., 96: p. 2895, and references therein. (26) Breckenridge W.H., and Umemoto, H. (1984) J. Chem. Phys., 80: p. 4168, and references therein, Adams, N., Breckenridge, and W.H., Simons (1981) J. Chem. Phys., 56: p. 327. (27) Baushclicher Jr, C.W. (1993) Chem. Phys. Lett., 201: p. 11. (28) Breckenridge, W.H. (1996) J. Phys. Chem., 100: p. 14840. (29) Breckenridge, W.H., and Umemoto, H. (1982) J. Chem. Phys., 77: p. 4464. (30) Wong, T.H., Freel, C., and Kleiber, P.D. (1998) J. Chem. Phys., 108: p. 5723. (31) Chaquin, P., Papakondylis, A., Giessner-Prettrer, C., and Sevin, A. (1990) J. Phys. Chem., 94, 7352. (32) Liu, D.K., Ou, Y.R., and Lin, K.C. (1996) J. Chem. Phys., 104: p. 1370. (33) Bauschlicher, Jr., C.W. and Sodupe, M. (1993) Chem. Phys. Lett., 214: p. 489.
9 SOLVATED METAL IONS AND ION CLUSTERS, AND THE EFFECT OF LIGANDS UPON THEIR REACTIVITY Vladimir E. Bondybey, Martin Beyer, Uwe Achatz, Brigitte Fox, and Gereon Niedner-Schatteburg
I. II. III. IV.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296 Generation of Solvated Metal Ions and Cluster Ions . . . . . . 297 Clusters Solvated by Inert Gases and their Structure . . . . . . 300 Cooling the Collision Complex: Inert Ligands as an Effective Heat Sink . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303 V. Temperature Control and “Freezing” of Reaction Intermediates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305 VI. Enhancing Reactivity by Inert Ligands: Stabilization of Collision Complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307 VII. Complexes of Metal Cations with Small Molecular Ligands 310 VIII.Hydrated Ions as Nanodroplets for Studies of Solution Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314 IX. Hydration of Ions and Reduction-Oxidation Reactions in Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316 X. Reactions of Metals with Hydrochloric Acid, and the Evolution of Hydrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319 XI. Neutralization and Precipitation Reactions in Hydrated Clusters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320 XII. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323
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I.
INTRODUCTION
Most industrially important reactions proceed either in condensed phases, or in gas phase systems at high pressure. The presence of the solvent often has, in more than one way, a profound effect upon the properties of the reactants, and upon the course of chemical reactions. In the first place, through the intimate contact and collisions with the solvent atoms or molecules, a well defined temperature can be maintained at the reaction site. The collisions remove energy resulting from a chemical reaction, or conversely supply the energy needed for an endothermic reaction to occur. In the second place, the solvent itself may through its interactions with the reactants change their reactivity or chemical properties. Furthermore, through such interactions between the reactants and the solvent on one hand, and the products and the solvent on the other, the energetics of the reaction can be changed. In many cases one can actually steer the course of the reaction by a suitable choice of a particular solvent. Finally, the condensed phase may change the time-scale of a “collision” between the reactant partners. While a gas phase collision between small atomic or molecular reactants is mostly over within a single vibrational period, the hindered motion in a condensed system slows down the approach and departure of the reactants, and guarantees an extended, sustained proximity between them, so that even an intrinsically slow reaction can take place. Reactions proceeding in condensed phase, or even on the surface of a solid catalyst, do often not take place in a single step, but the products one observes are the results of a whole series of consecutive reactions. One of course can obtain valuable information by analysing the products, but this often gives only quite incomplete microscopic insight into the actual course of the reaction. The information about the overall reaction is obtained, but the consecutive reaction steps often remain obscured. With the help of well conceived mass spectroscopic experiments, it is often possible to simulate and identify these individual reaction steps. One possibility is employing as reactants not a bare ion or cluster, but its complex with atoms or molecules of the desired solvent, which simulate the effects of the condensed environment. Using an external molecular beam ion source, it is possible to generate an ion or ionic cluster of basically any element, solvated with a shell of solvent atoms or molecules. Both anions and cations can be prepared with comparable ease, so that the effects of the complex charge upon its stability and chemical properties may be investigated. Interfacing the cluster source to a fourier transform
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ion cyclotron resonance (FT-ICR) mass spectrometer is particularly convenient. Unlike in many other experiments, in FT-ICR one does not have to work with a whole distribution of cluster sizes, but if unambiguous interpretation requires it, a cluster of any desired size and composition can be mass selected. Finally, the FT-ICR has the advantage of a rather high resolution, which permits an unambiguous identification of the elemental composition of both the reactants and reaction products. In our laboratory we have constructed such an external cluster source interfaced to an FT-ICR (cf. Fig. 1), which has the advantages of extreme versatility in the choice of the specific nature of the cluster and ligands, and the ability of unambiguously determining the elemental composition of the reaction products1–3. In the last few years we have investigated in some detail a large number of reactions of solvated metal ions and clusters, employing various ligands. The “solvents” ranged from the simplest, and theoretically easiest to describe rare gas atoms, over simple molecules like CO, N2 or O2 to polar polyatomic species like NH3, and to the most important solvent of them all, water. These studies have provided a number of interesting insights into the metal–ligand interactions and into the effect of the solvent upon the chemical properties of the metal. The object of the present chapter is to review and summarize some of these results. II.
GENERATION OF SOLVATED METAL IONS AND CLUSTER IONS
As explained in the experimental section, the metal ions and cluster ions are generated by vaporizing a solid target by a pulsed Nd:YAG laser in the presence of a high pressure cold carrier gas.1,4,5 Such a vaporization produces, besides mainly neutral atoms, also sufficient quantities of ions, typically both positively and negatively charged, so that separate ionization is usually not needed. Experimentally, there is naturally a number of possibilities of forming complexes between the metal ion or ion cluster, and the desired ligand. In our apparatus, we use at least three distinct methods to generate the complexes of interest. Perhaps the simplest method involves adding the desired solvent or ligand directly to the carrier gas flow. In most of our experiments the carrier gas is helium, with the helium atoms interacting with the ions weaker than just about any other atom or molecule. Usually whether one desires it or not, the ions produced in the vaporization interact with impurities which are either present in the gas flow, or are formed in the vaporization process, so that even
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Figure 1: Fourier-transform ion cyclotron resonance (FT-ICR) instrument equipped with an external pulsed supersonic beam ion source. The ions and cluster ions are guided from the source chamber through several stages of differential pumping into the ICR trapping cell. The reactant gases are introduced into the cell via a precision leak valve, raising the background pressure from the background value (p < 10–10 mbar) to ≈10–8mbar, corresponding to about one collision per second.
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without intentional addition of other species to the carrier gas one often observes complexes with water, molecular nitrogen or carbon dioxide. One of the disadvantages of the direct addition method is that the atoms and ions are initially produced translationally, vibrationally, or electronically hot, so that a chemical reaction may take place, resulting in an intimately bound product cluster, rather than a molecular complex. Usually, however, the dilution is sufficiently large, so that enough collisions with the inert carrier gas take place to cool the ions and atoms translationally and relax excited states. As an example, seeding the carrier gas with molecular O2 while vaporizing chromium, a weakly bound [Cr..O2]+ complex is predominantly produced. On the other hand, when N2O is used, a chemical reaction of the chromium ions takes place, producing the covalently bound chromyl cation, CrO2+. The two ions can easily be distinguished based on the differences of their chemical behaviour.6 A second possibility is to produce the solvated complexes by reactions of the desired central ion or cluster ion with the ligands directly in the FT-ICR mass spectrometer. At first sight one might expect that two body recombination in the high vacuum, where the collision rate is typically less than one per second, will be very inefficient. Actually, however, one often observes that formation of complexes between transition metal ions or clusters and even small molecules, such as nitrogen or carbon monoxide, can be amazingly efficient. This is undoubtedly due to the availability of a multitude of low lying electronic states in most transition metals, and the resulting high density of states of the complex, where the excess energy can be redistributed for a time sufficiently long, until the complex can be stabilized by subsequent collision, or radiatively, by emission of a photon. As an example, already trimers and tetramers of group 5b (V, Nb, Ta) attach rather efficiently small molecules like CO forming carbonyl cations such as for instance V4CO+, V4(CO)2+, etc. While for the small, n = 3 or 4 species the attachment efficiency is relatively low, it increases rapidly with size, and for n above ≈15 it takes place essentially with collisional rate.7 Important for the rate of attachment is not only the density of states on the cluster, but also that of the ligand. Thus while at least an n = 4 Rhn+cluster is needed for observable formation of complexes with CO or N2, already the monatomic Rh+ cation attaches efficiently undecomposed benzene in binary collisions, and if allowed to react for a sufficiently long time (several seconds), a Rh+(C6H6)2 “sandwich” cation forms as a final product.8 The fact that the product is a Rh+ with benzene ligands can be shown by exchanging the benzene for perdeuterobenzene, C6D6, which occurs without any isotopic scrambling.
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A third, and gentlest way of generating the desired complexes and clusters involves ligand exchange. In this case, one produces already in the supersonic expansion the central ion or ion cluster solvated with weakly bound ligands. Thus addition of argon to the carrier gas and increasing sufficiently the stagnation pressure results in the formation of cluster ions of the type Mn+Arm, that is “coated” with a layer of weakly bound argon ligands. This cluster can then in the mass spectrometer be reacted with the desired, stronger bound species. In this way one can produce complexes between the metal core and reactive ligands, which would otherwise chemically react. The ligand is “soft landed” on the metal, with the excess energy being carried away by the weakly bound rare gases. As an example the reaction of benzene with Nb+ can here be mentioned. In contrast with Rh+, which attaches undecomposed C6H6, reaction with Nb+ results in the loss of a hydrogen molecule and formation of Nb+C6H4. If, on the other hand, a solvated Nb+Arn, n ≥ 3 is used instead, no dehydrogenation takes place, and as in the rhodium case, Nb+C6H6 and eventually Nb+(C6H6)2 complexes are the observed reaction products.9 III.
CLUSTERS SOLVATED BY INERT GASES AND THEIR STRUCTURE
An interesting question regarding the clusters containing a metal core solvated by several rare gas ligands involves their structure and geometry: are they just “snowballs” with the relatively weakly interacting rare gases randomly distributed, are the positions of the ligands controlled by electrostatic repulsion or attraction forces, or are they to be viewed as complexes with well defined structures, and with the individual atoms held in specific locations by directional valence forces? To test this question we have examined in more detail the clusters of the type M+Arn, specifically with rhodium and niobium.10 In both cases we could prepare clusters with n up to about 20. Even though the observed distributions varied considerably depending on the argon stagnation pressure and other source parameters, over a relatively wide range of conditions we found a prominent maximum in the distribution at n = 4 for Nb+, and at n = 6 for Rh+, suggesting clearly that some kind of coordinative saturation or shell closure occurs for these numbers (Fig. 2). A similar interesting observation was in fact made several years earlier by Lessen and Brucat,11,12 who found that the isovalent ions V+Ar4 and Co+Ar6 also represented distribution maxima, and suggested they have tetrahedral and octahedral geometry, respectively. Even
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Figure 2: Coordinative saturation of the NbArn+ and RhArn+ solvation shells. Note the enhanced abundances of the n = 4 cluster ion for Nb+ and n = 6 for Rh+ due to the enhanced stability of the closed first solvation shell – see text. Notice the presence of Arn+ clusters in the niobium experiment.
though this would appear reasonable if the geometry was solely controlled for instance by the electrostatic repulsion forces, there was a problem with this interpretation: since Rh+ (and Co+) with their larger nuclear charge are smaller ions than Nb+ (and V+), if anything one would therefore expect solvation shell closure at a smaller, not larger value of n. A useful insight into this problem was provided by the trailblazing experiments of Soep and co-workers on the much simpler, diatomic species Al..Ar,13 and by subsequent work on the related group IIIArare gas atom complexes.14 When one of these atoms with an s2p valence electron configuration interacts with a closed shell rare gas atom, depending on the orientation of the p electron orbital, either a 2Σ, or a doubly degenerate 2Π state can form. Experimentally one finds that the former, where the p orbital is oriented towards the rare gas atom, is either very weakly bound or repulsive, while the latter is rather strongly bound. The perpendicular orientation
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permits the rare gas atom to approach along the nodal plane of the p orbital the positive ion core much more closely, resulting in the attractive interaction. This bonding model is easily extended to the positive Nb+ and Rh+ (and V+ and Co+) ions, with their partially filled d orbitals. Nb+ (V+) with their Kr 4d4 (Ar 3d4) configuration will possess four singly occupied and one empty d orbital. If the latter is identified with the dx2–y2 orbital, the electron density will be nonspherical, and will exhibit in the x–y plane four areas of lower electron density, providing four sites for rare gas ligands in a square planar arrangement. Additional ligands along the z axes will face the half filled dz2 orbital, and will be much less strongly bound. In the case of Rh+ and Co+ with a d8 configuration, three d orbitals will be doubly occupied, with two being only singly occupied. Here the half empty dx2–y2 and dz2 orbitals will provide six octahedrally arranged areas of lower electron density, allowing preferential attachment of six rare gas ligands. The prediction of these simple theoretical considerations found then full support also in ab initio density functional calculations.15 These find for Nb+ in agreement with the experiment four strongly bound Ar ligands at 2.96 Å, in a square planar arrangement, and not tetrahedral as previously suggested. When a fifth and a sixth ligand are added, these are predicted to be much more weakly bound, and at much larger distances of ≈3.8 Å. For Rh+ (and Co+) on the other hand, one finds six strongly bound ligands at 2.93 Å in an octahedral geometry. Interestingly, the computations would predict for instance for the Nb+Ar3 complex to be T-shaped (and polar), and would also suggest that for Rh+Ar3 two nearly isoenergetic isomers should be possible. Clearly, the computations suggest that the ligands are not simply attached by van der Waals and electrostatic forces to a spherical ionic core by its isotropic potential, but are held in a relatively rigid geometry by directional forces. The empty dx2–y2 orbital for d4 V+ and Nb+ and the half-filled dx2–y2 and dz2 in the d8 Co+ and Rh+ ions generate a highly anisotropic electrostatic potential, with increased binding in the areas of reduced electron density, that is along the axis of the empty or partly filled orbitals. We do not have detailed data for solvated cluster ions, and have therefore not tried to extend the coordinative saturation studies to the larger Mn+Rgn species. From the observations for solvated M+ cations it seems very likely that one can extrapolate these results to the larger species, and that even these should not be viewed as “snowballs” of randomly associated rare gas ligands, but as complexes with well defined structures and solvation geometries.
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COOLING THE COLLISION COMPLEX: INERT LIGANDS AS AN EFFECTIVE HEAT SINK
If one immerses niobium metal into room temperature liquid benzene, no apparent chemical reaction is observed. On the other hand, examination of the reactions of gas phase niobium ions or cluster ions with benzene has revealed efficient reaction, and for all the larger clusters formation of carbide with total hydrogen loss. If one tries to identify the reasons for this difference in behavior, three possible causes can be considered: (a)The degree of coordination: while the atoms on the bulk metal are coordinated to a number of other atoms, those in a small cluster have a much smaller degree of coordination. (b)The effect of charge: the atoms on a metal surface are in general neutral, while in the mass spectrometer ionic (positively or negatively charged) species are investigated. (c) The effect of temperature: binding of benzene to the surface of the metal releases a considerable amount of heat; this heat released can in the rarefied gas phase not be readily removed, and helps surmounting the activation barrier to benzene decomposition and dehydrogenation. One of the ways of distinguishing between these possibilities would be preparing the metal-benzene complex cold. As noted above, this can readily be done by a ligand exchange technique, in which the niobium cluster or ion cluster is first solvated by a weakly bound ligand such as argon, and these argon atoms are then exchanged for the reactant to be investigated, e.g. in the present case benzene. One advantage of the FT-ICR method is that one can do the experiment even more quantitatively: it is easy to prepare and mass select solvated clusters of the type NbnArm+, with essentially any desired values of n and m.9 The results can be exemplified by the results of an experiment with n = 1 and varying values of m. As noted above, m = 0, that is the bare Nb+ ion, results in the loss of two hydrogens, and formation of an NbC6H4+ cation. When now the reaction of the m = 1 cation, NbAr+, is investigated, one finds out that not only the overall reaction rate is increased, but in addition to formation of the dehydrogenated NbC6H4+ ion, at least two additional reaction channels are observed: NbAr+ + C6H6 → → →
Nb+C6H4 + H2 (≈76 %) Nb+ + C6H6 + Ar (≈17 %) Nb+C6H6 + Ar (≈7 %)
(1)
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The collisional fragmentation leads to a bare Nb+ ion, which then subsequently reacts with benzene to form the major NbC6H4+ product. The argon ligand can, however, apparently remove enough energy from the complex, so that a third process, ligand exchange with no dehydrogenation, takes place and a cold NbC6H6+ complex is stabilized. The removal of heat from the complex is made more efficient by increasing the number of argon ligands, m, so that for the NbAr2+ the stabilization of the complex and loss of H2 occur with comparable probability. Finally, for n ≥ 3 the dehydrogenation is no longer detected, and the Nb+C6H6 becomes the dominant primary reaction product, which in a secondary reaction step results in the Nb+(C6H6)2 “sandwich” complex. Naturally, in a similar way one can study the reactions of NbnArm+ ions with values of n > 1, and we have investigated them up to about n = 45. The general conclusion is the same as for the n = 1 case described above, by attaching to the niobium cluster enough argon atoms to remove the heat generated by nondissociatively chemisorbing the benzene, the dehydrogenation can be suppressed, and stable NbnC6H6+ complex ion products are generated. This answers clearly the question presented at the beginning of this paragraph: the dominant factor in the niobium cluster reactions is the effect of the heat generated by chemisorption of the ligand on the cluster surface, rather than the charge of the cluster or coordination of the atoms. By providing an efficient heat sink to remove this energy, stable complexes between the metal and undecomposed benzene ligands can be generated even for small charged clusters. Interestingly, the last sentence has to be said with some reservation. While complexes with undecomposed benzene ligands could be stabilized for most of the cluster sizes in the investigated range from n = 4 to n = 45, there were a few exceptions, as exemplified for n = 1 in Fig. 3. Regardless of the value of m, the Nb11Arm+ clusters always fully dehydrogenated benzene, and no Nb11C6H6+ complex ion could be detected: Nb11Arm+ + C6H6 → Nb11C6+ + 3H2
(2)
This demonstrates that even though the temperature may be dominant, also the local “structure” of the cluster surface, and the niobium atom coordination have an effect. Apparently the Nb11 cluster surface provides a reactive “site”, where the activation barrier to benzene dehydrogenation is sufficiently low, so that even when most of the chemisorption heat is removed, the benzene still efficiently reacts with the metal, resulting in hydrogen loss and
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Figure 3: Reactions of niobium cluster cations solvated by argon atoms with benzene. The top trace shows the initial NbnArm+ clusters for n = 9–14, with m ranging from 0 to ≈5, and in the bottom spectrum products after 3 seconds reaction are shown. Even though in this size range bare clusters fully dehydrogenate benzene and form NbnC6+ “carbide” clusters, exchange of benzene molecules for the argon ligands results in NbnC6H6+ products. An exception is the Nb11+ cluster which completely dehydrogenates benzene even when solvated with argon atoms.
niobium carbide formation. This again shows an analogy with processes on bulk catalysts, which are now known not to proceed uniformly over the entire surface, but preferentially or even exclusively on particular active “sites”. V.
TEMPERATURE CONTROL AND “FREEZING” OF REACTION INTERMEDIATES
As explained above, one can actually control the number of the inert ligand atoms on the surface, and in this way control the effective “temperature” of the collision complex, and steer the catalytic
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process. A recent study of the reaction of platinum cations with methane is another nice demonstration of such control.16 From several previous studies, unlike most other transition metal cations, Pt+ was known to exothermically dehydrogenate methane, yielding PtCH2+ and molecular hydrogen. We have now reinvestigated this same reaction not only with bare Pt +, but also with cations solvated by rare gas atoms. Under these circumstances one observed not only dehydrogenation, but also two parallel processes, ligand exchange and fragmentation. PtArm+ + CH4
→ → →
PtCH2+ PtCH4Arm–n+ PtArm–n+
+ m Ar + H2 + n Ar + n Ar + CH4
(3)
The branching between these three processes depended critically on the initial number of the argon ligands, m. For m = 0, dehydrogenation is the only observed process, but already with m = 1, the second process prevails, and the overall efficiency of the reaction increases. For m = 2 and 3 the dehydrogenation completely disappears, and only the “ligand exchange” forming the “methane complex” is observed, besides a small degree of fragmentation. For m = 4–5 the efficiency of complex formation decreases, and fragmentation becomes dominant, and for m > 5 the only process. One often considers ionic reactions of this type, which take place with high efficiency during “low temperature”, low energy collisions, as proceeding without a barrier. Actually, when one examines carefully the problem of the Pt+ reaction with methane, one finds out not only that the potential surface is quite complex, and involves in fact several barriers (cf. Fig. 4), but also that the reaction under the single collision conditions can hardly be considered a “low temperature” process, but it takes place in a highly excited, “hot” collision complex. DFT computations reveal that the first step in the reaction involves a highly exothermic formation of a Pt+–CH4 complex, which is separated by a low barrier from the global minimum, an inserted CH3PtH+ ion. Another, relatively high, barrier has to be surmounted in order to form the methylene-platinum-dihydride (CH2PtH2+) ion lying at much higher energy than the global minimum. This then proceeds via a complex of CH2Pt+ with H2 towards a final barrier needed for its dissociation. Since, however, all the barriers are low compared with the large amount of internal vibrational energy in the complex, their presence is essentially irrelevant in a single collision, high vacuum gas phase process, and an efficient reaction takes place. Even if the initial internal energies of the two reactants as well as their kinetic energies were
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Figure 4: A potential energy diagram showing the tortuous path from the Pt+ and methane reactants to the PtCH2+ and methylene products. Even though the reaction proceeds via a number of reaction intermediates and over several rather high potential barriers, it runs in the gas phase to completion, since the reactive complex is formed “hot” due to redistribution of the high, ≈160 kJ/mol, Pt+–CH4 interaction energy. Evaporating argon ligands removes the excess energy, resulting in cooling the complex, and “freezing” the inserted reaction intermediate.
exactly zero, their interaction energy becomes available as the ion and its collision partner recombine. It heats the collision complex, and permits surmounting the activation barriers. The argon ligands thus provide a means of removing this large internal energy, and in this way one can control the course of the reaction, and “freeze” or stabilize the inserted reaction intermediate. VI.
ENHANCING REACTIVITY BY INERT LIGANDS: STABILIZATION OF COLLISION COMPLEXES
In the above paragraph we have discussed how the weakly bound ligands on the metal cluster surface can provide a heat sink, which can control the reaction by gently removing the chemisorption heat, and prevents a reaction which would otherwise take place. This effect is well known from matrix isolation, where there are many experiments of reactants which react, often violently, in the gas phase, but can coexist peacefully in a low temperature matrix.
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On the other hand, also from matrix studies examples are known, where a reaction which in the gas phase does not occur, is found to proceed in the low temperature solid. In a room temperature gas phase system, a collision between two small molecules typically occurs on a subpicosecond timescale; under these circumstances the probability of a reaction whose rate is intrinsically slow is low, and may not be observed. Furthermore, the interaction potentials are often strongly anisotropic, and colliding partners in the gas phase may not have the correct relative orientation favoring the reaction. The presence of the two reactants as nearest neighbors in the matrix provides the “sustained proximity” which is needed for the slow reaction to take place. A similar effect can also be observed in the mass spectrometric studies, where the presence of ligands permits the formation of a long lived complex, and changes thus the timescale by some 9–11 orders of magnitude from sub-picosecond into the second range. An example was already apparent above: even though the presence of several argon atoms on the Nb+ ion could completely suppress dehydrogenation, for the NbAr+ diatomic ion with just a single argon ligand, its rate is actually increased by about 30%, and if one considers the parallel reaction channels, the increase is more than 50%. The reason is that for the bare ion, the collision occurs on a very short, subpicosecond timescale, this may reduce the product yield even if the reaction is extremely fast; in part of the collisions the reaction partners separate again, before the chemical reaction could take place. When the weakly bound argon ligand is present, it may detach or “evaporate” from the complex. The energy removed by the departing argon will in most cases be sufficient to stabilize the Nb+–C6H6 collision complex, and thus assure that they remain in proximity for an extended time. The removed energy may or may not be enough to prevent further chemical reaction and dehydrogenation of the benzene from taking place, so that both unreacted complexes and dehydrogenated species are observed. Only evaporation of two or three argon ligands removes enough energy to completely stop the dehydrogenation. While the reaction of benzene with niobium is apparently intrinsically efficient, and furthermore the collisions of the polyatomic benzene molecules with the transition metal are relatively “sticky”, so that even without the presence of a ligand efficient dehydrogenation may proceed, when less reactive small molecules are involved, this may not be the case. A more clearcut case is observed in reactions of rhodium clusters with methane.17 Bare rhodium cationic clusters, with the exception of the dimer, do not react with methane
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at all. On the other hand, when for instance Rh3+ solvated with argon are reacted, an efficient reaction with a loss of molecular hydrogen is observed (cf. Fig. 5): Figure 5: Effect of argon ligands upon methane activation by rhodium clusters. (a) The reaction of atomic Rh+ with methane is endothermic, and cannot occur in thermal collisions. By exhanging for Ar ligands, a Rh+ methane complex can be formed. (b) Rh2+ is the only bare rodium cluster that reacts with methane. Presence of one or two Ar ligands makes the reaction more efficient, since they stabilize the collision complex. Evaporation of three or more ligands cools the complex to the extent that the reaction rate drops significantly, and a competitive process, formation of a Rh2+CH4 complex, appears. (c) While no reaction of bare Rh3+ with methane is observed, ligand exchange with Ar ligand makes possible the formation of a long lived complex, in which dehydrogenation can then take place. Evaporation of two or more ligands cools the complex too much for the reaction to occur. (d) Rh4+ can only form a complex by exchanging argon ligands for methane.
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Rh3Arm+ + CH4 → Rh3CH2+ + m Ar + H2
(4)
Again, the ligand exchange of methane for the argon ligands yields a long lived complex, which can then leisurely react with hydrogen loss. Actually, one can in this case directly observe the intermediate before dehydrogenation, so that one can formulate the reactions as proceeding in two steps: RhnArm+ + CH4 → RhnArkCH4+ + m-k Ar → RhnCH2+ + m Ar + H2 (5) In the case of n = 3, one can indeed observe the intermediates prior to dehydrogenation, for instance Rh3ArCH4+ or Rh3CH4+; in further collisions with methane these then gradually lose hydrogen and the remaining argon ligands, yielding the Rh3CH2+ final product. It should be noted that for Rhn+ with n ≥ 4 the dehydrogenation step is either too slow, or the barrier too high, so that only ligand exchange of argon for undecomposed methane is detected. To summarize this section, besides retarding the reaction by removing the reaction chemisorption heat, alternatively the presence of inert ligands can make a reaction more efficient. This will in general be observed in cases when two conditions are met. In the first place when the density of states of the collision complex is too low for a long lived complex to efficiently form in the absence of ligands, and the ligands are essential for its stabilization. In the second place, the intrinsic reaction rate must even in the cold, stabilized complex be sufficiently high, so that the reaction does occur on the timescale of the ICR experiment (typically seconds). VII.
COMPLEXES OF METAL CATIONS WITH SMALL MOLECULAR LIGANDS
The laser vaporization-supersonic expansion source permits the production of a large variety of ions or ion clusters solvated not only with rare gas atoms, but also with small molecular species. The best known group of compounds belonging to this class are naturally carbonyls, extensively studied since their discovery by Mond. Much less understood is the chemistry of complexes with other molecular ligands, such as O2, N2, or CO2, even though recently increasing numbers of studies are addressing this problem. Species of this type are easily produced by several methods in our apparatus, either by simply adding the desired ligand to the carrier gas, by ligand exchanging it for a more weakly bound ligand, or by chemical reaction within the ICR cell.
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Interestingly, by using different preparation methods, often isomeric species can be produced, which exhibit quite different chemical properties. As an example we have recently reported, one can produce the [Cr,O2]+ ion by vaporizing chromium metal and add to the inert carrier gas either N2O or molecular oxygen.6 In spite of the same elemental composition, and the same temperature in both cases, the two species exhibit quite different chemical properties. The former ion exhibits a CID pattern with preferential loss of an O atom and CrO+ formation, and a fairly high threshold for O2 loss. It also exhibits no isotopic exchange with 18O2. The CID fragmentation of the latter species is characterized by a quite different CID fragmentation pattern, with a low threshold for O2 loss, and it also quantitatively exchanges 16O2 for 18O2 without any isotopic scrambling. Clearly the ion produced with molecular oxygen is identified as a Cr(O2)+ complex, whereas expansion with N2O results in a covalently bound chromyl cation, CrO2+. Also interesting are the reactions of the Cr(O2)+ complex with water, which apparently proceed via a “hot” [CrO3H2]+ complex with three equivalent oxygen atoms, and which then immediately dissociates to give back water and CrO2+, as evidenced by isotopic scrambling when H218O is used. The transient interaction with the strongly bound water ligand provides energy which heats the reaction intermediate and allows surmounting the activation barrier to the breakage of the O–O bond. The collision with the water ligand thus “catalyzes” isomerization of the chromium peroxide entity to CrO2+, the covalently bound chromyl cation. Production of such isomeric ions by different methods is apparently quite common, and several examples were observed in our studies. Thus ReO2+ produced by addition of O2 to the source expansion reacts within the ICR cell with water, yielding ReO3+ and hydrogen, H2. Conversely, the reaction of ReO3+ with molecular hydrogen proceeds with rather high efficiency in exactly the opposite direction, yielding ReO2+ and water. Clearly, two different isomers of ReO2+ are involved (Fig. 6).18 Apparently, the higher energy metastable complex Re(O2)+ formed in the supersonic expansion again isomerizes upon binding a water ligand. The energy of the isomerization plus the binding energy of the water produce a hot collision complex with so much excess internal excitation that molecular H2 can evaporate. On the other hand, the stable, cold ReO3+ from the source can be reduced by molecular hydrogen to a covalent ReO2+ ion. The expansion with added oxygen often produces metal cations in a variety of oxidation states. Thus in the above mentioned case of rhenium, ions of the type ReOn+ are observed, with the
Computed structures of rhenium oxides and complexes with molecular oxygen. The structures were computed by DFT-techniques.
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Figure 6:
V. E. Bondybey, M. Beyer, U. Achatz, B. Fox, and G. Niedner-Schatteburg
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distribution essentially ending with n = 8. Interestingly, the n distribution is not random, but while for instance n = 2–6 and n = 8 are usually quite abundant, n = 1 and n = 7 are under most conditions nearly absent. Information about the structures of these oxide and peroxide ions can be obtained with the help of their collisional dissociation, CID (Fig. 7). Such studies reveal that, Figure 7: Examples of collisional fragmentation of ReOn+ species. ReO5+ in the top part looses O2 ligand with a low fragmentation threshold of ≈0.5 eV; an order of magnitude more energy is needed for the loss of one additional atom. The collisional fragmentation pattern of ReO8+ shows that the first CID products are ReO6+ and ReO4+ appearing with threshold energies of ≈0.5 and 1.5 eV, respectively. These data are quite consistent with the computed structures in Fig. 5.
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for instance, the n = 8 molecule is probably best formulated as Re+ with four O2 dioxygen ligands, that is Re(O2)4+. With very low energetic thresholds it gives up two O2 molecules, resulting in Re(O2)3+ and Re(O2)2+, with the n = 7 and n = 5 species not appearing among the fragmentation products at all. On the other hand, the n = 5 ion from the source easily gives up in the first fragmentation step one O2 molecule, but a much higher collision energy is needed for the loss of a single additional atom. This is consistent with a structure consisting of a covalent ReO3+ cation with three Re=O double bonds, and with a weaker bound additional peroxidic O2 group, that is ReO3(O2)+. The structure of the n = 5 ion is also easily demonstrated by its reaction in the ICR cell, since it exchanges very efficiently its O2 molecular ligand for other molecular species, N2, CO2, CO, and H2O, in the order of increasing binding energies.19 It is perhaps again interesting to note that even though the three of four O2 of the n = 6 and n = 8 ions are considerably weaker bound to the rhenium cation than the single molecular oxygen in the n = 5 ion, they exchange their ligands for CO or CO2 two to three orders of magnitude less efficiently. This is probably the effect of coordinative saturation: with the molecular ligands around, sterical effects prevent the collision partner from interacting with the core metalion. VIII.
HYDRATED IONS AS NANODROPLETS FOR STUDIES OF SOLUTION REACTIONS
With the help of a laser vaporization source it is easy to prepare metal cations with a shell of solvent molecules again by simply adding the desired solvent to the carrier gas. While there is basically no end to the variety of solvents which can be used, of particular interest is the most important solvent on earth, water. Numerous important industrial reactions involve aqueous solutions – the chemistry of life is basically an aqueous chemistry – and oceans, rivers, and even the rain falling down is essentially water containing varying concentrations of ions, including metal cations. Clusters of the type M(H2O)n+ are therefore very convenient systems for investigating a large variety of solution processes in microscopic detail. With our laser vaporization source such hydrated clusters, where M can be essentially any metal, and where n ranges from 0 to >100, are easily generated.3,20 A slight complication which, however, can be turned into an advantage is the black body fragmentation of the hydrated clusters. Water is an excellent absorber of infrared radiation, and
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the oscillator strength of infrared absorptions is usually further significantly increased in hydrogen bonded systems, such as water clusters and hydrated ions. Many of the cluster vibrational modes corresponding to the “rotational” and “translational” degrees of freedom in liquid water happen to lie close to the maximum of the Planck curve at 300K, and the clusters therefore efficiently absorb radiation from the apparatus wall. As a consequence one finds that even though the large hydrated clusters are initially in the source produced cold, their temperature in the ICR cell is controlled by a competition between radiative heating and evaporative cooling. The rate of energy absorption is proportional to the number of absorbing molecules, and indeed one finds experimentally that the rate of the cluster fragmentation is roughly proportional to the number of water ligands n2. This simply reflects the fact that the time needed to accumulate enough energy to evaporate one ligand molecule is proportional to 1/n. The above discussion does not need to be restricted only to hydrated metal cations; the laser vaporization source can equally well generate clusters where the central ion is an anion or involves nonmetallic elements. In view of the above discussion it is also quite understandable why the proportionality constant is basically independent of the specific nature of the central ion, that is if it is an anion or cation, or if it is a metal or an ion such as OH– or H3O+.21 The solvent molecules at the periphery of the cluster where the evaporation occurs are sufficiently far from the central ion to make its specific nature relatively irrelevant, except for the last stages of fragmentation, that is for very small values of n. It might also be mentioned here, that such fragmentation is not an exclusive property of water, but will occur for any other solvents strongly absorbing in the far infrared; for instance we observed equally efficient black body fragmentation for ammoniated clusters M(NH3)n±.22 From the experimental point of view, the efficient fragmentation of the hydrated species limits the size of clusters that can be conveniently studied. In our apparatus, this restricts us to ions with less than about 100 ligands. Obviously, the range could be significantly extended with an ICR cell and apparatus with controllable wall temperature. On the other hand, the black body fragmentation also makes it possible to start with clusters of a given size, and then gradually remove solvent molecules one by one. Since many ionic systems owe their stability to the polar water solvent, one can then observe reactions and rearrangements which occur as the stabilizing solvent is removed.
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HYDRATION OF IONS AND REDUCTION-OXIDATION REACTIONS IN SOLUTION
We have thus far studied a variety of ionic hydrated M(H2O)n+ clusters, with metals M including Na, Ag, Mg, and Al. Particularly interesting and instructive were the studies of the rare earth metals as exemplified by Mg. As shown both by the group of Fuke et al23–27, and by the FT-ICR studies in our group, the hydrated magnesium cations behave differently depending on the value of n. For very small values of n < 5 and very large values of n ≥ 20 one obtains readily clusters of the Mg(H2O)n+ composition. A different situation is in the intermediate range, 19 ≥ n ≥ 5, where usually only hydroxide clusters, MgOH(H2O)n+, are observed. Obviously, magnesium occurs in these clusters in two different oxydation states. While in the small clusters with just a few water ligands the Mg+ ion is obviously monovalent, in the hydroxide clusters it clearly is in its usual oxydation state as Mg2+. A clearer insight into this problem is gained when one starts with a large, e.g. n > 20 cluster and follows its black body fragmentation. Initially as discussed above, water ligands are lost one by one. When, however, the transition region of around n ≈ 19 is reached, a different reaction takes place: Mg(H2O)n+ (+ hν) → MgOH(H2O)n–1+ + H
(6)
Seemingly magnesium is oxidized by water to Mg2+, the hydrated magnesium cation cluster is converted into a hydrated magnesium hydroxide, and the simultaneously formed hydrogen atom “evaporates” from the cluster. The interpretation of this process, and the exact time when the magnesium oxidation takes place is, however, not as obvious as it might seem. A possible key may be provided already by the observation of Humphrey Davy that alkali metals, e.g. sodium, can be dissolved in liquid ammonia; a blue solution is formed, which contains the alkali atoms oxidized to their favorite oxidation state, i.e. Na+, with the blue color being due to solvated electrons. When an adequate supply of water ligands is available, a process similar to dissolving alkali atoms in ammonia could take place. The Mg+ ions, isovalent with alkali atoms, could be spontaneously oxidized to their favorite oxidation state, resulting in clusters containing a hydrated Mg2+ cation, and a hydrated electron (Fig. 8). As then the solvent is gradually removed, at some point the number of water molecules is not sufficient to stabilize both the doubly charged ion and the electron, and their recombination takes place. The resulting open shell Mg+ ion immediately reacts with a water molecule producing the MgOH+
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Figure 8: Fragmentation of hydrated Mg+(H2O)n clusters. Large clusters containing presumably separately hydrated Mg++ and e– lose water ligands until they reach the critical size of n ≈ 16–21. In this region the system becomes unstable, the hydrated electron recombines with the Mg2+. The open shell Mg+ instantly react with a nearby water molecule, resulting in a magnesium hydroxide cation, and a loss of hydrogen atom, as observed experimentally.30
hydroxide, and leaving behind a hydrogen atom which being weakly bound is ejected from the cluster. Stable Mg2+ ions do exist in bulk water solutions, even though the second ionization potential of magnesuim, 15.031 eV, considerably exceeds the 12.61 eV first ionization potential of water. The high solvation energy of the small doubly charged alkaline earth metal cations is more than sufficient to compensate the difference in the ionization potentials. Not surprisingly, it has been shown conclusively by Kebarle and co-workers that small doubly ionized clusters Mg2+(H2O)n can easily be generated in the gas phase, and survive at least on the time scale of mass spectrometric experiments.28,29
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Quite interestingly both experiment and theory indicate that the metastable small hydrated Mg2+(H2O)2 cations do not fragment via charge transfer, but with proton transfer yielding MgOH+ and H3O+.29 We have therefore investigated the stability of doubly ionized ions by DFT ab initio techniques.15 Our recent theoretical DFT study has shown that a hydrated M2+(H2O)2 cation (where M can be any of the rare earth metals) is separated from the MOH+ + H3O+ ground state by two potential barriers. The first, quite high and broad barrier involves moving one of the two water ligands from the first into the second solvation shell. The second, lower barrier then involves a proton transfer across the hydrogen bond from the water in the first solvation shell to the one in the second one, resulting in a “salt bridge” M2+ OH– H3O+ structure. This is then followed by a coulombic explosion and separation of the two singly charged ions, MOH+ + H3O+. It is quite likely that this “salt bridge” mechanism may also be at work in the above discussed hydrogen atom loss and hydroxide formation in the singly charged M(H2O)n+ clusters. In the large cluster there naturally already are water molecules in the second solvation shell around the doubly charged M2+ cation. Evaporation and shrinking of the solvation shell must eventually lead to a close approach of the solvated electron to one of the second shell ligands. This will naturally facilitate the transfer of a proton from a molecule in the first solvation shell and lower further the second activation barrier. In this case, however, the H3O+ ion formed by the transfer will recombine with the electron, resulting in the unstable neutral H3O, which will in turn decompose to form water and a hydrogen atom. To gain further information about such redox processes, we have carried out similar experiments with hydrated aluminum ions, Al+(H2O)n, n = 3–50. Again, for small n ≤ 10 and large n ≥ 25 loss of a single water molecule was observed, while in the intermediate size region, 11 ≤ n ≤ 24, water loss was competing with the formation of aluminum dihydroxide and molecular hydrogen: Al+(H2O)n → Al(OH)2+(H2O)n–2–m + H2 + m H2O,
(7)
Similar to the hydrated magnesium case, one might advance an explanation involving two hydrated electrons in the vicinity of a hydrated Al3+ core, which upon loss of solvent become unstable and recombine to reactive Al+, leading to the formation of H2 and of the aluminum dihydroxide cation. The energetic situation, however, is less favorable, and it is less obvious if the hydration energy Al3+ in the small cluster is sufficient to offset the high second and third
Solvated Metal Ions and Ion Clusters
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ionization potential. It also fails to explain why the transition range of coexistence of the hydroxide and Al+ is broader than in the magnesium case. In the above pre-ionized model the oxidized Mg2+ or Al3+ are present in the cluster from the start, and it is their recombination with the electron which triggers the reaction with water, and the formation of hydroxide and hydrogen. An alternative possibility would be that hydrated clusters indeed contain monovalent ions, whose oxidation only takes place at or close to the time of the hydrogen evolution. In such a mechanism, a proton transfer could occur between water molecules in the first and second solvation shell, yielding a “salt bridge” structure described above, e.g. •Mg+..OH–..H3O+. This would then be followed by correlated electron transfers from the OH– to H3O+ and from •Mg+ to OH–, yielding Mg2+OH– and the unstable, neutral H3O. Explaining why this process does not take place in the large clusters, but only when a certain critical size is reached is one of the problems of this model. Perhaps the proton transfer described above does not occur with appreciable rate in a fully developed hydrogen bonded liquid, but only takes place when the solvation structure is destabilized by the loss of ligands from the second or third solvation shell. X.
REACTIONS OF METALS WITH HYDROCHLORIC ACID, AND THE EVOLUTION OF HYDROGEN
The reactions described above have a similarity to the evolution of hydrogen in statu nascendi in reactions of metals with strong acids. To further examine the properties of hydrated metal ions in unusual oxidation states, and to gain more evidence in favor of or against the proposed mechanisms, we have studied their reactions with hydrogen chloride.30,31 Quite interestingly, a reaction only takes place in clusters above a certain size limit – when enough water ligands were available to ionically dissolve the HCl – Mg+(H2O)n with n < 15 and Al+(H2O)n with n < 11 exhibited only fragmentation. On the other hand, the uptake of hydrogen chloride by the larger clusters was, without an upper limit, promptly followed by the hydrogen evolution reaction, which without the HCl only took place below a certain size: Mg+(H2O)n + HCl → MgCl+(H2O)n-m + H + m H2O, n < 15 Al+(H2O)n + HCl → Al+(H2O)n-kHCl + k H2O → Al(OH)Cl+(H2O)n-1-m + H2 + m H2O, n < 11 (8)
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For very large Al+(H2O)n, with n above ≈40 a “ligand exchange” Al+(H2O)nHCl intermediate could be detected with very low intensities in the mass spectra; based on their intensities, one could estimate a delay of ≈100 ms between the intake of HCl and the H2 evolution. Again the observations can be explained with the help of both the “preionization” and “proton transfer” models, even though arguments can be presented for and against either of them. At this point, the available data do not allow a final judgement on the validity of either of the two mechanisms. It would surely be quite desirable to prove spectroscopically if e.g. the open shell Mg+ is – or is not – present in the large hydrated clusters. The proton transfer mechanisms may be examined with state of the art theoretical methods, but electrons delocalized from cores require special techniques. These days considerable efforts are being spent on computational treatments of hydrated electrons without involving metal ions; the extension of these models to hydrated metal ions seems challenging, but promising at the same time. XI.
NEUTRALIZATION AND PRECIPITATION REACTIONS IN HYDRATED CLUSTERS
Of some interest are the reactions of the solvated metal cations with acids, such as hydrochloric acid. It is well known that when HCl is reacted with a bulk solution of NaOH, containing the basic Na+ cations, a very exothermic reaction takes place, with a considerable development of heat. When, on the other hand, one exposes the Na+(H2O)n clusters to gaseous hydrochloric acid, one finds out that clusters with n ≤ 12 exhibit only fragmentation, but do not seem to react with HCl at all.32 If larger clusters are allowed to react for a sufficiently long time, one finds that clusters with n = 13–15 have “dissolved” one HCl, while those with n ≥ 16 contain two (Fig. 9, top spectrum). If now the clusters are allowed to fragment, activated collisionally or by black body infrared radiation, they lose the water ligands, but when one of the above limits is reached, an HCl molecule is evaporated instead. The last HCl is lost around n = 13, and below that limit only hydrated Na+ clusters will be present. This can easily be understood if one remembers that HCl ionizes to H+ and Cl– when dissolved in water; upon dissolution in a discrete Na+(H2O)n cluster, this will contain three ions: H+, Na+ and Cl–, since also NaCl as a highly soluble salt of a strong base and strong acid is expected to be fully ionized. To stabilize three ions and prevent their recombination, a sufficient number of water molecules is required. If one remembers that a proton forms very
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Figure 9: Reactions of hydrated metal cations with HCl. Hydrated Na+(H2O)n clusters react with and “dissolve” HCl only for n > 13. As shown in the top spectrum, when larger clusters with dissolved HCl are allowed to fragment, and when the n ≈ 13 limit is reached, the HCl molecule, rather than a water ligand, is lost. The bottom spectrum shows similar processes for Ag+(H2O)n, which retain the HCl down to n = 5. The reason for this difference in behavior is the “solubility” of the salts. While the NaCl is ionically dissolved in the cluster and the Na+ and Cl– ions have to be separately hydrated, AgCl “precipitates” and forms within the cluster an undissociated silver chloride molecule.32
stable H3O+(H2O)3 ions, while Na+ prefers hexacoordination, then ten water molecules will be needed just to solvate the two cations, with several remaining water ligands being needed to solvate the chloride and bind the ions together. When the amount of water gets too small, a recombinatin through proton transfer from the H3O+ to
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the Cl– takes place, and covalent HCl is reformed. This then evaporates preferentially from the cluster. A nice confirmation of this is provided by experiment where the Na+ metal is replaced by Ag+. In this case already clusters with four water ligands, Ag+(H2O)4, are able to contain an HCl molecule, and clusters with n ≥ 7 can dissolve two (Fig. 9, bottom spectrum).32 The difference here is that AgCl is a very insoluble salt, and even in a small cluster the chlorine will not be present as a chloride anion, Cl–, but will form a silver chloride molecule with the silver cation. The complex will then not contain three ions, but only a single H3O+ cation, and the polar but largely covalent AgCl molecule. The same situation is also found for HBr and AgBr. It should be noted that when the n = 4 cluster, which is probably best written as H+(AgCl)(H2O)4, is allowed to fragment further, it does not lose a water molecule, but the chlorine in the form of HCl. The reason for this is the high ionization energy of hydrogen. A bare proton has from all the singly charged ions the highest hydration energy. When an adequate supply of water ligands is available, it is therefore energetically more favorable to have the charge on hydrogen in spite of the much lower ionization potential of silver. In other words, while in the gas phase the ionization potential of silver (731 kJ/mol) is much lower than that of hydrogen (1311.8 kJ/mol), in aqueous solution the situation is reversed. When, however, the number of water molecules drops below a certain minimum, a charge transfer takes place, yielding presumably AgCl+ and a neutral H atom, which then in turn reacts with the chlorine, regenerating HCl, as suggested schematically by Equation 9: H+(H2O)4(AgCl) → H(H2O)4 (Ag+Cl) → Ag+(H2O)4 + HCl (9) These results seem to imply that ions solvated in the water clusters behave similarly to ions in bulk aqueous solutions. Thus “neutralization” of clusters containing alkali cations results in alkali halides which are dissolved and ionically dissociated. On the other hand, a similar reaction involving insoluble halides results, in spite of the absence of the lattice stabilization energy, in a cluster containing a single metal cation, in “precipitation” of a covalently bound (albeit polar) metal halide molecule, e.g. AgCl or AgBr. XII.
SUMMARY
Many industrially important reactions proceed in solutions, and considerable effort is being directed towards the detailed understanding of the effect of the solvent upon the reactions and the
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course of the reaction. While bulk solutions are extremely complex systems whose studies, experimental as well as theoretical, are quite difficult, modern molecular beam techniques make it possible to generate finite clusters, involving the “solute” with just a limited number of “solvent” atoms or molecules. In this way, one can strategically design the system to simplify this task, and focus only on particular aspects of solute-solvent interactions. The systems which we describe in this review range from metal ions solvated by rare gases, to small molecular ligands and to hydrated ions. We show that just one or several inert ligands can significantly affect the reactivity of a metal ion or ion cluster, and that these effects are analogous to those observed in condensed solutions. Using small reactive ligands, such as CO or oxygen, one can generate metal ions in unusual valence states, and investigate their structures and other properties. Finally, with the help of hydrated ions, one can in considerable detail investigate a number of processes known from aqueous solutions: evaporation, dissolution, redox-processes or precipitation. REFERENCES (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15)
Berg, C., Schindler, T., Niedner-Schatteburg, G., and Bondybey, V.E. (1995) J. Chem. Phys., 102: pp. 4870–84. Schindler, T., Berg, C., Niedner-Schatteburg, G., and Bondybey, V.E. (1996) Chem. Phys. Lett., 250: pp. 301–8. Berg, C., Achatz, U., Beyer, M., Joos, S., Albert, G., and Schindler, T. (1997) Int. J. Mass Spectrom. Ion Processes, 167: pp. 723–734. Bondybey, V.E. and English, J.H. (1981) J. Chem. Phys., 74: pp. 6978–9. Dietz, T.G., Duncan, M.A., Powers, D.E., and Smalley, R.E. (1981) J. Chem. Phys., 74: pp. 6511. Beyer, M., Berg, C., Achatz, U., Joos, S., Niedner-Schatteburg, G., and Bondybey, V.E. (2001) Molec. Phys. In press. Achatz, U., Fox, B., and Bondybey, V.E. In preparation. Berg, C., Beyer, M., Schindler, T., Niedner-Schatteburg, G., and Bondybey, V.E. (1996) J. Chem. Phys., 104: pp. 7940–7946. Bondybey, V.E. and Beyer, M (2001) J. Phys. Chem. A, 105: p.951. Beyer, M., Berg, C., Albert, G., Achatz, U., and Bondybey, V.E. (1997) Chem. Phys. Lett., 280: pp. 459–463. Lessen, D. and Brucat, P.J. (1989) J. Chem. Phys., 90: p. 6296. Lessen, D. and Brucat, P.J. (1989) J. Chem. Phys., 91: p. 4522. Duval, M.C., D'Azy, O.B., Breckenridge, W. H., Jouvet, C., and Soep, B. (1986) J. Chem. Phys., 85: p. 6324. Stangassinger, A., Mane, I., and Bondybey, V.E. (1995) Chem. Phys., 201: pp. 227–235. Beyer, M., Williams, E.R., and Bondybey, V.E. (1999) J. Am. Chem. Soc., 121: pp. 1565–1573.
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(16) Achatz, U., Beyer, M., Joos, S., Fox, B. S., Niedner-Schatteburg, G., and Bondybey, V.E. (1999) J. Phys. Chem.A, 103: p. 8200. (17) Albert, G., Berg, C., Beyer, M., Achatz, U., and Joos, S., Niedner-Schatteburg, G., and Bondybey, V.E. (1997) Chem. Phys. Lett., 268: pp. 235–241. (18) Beyer, M., Berg, C., Joos, S., Achatz, U., Hieringer, W., Niedner-Schatteburg, G., and Bondybey, V.E. (1999) Int. J. Mass Spectrom. Ion Proc., 185/186/187: pp. 625–638. (19) Beyer, M., Berg, C., Albert, G., Achatz, U., and Joos, S., Niedner-Schatteburg, G., and Bondybey, V.E. (1997) J. Am. Chem. Soc., 119: pp. 1466–1467. (20) Beyer, M., Berg, C., Goerlitzer, H., Schindler, T., and Achatz, U., Albert, G., Niedner-Schatteburg, G., and Bondybey, V.E. (1996) J. Am. Chem. Soc., 118: pp. 7386–7389. (21) Bondybey, V.E., Schindler, T., Berg, C., Beyer, M., Achatz, U., Joos, S., and Niedner-Schatteburg, G. (2000) In: NATO ASI Series on Recent Theoretical and Experimental Advances on Hydrogen Bonded Clusters, (Xantheas, S., ed.), Kluwer Academic Publishers: Dordrecht, p. 323. (22) Fox, B., Reinhard, B. M., Beyer, M.K., and Bondybey, V.E. J. Phys. Chem. Submitted for publication. (23) Misaizu, F., Tsukamoto, K., Sanekata, M., and Fuke, K. (1992) Chem. Phys. Lett., 188: p. 241. (24) Misaizu, F., Sanekata, M., and Fuke, K. (1994) J. Chem. Phys., 100: p. 1161. (25) Fuke, K., Misaizu, F., Sanekata, M., Tsukamoto, K., and Iwata, S. (1993) Z. Phys., D26: p. 180. (26) Sanekata, M., Misaizu, F., Fuke, K., Iwata, S., and Hashimoto, K. (1995) J. Am. Chem. Soc., 117: p. 747. (27) Watanabe, H., Iwata, S., Hashimoto, K., Misaizu, F., and Fuke, K. (1995) J. Am. Chem. Soc., 117: p. 755. (28) Peschke, M., Blades, A.T., and Kebarle, P. (1998) J. Phys. Chem. A., 102: pp. 9978–9985. (29) Peschke, M., Blades, A.T., and Kebarle, P. (1999) Int. J. Mass Spectrom, 185: pp. 685–699. (30) Berg, C., Beyer, M., Achatz, U., Niedner-Schatteburg, G., and Bondybey, V.E. (1998) Chem.Phys., 239: pp. 379–392. (31) Beyer, M., Achatz, U., Berg, C., Joos, S., Niedner-Schatteburg, G., and Bondybey, V.E. (1999) J. Phys. Chem., 103: p. 671. (32) Fox, B.S., Beyer, M.K., Achatz, U., Joos, S., Niedner-Schatteburg, G., and Bondybey, V.E. (2000) J. Phys. Chem., 104: pp. 1147–1151.
10 TRANSITION METAL MONOHYDRIDES Peter F. Bernath
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326 ScH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 YH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 LaH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 TiH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331 ZrH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331 HfH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333 VH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333 NbH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333 TaH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333 CrH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334 MoH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334 WH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334 MnH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335 TcH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335 ReH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336 FeH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336 RuH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336 OsH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337 CoH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337 RhH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338 IrH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338 NiH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338 PdH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339 Advances in Metal and Semiconductor Clusters Volume 5, pages 325–345 © 2001 Elsevier Science B.V. All Rights Reserved. ISBN: 0-444-50726-4
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PtH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .339 CuH, AgH and AuH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .339 ZnH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .341 CdH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .341 HgH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .341 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .343 INTRODUCTION The metal hydrides are the simplest possible molecules and form the basis for much of our understanding of chemical bonding. Since Armentrout and Sunderlin1 last reviewed transition metal hydrides in 1991, there has been extensive new spectroscopic work. The best review of the classical work on metal hydrides is still the book by Huber and Herzberg.2 The focus of this review is the ground states of all transition metal monohydrides. We take transition metal hydrides to be the 30 molecules from ScH to HgH containing metals from the d-block of the periodic table, and we exclude the lanthanide and actinide monohydrides. In many ways ab initio theory is well ahead of laboratory measurements because high quality calculations are available for the ground states of all transition metal monohydrides. Indeed, several groups have predicted the properties for the ground states of the transition metal hydrides of the entire 3d (ScH to ZnH)3 and 4d rows (YH to CdH)4,5 of the periodic table using a uniform level of theory. This approach is more difficult for the 5d row (LaH to HgH) because the strong effects of spin-orbit coupling need to be included. Even for the LaH to HgH series, however, Balasubramanian and co-workers (for example) have carried out relativistic ab initio calculations for the ground and low-lying electronic states. In order to interpret the electronic structure of transition metal monohydrides, the simple qualitative valence molecular orbital diagram (Fig. 1) is helpful. The details, of course, depend strongly on the particular molecule. The 1σ orbital can be considered to be a bonding orbital formed by the interaction of the (s+p)-metal hybrid orbital with the hydrogen 1s orbital.6 The 1σ orbital always remains bonding, although the relative portions of the metal s, p and d orbitals change depending on the molecule. The 2σ orbital is basically non-bonding. It can be considered to be formed from the (s-p)-metal hybrid orbital and has, therefore, electron density on the back side of the metal away from the hydrogen. The next three orbitals, 1δ, 1π, and 3σ, are the non-bonding metal ndδ, ndπ and ndσ orbitals perturbed by the Hδ– ligand field. The metal hydride polarity is generally Mδ+–Hδ– for the ground state. The ground states
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327
Figure 1: Qualitative molecular orbital diagram for the transition metal monohydrides.
are derived by adding the valence electrons of the metal plus one electron from hydrogen to the orbitals in the usual way. The resulting ground states are summarized in Table 1, with parentheses used for symmetries that are not yet confirmed by experiment. The primary molecular constants that define the basic shape of the molecular potential are the equilibrium internuclear separation, Re, the equilibrium vibrational frequency, ωe, and the equilibrium bond dissociation energy, De. We, therefore, provide the current best estimates of these quantities as well as the symmetry and electron configuration of the ground state. For the dissociation energy, however, we follow the example of Huber and Herzberg2 and report experimental D00 values, i.e., the energy required to dissociate the molecule from v = 0 in the ground state to the lowest energy atomic limit, measured in eV at 0 K. The basic vibrational constant ωe is augmented with the first anharmonic correction ωexe, defined as 7 G(v) = ωe(v+½) – ωexe(v+½)2. In this case the fundamental vibrational interval ΔG1/2 = G(1)–G(0) is given by,
ΔG1/2 = ωe–2ωexe.
328 Peter F. Bernath
Table 1: Ground states of the transition metal monohydrides. 3
4
5
6
7
8
9
10
11
12
ScH
TiH
VH
CrH
MnH
FeH
CoH
NiH
CuH
ZnH
X1Σ+
X4Φ3/2
(X5Δ)
X6Σ+
X7Σ+
X4Δ7/2
X3 Φ 4
X2Δ5/2
X1Σ+
X2Σ+
YH X1Σ+
ZrH
NbH
MoH
TcH
RuH
RhH
PdH
AgH
CdH
(X2Δ3/2)
(X5Δ)
(X6Σ+)
(X5Σ+)
(X4Σ1/2 )?
X3 Δ 3
X2Σ+
X1Σ+
X2Σ+
LaH
HfH
TaH
WH
ReH
OsH
IrH
PtH
AuH
HgH
X1Σ+
X2Δ3/2
(X0+)
(X6Σ+)
(X7Σ+)
(X7Π5/2)
(X3Σ0+ )
X2Δ5/2
X1Σ+
X2Σ+
Transition Metal Monohydrides
329
The equilibrium rotational constant Be is also provided along with the first vibration-rotation interaction constant, αe, defined as7 Bv = Be – αe(v+½). One standard deviation errors in the last digits of the values of the constants are reported in parentheses. Note that no effort has been made to make the review comprehensive. The references are those necessary to support the selected constants. ScH Some early ab initio calculations (now best forgotten) helped sow confusion in the spectroscopy of ScH, YH and LaH. The ground state is now experimentally8,9 and theoretically3,10 established as X1Σ+ arising from a 1σ22σ2 configuration (Fig. 1). Experimentally the ground state constants of ScH are available from near infrared and visible electronic emission spectra from a hollow cathode lamp.8,9 The Re value is found to be 1.775427(8) Å but only a ΔG1/2 value (1546.9730(14) cm–1) is known (Table 2). For ScD, however, both ωe and ωexe are available.8,9 The dissociation energy D00 of 47.5±2 kcal/mol (2.06(9) eV) is a thermochemical value determined from mass spectrometric monitoring of high temperature equilibria.11 YH YH like ScH has a X Σ ground state from a 1σ22σ2 configuration. Electronic emission spectra from a hollow cathode lamp give (Table 2) ωe = 1530.456(15) cm–1, Βe = 4.575667(39) and Re = 1.922765(8) Å.12,13 No experimental values of the dissociation energy are available but Balasubramanian5,14 calculates a value of 2.93 eV, while Langhoff et al. 4 calculate 2.95 eV for De. 1 +
LaH LaH also follows the periodic trend with a X1Σ+ ground state (1σ22σ2 configuration). Ram and Bernath15 again used a hollow cathode lamp (made with La foil) to record infrared electronic spectra of the A1Π–X1Σ+ transition. Equilibrium rotational constants for LaH are 4.080534(80) cm–1 for Be and 2.031969(20) for Re (Table 2). Unfortunately no off-diagonal vibrational bands were detected so the gas phase vibrational frequencies remain unknown.
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Molecule
ωe/cm
ωexe/cm
–1
Peter F. Bernath
Table 2: –1
Constants for ScH, YH and LaH. Βe/cm–1
αe/cm–1
Re/Å
D00/eV
ScH X1Σ+
[1546.9730(14)]a
–
5.425432(48)
0.124802(84)
1.775427(8)
2.06(9)
YH X1Σ+
1530.456(15)
19.4369(72)b
4.575667(38)
0.091449(23)
1.922765(8)
–
LaH X1Σ+
–
–
4.080534(80)
0.07739(10)
2.031969(20)
–
a
ΔG1/2 value.
b
ωeye = 0.0361(9) cm–1.
Transition Metal Monohydrides
331
The ab initio values of Re = 2.08 Å, De = 2.60 eV and ωe = 1433 cm–1 were calculated by Das and Balasubramanian.16 No experimental dissociation energy is available for comparison. TiH The complex spectra of TiH defied analysis for many years until the recent work of Launila and Lindgren17 on the 4Γ–X4Φ electronic transition. Theory18 and experiment17 are in accord with a regular 4 Φ ground state from the high spin 1σ22σ11δ11π1 configuration. The 1σ and 2σ orbitals are similar to those in ScH. The 1π and 1δ orbitals, however, are essentially unchanged non-bonding metal 3dπ and 3dδ orbitals. TiH lowers its energy by opening the 2σ orbital and distributing the three non-bonding electrons in three different spatial orbitals, 2σ, 1π and 1δ. In this way the electron repulsion is minimized. The first correct rotational analysis of TiH was by Steimle et al.19 who made TiH in electrical discharges (DC and microwave) and by laser vaporization in a Smalley-type jet expansion. They rotationally analysed the 0–0 vibrational band of the 4Γ5/2–X4Φ3/2 subband. Their B0 value of 4.359(3) cm–1 leads to an effective R0 = 1.979(1) Å (contaminated by spin-orbit effects) for the 3/2 spin component. From the Stark effect Steimle et al.19 determined the ground state dipole moment to be 2.455 D. Launila and Lindgren17 were able to analyse all four subbands of the 4Γ–X4Φ transition. The four ground state spin components (4Φ9/2, 4Φ7/2, 4Φ5/2, 4Φ3/2) were fitted together to give B0 = 5.36206(19) cm–1 and A0 = 33.083(29) cm–1 (A0 is the spin-orbit coupling constant). This B0 value gives a recommended R0 value of 1.7847 Å (Table 3). No gas phase vibrational frequencies are available but Chertihin and Andrews20 measured the infrared spectrum in an argon matrix. By empirically correcting for the matrix shift they predict a value of 1405±10 cm–1 for the gas phase ΔG1/2. Chen, Clemmer and Armentrout21 used ion beam techniques to measure the threshold for Ti+ reactions with amines. Using additional thermochemical information they deduce a bond dissociation energy D00 = 2.08(9) eV (48.0±2.1 kcal/mol). ZrH There are no high resolution spectroscopic measurements available for ZrH. The ab initio calculation of Balasubramanian and Wang22 predicts a regular 2Δ ground state from the 1σ22σ21δ1 configuration. The high spin configuration adopted by TiH is evidently less
332
Molecule TiH X4Φ
ωe/cm
([1405])a
Βe/cm–1
αe/cm–1
Re/Å
D00/eV
[5.36206(19)]b
–
1.7847c
2.08(9)
ZrH (X Δ3/2)
([1541])
–
–
–
–
HfH X2Δ3/2
[(1638)]a
5.01911(8)
0.12026(11)
1.830691(15)
–
2
a
a
Estimated ΔG1/2 values from Ar matrix isolation experiments (see text).
b
B0 value.
c
R0 value.
Peter F. Bernath
Table 3: Constants for TiH, ZrH and HfH. –1
Transition Metal Monohydrides
333
favorable for ZrH. There is a trend for increased stability for low-spin configurations for the 4d and 5d transition metal diatomics as compared to the 3d molecules. The ab initio predictions for the X4Δ3/2 state (including spin-orbit coupling) are Re = 1.77 Å, ωe = 1777 cm–1 and De = 2.64 eV.22 Chertihin and Andrews20 make a tentative assignment of 1541 cm–1 for ΔG1/2 in an argon matrix (Table 3). HfH The ground state of HfH is found to be X2Δ3/2 (from the 1σ22σ21δ1 configuration as for ZrH) by both experiment23 and theory.24 Ram and Bernath measured two electronic transitions of HfH using a hollow cathode lamp. The equilibrium rotational constant of 5.01911(8) cm–1 led to a Re = 1.830691(15) Å in the ground state (Table 3). Unfortunately no off-diagonal bands were detected so the best estimate for ΔG1/2 is the Ar matrix value of 1638 cm–1 from Chertihin and Andrews.20 No experimental dissociation energy has been measured but Balasubramanian and Das24 predict a value of De = 2.88 eV. VH There are no published high resolution spectroscopic measurements for VH. Theory3,6 predicts a regular X5Δ arising primarily from the 1σ22σ11δ11π2 configuration. Again the high spin configuration with four unpaired non-bonding electrons in four different spatial orbitals is favored. The ab initio predicted3 constants are Re = 1.73 Å, ωe = 1524 cm–1 and De = 2.30 eV. Xiao et al.25 measured the ΔG1/2 value of 1437 cm–1 in a Kr matrix. There is an experimental value for the dissociation energy D00 = 2.13(7) eV derived from the ion beam reaction threshold of V+ with various amines.26 NbH No experimental data are available for NbH but the ground state is predicted4,5,27 to be X5Δ from the 1σ22σ11δ11π2 configuration. The 5 Π state, however, from the 1σ22σ11δ21π1 configuration is predicted to lie only about 700 cm–1 above the ground state. The predicted ground state spectroscopic constants27 are Re = 1.787 Å, ωe = 1750 cm–1 and De = 2.67 eV. TaH As for NbH, no experimental information has been published for TaH. Cheng and Balasubramanian28 predict a X0+ ground state that
334
Peter F. Bernath
is derived primarily from the 5Δ0+ spin component but with a strong admixture of 3Π0+, 5Π0+ and 3Σ0+ , when spin-orbit coupling is + included. The X0 state is estimated28 to have Re = 1.775 Å, ωe = 1851 cm–1 and De = 2.4 eV. CrH Of all of the transition metal hydrides, CrH is one of the best characterized. The ground state is X6Σ+ from the high spin 1σ22σ11δ21π2 configuration that has five unpaired electrons in five spatially distinct orbitals.3,6 Recent work includes a re-analysis of the A6Σ+–X6Σ+ electronic emission spectrum from a hollow cathode lamp29,30 and the vibration-rotation absorption spectrum recorded by laser magnetic resonance.31 Laser magnetic resonance was also used to record the pure rotational spectrum.32 The 1–0 and 2–1 vibration-rotation bands31 gave ωe = 1656.0515(3) cm–1, ωexe = 30.4914(1) cm–1 and αe = 0.18099(3) cm–1. The best value of B0 is from the work of Ram et al.,29 which leads to a Be = 6.22224(2) cm–1 and Re = 1.655409(3) Å (Table 4). The dissociation energy of D00 = 1.93(7) eV originates from the ion-beam work of Chen et al.21 MoH There is no high resolution experimental information for MoH, but theory predicts4,5 it will follow the periodic trend set by CrH. Balasubramanian and Li33 predict that the X6Σ+ state will have substantial spin-spin splitting (caused by second order spin-orbit coupling) that places the 6Σ+3/2 spin component at 118 cm–1 and 6Σ+5/2 at 177 cm–1 above the lowest energy 6Σ+1/2 spin component. The X6Σ1/2 spin component33 is predicted to have Re = 1.68 Å, ωe = 1807 cm–1 and De = 2.43 eV. Xiao et al.34 have measured ΔG1/2 = 1675 cm–1 in a Kr matrix. Armentrout and Sunderlin1 recommend a value of 203(19) kJ/mol (2.10(20) eV) for D00, based on two previous ion reactivity measurements. WH WH follows the high spin pattern set by CrH and MoH with a X 6Σ+ ground state. The only spectroscopic information published to Table 4: Constants for CrH. State
ωe/cm–1
ωexe/cm–1
Βe/cm–1
αe/cm–1
Re/Å
D00/eV
XΣ
1656.0515(3)
30.4914(1)
6.22224(2)
0.18099(3)
1.655409(3)
1.93(7)
6 +
Transition Metal Monohydrides
335
date35 is a low resolution arc jet emission spectrum near 14842 cm–1. The B0 value of 5.21 cm–1 leads to an r0 bond distance of 1.79 Å. Although these values are reasonable, only one spin component was observed and the centrifugal distortion constant is about an order of magnitude too large. Ma and Balasubramanian36 predict that the X6Σ+3/2 spin component will be 602 cm–1 above the X6Σ1/2 ground state (with X6Σ+5/2 at 1031 cm–1). The calculated36 X6Σ+1/2 constants are Re = 1.737 Å, ωe = 1936 cm –1 and De = 2.69 eV. MnH The ground state of MnH is X7Σ+ from the 1σ22σ13σ11δ21π2 configuration.37 The 3σ orbital has appeared for the first time and it can be approximated as the non-bonding 3dσ orbital. The six nonbonding electrons are distributed into the five metal d-orbitals and the non-bonding 2σ orbital. The 0–0 band of the A7Π–X7Σ+ electronic transition has been rotationally analysed.38 The infrared vibration-rotation absorption spectrum recorded with a diode laser39 and the equilibrium constants (Table 5) are ωe = 1546.8536(15) cm–1 and Be = 5.685795(37) cm–1 from the 1–0, 2–1 and 3–1 bands.39 The dissociation energy (D00) has been determined to be 1.31(19) eV by Sunderlin and Armentrout40 on the basis of a somewhat uncertain threshold for reactivity of Mn+ with various organic molecules. TcH Tc is radioactive and there are no experimental data for TcH. On the basis of the ab initio calculations,4,5 the ground state is X5Σ+ from the Tc(6S)+H(2S) atomic limit. The presence of a low-spin ground state, in contrast to X7Σ+ for MnH, is not completely secure because the 7Σ+ state from the same atomic limit lies very low in energy (~1000 cm–1). Theoretical estimates for the spectroscopic constants by Langhoff et al.4 are Re = 1.678 Å, ωe = 1742 cm–1 and De = 1.95 eV. Table 5: Constants for MnH. State
ωe/cm
–1
ωe/cm–1
Βe/cm–1
αe/cm–1
Re/Å
X7Σ+ 1546.8536(15) 27.60280(91)a 5.685795(37) 0.160488(22) 1.730842(6) a
ωeye = –0.30822(15).
D00/eV 1.31(19)
336
Peter F. Bernath
ReH The situation for ReH is very similar to that for TcH and MnH. The high spin X7Σ+ state (1σ22σ13σ11δ21π2) is predicted to be the ground state41 with a low-lying a5Σ+ state (1σ22σ21δ21π2) at about 3000 cm–1. The situation becomes more complicated when second order spin-orbit coupling (a relativistic effect) is included, but the X0– ground state still originates mainly from the 7Σ+ state.41 The X7Σ+0- spin component is predicted to have Re = 1.833 Å and ωe = 1675 cm–1, with the first excited 7Σ+1 spin component lying at about 1355 cm–1. The X7Σ+ dissociation energy (De) is predicted41 to be 1.26 eV. FeH The ground state of FeH is X4Δi arising from the 1σ22σ21δ31π2 configuration with a low-lying a6Δi state from the 1σ22σ13σ11δ31π2 configuration.3,6 The a6Δ9/2 spin component lies 1766 cm–1 above the X4Δ7/2 spin component42 and for many years the identity of the ground state of FeH was unclear. The first complete analysis of FeH was through the F4Δ–X4Δ electronic transition observed in emission near 1 μm by Phillips et al.43 using a King furnace. More recently J. Brown and co-workers44,45 have located nearly all of the spin components of the low-lying electronic states. The four spin components (Ω = 7/2, 5/2, 3/2, 1/2) of the X4Δ do not fit together in a proper Hund’s case (a) fit and the vibrational intervals also differ slightly for each spin component.45 The vibrational and rotational constants for the X4Δ state of ωe = 1826.86 and Be = 6.59065 (Table 6) derived or implied (from B0 and B1) by the work of Phillips et al.43 are therefore still useful in spite of recent improvements in the precision of the term values by laser spectroscopy.44,45 The dissociation energy D00 = 1.59(8) eV (at 0 K) was determined from the threshold of reactivity of Fe+ with several organic molecules.46 RuH The RuH and OsH molecules do not seem to follow the periodic trend set by FeH. The ground state of RuH is calculated to be Table 6: Constants for FeH. State
ωe/cm–1
ωexe/cm–1
Be/cm–1
αe/cm–1
Re/Å
D00/eV
X4 Δ
1826.86
31.96
6.59065
0.21166
1.60738
1.59(8)
Transition Metal Monohydrides
337
X4Σ– from the 1σ22σ11δ21π4 configuration.5,47 The calculated spectroscopic parameters5 are Re = 1.609 Å, ωe = 1934 cm–1 and De = 2.61 eV. When spin-orbit coupling is included Balasubramanian5 finds that the 4Φ9/2 spin component lies only 256 cm–1 above the 4 Σ1/2 spin component, so the assignment of the ground state is not secure. Indeed Langhoff et al.4 argue for a 4Φ ground state but have not included relativistic effects in their calculations. When second order spin-orbit coupling is included, the 4Σ3/2 spin 57 –1 4 component is calculated to be 87 cm above the Σ1/2 spin component. The dissociation energy of D00 = 2.43(22) eV (at 0 K) is determined by Tolbert and Beauchamp48 from Ru+ ion reactivity. OsH As already noted, OsH does not closely resemble FeH or RuH in electronic structure. The ground state is calculated to be an inverted X4Π state from the 1σ22σ21δ21π3 configuration.49,50 With spin-orbit coupling included, the X5/2 state, which originates primarily from the 4Π term, but has a nearly equal 4Δ contribution, is predicted49 to have Re = 1.606 Å, ωe = 2199 cm–1 and De = 2.32 eV (for X4Π term). CoH The electronic spectra of CoH have been known for some time2 and the ground state is X3Φi from the 1σ22σ21δ31π3 configuration. Only the X3Φ4 spin component is well characterized51 although 3 Φ3 has been located at 728 cm–1 by laser-induced fluorescence.52 Two rotational lines (J = 4←3 and 5←4) of the 3Φ3 spin component have also been measured by far infrared laser magnetic resonance53 and a Hund’s case (a) fit for two of the three spin components gives B0 = 7.313713(67) cm–1. The 0–0 and 0–1 bands of the A′3Φ4–X3Φ4 electronic transition of CoH near 12000 cm–1 give (Table 7) ΔG1/2 = 1858.7932(32) cm–1 and an effective αe = 0.212444(93) cm–1. Combining the B0 of Beaton et al.53 with αe of Ram et al.51 gives a Be = 7.419935(81) cm–1 and Re = 1.508060(8) Å. The v = 2 vibrational level of the ground state and the 3Φ2 spin component have not been seen yet. The dissociation energy D00 = 1.97(13) eV has been recommended by Armentrout and Sunderlin1 based on the threshold for reactivity of Co+ with a few organic molecules and some thermochemical work by Kant and
338
Peter F. Bernath Table 7: Constants for CoH and RhH. ωe/cm
State CoH
–1
ωexe/cm–1
[1858.7932(32)]a
–
2040(10)
46(4)
Βe/cm–1
αe/cm–1
Re/Å
D00/eV
7.419935(81)b 0.212444(93) 1.508060(8) 1.97(13)
X Φ4 3
RhH
[6.55(1)]c
–
[1.59(21)]d
2.42(6)
X Δ3 3
a
ΔG1/2 value.
b
Be and Re for 3Φ4 and 3Φ3 spin components (see text).
c
B0 value.
d
R0 value.
Moon.11 Freindorf et al.54 have made a detailed ab initio study of the low-lying states. RhH The RhH and IrH molecules also do not follow the periodic pattern set by CoH for their electronic structure. The ground state of RhH is predicted4,5 to be an inverted X3Δ state from the 1σ22σ11δ31π4 configuration. Very recently this has been confirmed by Balfour et al.,55 who characterized the X3Δ3 spin component and located 3Δ2 at 850(25) cm–1 by laser-induced fluorescence. When spin-orbit coupling is included, Balasubramanian and Wang56 predict that the 3 Δ2 is at 527 cm–1 above X3Δ3 and 3Δ1 is at 1377 cm–1. Balfour et al.55 find B0 = 6.55(1) cm–1 for X3Δ3 spin component (Table 7) from pulsed laser excitation studies and ωe = 2040(10) cm–1 from laserinduced fluorescence.55 The RhH bond energy D00 = 2.42(6) eV, again from Rh+ reactivity studies.57 IrH There is only one published paper on IrH.58 Dai and Balasubramanian58 predict a X3Σ– ground state from the 1σ22σ21δ21π4 configuration with Re = 1.557 Å, ωe = 2476 cm–1 and De = 2.63 eV. When spin-orbit coupling included the ground state becomes X0+ with some mixing of X3Σ–0+ and 3Π0+. NiH The optical spectra of NiH have been known since 1934.2 The ground state is an inverted X2Δ state from the 1σ22σ21δ31π4
Transition Metal Monohydrides
339
configuration, i.e., a hole in the 3dδ orbital.3,6,59 There are also low-lying 2Π and 2Σ+ states that can be considered as holes in the 3dπ and 3dσ orbitals.60 The three low-lying states, X2Δ, 2Π and 2Σ+, interact extensively and form a Ni+ 3d9 2D “supermultiplet”.60 The v = 0 and 1 levels of X2Δ5/2 (ΔG1/2 = 1927.68451(56)) and v = 0 of the X2Δ3/2 spin component61 at 782.970817 cm–1 are relatively unperturbed, and give Re = 1.4694493(63) Å (Table 8). The anharmonicity constant ωexe in Table 8 is derived from the Ni isotopic shifts7 in the v = 1–0 intervals.61 The dissociation energy D00 of 2.58(9) eV is a thermochemical value determined by Kant and Moon62 by high temperature mass spectrometry. This value is in agreement with that of Georgiadis et al.63 PdH The 4dσ hole state X2Σ+ from the 1σ22σ11δ41π4 configuration has become the ground state of PdH.4,5,64 The electronic spectrum of PdH and PdD dates2 from 1968, but only PdD was analysed because of perturbations. The first high resolution spectrum of PdH was recorded by McCarthy and Field65 and they determined B0 = 7.099(2) cm–1. The ground state constants of PdH are best estimated from those of 108PdD using isotope relations7 for ωe, ωexe and αe. The resulting values are ωe = 2034.82 cm–1 Be = 7.2123 cm–1 and Re = 1.5300 Å, not including Born-Oppenheimer breakdown. The best dissociation energy (D00 = 2.43(26) eV) is from the ion beam work of Tolbert and Beauchamp.48 PtH Curiously while PdH has a X Σ ground state, PtH is like NiH with an inverted X2Δ ground state.66 The X2Δ3/2 spin component is 3224.9 cm–1 above the X2Δ5/2 spin component (for v = 0) and there are strong Hund’s case (c) tendencies.67 NiH, PdH and PtH66 all have strongly interacting 2Δ, 2Π, 2Σ+ states from the metal ion d9 2D “supermultiplet”. For PtH only the vibrational interval ΔG1/2 = 2293.49(3) cm–1 (for X2Δ5/2) is known along with effective Be = 7.1962 cm–1 and Re = 1.5285 Å.67 No reliable experimental dissociation energy is available but a theoretical value (one of many) is 72 kcal/mol (3.12 eV)68 for De. 2 +
CuH, AgH AND AuH The coinage metal hydrides have been studied for many years.2 The ground states are X1Σ+ from the closed-shell 1σ22σ21δ41π4
340
State
ωe/cm
ωexe/cm
–1
Peter F. Bernath
Table 8: –1
Constants for NiH, PdH and PtH. Βe/cm–1
αe/cm–1
Re/Å
D00/eV
NiH X2Δ
[1927.68451(56)]a
(39.71(18))b
7.8812175(88)
0.256403(78)
1.4694493(63)
2.58(9)
PdH X2Σ+
(2034.82)b
(38.79)b
(7.2123)b
(0.2262)b
1.5300
2.43(26)
PtH X2Δ5/2
[2293.49(3)]a
–
7.1962
0.2001(7)
1.5285
–
a
ΔG1/2 value.
b
Estimated from isotope relationships (see text).
Transition Metal Monohydrides
341
configurations and they have been popular species for the calculation of relativistic effects. 69 The most recent paper on CuH/D, AgH/D and AuH/D reports on vibration-rotation emission from a King furnace.70 Dunham fits and direct fits to potential energy functions of all available modern data results in the constants reported in Table 9. The dissociation energies are all from the high temperature mass spectrometric work of Kant and Moon.62
ZnH The ground state of ZnH is X2Σ+ from the 1σ22σ23σ11δ41π4 configuration.3,71 The best current molecular constants originate from the diode laser absorption work of Urban et al.72 for the 1–0 and 2–1 bands (Table 10). Recently new pure rotational measurements73,74 and A2Π–X2Σ+ electronic emission spectra have become available75 so the ground state constants will be re-evaluated. The spectroscopic value of the dissociation energy D00 = 0.851 eV is recommended.2
CdH The electronic structure of CdH is very similar to ZnH with a X2Σ+ ground state. The best ground state constants also come from the diode laser absorption measurements of Urban et al.72 for the 1–0 and 2–1 bands (Table 10). Huber and Herzberg recommend D00 = 0.678 eV based on a short extrapolation of the shallow ground state.2
HgH The X Σ state of HgH is bound by only 0.3744 eV (D00) and the spectroscopic constants have a strong vibrational dependence.2 There has been little spectroscopic work since Huber and Herzberg2 evaluated the spectroscopic constants. We therefore adopt their values2 and also quote ΔG1/2 = 1203.24 cm–1, B0 = 5.3888 cm–1 and R0 = 1.76620 Å (Table 10). Information is available for v = 0 to 4, essentially for all of the bound vibrational levels of the ground state (v = 5 is slightly bound76) but conventional spectroscopic constants are not useful because the ground state has such a shallow potential well. 2 +
342
Molecule
ωe/cm–1
ωexe/cm–1
Βe/cm–1
αe/cm–1
Re/Å
D00/eV
CuH X1Σ+
1941.6105(25)
37.8870(21)
7.9448171(82)
0.255702(23)
1.46254378(24)
2.53(9)
AgH X1Σ+
1759.7496(23)
33.9801(15)
6.450066(39)
0.202137(35)
1.6179110(27)
2.20(9)
AuH X1Σ+
2305.5008(20)
43.3661(16)
7.241538(21)
0.213724(24)
1.5236752(13)
2.99(9)
Table 10: Molecular constants for ZnH, CdH and HgH. Molecule
ωe/cm–1
ωexe/cm–1
Βe/cm–1
αe/cm–1
Re/Å
D00/eV
ZnH X2Σ+
1615.7164(17)
59.61793(52)
6.686984(50)
0.269789(36)
1.593996(7)
0.851
CdH X2Σ+
1460.8978(16)
61.97017(59)
5.441172(70)
0.221356(81)
1.76105(9)
0.687
HgH X2Σ+
[1203.24]a
–
[5.3888]b
–
[1.76620]c
0.3744
a
ΔG1/2 value (see text).
b
B0 value (see text).
c
R0 value (see text).
Peter F. Bernath
Table 9: Constants for CuH, AgH and AuH.
Transition Metal Monohydrides
343
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P.B. Armentrout and L.S. Sunderlin (1991) Transition Metal Hydrides, (A. Dedieu, ed.), VCH, New York. K.-P. Huber and G. Herzberg (1979) Constants of Diatomic Molecules, Van Nostrand Reinhold, NY. D.P. Chong, S.R. Langhoff, C.W. Bauschlicher, S.P. Walch and H. Partridge (1986) J. Chem. Phys., 85: p. 2850. S.R. Langhoff, L.G.M. Pettersson, C.W. Bauschlicher and H. Partridge (1987) J. Chem. Phys., 86: p. 268. K. Balasubramanian (1990) J. Chem. Phys., 93: p. 8061. S.P. Walch and C.W. Bauschlicher (1983) J. Chem. Phys., 78: p. 4597. G. Herzberg (1950) Spectra of Diatomic Molecules, 2nd edn, Van Nostrand Reinhold, NY. R.S. Ram and P.F. Bernath (1996) J. Chem. Phys., 105: p. 2668. R.S. Ram and P.F. Bernath (1997) J. Mol. Spectrosc., 183: p. 263. J. Anglada, P.J. Bruna and S.D. Peyerimhoff (1989) Mol. Phys., 66: p. 541. A. Kant and K.A. Moon (1981) High Temp. Sci., 14: p. 23. R.S. Ram and P.F. Bernath (1994) J. Chem. Phys., 101: p. 9283. R.S. Ram and P.F. Bernath (1995) J. Mol. Spectrosc., 171: p. 169. K. Balasubramanian and J.Z. Wang (1989) J. Mol. Spectrosc., 133: p. 82. R.S. Ram and P.F. Bernath (1996) J. Chem. Phys., 104: p. 6444. K.K. Das and K. Balasubramanian (1990) Chem. Phys. Lett., 172: p. 372. O. Launila and B. Lindgren (1996) J. Chem. Phys., 104: p. 6418. J. Anglada, P.J. Bruna and S.D. Peyerimhoff (1990) Mol. Phys., 69: p. 281. T.C. Steimle, J.E. Shirley, B. Simard, M. Vasseur and P. Hackett (1991) J. Chem. Phys., 95: p. 7179. G.V. Chertihin and L. Andrews (1995) J. Phys. Chem., 99: p. 15004. Y.-M. Chen, D.E. Clemmer and P.B. Armentrout (1991) J. Chem. Phys., 95: p. 1228. K. Balasubramanian and J.Z. Wang (1989) Chem. Phys. Lett., 154: p. 525. R.S. Ram and P.F. Bernath (1994) J. Chem. Phys., 101: p. 74. K. Balasubramanian and K.K. Das (1991) J. Mol. Spectrosc., 145: p. 142. Z.L. Xiao, R.H. Hauge and J.L. Margrave (1991) J. Phys. Chem., 95: p. 2696. Y.-M. Chen, D.E. Clemmer and P.B. Armentrout (1993) J. Chem. Phys., 98: p. 4929. K.K. Das and K. Balasubramanian (1990) J. Mol. Spectrosc., 144: p. 245. W. Cheng and K. Balasubramanian (1991) J. Mol. Spectrosc., 149: p. 99. R.S. Ram, C.N. Jarman and P.F. Bernath (1993) J. Mol. Spectrosc., 161: p. 445. R.S. Ram and P.F. Bernath (1995) J. Mol. Spectrosc., 172: p. 91. K. Lipus, E. Bachem and W. Urban (1991) Mol. Phys., 73: p. 1041. J.M. Brown, S.P. Beaton and K.M. Evenson (1993) Astrophys. J., 414: p. L125. K. Balasubramanian and J. Li (1990) J. Phys. Chem., 94: p. 4415. Z.L. Xiao, R.H. Hauge and J.L. Margrave (1992) J. Phys. Chem., 96: p. 636. J.F. Garvey and A. Kupperman (1988) J. Phys. Chem., 92: p. 4583. Z. Ma and K. Balasubramanian (1991) Chem. Phys. Lett., 181: p. 467. S.R. Langhoff, C.W. Bauschlicher and A.P. Rendell (1989) J. Mol. Spectrosc., 138: p. 108.
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(38) T.D. Varberg, J.A. Gray, R.W. Field and A.J. Merer (1992) J. Mol. Spectrosc., 156: p. 296. (39) R.-D. Urban and H. Jones (1989) Chem. Phys. Lett., 163, 34. (40) L.S. Sunderlin and P.B. Armentrout (1990) J. Phys. Chem., 94: p. 3589. (41) D. Dai and K. Balasubramanian (1993) J. Mol. Spectrosc., 158: p. 455. (42) D.F. Hullah, C. Wilson, R.F. Barrow and J.M. Brown (1998) J. Mol. Spectrosc., 192: p. 191. (43) J.G. Phillips, S.P. Davis, B. Lindgren and W. Balfour (1987) Astrophys. J. Suppl., 65: p. 721. (44) For example, D.F. Hullah, R.F. Barrow and J.M. Brown (1999) Mol. Phys., 97: p. 93. (45) C. Wilson and J.M. Brown (1999) J. Mol. Spectrosc., 197: p. 188. (46) R.H. Schultz and P.B. Armentrout (1991) J. Chem. Phys., 94: p. 2262. (47) K. Balasubramanian and J. Wang (1990) Chem. Phys., 140: p. 243. (48) M.A. Tolbert and J.L. Beauchamp (1986) J. Phys. Chem., 90: p. 5015. (49) M. Benavides-Garcia and K. Balasubramanian (1991) J. Mol. Spectrosc., 150: p. 271. (50) K. Balasubramanian, D. Andrae, M. Dolg, H. Stoll and H. Preuss (1993) J. Mol. Spectrosc., 160: p. 585. (51) R.S. Ram, P.F. Bernath and S.P. Davis (1996) J. Mol. Spectrosc., 175: p. 1; see also, M. Barnes, A.J. Merer and G.F. Metha (1995) J. Mol. Spectrosc., 173: p. 100. (52) T.D. Varberg, E.J. Hill and R.W. Field (1989) J. Mol. Spectrosc., 138: p. 630. (53) S.P. Beaton, K.M. Evenson and J.M. Brown (1994) J. Mol. Spectrosc., 164: p. 395. (54) M. Freindorf, C.M. Marian and B.A. Hess (1993) J. Chem. Phys., 99: p. 1215. (55) W.J. Balfour, J. Cao and C.X.W. Qian (2000) J. Mol. Spectrosc. 201: p. 244. (56) K. Balasubramanian and D.-W. Wang (1988) J. Chem. Phys., 88: p. 317. (57) Y.-M. Chen and P.B. Armentrout, (1995) J. Am. Chem. Soc., 117: p. 9291. (58) D. Dai and K. Balasubramanian (1991) New J. Chem., 15: p. 721. (59) C.M. Marian, M.R.A. Blomberg and P.E.M. Siegbahn (1989) J. Chem. Phys., 91: p. 3589; C.M. Marian (1990) J. Chem. Phys., 93: p. 1175. (60) J.A. Gray, M. Li, Th. Nelis and R.W. Field, (1991) J. Chem. Phys., 95: p. 7164. (61) Th. Nelis, S.P. Beaton, K.M. Evenson and J.M. Brown (1991) J. Mol. Spectrosc., 148: p. 462. (62) A. Kant and K.A. Moon (1979) High Temp. Sci., 11: p. 52. (63) R. Georgiadis, E.R. Fisher and P.B. Armentrout (1989) J. Am. Chem. Soc., 111: p. 4251. (64) T. Fleig and C.M. Marian (1998) J. Chem. Phys., 108: p. 3517. (65) M.C. McCarthy and R.W. Field (1994) J. Chem. Phys., 100: p. 6347. (66) T. Fleig and C.M. Marian (1996) J. Mol. Spectrosc., 178: p. 1. (67) M.C. McCarthy, R.W. Field, R. Engleman and P.F. Bernath (1993) J. Mol. Spectrosc., 158: p. 208. (68) K. Balasubramanian and P.Y. Feng (1990) J. Chem. Phys., 92: p. 541. (69) For example, C.L. Collins, K.G. Dyall and H.F. Schaefer (1995) J. Chem. Phys., 102: p. 2024 and references therein. (70) J.Y. Seto, Z. Morbi, F. Charron, S.K. Lee, P.F. Bernath and R.J. LeRoy (1999) J. Chem. Phys., 110: p. 11756.
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(71) Ch. Jamorski, A. Dargelos, Ch. Teichteil and J.P. Daudey (1994) J. Chem. Phys., 100: p. 917. (72) R.-D. Urban, U. Magg, H. Birk and H. Jones (1990) J. Chem. Phys., 92: p. 14. (73) M. Goto, K. Namiki and S. Saito (1995) J. Mol. Spectrosc., 173: p. 585. (74) F.A. Tezcan, T.D. Varberg, F. Stroh and K.M. Evenson (1997) J. Mol. Spectrosc., 185: p. 290. (75) T. Hirao and P.F. Bernath, unpublished. (76) W.C. Stwalley (1975) J. Chem. Phys., 63: p. 3062.
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11 THE BINDING IN NEUTRAL AND CATIONIC 3d AND 4d TRANSITION-METAL MONOXIDES AND -SULFIDES Ilona Kretzschmar, Detlef Schröder, Helmut Schwarz and Peter B. Armentrout
I. II.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348 Instrumentation and Computational Methods . . . . . . . . . . . 350 A. The Guided Ion Beam (GIB) Apparatus. . . . . . . . . . . . . . 350 B. Fourier-Transform Ion Cyclotron Resonance Mass Spectrometry (FTICR-MS) . . . . . . . . . . . . . . . . . . . . . . . . . 352 C. Reaction Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353 D. Computational Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . 354 III. General Bonding in Diatomic Transition-Metal Oxides and Sulfides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355 IV. Periodic Trends in D0(M+–S) of the 3d Transition-Metal Sulfide Cations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358 V. Comparison of D0(M+–S) with D0(M+–SiH2) and D0(M–S) . 365 VI. Periodic Trends in D0(M+–S) of the 4d Transition-Metal Sulfide Cations and the Comparison with their 3d Congeners. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372 VII. Comparison of the Cationic and Neutral Transition-Metal Monoxides and Sulfides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379 VIII.Electronic Ground States and the Bonding in MX0/+ (X = O, S). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388 Advances in Metal and Semiconductor Clusters Volume 5, pages 347–395 © 2001 Elsevier Science B.V. All Rights Reserved. ISBN: 0-444-50726-4
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IX. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .390 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .391 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .391 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .391 I. INTRODUCTION The chemistry of transition-metal oxides and sulfides has been summarized in several books1 and reviews2–5 during the last decade. The interest in transition-metal chalcogenides evolves primarily from the numerous applications of transition-metal oxides and sulfides, e.g. catalysts, lubricants, support materials, superconductors, gas sensors for pollution monitoring and control as well as electrode materials in photoelectrolysis to mention only a few.1a Moreover, transition-metal oxides and sulfides are found in the reaction centers of many enzymes, and metal sulfides have even been postulated to be essential for the evolution of life.6 In industry, transition-metal oxides are used as versatile catalysts in many applications; however, for some processes their reactivity is too high and non-specific product formation occurs. In contrast, transition-metal sulfides are less reactive, and sulfur is often deliberately added as a catalyst moderator or poison in order to improve selectivity. Despite their successful application in industry and their relevance in biology, the thermochemical data base acquired for the transition-metal sulfides is still very small. In order to get more insight into the diversity of the intrinsic reactivity and to gain a better understanding of the similarities and the differences observed for the various transition-metal chalcogenides, the cationic and neutral monoxides and sulfides appear to be suitable model systems. The comparison of properties such as electronic ground states, bond dissociation energies, bond lengths, charge distributions, ionization energies, bonding patterns etc. may help to elucidate the intrinsic nature of the metal–oxygen and metal–sulfur interactions. This knowledge could in turn be used for the development of better catalysts, which combine the characteristics of the M/O and M/S systems. The inclusion of the neutral metal chalcogenides in this comparison is intended to help clarify the role of charged species in catalytic processes. Over the past two decades, mass spectrometry has undoubtedly proven to be one of the most powerful tools for the study of the intrinsic properties of molecules and for the elucidation of their structures and energetics at a truly molecular level. The main advantage of mass-spectrometric techniques is that the species of interest
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can be isolated and investigated in a solvent-free environment. This is particularly useful for the study of periodic trends, because all species are generated under equal, well-defined conditions, allowing a direct comparison of their physical and chemical properties. Further, the results of gas-phase experiments can be successfully complemented by sophisticated quantum-chemical calculations. A challenging task for gas-phase chemists is, however, the conversion and the use of such gas-phase data for the explanation of solid- or liquid-phase phenomena. Among gas-phase studies dealing with transition metals, metal oxides have received particular attention.3,7 Some of these studies reveal parallels between the reactivities of the gas-phase species and their condensed-phase analogs, e.g., the recent extrapolation from gas-phase results to the condensed phase for cytochrome c-P450.8 However, for a valid comparison of gas- and condensedphase experiments, it is necessary to take into account the extremely different environments encountered in the two fields.3,9 Despite an ever increasing interest, knowledge of the gas-phase chemistry of metal sulfides is still quite limited,10 and few thermochemical data of transition-metal sulfides are available.11 The task of this chapter is to provide a complete set of thermochemical data, such as bond dissociation energies, heats of formation, and ionization energies, for the neutral and monocationic first- and secondrow transition-metal monosulfides. The comparison of these data with known thermochemistry of metal oxides and relevant compounds should provide the reader with an understanding of the intrinsic properties of the metal-chalcogenide interaction. Further, the data can serve as anchor points for quantum-chemical electronic structure calculations in that they allow tests of the performance of quantum-chemical methods in the description of transition-metal sulfides. Another area of application has been proposed recently by Cundari and Moody.12 These authors report the use of neural networks for the prediction of bond dissociation energies. A major requirement for the good performance of neural networks in the prediction of bond dissociation energies is a sufficient experimental data base. This chapter will be organized as follows. First, a short overview of the experimental and theoretical methods used for the determination of bond energies and other spectroscopic constants, such as bond distances, vibrational frequencies, and electronic states, is given. Further, the reader is introduced to the general molecularorbital scheme suited to describe the bonding in transition-metal chalcogenides. Next, the bond dissociation energies of the first-row transition-metal sulfide cations are discussed with regard to trends
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across the period. Further, the binding of the isolobal fragments S and SiH2 to transition-metal cations is compared. The neutral transition-metal sulfides are also included in the comparison in order to extract the influence of charge and occupation on the binding. Section VI covers the comparison of the first-row transition-metal sulfide cations with those of the second transition row. Finally, the neutral and cationic transition-metal sulfides are compared with the corresponding oxides. I. INSTRUMENTATION AND COMPUTATIONAL METHODS Two complementary mass spectrometers have been used for the investigation of the transition-metal sulfide cations: (i) a guided ion beam (GIB) apparatus that allows the determination of thermochemical data for MX+ (X = O, S) by threshold collision-induced dissociation (CID) and ion-molecule reactions at elevated kinetic energies, and (ii) a Fourier-transform ion cyclotron resonance (FTICR) mass spectrometer employed for the determination of rate constants and branching ratios of exothermic reactions which, under fortunate circumstances, allows the study of chemical equilibria. Further spectroscopic data, such as vibrational frequencies, bond lengths, ground states, and state splittings, are computed with a density functional approach. All experimental techniques used for the determination of D0 values in this study have been described in detail before.13–18 Therefore, a brief description of the general methodologies will suffice here. A. The Guided Ion Beam (GIB) Apparatus13,14 The GIB tandem mass spectrometer consists of an ion source, a flow tube, a magnetic sector, a reaction zone, a quadrupole mass analyzer, and an ion detector. In a typical experiment, the reactant ions are created in the ion source, thermalized in the flow tube, mass-selected with the magnetic sector, decelerated to a particular kinetic energy, and reacted with a neutral present in the reaction zone. The path length for reaction in the reaction zone is welldefined and the neutral pressure is optimized such that, on average, only single ion-neutral encounters take place. The latter is verified by conducting the experiment at several different pressures. Further, the reaction zone is surrounded by an rf octopole ion beam ‘guide’ that ensures efficient collection of all ions. The reactant and product ions are mass-selected in the quadrupole located after the reaction zone and detected afterwards.
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The raw data, ion intensities as a function of the kinetic energy of the incident ion beam, are converted to absolute reaction cross sections, σ(E), where E is in the center-of-mass energy frame. The cross sections provide direct measures of the reaction probabilities under study at given kinetic energies. For endothermic reactions, the cross section exhibits a threshold (E0), which measures the minimum energy required for a given process under strictly bimolecular conditions. E0 corresponds to the thermodynamic threshold, i.e., the reaction enthalpy ΔRH, if the reaction does not exhibit a barrier in excess of the reaction endothermicity. In the case of an exothermic reaction, the cross section decreases with increasing energy. No thresholds are obtained, but a phenomenological rate constant can be extracted instead. Quantitative analysis of the energy dependence of the cross sections is achieved using Equation 1; details of the methods are outlined elsewhere.19
σ(E) = σ0 Σ gi (E + Ei – E0)n / Em
(1)
In Equation 1, E is the relative kinetic energy of reactants, E0 is the threshold for the reaction at 0K, σ0 is a scaling parameter, and n and m are fitting parameters, where m = 1 in all but unusual circumstances. The summation is over all rovibrational states of the reactants having internal energies Ei and populations gi (Σgi = 1). The vibrational frequencies of the neutral reagents are taken from the literature,20 and the vibrational frequencies for MX+ are calculated at the B3LYP/6-311+G* (M = Sc – Zn) and B3LYP/3-21G (M = Y – Ag) levels of theory (see computational details, Part D of this section). The model cross sections are then compared to the experimental data after convolution with the thermal energy distributions of the reactants. The parameters σ0, n, and E0 are optimized to best reproduce the data using a least-square criterion. Reported uncertainties in E0 reflect the range of values obtained for several data sets and the absolute uncertainty of the energy scale. Equation 1 is expected to be appropriate for translationally driven reactions21 and has been found to reproduce cross sections in numerous previous studies of di- and polyatomic reactions19,22 including collision-induced dissociation (CID).23 Equation 1 explicitly includes the internal energy of the reactants and makes the assumption that all of the internal energy is capable of statistically coupling into the reaction coordinate. This is the most reasonable assumption in the absence of any other information concerning state-specific, dynamic effects. Thus, the thresholds correspond to the formation of products with no internal excitation and therefore
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represent thresholds at 0K. The use of these assumptions has been justified in several studies.19,23,24 B. Fourier-Transform Ion Cyclotron Resonance Mass Spectrometry (FTICR-MS)15 In contrast to the GIB experiment, FTICR mass spectrometry is primarily used to monitor exothermic reactions of ions trapped in a cell located in a magnetic field B. Specifically, the ions are generated by laser ionization/laser desorption (LI/LD) of a metal target and transferred into a cylindrical cell situated in a superconducting magnet. The ions are forced onto a circular orbit with the cyclotron frequency ωc, which is related to the ion’s charge q and its mass m according to the fundamental Equation 2. ωc =
q⋅B m
(2)
The cyclotron motion of the ions in the cylindrical cell induces an image current in the detection plates, which is the stronger the closer the ions get to the plates during their circular orbit. The image current is caused by the motion of electrons in the plates as the ion moves toward and away from them. In a statistical picture, the image currents of the ions would wipe out each other. Thus, the ions need to be brought into coherence. The coherent motion of the ions is achieved by application of an radio frequency (rf) broadband pulse to the second pair of opposite plates of the ICR cell, the excitation plates. Ions having cyclotron frequencies identical with the frequencies of the rf broadband pulses applied can absorb energy and increase their velocities and radii. Simultaneously, ion packages of ions with identical m/z ratios are formed and cause coherent summation of the image currents. The m/z ratios of the different ions in the cell are then obtained via Fourier-transformation25 of the time-dependent signal (FID), which is the summation of the image currents of all ions in the cell, followed by conversion of the frequencies to masses using Equation 2. By the same technique, rf pulses at the cyclotron frequency of a particular ion can be used for the ejection of these ions from the cell and thereby afford mass selection. The main purpose of the experiments performed in the FTICR is to establish reaction rate constants of thermalized ions in their electronic ground states. LD/LI generation is known to produce the reactant ions in ground and excited states.26,27 In addition, the ions
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are kinetically ‘hot’ when transferred from an external source to the ICR cell. In order to allow thermalization, the ions are collided with pulsed-in methane or argon (∼2000 collisions). The kinetics of all reactions are carefully studied as a function of thermalizing collisions in order to ensure that the ions undergoing ion-molecule reactions are not kinetically or electronically excited. The following four conditions should be fulfilled when complete thermalization is to be assumed: • • • •
Variation of the thermalizing collision events should not affect the measured reaction rates and especially product branching ratios. The reactant-ion intensity should follow strict pseudo first-order kinetics. The intensities of the observed products should rise with increasing reaction time, provided they do not undergo secondary reactions. Complete conversion of the reactant ions into products should be achieved.
When ΔRG covers a range from +0.2 to –0.2 eV,28 the determined reaction rate constants can be further used for the derivation of the equilibrium constants Keq.29–31 These can be derived from steadystate ion intensities at given pressures of the relevant neutrals or as the quotient of the rate constants determined for forward and backward reactions in a system. Subsequently, Keq is converted into Δ RG by means of the Gibbs-Helmholtz equation when an effective temperature of 298K is assumed. Using the TΔS term derived from quantum-chemical calculations, Δ RH is obtained. The error of the equilibrium constant is estimated as 30%, comprising the experimental uncertainties as well as systematic errors.32 Note that the considerable error in the absolute pressure measurement is not relevant here.
C. Reaction Systems The following four general reaction systems 3–6 have been employed for the determination of D0(M+–S): M+ + XS → MS+ + X
(3)
MS+ + Xe → M+ + S + Xe
(4)
MS+ + XO → MO+ + XS
(5)
MO + XS → MS + XO
(6)
+
+
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These reactions can be either exothermic or endothermic, except for CID in reaction 4, which is an intrinsically endothermic reaction. In the case of endothermic reactions, the thermochemical information required can be calculated from the thresholds obtained with the GIB technique by use of the following equations: D0(M+–S) = D0(X–S) – E0(3)
(7)
D0(M+–S) = E0(4) +
(8) +
D0(M –S) = D0(X–S) + D0(M –O) – D0(X–O) + E0(5)
(9)
D0(M+–S) = D0(X–S) + D0(M+–O) – D0(X–O) – E0(6)
(10)
The major assumption made in Equations 7–10 is that no activation barrier in excess of the reaction endothermicity is operative. This assumption is often a good one for ion-molecule reactions because of the long-range attractive forces involved; however, empirically it has been found that the CID reaction (4) for strongly bound species such as MS+ often leads to upper limits on the true bond energy.19a,33 For exothermic reactions, GIB as well as FTICR data provide reaction rate constants, which also indicate the role of actual barriers in the particular reactions examined. In fortunate cases, additional thermochemical information can be obtained via equilibrium studies (see above). D. Computational Methods The bond lengths and the ground state/excited state splittings of MX+ (M = 3d, 4d-metal; X = O, S) are calculated with density functional theory (DFT). The DFT calculations are carried out using the Amsterdam density functional (ADF, version 2.0.1) suite of programs34 with the inner-shell electrons ([He] for O, [Ne] for S, [Ar] for 3d-metals, and [Kr] for 4d-metals) treated in the frozen-core approximation.35 The valence orbitals are expanded as linear combinations of Slater-type basis functions. Triple-zeta basis sets are used for metal, oxygen, and sulfur. All molecular and atomic energies are calculated using the local spin density approximation (LDA) with Slater’s exchange functional and the Vosko-Wilk-Nusair parametrization (VWN)36 augmented by Becke’s37 and Perdew’s38 (BP) gradient corrections for the exchange and correlation potential, respectively.39 This method will be referred to as ADF/BP. Advantageous characteristics of the ADF program are that it provides control over the symmetry of the wave function created during geometry optimizations and permits the calculations of excited states.
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For ground state MX+, the bond lengths obtained with ADF are reoptimized using the B3LYP functional as implemented in Gaussian9440 with the 6-311+G* and 3-21G basis sets for the 3d and 4d-metal containing species, respectively. Vibrational frequencies are also calculated at these levels and used for zero-point vibrational energy (ZPVE) correction. III. GENERAL BONDING IN DIATOMIC TRANSITION-METAL OXIDES AND SULFIDES In order to understand trends in the bonding of the transitionmetal monoxides and sulfides, it is necessary to know more about the nature of the MX+ bonds. The orbitals involved in the formation of M+–X bonds are mainly the valence orbitals, i.e., 3d(4d)/4s(5s) of the metal center and the 2s/2p (3s/3p) of oxygen (sulfur). The 2s (3s) orbital on oxygen (sulfur) is low in energy with respect to the metal valence orbitals and thus interacts weakly with orbitals from the metal resulting in a ligand-centered 1σ orbital. Further, the 2pπ (3pπ) orbitals overlap with the 3dπ (4dπ)-orbitals present on the metal center in a bonding and antibonding fashion yielding sets of degenerate 1π and 2π orbitals. The dδ-orbitals find no symmetry match on the oxygen or sufur ligand and thus lead to two metalcentered, degenerate, nonbonding 1δ orbitals. Finally, the 4s (5s) and 3dσ (4dσ) orbitals of the metal and the 2pσ (3pσ) orbitals on the ligand form three σ-orbitals, a bonding (2σ), a nonbonding (3σ), and an antibonding (4σ) orbital. Combining these orbitals yields the qualitative molecular-orbital scheme depicted in Fig. 1. Note, however, that this approach is a formalism that cannot account for the differences in orbital energies caused by occupation. Thus, the scheme depicted in Fig. 1 is assumed to apply for all 3d-block metals from Sc through Zn, although the orbitals certainly reorder across the periodic table (see for example, the 1δ → 3σ excitation energies discussed in Section V). Nevertheless, this simplistic approach is instructive. Comparing this scheme with those known for main group elements of the second and third row reveals close similarities with CO, CS, O2, and S2. The major difference is the lack of the three nonbonding (3σ and two 1δ) orbitals for the main group species. This similarity has already been discussed for the transition-metal oxide cations in some detail.41–43 A particular feature of Fig. 1 is that the 1δ, 3σ, and 2π orbitals are close in energy, such that they can be considered as being quasi-degenerate. Occupation of these orbitals is therefore determined by the combined interaction of Hund’s rule, electron correlation, and orbital-gap effects. The energetic
Qualitative molecular-orbital scheme for MX+.
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Figure 1:
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The Binding in Neutral and Cationic 3d and 4d
357
spacing of these orbitals depends on the relative energies of the valence orbitals and their occupations. In previous theoretical work on cationic molybdenum monoxides and sulfides, it has been reported that the orbital gap between the 1δ and 3σ orbitals decreases from 1.6 eV in MoO+ to 0.4 eV in MoS+.10f This observation points to the fact that the above-mentioned interplay of electronic and orbital effects will be even more severe for the sulfide cations. A similar effect of decreasing orbital gaps is seen for the valence orbitals in the isolobal CO and CS molecules.44 Figure 2 shows the occupations of these molecular orbitals for the cations ScO+ and FeO+,10e,45a,46 as well as neutral ZnO as examples.47 These three species are chosen because they represent extremes along the 3d series, have already been studied in more detail, and help to highlight the change of bond order and charge distribution along a period. For example, in ScO+ only the bonding 1σ, 2σ, and 1π orbitals are occupied leading to a bond order of 3. This bonding pattern is similar to that of carbon monoxide, and the stability of the closed-shell configuration of ScO+ is also manifested in the large Figure 2: Qualitative molecular-orbital scheme for ScO+, FeO+, and ZnO. Note that the sequence of the orbitals may change upon their occupation with electrons.
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amount of energy (3.45 eV)45a required for the excitation of an electron from the 2σ to the 1δ orbital yielding the 3Δ state. Natural bond orbital (NBO) analysis48 yields a charge on the metal, qNBO(Sc), of 1.81, which points to the importance of the M2+–O− configuration for the early transition-metal chalcogenides. In contrast to the occupation in ScO+, non- and antibonding orbitals are singly occupied in FeO+ (6Σ+) yielding a high-spin ground state. Assuming that the 3σ and 1δ orbitals have nonbonding character (see above), a bond order of 2 results, which matches the bond order and occupation found for the O2 molecule (3Σ−). The lowest-lying excited states of FeO+ are the quasi-degenerate 4Δ (1σ22σ21π41δ32π23σ0) and 4Φ (1σ22σ21π41δ32π13σ1) states at 1.0 and 1.1 eV, respectively.46 The presence of low-lying, but well-separated quartet and sextet spin states renders FeO+ a suitable candidate for the observation of twostate reactivity.49,50 For the chalcogenides of the metals from the middle of the 3d-row, M+–O configurations seem to be most important; e.g., Mulliken analysis yields q(Fe) = 1.05 for FeO+. The last element of the 3d row, zinc, exhibits a 1Σ+ ground state when bonded to oxygen in neutral ZnO. In this molecule, all non- and antibonding orbitals except the very energetic 4σ orbital are doubly occupied. As a result, the formal bond order calculated for this species is 1, consistent with an experimental bond dissociation energy of D0(Zn–O) = 1.61 ± 0.04 eV.51 However, analysis of orbitals obtained from modified-coupled pair functional calculations47 shows that 4s4p hybridization of zinc plays a role in ZnO, and that these hybrid orbitals form a bonding and an antibonding orbital with the 2pσ orbital of oxygen. The 2π orbitals are mostly 2pπ of O with some donation to the Zn. According to the calculations, the bonding in ZnO (1Σ+) can be viewed as arising from Zn+ 2S(4s1) + O− 2P(2pσ12pπ4) and Zn 1S + O 1 D(2pσ02pπ4) in a ca. 1:1 ratio; the calculations predict q(Zn) = 0.48. IV. PERIODIC TRENDS IN D0(M+–S) OF THE 3d TRANSITION-METAL SULFIDE CATIONS The M+–S bond dissociation energies derived from the reaction systems described above are summarized in Table 1 and can be converted to heats of formation by use of Equation 11 where atomic data are taken from literature compilations and data bases.
ΔfH°(M+–S) = ΔfH°(M+) + ΔfH°(S) – D0(M+–S)
(11)
Further, Table 1 contains term symbols and configurations of the MS+ ground states determined at the ADF/BP level of theory. Re-optimization of the bond lengths and frequency calculations are performed at
The Binding in Neutral and Cationic 3d and 4d
359
Table 1. Experimental 0K bond dissociation energies and heats of formation, calculated electronic states, vibrational frequencies and bond lengths for first-row transition metal sulfide cations. MS+ ScS+
Configurationa
Ground statea,b
Σ
1σ22σ21π4
D0(M+–S) [eV]d
ν [cm–1]b
r [Å]b
8.28 ± 0.13
4.97 ± 0.05e
618
2.087
Δ
1σ 2σ 1π 1δ
1
9.97 ± 0.14
4.71 ± 0.07e
610
2.039
VS+
3 −
1σ22σ21π41δ2
11.12 ± 0.13
3.78 ± 0.10f
532
2.023
CrS+
4 −
Σ
1σ22σ21π41δ23σ1
11.00 ± 0.07
2.71 ± 0.07
388
2.121
MnS+
5
Π
1σ22σ21π41δ23σ12π1
10.75 ± 0.09
2.46 ± 0.09
407
2.156
FeS+
6 +
Σ
1σ22σ21π41δ23σ12π2
11.91 ± 0.09
3.09 ± 0.04g
463
2.060
TiS
+
1 +
ΔHf(MS+) [eV]c
2
Σ
2
2
4
Δ
1σ22σ21π41δ33σ12π2
12.30 ± 0.09
2.82 ± 0.09
419
2.069
4 −
Σ
1σ22σ21π41δ43σ12π2
12.59 ± 0.12
2.33 ± 0.09
374
2.088
CuS+
3 −
Σ
1σ22σ21π41δ43σ22π2
12.32 ± 0.09
1.74 ± 0.09
338
2.156
ZnS+
2
Π
1σ22σ21π41δ43σ22π3
11.57 ± 0.06
1.96 ± 0.06
382
2.182
CoS+ NiS
a b c
d e f g
+
5
ADF/BP. B3LYP/6-311+G*. Calculated using ΔfH°(S) = 2.847 ± 0.003 eV and ΔfH°(M+) from Chase, M.W., Jr.; Davies, C.A.; Downey, J.R., Jr.; Frurip, D.J.; McDonald, R.A.; Syverud, A.N. (1985) J. Phys. Chem. Ref. Data, 14, Suppl. 1 (JANAF Tables). Ref. 10m. Ref. 10n. Refs 10j,k. Ref. 10l.
the B3LYP/6-311+G* level of theory and yield the bond lengths r and the (harmonic) frequencies ν as spectroscopic parameters.(a) The bond strengths given in Table 1 decrease from ScS+ through MnS+, exhibit a second maximum at FeS+, then decrease monotonically to CuS+, and end with a slight increase for ZnS+. The binding scheme shown in Fig. 1 can be used to explain the observed trends in the MS+ bond energies. For ScS+ (Sc+: [Ar]4s13d1; S: [Ne]3s23p4) in its 1 + Σ ground state, the bonding 1σ, 2σ, and 1π orbitals are doubly occupied, whereas all other orbitals are empty. Thus, ScS+ should have the strongest bond of all metal sulfides with a formal bond order of three. TiS+ has a 2Δ ground state, in which the uncoupled electron occupies one of the two degenerate nonbonding 1δ orbitals. As can be extracted from Table 1, occupation of the 1δ orbital leads to a decrease of the bond energy by about 5%. The single occupation of the second 1δ orbital in VS+ causes another 20% decrease in bond energy. This observation is somewhat surprising because the 1δ orbitals are considered to be the 3dδ orbitals localized on the metal center with no counterpart for overlap on the sulfur ligand. This fact renders the 1δ orbitals nonbonding and occupation of these orbitals should not have a strong influence on the bond energy. Thus, simple electron counting in the TiS+ and VS+ molecules yields a formal bond
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Ilona Kretzschmar et al.
order of three. However, the observed decrease in D0(M+–S) (M = Sc, Ti, and V) can be rationalized by consideration of electron correlation. Theoretical approaches include electron correlation by consideration of configuration interaction (CI); DFT applies a correlation functional for this purpose. The doubly-excited open-shell 1Σ+ configuration [1σ22σ21π21δ2] will contribute most to the [1σ22σ21π4] ground-state configuration of ScS+. In this excited configuration, two of the four 1π electrons with like spin are excited to the nonbonding 1δ orbitals. The interaction with the same double-excitation configuration is likely to be much lower for TiS+, because of the repulsion (spinpairing energy) and lower electron correlation caused by the additional electron that already occupies the 1δ orbital in the 2Δ ground state of TiS+ (Table 1). In ground-state VS+ (3Σ−) both 1δ orbitals are singly occupied, such that there can be no doubly-excited open-shell configuration corresponding to excitation of two like spin electrons from the 1π to the 1δ orbitals. Configurations with double excitations to higher orbitals (2π, 3σ/4σ) also contribute to the true ground-state wave function. For those excitations, higher contributions to the electron-correlation term would be expected for VS+ and TiS+, because of the larger number of unpaired electrons involved. However, the 2π and 4σ orbitals are antibonding and much higher in energy, thus lowering any stabilizing contributions from these configurations. Addition of yet another electron to the MS+ system further decreases the bond energy, D0(Cr+–S) amounts to only 55% of D0(Sc+–S). Chromium sulfide cation exhibits a 4Σ− ground state at the ADF/BP level with the additional electron occupying the 3σ orbital. The lowest-lying 4Π excited state lies 0.77 eV above the ground state. According to the binding scheme shown in Fig. 1, the 3σ orbital should have mainly nonbonding character while the 2π orbitals are clearly antibonding. This assignment is in good agreement with 0.77 eV required for the 4Σ− → 4Π transition in CrS+, but contrasts with the drastic decrease in bond energy compared to the early transition metals. A strongly antibonding character of the 3σ orbital would help to rationalize the decrease in D0(M+–S). It would also be in agreement with the surprisingly small change in D0 observed, as one moves along the row to MnS+, because in the 5Π ground state of MnS+ both the 3σ and the antibonding 2π orbitals are singly occupied. However, the similar excitation energies (ADF/ BP) required for the promotion of an electron from the 3σ orbital into an empty, antibonding 2π orbital in CrS+ (4Σ− → 4Π : 0.77 eV) and MnS+ (5Π → 5Σ+ : 0.92 eV), respectively, argue against a strongly antibonding character of the 3σ orbital. The rationale for the reduction of D0(M+–S) going from VS+ to CrS+ has a different origin, namely the dissociation asymptotes. The
The Binding in Neutral and Cationic 3d and 4d
361
D0(M+–S) values given in Table 1 refer to the dissociation of the MS+ molecules into ground-state M+ and ground state S (3P). Cr+ has a 6S ground state with a half-filled 3d-shell (3d5).52 Half-filled subshells are known to exhibit a particular stability and chemical inertness due to the spherical symmetry of such configurations. The loss of this particular stabilization energy in the case of Cr+ (6S) leads to the strong reduction in D0(M+–S) going from V+ to Cr+. Considering the dissociation asymptote of ground-state MnS+, we find half-filled 3d and 4s shells for Mn+ (7S). Two half-filled shells should lead to an additional stabilization of the dissociation products with respect to MnS+, resulting in an even smaller D0(Mn+–S) compared to D0(Cr+–S). Further, an antibonding 2π orbital is occupied in MnS+, which also destabilizes the MnS+ bond. A look at Table 1 reveals that there is only a small difference of 10% between D0(Cr+–S) and D0(Mn+–S). How can we explain this observation? Indeed, MnS+ is somewhat exceptional from the other transitionmetal sulfide cations. It is the only transition-metal sulfide cation, which has a medium-spin 5Π ground state accompanied by closelying high-spin 7Π (1σ22σ21π31δ23σ12π2; 0.47 eV) and low-spin 3Σ− (1σ22σ21π31δ23σ2; 1.26 eV) states. The splitting of 0.47 eV between the 5Π ground state and the 7Π excited state is unexpectedly small, considering that it includes the promotion of an electron from a bonding 1π orbital into an antibonding 2π orbital. A reasonable explanation for this finding is that the excitation energy is partly compensated by a favorable exchange energy in the high-spin state. In fact, it could be this exchange compensation that is responsible for the enhanced stability of the MnS+ 5Π ground state compared to the Mn+ and S fragments, resulting in a stronger D0(Mn+–S) bond. The bond orders in CrS+ and MnS+ are between 2.5 and 3 depending on the amount of antibonding character attributed to the 3σ orbital. This displays the intermediate bond situation of these two metal sulfides in between the early and late transitionmetal sulfide cations. Moving further to the right in the periodic table leads to the ironsulfide cation. In FeS+, the 1δ, 3σ, and 2π orbitals are singly occupied leading to a high-spin 6Σ+ ground state with a formal bond order of 2. Nevertheless the MS+ bond energy (Table 1) has a local maximum at D0(Fe+–S). This is in good agreement with consideration of the dissociation asymptotes discussed above for CrS+ and MnS+, because Fe+ (6D, 3d64s1) no longer has a half-filled 3d shell. Going from FeS+ to NiS+ (4Σ−) via CoS+ (5Δ), the two singly-occupied nonbonding 1δ orbitals are doubly occupied causing a reduction in D0(M+–S) similar to that seen for ScS+, TiS+, and VS+. This can again be explained by loss of more and more electron correlation.
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Ilona Kretzschmar et al.
According to the occupation given in Table 1, the formal bond order in FeS+ (6Σ+), CoS+ (5Δ), NiS+ (4Σ−), and CuS+ (3Σ−) is 2 in all cases. However, CuS+ has the weakest M+–S bond among the metal cations of the first transition row. This failed correlation between bond order and bond strength demonstrates the weakness of the molecular-orbital formalism when neglecting the trends in orbital energies among the 3d series. Thus, unlike the early 3d-elements, the 3d orbitals become core-like for copper such that the 2σ and 1π become essentially nonbonding in CuS+. Further, the dissociation asymptote comes into play as ground-state Cu+ has a very stable closed-shell 3d10 configuration (excitation to the 3d94s1 configuration requires 2.80 eV)53 rendering the formation of a bond to any ligand energetically demanding. The bond energy of ZnS+ is slightly larger than that of CuS+. This trend can neither be rationalized with the occupation of the MOs (all orbitals are doublyoccupied, except one singly-occupied 2π and the empty 4σ) nor with the dissociation asymptote (Zn+ has a filled 3d shell and a halffilled 4s shell). However, the higher nuclear charge of Zn+ compared to Cu+, which causes a contraction of the 3d orbitals, could serve as an explanation, because it might render the 3σ orbital slightly more bonding than in CuS+ resulting in a stronger bond. Further, one should keep in mind that the contributions of ionic configurations such as Zn2+–S− and Zn–S+ become more important the further one moves to the right in the periodic table, because covalent bonding becomes less likely the higher the number of electrons in antibonding orbitals (see Fig. 2). An alternate means to interpret the bonding pattern is with valence-bond (VB) theory. This concept has been employed for the description of the bonding in metal-oxide cations by Carter and Goddard.42 In their considerations of VO+, the authors compare the bonding in VO+ to the triple bond in CO. The authors conclude that the bond in VO+ is viewed best as one covalent σ bond, one covalent π bond, and one donor-acceptor (dative) π bond. Similar considerations on ScO+ and ScS+ lead Tilson and Harrison45 to the two asymptotic configurations depicted in Fig. 3, which contribute to the ground-state equilibrium structure of ScS+. The Lewis structure depicted in Fig. 3a requires Sc+ in its 3D ground state (4sσ13dπ1) and resembles the bonding pattern proposed by Carter and Goddard, whereas the structure in 3b uses the 3F first excited state of Sc+ (3dπ2) and involves two covalent π bonds and one donor-acceptor σ bond. The strength of the metal-sulfur bond in the bonding scheme proposed by Carter and Goddard is governed by two factors: (i) the fulfillment of the requirements for the metal center to enable bonding and (ii) the loss of 3d–3d and 3d–4s
The Binding in Neutral and Cationic 3d and 4d
363
Figure 3: Schematic picture of the two possible asymptotic configurations contributing to the ground state of ScS+ taken from Ref. 45b.
exchange energies (Kdd and Ksd), due to the use of 3d and 4s electrons for bond formation. The requirements for the metal center are two singly occupied orbitals, one with σ (3dσ or 4s ) and one with π (3dπ) symmetry, and an empty acceptor orbital of π symmetry. The ligand (here sulfur) needs a lone pair in addition to singlyoccupied σ- and π-orbitals. The amount of exchange energy lost upon bond formation is higher the more unpaired 3d electrons the free metal cation has. Sc+, Ti+, and V+ fulfill all requirements for the metal center and sulfur those for the ligand. Thus, ScS+, TiS+, and VS+ are expected to have similar bonding patterns, which can be compared with the triple bond in CS.44 In the VB picture, the decrease in the bond energies among the early transition-metal sulfide cations can be attributed to the interplay of the higher electron density at the metal center, which renders the π-donation of the sulfur lone pair into the empty 3dπ metal orbitals less favorable, and the higher amount of exchange energy lost upon bond formation. As mentioned above, Cr+ has all 3d orbitals singly occupied resulting in a very stable 3d5 configuration. The severe decrease in the bond strength of CrS+ can be rationalized by the fact that (i) the single occupation of all 3d orbitals interferes with efficient π-donation from sulfur and (ii) formation of the Cr+–S bond involves disruption of a half-filled subshell, which is an energy demanding process because the loss of 3d–3d exchange energy is at a maximum. The Mn+ cation has a 3d54s1 ground-state configuration with two halffilled subshells. Bond formation with sulfur leads to a maximum of 3d–3d and 3d–4s exchange loss, rationalizing the low D0(Mn+–S) value. Fe+ has singly occupied dσ and dπ orbitals that allow the formation of a double bond with sulfur. In addition, one of the 3d orbitals is doubly-occupied reducing the maximum amount of exchange energy that can be lost upon bond formation compared to Cr+ and Mn+. Interestingly, D0(Fe+–S) exceeds D0(Co+–S) despite the fact
364
Ilona Kretzschmar et al.
that the exchange-energy loss is smaller in CoS+ compared to FeS+, because Co+ (3F, 3d8) has three doubly-occupied orbitals. This reduction of D0 can be rationalized by a worsening of the overlap between the 3d and 3p orbitals of Co+ and S, respectively, which results from the contraction of the 3d orbitals, caused by the higher nuclear charge of Co+. Ni+ (2D) with its 3d9 configuration no longer meets the requirement of two unpaired electrons (see above). The bonding of sulfur in terms of a covalent double bond therefore requires the involvement of the first excited 4F(3d84s1) state, which is 1.17 eV higher in energy, rendering the Ni+–S bond less stable compared to FeS+ and CoS+. One could imagine a binding scheme for NiS+ where a single covalent π bond is formed between the unpaired electrons of the metal and the sulfur and a second bond arises from σ donation of the sulfur lone pair to the empty 4s orbital of the metal cation. However, because covalent π bonds are weaker than covalent σ bonds such a bonding pattern is less preferential. For Cu+, we encounter a d10 configuration that no longer allows formation of covalent bonds. Bond formation must involve excited states or dative bonds, thus explaining the decrease in bond energy. The bonding of Cu+ to sulfur can be visualized in three ways: 1. a single dative σ bond of the sulfur lone-pair to the empty metal 4s orbital, 2. involvement of the first excited 3D state of Cu+ with a 4s13d9 configuration (ΔE = 2.80 eV),53 which allows formation of covalent σ and π bonds, or 3. involvement of the first excited 1D state of sulfur (ΔE = 1.15 eV)53 with a p4 configuration enabling dative σ- and π-bonding between the metal and the sulfur. Chemical intuition prefers cause (ii) over (i) and (iii), because (i) is unlikely to yield a stable metal-sulfur bond (electronegativity54 of Cu+ = 1.75 vs. S = 2.44) and (iii) involves only dative bonds. However, option (ii) demands a 2.80 eV excitation energy, whereas excitation of sulfur, (iii), requires only 1.15 eV rendering (iii) energetically more favorable. No matter which of the three bonding schemes is actually realized, all options include terms of destabilization resulting in a weak interaction between Cu+ and S, and thus the smallest M+–S bond energy in the 3d series. The slightly increased bond energy of ZnS+ can be rationalized in several ways. The most obvious reason is the 4s13d10 ground state configuration of Zn+. Here, the single 4s electron allows straightforward σ-bond formation with one of the unpaired electrons of sulfur. Another rationale is the stabilization of the Zn+–S bond by ionic contributions (see below).
The Binding in Neutral and Cationic 3d and 4d
365
V. COMPARISON OF D0(M+–S) WITH D0(M+–SiH2) AND D0(M–S) Comparison of the D0(M+–S) values given in Table 1 with bond energies of other transition-metal species may also help elucidate the bonding situation in the transition-metal sulfide cations. It has been proven useful to compare the bond situation in the species of interest with that of other molecules by varying the ligand. The variation can either (i) be along a column (i.e., the chalcogenides O, S, Se, and Te) or (ii) along a row (i.e., isolobal fragments SiH2, PH, and S) of the periodic system. The influence of charge and spin is best viewed by comparison with neutral or anionic counterparts of the species under investigation (i.e., MS vs. MS+). From these comparisons, more insight into the factors affecting the M+–X bond should evolve and help to identify and explain deviations from general trends. The comparison of oxides and sulfides (i) will be treated in Sections VI and VII for the 3d and 4d transition metals, whereas the comparison of MS+ with MS and MSiH2+ is discussed here. Figure 4 shows the M+–S bond energies (full circles) along the 3d series. The open circles display the M+–SiH2 bond energies derived from threshold analysis of GIB cross sections measured for reaction (12)55 with the exception of D0(Ni+–SiH2), which is obtained from the exothermicity of reaction (12) and the endothermic formation of NiSiH2+ in the reaction of Ni+ with dimethylsilane.56 Figure 4: D0(M+–S) of the first-row transition-metal sulfide cations (●). Open circles (❍) show D0(M+–SiH2), taken from Refs. 55 and 56; note that the value for D0(Cu+–SiH2) is only a lower limit as indicated by the arrow.
366
Ilona Kretzschmar et al.
M+ + SiH4 → MSiH2+ + H2
(12)
It is obvious from Fig. 4 that D0(M+–S) and D0(M+–SiH2) roughly parallel one another for the early transition metals, but differ for the late ones. The lower M+–SiH2 bond energies found for the early transition metals compared to M+–S can be rationalized by the lower number of available valence electrons at the SiH2 ligand compared to the sulfur ligand (4 vs. 6 electrons). Thus, bond formation of M+ with the sulfur ligand can result in a bond order of 3, whereas the silylene ligand can only lead to a double bond. The differing trends for D0(M+–S) and D0(M+–SiH2) for the late transition metals can be traced back to a change in the bonding mechanism. Cundari and Gordon57 showed in a theoretical study of metal–silicon bonds in MSiH2+ that covalency prevails for the early 3d elements while dative σ bonds from SiH2 in its 1A1 ground state to M+ together with dative π backbonding from M+ to the SiH2 unit dominate the bonding patterns for the late transition metals. The comparison of D0(M+–S) with D0(M+–PH) cannot be performed, because no accurate data for D0(M+–PH) are reported in the literature. There are upper limits of D0(M+–PH) < 2.39 eV for M = Cr – Ni derived from the non-occurrence of reaction 13 under FTICR conditions.58,59 M+ + PH3
MPH+ + H2
(13)
The situation is somewhat different for the neutral transitionmetal sulfides. The liquid and solid phases of binary transition-metal sulfides have been investigated and reviewed thoroughly in the past.60 The study of the bond energies of the neutral, gaseous transition-metal monosulfides was initiated by a publication of Colin, Goldfinger, and Jeunehomme in 1962.61 In their publication, the authors reported the determination of D0(Mn–S). The MnS bond energy was derived from a mass-spectrometric study in which the vaporization of solid MnS was investigated using the Knudsen-effusion method.62 In the following years, D0(M–S) for all metals of the first transition row were established using the Knudsen-effusion method. A summary of the experimentally determined bond energies, D0(M–S), and some spectroscopic constants obtained from quantum chemical studies5,63 is given in Table 2. The accuracy of the thermochemistry derived from the Knudseneffusion method depends on the uncertainties of temperature and pressure measurements and of the thermodynamic functions used. The major contribution of the uncertainty comes from the thermodynamic functions, because they require accurate knowledge of
The Binding in Neutral and Cationic 3d and 4d
367
Table 2. Experimental 0K bond dissociation energies and heats of formation, calculated electronic states, vibrational frequencies and bond lengths for first-row transition metal sulfide neutrals. MS
Ground statea 2 +
Configuration
ΔfH°(MS) [eV]b
D0(M–S)[eV]
νaMS – [cm 1]
raMS [Å]
Σ
1σ22σ21π43σ1
1.90 ± 0.15
4.93 ± 0.13c
563
2.155
3
Δ
1σ 2σ 1π 1δ 3σ
1
2.98 ± 0.22
4.75 ± 0.13d
575
2.083
4 −
Σ
1σ22σ21π41δ23σ1
3.55 ± 0.17
4.61 ± 0.15e
521
2.081
5
Π
1σ22σ21π41δ23σ12π1
3.57 ± 0.16
3.37 ± 0.15e,f
435
2.128
6 +
Σ
1σ22σ21π41δ23σ12π2
2.92 ± 0.12
2.85 ± 0.11e
467
2.110
FeSg
5 +
Σ
1σ22σ21π41δ23σ22π2
3.82 ± 0.15
3.31 ± 0.15e,f
536g
2.010g
CoS
4
Δ
1σ22σ21π41δ33σ22π2
3.86 ± 0.15
3.39 ± 0.15e,f
537
1.980
3 −
Σ
2
1σ 2σ 1π 1δ 3σ 2π
3.76 ± 0.17
3.53 ± 0.15e,f
636
1.980
2
Π
1σ22σ21π41δ43σ22π3
3.52 ± 0.15
2.81 ± 0.15h
385
2.106
1 +
1σ22σ21π41δ43σ22π4
2.11 ± 0.13
2.08 ± 0.13i
ScS TiS VS CrS MnS
NiS CuS ZnS a b
c
d
e f g h
i
Σ
2
2
2
2
4
4
1
4
2
Taken from Ref. 5. Calculated using ΔfH°(S) = 2.847 ± 0.003 eV and ΔfH°(M) from Chase, M.W., Jr.; Davies, C.A.; Downey, J.R., Jr.; Frurip, D.J.; McDonald, R.A.; Syverud, A.N. (1985) J. Phys. Chem. Ref. Data, 14, Suppl. 1 (JANAF Tables). Average of the values derived in: Coppens, P.; Smoes, S.; Drowart, J. (1967) Trans. Faraday Soc., 63: p. 2140; Steiger, R.A.; Cater, E.D. (1975) High Temp. Sci., 7: p. 288. Smoes, S.; Coppens, P.; Bergman, C.; Drowart, J. (1969) Trans. Faraday Soc., 65: p. 682; Pelino, M.; Viswanadham, P.; Edwards, J.G. (1979) J. Phys. Chem., 83: p. 2964. Ref. 62. Values for CrS, FeS, CoS, and NiS are based on D0(MnS) = 2.85 ± 0.11 eV. Ref. 63. Smoes, S.; Mandy, F.; Vander Auwera-Mahieu, A.; Drowart, (1972) J. Bull. Soc. Chim. Belg., 81: p. 45. De Maria, G.; Goldfinger, P.; Malaspina, L.; Piacente, V. (1965) Trans. Faraday Soc., 61: p. 2146; see also: Grade, M.; Hirschwald, W. (1982) Ber. Bunsenges. Phys. Chem., 86: p. 899.
vibrational frequencies and bond lengths of the species investigated. At the time when most of the Knudsen-effusion experiments were performed, few data on gaseous, neutral transition-metal sulfides were available. Bond lengths and vibrational frequencies were estimated from comparison with the better investigated metal oxides or from extrapolation of the known values for the solid transition-metal sulfides. However, a recent theoretical study of Bauschlicher and Maitre5 at the CCSD(T) level of theory shows reasonably good agreement between estimated, experimental, and calculated data for gaseous MS. Another source of error is the clear identification of the process that leads to the formation of the species investigated. This source of error is particularly important when thermodynamic data are derived from reactions such as 14 and 15, which involve evaporation from amorphous solids (s) or crystalline (c) materials.
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Ilona Kretzschmar et al.
(MxSy)s
MS
(14)
(MxSy)c
MS
(15)
Figure 5 shows the variation of the bond energies of the neutral and the cationic transition-metal sulfides in the 3d series. The general trends in the bond energies along the first transition row are very similar for the neutral and the cationic transition-metal sulfides. In addition, except for scandium, the M–S bonds of the neutral exceed those of the cationic transition-metal sulfides. Two factors can be straightforwardly identified as influencing the strengths of the M–S and M+–S bonds: (i) the electron density at the metal center and (ii) the character of the orbital from which an electron is removed upon ionization. The electron density on the metal center is influenced by the charge of the molecule and the electronegativity of the ligands attached to the metal center. A convenient way to demonstrate the effect of charge and ligation is to compare the ionization energies (IEs) of the bare metals (M) and the ligated species (MS). The D0(M–S) and D0(M+–S) values given in Tables 1 and 2 are used to calculate the IEs of the neutral transition-metal sulfides (Table 3). The comparison of the IE(M) and IE(MS) values reveals that ionization of the bare metal atom is energetically more favored than Figure 5: Bond energies of the first-row transition-metal sulfides (▲) and sulfide cations (●). Open triangles (Δ) show calculated D0(M–S) taken from Ref. 5 with the exception of D0(Fe–S) taken from Ref. 63.
The Binding in Neutral and Cationic 3d and 4d Table 3. Ionization energies for M, MO, and MS. M
IE(M)a c
IE(MS)b
IE(MO) d
Sc
6.562
6.44 ± 0.16
6.50 ± 0.18
Ti
6.820c
6.8198 ± 0.0007e
6.86 ± 0.24
V
6.746f
7.2386 ± 0.0006g
7.57 ± 0.22
Cr
6.767c
7.46 ± 0.32h
7.43 ± 0.17
Mn
7.434c
8.30 ± 0.15h
7.83 ± 0.15
Fe
7.902c
8.61 ± 0.16d
8.09 ± 0.17
Co
7.881i
8.51 ± 0.15h
8.43 ± 0.17
Ni
7.640i
8.77 ± 0.18d
8.83 ± 0.21
Cu
7.726j
8.86 ± 0.27d
8.80 ± 0.17
Zn
9.394k
9.28 ± 0.06l
9.45 ± 0.14
Y
6.217m
6.113 ± 0.002e
6.26 ± 0.16
Zr
6.634n
6.812 ± 0.002e
7.03 ± 0.28
Nb
6.759o
7.154 ± 0.001e
Mo
o
Tc
7.092 7.28
r
7.361 7.459
s
8.337
s
Ag
7.576
j
Cd
7.576k
Ru Rh Pd
a
7.450 ± 0.0005 –
s
–p e
p
7.7 ± 0.3q –p
t
–p
t
–p
t
–p
t
8.60 ± 0.22
8.51 ± 0.20
–p
–p
8.89 ± 0.43 8.63 ± 0.43 9.76 ± 0.17
http://physics.nist.gov/PhysRefData/IonEnergy/tblNew.html. Calculated according to Equation 16. c Ref. 52. d Ref. 7 using D0(Sc+–S) = 7.14 ± 0.06 eV. e Ref. 69. f James, A.M.; Kowalczyk, P.; Langlois, E.; Campell, M.D.; Ogawa, A.; Simard, B. (1994) J. Chem. Phys., 101: p. 4485. g Harrington, J.; Weisshaar, J.C. (1992) J. Chem. Phys., 97: p. 2809. h Ref. 7. i Page, R.H.; Gudeman, C.S. (1990) J. Opt. Soc. Am. B, 7: p. 1761. j Loock, H.-P.; Beaty, L.M.; Simard, B. (1999) Phys. Rev., A 59: p. 873. k Brown, C.M.; Tilford, S.G.; Ginter, M.L. (1975) J. Opt. Soc. Am., 65: p. 1404. l Ref. 51. m Garton, W.R.S.; Reeves, E.M.; Tomkins, F.S.; Ercoli, B. (1973) Proc. Roy. Soc. Ser. A, 333: p. 1. n Hackett, P.A.; Humphries, M.R.; Mitchell, S.A.; Rayner, D.M. (1986) J. Chem. Phys., 85: p. 3194. o Rayner, D.M.; Mitchell, S.A.; Bourne, O.L.; Hakkett, P.A. (1987) J. Opt. Soc. Am. B, 4: p. 900. p Neither D0(M–X) nor IE(MX) are available in the literature. q Ref. 10f. r Finkelnburg, W.; Humbach, W. (1955) Naturwiss., 42: p. 35. s Callender, C.L.; Hackett, P.A.; Rayner, D.M. (1988) J. Opt. Soc. Am. B, 5: p. 614. t Ref. 71. b
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Ilona Kretzschmar et al.
the ionization of the metal sulfide molecule in all cases but M = Sc. This is in agreement with the fact that the electron density at the metal center is reduced by the formation of bonds to the electronegative sulfur ligand, which renders the removal of an electron from the MS molecule more energetic. The opposite trend for the IE(Sc)/IE(ScS) couple and the close proximity of the ionization energies for titanium and titanium sulfide can be explained by the increased electron densities on the metal centers in the early transition-metal sulfides compared to the free metals, which can be rationalized by the π-donation of the sulfur lone-pair electrons into the metal dπ-orbitals (see above). A thermochemical cycle, which includes the ionization processes M → M+ and MS → MS+ as well as the dissociation of MS and MS+ into M/M+ and S, yields Equation 16. D0(M+–S) = D0(M–S) – IE(MS) + IE(M)
(16)
This formula nicely explains the correlation of the data presented in Fig. 5 and Table 3. The effect of the orbital character (bonding, nonbonding, or antibonding) on the M–S bonds in the neutral and cationic transition-metal sulfides is best viewed by consideration of the M–S bond lengths. The removal of an electron from an antibonding orbital should result in a reduction of the M–S bond length accompanied by a stabilization of the bond due to better overlap. In contrast, the removal of an electron from a bonding orbital results in an increase of rMS and a destabilization of the bond. The change in rMS is expected to be small if electrons from nonbonding orbitals (1δ) are involved. The orbital scheme developed for MX+ (Fig. 1) suggests that the electron removed upon ionization of MS stems either from an 1δ-, 3σ-, or 2π-orbital. According to the binding scheme, these orbitals are either non- or antibonding. Thus, the ionization of MS should either have little effect on the M–S bond or result in a shortening. The bond lengths of the cationic and neutral transitionmetal sulfides given in Tables 1 and 2 are shown in Fig. 6. Analysis of Fig. 6 reveals that rMS is larger than rMS+ for the early transition metals Sc, Ti, V, and Cr. This indicates that the electron is removed from an orbital with antibonding character. Interestingly, the trend in the bond length difference reverses for the late transition metals, implying that in contrast to the assumptions made above, the electron originates now from a bonding orbital. Tables 1 and 2 contain the occupations for the neutral and cationic transition metals in their ground states when described in a single-configuration picture. Comparison of the configurations for MS and MS+
The Binding in Neutral and Cationic 3d and 4d
371
Figure 6: Computed bond lengths of the M–S bond of the cationic (■, B3LYP/6311+G*) and neutral (❏, Refs. 5,63) first-row transition-metal sulfides.
reveals that the electron is removed from the 3σ orbital for M = Sc, Ti, V, Fe, Co, and Ni and from a 2π orbital for M = Cr, Mn, Cu, and Zn. The observed decrease in the M–S bond lengths for the early transition metals Sc–Cr upon ionization of the neutral metal sulfides to the cations can be rationalized by antibonding characters of the 3σ and 2π orbitals. However, the electron removed from MnS also stems from an antibonding 2π orbital, but results in an elongation of the Mn–S bond in MnS+. A rationale for this trend is the reduction of the electron correlation due to the removal of one uncoupled electron, which causes a destabilization of the MnS+ molecule (see above). Further, the increase of rMS for M = Fe, Co, and Ni suggests bonding character of the 3σ orbital. The elongation of the M–S bond upon ionization of CuS and ZnS cannot be rationalized by bonding character of the antibonding 2π orbitals, but rather points to the presence of different bonding interactions, i.e., ionic and dative, in these molecules. The change of the 3σ-orbital character from antibonding to bonding is further demonstrated by the amount of energy needed for the excitation of an electron from the 1δ to the 3σ orbital in the early and late transition-metal sulfide cations. At the ADF/BP level of theory, the 1δ → 3σ excitation requires 0.65 eV for TiS+ (2Δ → 2Σ+) and 0.59 eV for VS+ (3Σ− → 3Δ), whereas these orbitals are inverted for the late metals, such that the 3σ → 1δ excitation requires 1.55 eV for FeS+ (6Σ+ → 4Δ) and 1.40 eV for CoS+ (5Δ → 3Σ−). The explanation
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Ilona Kretzschmar et al.
for the change of the 3σ orbital character is given by the contraction of the 3d orbitals, which results from the increasing nuclear charge of the metal going from the left to the right of a period. VI. PERIODIC TRENDS IN D0(M+–S) OF THE 4d TRANSITIONMETAL SULFIDE CATIONS AND THE COMPARISON WITH THEIR 3d CONGENERS Let us now address trends in bond energies, electronic structures, and reactivities between first and second-row transition-metal sulfide cations.64 The bond energies obtained from reactions 3 to 6 are summarized in Table 4 together with some complementary data obtained from quantum-chemical calculations. The electronic ground states have been obtained at the ADF/BP level of theory and are confirmed by B3LYP/3-21G calculations,(b) which also yield bond lengths r and vibrational frequencies ν.(c) Comparing the data given in Table 4 with those given for the firstrow transition-metal sulfide cations in Table 1 reveals that the sulfide cations of both transition rows exhibit equivalent ground states and electronic configurations. This finding points to the fact that bond formation to sulfur occurs with a similar pattern for the metal cations of the first and the second transition row and does not Table 4. Experimental 0K bond dissociation energies and heats of formation, calculated electronic states, vibrational frequencies and bond lengths for second-row transition metal sulfide cations. MS+
Statea,b
YS+
1 +
Configurationa
ΔHf(MS+) [eV]c
D0(M+–S) [eV]d
ν [cm–1]
r [Å]b
Σ
1σ22σ21π4
7.93 ± 0.09
5.49 ± 0.08
540
2.244
2
Δ
1σ22σ21π41δ1
10.49 ± 0.34
5.52 ± 0.22
547
2.196
NbS+
3 −
1σ22σ21π41δ2
11.78 ± 0.13
5.51 ± 0.10
541
2.154
MoS+
4 −
Σ
1σ22σ21π41δ23σ1
13.08 ± 0.11
3.68 ± 0.05e
421
2.171
TcS+
5
ZrS
+
RuS
+
Σ
Π
1σ22σ21π41δ23σ12π1
384
2.231
6 +
Σ
1σ22σ21π41δ23σ12π2
13.77 ± 0.09
2.99 ± 0.06
413
2.233
RhS+
5
Δ
1σ22σ21π41δ33σ12π2
13.81 ± 0.14
2.34 ± 0.13
378
2.243
PdS+
4 −
Σ
1σ22σ21π41δ43σ12π2
13.05 ± 0.07
2.04 ± 0.06
343
2.258
AgS+
3 −
Σ
1σ22σ21π41δ43σ22π2
12.10 ± 0.14
1.27 ± 0.13
383
2.643
CdS+
2
Π
1σ22σ21π41δ43σ22π3
290
2.491
a b c
d e
ADF/BP. B3LYP/3-21G. Calculated using ΔfH°(S) = 2.847 ± 0.003 eV and ΔfH°(M+) from Chase, M.W., Jr.; Davies, C.A.; Downey, J.R., Jr.; Frurip, D.J.; McDonald, R.A.; Syverud, A.N. (1985) J. Phys. Chem. Ref. Data, 14, Suppl. 1 (JANAF Tables). Ref. 10m. Ref. 10f.
The Binding in Neutral and Cationic 3d and 4d
373
depend on the ground-state configuration of the metal cation, which does vary from row to row. The best way to compare the effect of the metal on the bond strengths is to plot the bond strengths along the 3d and 4d rows (Fig. 7). The general trend for the bond energy to decrease from the left to the right of a period is also found for the metal-sulfide cations of the second transition row pointing to a similar bond situation as discussed above for the metal sulfides of the first transition row. However, there are two distinct differences. First, the trends in the D0(M+–S) values of the early transition metals are somewhat different for first- and second-row transition metals in that D0(M+–S) decreases by 25% going from scandium to vanadium, while D0(M+–S) remains similar for M = Y, Zr, and Nb. Second, the bond energies of the MS+ cations of the early 3d metals are lower than those of their 4d congeners, whereas this trend reverses for the late transition metals. For the first-row transition-metal sulfide cations, the decrease in bond energy has been attributed to the reduction of the electroncorrelation term caused by the single occupation of the nonbonding 1δ orbitals moving from ScS+ to VS+ (see above). As is apparent from Fig. 7, the trend vanishes for the second-row congeners YS+, ZrS+, and NbS+. The more diffuse nature of the 4d orbitals gives the electrons more space to avoid each other, which leads to a reduction of the Figure 7:
Bond energies of the first-row (●) and the second-row transition-metal sulfide cations (❍).
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Ilona Kretzschmar et al.
electron–electron repulsion. This effect is demonstrated best by the smaller Kdd-exchange integrals calculated for the metal cations of the second transition row (0.4 < Kdd < 0.8 eV) compared to the corresponding metal cations of the first transition row (0.5 < Kdd < 1.0 eV).65 The reversal of the absolute magnitudes of D0(M+–S) for 3dand 4d metals when moving from early to late metals of the periodic table is more difficult to rationalize, although the more diffuse 4d orbitals could mean decreased overlap with the sulfur orbitals as the 4d orbitals contract. Careful consideration of the effects that influence the bonding interaction between a metal cation and a ligand might give more insight into the origins of this trend. Factors affecting the bond strengths are charge distributions, electronegativity differences, and relative stabilities of the fragments. NBO population analysis of the first- and second-row transition-metal sulfide cations at the B3LYP/6-311+G* and 3-21G levels of theory, respectively, yields the charge distributions qNBO for sulfur shown in Fig. 8. Two conclusions can be drawn from the plot in Fig. 8. 1. The configurations M2+–S− are very important for a correct description of the early transition-metal sulfide cations, while for the late transition-metal sulfide cations, M–S+ configurations also contribute. Figure 8: NBO-charges of sulfur for the first-row (■, B3LYP/6-311+G*) and the second-row transition-metal sulfide cations (❏, B3LYP/3-21G).
The Binding in Neutral and Cationic 3d and 4d
375
Figure 9: NBO-charges of the metal center for the first-row (■, B3LYP/6-311+G*) and the second-row transition-metal sulfide cations (❏, B3LYP/3-21G) as function of D0(M+–S). The full and dashed lines represent the linear regression fit for the first and second transition row, respectively. The correlation coefficients are 0.78 (0.97 after excluding D0(Mn+–S) and D0(Zn+–S), see text) and 0.91 excluding D0(Y+–S), respectively.
2. Similar to the observations made for D0(M+–S), the relative trend between first- and second-row transition-metal species reverses in the middle of the row. Correlation of D0(M+–S) with the qNBO located on the metal center yields the plots shown in Fig. 9. For the metals of the first transition row (full squares), the correlation coefficient is rather poor (r = 0.78). Closer inspection of the data shown in Fig. 9 reveals that the points for MnS+ and ZnS+ substantially deviate from the line for the other first row metals. Excluding these two points from the correlation, we obtain the full line with an improved correlation coefficient of r = 0.97.(d) Thus, we can conclude from the correlation that a higher charge localized on the metal correlates with a stronger bond dissociation energy. The failure of D0(Zn+–S) nicely underlines the conclusion made in Section III that the bonding mechanism in ZnS+ involves ionic contributions rendering the charge at the Zn higher than it should be according to the correlation and the experimental D0 value. Apparently, Mn+(3d54s1) bears some similarity to Zn+(3d104s1) in this regard. For the 4d-metals, the
376
Ilona Kretzschmar et al.
situation is different. The D0 values for technetium and cadmium are not known and therefore not included in the correlation. The entry for D0(Y+–S) deviates somewhat from the other points and is not included in the correlation (dashed line, r = 0.91). The deviation of D0(Y+–S) and the less satisfying correlation coefficient can probably be traced back to the much smaller basis sets (3-21G) used for the description of the 4d-metals. The relationship between the charge distribution in a molecule and the bond strength is determined by the electronegativities Χ. As all of the molecules discussed here contain sulfur, the electronegativities of the metal fragments need to be considered. From conclusion (i) derived above, it follows that the electronegativities of M2+, M+, and M all contribute to the overall bonding. Several models66 have been proposed in the literature for the calculation of Χ, including those of Pauling, Mulliken, and Allred-Rochow. In the present study, we have chosen the method developed by Mulliken. The empirical Equation 17 suggests that the attraction of an atom/ ion for electrons should be an average of the ionization energy (IE)53 and the electron affinity (EA)67 of the atom/ion.
Χ M = 0.168 eV–1 • (IEM + EAM – 1.23 eV)
(17)
Figures 10a–10c show the electronegativities of M, M+, and M2+ obtained with Equation 17 as a function of the corresponding D0(M+–S) values. It is evident from Fig. 10 that there exist correlations between Χ(M0/+/2+) and D0(M+–S). This result is consistent with similar bonding situations in all species examined, and further highlights the role of ionic contributions. However, for the first-row transitionmetal sulfide cations there are some exceptions, such as CrS+ in Fig. 10a and ZnS+ in Figs. 10b and 10c. The deviation of the latter may again result from a different, more ionic bonding mechanism apparent in ZnS+ compared with the other metal sulfides, which renders the metal–sulfur interaction stronger than the electronegativities of Zn+/2+ suggest. The discrepancy observed for CrS+ can arise either from a too low D0 value or a too low electronegativity. The former can probably be excluded as a reason because D0(CrS+) does not deviate as much, when it is plotted versus Χ(M+) and Χ(M2+). From this it follows that the derivation of Χ(Cr) according to Equation 17 might be inadequate. Comparison of the IEs of vanadium (6.74 eV) and manganese (7.43 eV) with that of chromium (6.77 eV) reveals that despite the increased effective nuclear charge in Cr the IE of chromium is not much different from that found for vanadium. The rationale for this observation is the
The Binding in Neutral and Cationic 3d and 4d
377
Figure 10: (a) Electronegativities Χ of the neutral first-row (■) and the second-row transition-metal atoms (❏) as function of D0(M+–S). The correlation coefficients are –0.91 (–0.98 after exclusion of D0(Cr+–S), see text) and –0.93, respectively. Note that D0(Mn+–S) and D0(Zn+–S) are not included because of the non-existence of the Zn− and Mn− anions. (b) Electronegativities Χ of the first-row (■) and the second-row transition-metal cations (❏) as function of D0(M+–S). The correlation coefficients are –0.87 (–0.92 after excluding D0(Zn+–S), see text) and –0.97, respectively. (c) Electronegativities Χ of the first-row (■) and the second-row transition-metal dications (❏) as function of D0(M+–S). The correlation coefficients are –0.93 (–0.96 after excluding D0(Zn+–S), see text) and –0.97, respectively. The full and dashed lines represent the regression fit for the first- and second transition row, respectively.
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Ilona Kretzschmar et al.
stable 3d5 configuration in Cr+ (6S). The best correlation (r = –0.96 and the standard deviation for the bond dissociation energy is 0.38 eV)(e) of all values from the first and second-row transition-metal sulfide cations is found with the electronegativity of the dications. However, due to the fact that Χ(M), Χ(M+), and Χ(M2+) correlate strongly with each other,(f) it is not trivial to deduce from the present data, which of the configurations (M–S+, M+–S, or M2+–S−) is most important. Another way to correlate the stability of M n+ (n = 0–2) with the bond strength is to plot the difference of the second and first ionization energies, ΔIE, versus D 0(M +–S) as is shown in Fig. 11. Good correlations are observed with two notable exceptions, MnS+ for the first transition row and AgS+ for the second transition row. According to this plot, the bond strength of a transition-metal sulfide cation is stronger the smaller the difference in ΔIE. Smaller ΔIEs indicate a more stable dication M2+ compared to the monocation. Thus, the most stable transition-metal sulfide cations are Figure 11: Difference of second and first ionization energies plotted as function of D0(M+–S) for the first-row (■) and the second-row transition-metal atoms (❏). The full and dashed lines represent the regression fits for the first and second transition row, respectively. The correlation coefficients are –0.92 (–0.96 after exclusion of D0(Mn+–S), see text) and –0.96 (–0.97 after excluding D0(Ag+–S), see text), respectively.
The Binding in Neutral and Cationic 3d and 4d
379
formed with metals for which the dication is stabilized, i.e., low second ionization energy, and the monocation is destabilized, i.e., high first ionization energy. This trend is further confirmed by the NBO charge distributions obtained for the metal-sulfide cations given in Fig. 8. In summary, it is obvious that the M2+–S− configuration plays a significant role in the bonding of MS+ monocations, consistent with a strongly polarized bond. VII. COMPARISON OF THE CATIONIC AND NEUTRAL TRANSITION-METAL MONOXIDES AND SULFIDES The bond dissociation energies of the cationic transition-metal oxides are summarized in Table 5. Table 6 contains the data for the neutral transition-metal oxides and sulfides mainly obtained with Knudsen-effusion mass spectrometry.62 The values for the cationic oxides and sulfides are derived from thermodynamic thresholds measured with the GIB apparatus. The bond energies of the neutral and the cationic molecules are related with the ionization energies of the transition metal and the transition-metal chalcogenides according to the Born-Haber cycle, see Equation 16 in Section V. Most of the commonly used methods for the determination of ionization energies, e.g., appearance-energy measurements, result in IE values with large errors of 0.5 to 1 eV. The use of Equation 16 represents an indirect way for the calculation of ionization energies. Because of the high precision, which is nowadays achievable for bond dissociation energies, the IE values derived by means of Equation 16 exhibit much smaller uncertainties. More precise IE values in return allow the use of more accurate methods, such as two-color photoionization (R2PI) spectroscopy and mass-analyzed threshold ionization (MATI) for the determination of IEs.68 Recently, the IEs of TiO, YO, ZrO, NbO, and MoO have been evaluated by a combination of R2PI and MATI measurements to an accuracy of 0.5 to 2 meV (Table 3).69 The IEs of most transition-metal oxides of the first and second transition rows have been determined experimentally, whereas only a few, rather imprecise IE values are available for the transitionmetal sulfides. Because of the large uncertainties (ΔE = 0.5–1.0 eV) of the IE(MS) values and their limited number, the IE(MS) values given in Table 3 are consistently derived using Equation 16. Figures 12 and 13 show the bond energies of the cationic and neutral transition-metal oxides and sulfides in a graphical form. Overall, the metal oxides and sulfides show very similar trends along the first and second transition rows, suggesting similar
380
Ilona Kretzschmar et al.
Table 5. Experimental 0K bond dissociation energies and heats of formation, calculated electronic states, vibrational frequencies and bond lengths for first- and second-row transition-metal oxide cations. MO+
Statea,b
ScO+
1 +
Configurationa
Σ
1σ22σ21π4
ΔHf(MO+) [eV]c
D0(M+–O) [eV]d
ν [cm–1]b
r [Å]b
5.88 ± 0.10
7.14 ± 0.06e
1076
1.612
Δ
1σ 2σ 1π 1δ
1
7.38 ± 0.10
6.88 ± 0.07f
1125
1.570
VO+
3 −
1σ22σ21π41δ2
8.62 ± 0.13
5.99 ± 0.10f
1140
1.537
CrO+
4 −g
Σ
1σ22σ21π41δ23σ1
9.70 ± 0.06
3.72 ± 0.06
768
1.592
MnO+
5
Πh
1σ22σ21π41δ23σ12π1
9.97 ± 0.13
2.95 ± 0.13
925
1.587
FeO+
6 +
Σ
1σ22σ21π41δ23σ12π2
11.24 ± 0.13
3.47 ± 0.10
820
1.640
CoO+
5
Δ
1σ22σ21π41δ33σ12π2
11.54 ± 0.10
3.29 ± 0.06
761
1.640
NiO+
4 −
Σ
1σ22σ21π41δ43σ12π2
11.89 ± 0.13
2.74 ± 0.10d
690
1.645
3 −
Σ
1σ22σ21π41δ43σ22π2
12.15 ± 0.15
1.62 ± 0.15
470
1.817
Π
1σ22σ21π41δ43σ22π3
11.57 ± 0.05
1.67 ± 0.05i
586
1.821
ν [cm–1]j
r [Å]j
TiO
+
2
Σ
CuO+ ZnO
+
MO+
2
2
4
Configurationa
ΔHf(MO+) [eV]c
Σ
1σ22σ21π4
Statea,j 1 +
YO+
2
D0(M+–O) [eV]
5.62 ± 0.12
7.51 ± 0.11k
1014
1.757
Δ
1σ 2σ 1π 1δ
1
7.93 ± 0.28
7.79 ± 0.11k
1052
1.719
NbO+
3 −
1σ22σ21π41δ2
9.44 ± 0.13
7.57 ± 0.10k
1082
1.685
MoO+
4 −
Σ
1σ22σ21π41δ23σ1
11.41 ± 0.05
5.06 ± 0.02l
1004
1.711
TcO+
5 +
1σ22σ21π41δ22π2
976
1.742
RuO+
6 +
1σ22σ21π41δ23σ12π2
12.66 ± 0.08
3.81 ± 0.05m
773
1.828
3 −n
1σ 2σ 1π 1δ 2π
12.84 ± 0.06
3.02 ± 0.06m
954
1.712
PdO+
4 −
Σ
1σ22σ21π41δ43σ12π2
13.35 ± 0.11
1.46 ± 0.11m,o
656
1.857
AgO+
3 −
Σ
1σ22σ21π41δ43σ22π2
11.85 ± 0.08
1.23 ± 0.05m
224
2.316
CdO+
2
Π
1σ22σ21π41δ43σ22π3
498
2.070
ZrO
+
RhO
a-c d e f
g h i j k l m n o
+
2
Σ Σ Σ Σ
2
2
2
2
4
4
4
2
See Table 1. Ref. 7. Chen, Y.-M.; Clemmer, D.E.; Armentrout, P.B. (1994) J. Phys. Chem., 98: p. 11490. Clemmer, D.E.; Elkind, J.L.; Aristov, N.; Armentrout, P.B. (1991) J. Chem. Phys., 95: p. 3387. 4 – Σ → 4Π = 0.1 eV, Ref. 3. 5 Π → 5Σ+ = 0.1 eV, Ref. 3. Ref. 11. B3LYP/3-21G. Ref. 10m. Sievers, M.R.; Chen, Y.-M.; Armentrout, P.B. (1996) J. Chem. Phys., 105: p. 6322. Loock, H.-P.; Beaty, L.M.; Simard, B. (1999) Phys. Rev., A 59: p. 873. 3 − Σ → 5Δ = 0.12 eV. D0(Pd+–O) of 2.08 eV is obtained with Equation 16 using IE(PdO) of 9.1 eV.71
bonding mechanisms. This similarity is not very surprising considering the comparable electronic properties of oxygen and sulfur. For instance, both atoms exhibit 3P ground states with the lowest singlet states (1D) at 1.97 and 1.15 eV,70 respectively. The bond energies of the two corresponding homonuclear dimers are 5.116 ± 0.001 eV
The Binding in Neutral and Cationic 3d and 4d
381
Table 6. 0K bond dissociation energies D0(M–O) and D0(M–S), calculated electronic states, vibrational frequencies and bond lengths for first- and second-row transition metal oxide and sulfide neutrals. M Sc Ti
Statea 2 +
Cr Mn Fe Co Ni Cu Zn M
7.01 ± 0.12
[3σ]
971 1.679
Δ
6.87 ± 0.02d
[3σ]
1014 1.628
Σ
6.49 ± 0.09
[3σ]
1028 1.601
Π
4.41 ± 0.30
[2π]
888 1.633
3.82 ± 0.08
[2π]e
794 1.664
Σ
4.21 ± 0.09
[3σ]
885 1.609
Δ
3.94 ± 0.14
[3σ]
909 1.620
Σ
3.91 ± 0.17
[3σ]
850 1.626
Π
2.75 ± 0.22
[2π]
572 1.771
1 +
1.61 ± 0.04g
[2π]
727 1.719
5
6 +
Σ
5 + 4
3 − 2
Σ
Stateg,h D0(M–O)b HOMO νMOh 2 +
Σ
Y Zr Nb Mo Tc Ru Rh
rMOa
Σ
3
4 −
V
D0(M–O)b HOMO νMOa
7.41 ± 0.12
[3σ]
975 1.786
8.00 ± 0.14
[3σ]
1047 1.736
Σ
8.02 ± 0.19
[3σ]
1044 1.712
Π
5.76 ± 0.22
[2π]
968 1.733
[3σ]
997 1.761
5.34 ± 0.43
[1δ]
800 1.753
4.19 ± 0.43
[3σ]
882 1.753
1 +
Σ
4 − 5
6 +
Σ
5
rMOh
Δ
4 −
Σ
State 2 +
4.93 ± 0.13
[3σ]
563 2.155
Δ
4.75 ± 0.13
[3σ]
575 2.083
Σ
4.61 ± 0.15
[3σ]
521 2.081
Π
3.37 ± 0.15
[2π]
435 2.128
2.85 ± 0.11
[2π]e
467 2.110
Σ
3.31 ± 0.15
[3σ]
521 2.024
Δ
3.39 ± 0.15
[3σ]
537 1.980
Σ
3.53 ± 0.15
[3σ]
636 1.980
Π
2.81 ± 0.15
[2π]
385 2.106
Σ
2.08 ± 0.13
[2π]
Stateg,h
D0(M–S)
4 − 5
6 +
Σ
5 + 4
3 − 2
1 +
2 +
Σ
5.44 ± 0.11
[3σ]
506 2.288
5.92 ± 0.17i
[3σ]
544 2.199
[3σ]
516 2.191
[2π]
433 2.217
Σ
4 −
Σ
Π
5
–j
[2π]
497 2.201
5
Δ
–j
[1δ]
480 2.176
4 −
Σ
–j
[3σ]
470 2.159
Π
–j
[2π]
360 2.259
[2π]
270 2.432
[2π]
331 2.356
[2π]
650 1.858
Ag
2
Π
2.25 ± 0.22
[2π]
507 2.039
2
[2π]
626 1.938
c d e f g h i j k l
4.29 ± 0.30k
Σ
2.84 ± 0.13
b
–j
6 +
Π
a
rMSh
1 +
Pd
Σ
HOMO νMSh i
3
1 +
rMSa
Σ
3
3
Cd
HOMO νMSa
D0(M–S)c
Π
1 +
Σ
2.21 ± 0.15l –j
Taken from Ref. 5. Ref. 7. Table 2. Clemmer, D.E.; Aristov, N.; Armentrout, P.B. (1993) J. Phys. Chem., 97: p. 544. Ionization to the cation involves [3σ] if MnS+(5Σ+) is formed. Ref. 51. ADF/BP. B3LYP/3-21G. Steiger, R.P.; Drowart, E.D. (1975) High Temp. Sci., 7: p. 288. Neither D0(M–S) nor IE(MS) available in the literature. Calculated according to Equation 16. Smoes, S.; Mandy, F.; Vander Auwera-Mahieu, A.; Drowart, J. (1972) Bull. Soc. Chim. Belg., 81: p. 45.
and 4.364 ± 0.005 eV in O2 and S2, respectively. The ground states of the diatomic species are both 3Σg− with the lowest singlet state 1Δ at 0.98 and 0.62 eV for O2 and S2, respectively.70 Although the four plots look rather similar, there are a few deviations, which are worth more detailed discussion. First, the bonding in the oxides is, with the exception of the CuO+/CuS+, ZnO+/ZnS+, and PdO+/PdS+ couples, always stronger than that of the corresponding
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Figure 12: Bond dissociation energies of the cationic transition-metal oxides (❍) and sulfides (●) of (a) the first transition row and (b) the second transition row. (Ë) D0(Pd+–O) derived from IE(PdO) = 9.1 eV (see text).
sulfides. The difference decreases with an increasing number of valence electrons. In order to rationalize the decreasing difference between M–O and M–S bond strengths, one needs to consider the changes in the bonding patterns along the transition-metal rows. The bonding in the early transition-metal oxides can be described as a triple bond comparable to that present in the CO molecule, whereas
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Figure 13: Bond dissociation energies of the neutral transition-metal oxides (Δ) and sulfides (▲) of (a) the first transition row and (b) the second transition row.
the later transition-metals bind the oxygen atom in a fashion comparable to the bonding in triplet oxygen.42 Similarly, the M–S bonds can be compared with those in CS and S2. The triple bonds in CO and CS arise from one covalent σ-bond and one covalent π-bond together with a donor-acceptor π-bond. The strength of the donor-acceptor πbond in MX0/+ depends on the electronegativity difference ΔΧ
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between the metal cation and the ligand. The higher ΔΧ is, the stronger the donor-acceptor π-bond. Thus, the lower electronegativity of sulfur compared to oxygen may cause a reduced donoracceptor interaction in the metal sulfides, which manifests itself in reduced bond strengths in the MS+ cations. Moving further to the right in the periodic system reduces the contribution of the donoracceptor interaction and thus leads to the observed adjustment of D0(M+–O) and D0(M+–S). A better way to visualize the bond-energy difference in the M–O and M–S bonds is to plot the reaction enthalpies ΔRH for a chosen reaction, which involves the conversion of the transition-metal sulfide into the corresponding oxide, e.g., reaction 18. MS+ + H2O → MO+ + H2S
(18)
In such a plot, Fig. 14, the absolute scale is determined by the difference in the enthalpies of formation of the neutrals, i.e., ΔHf(H2S) – ΔHf(H2O) = 2.294 ± 0.008 eV, and the relative scale displays Δ[D0(M+ –S) – D0(M+–O)]. Obviously, the reaction becomes more endothermic with increasing number of valence electrons on the metal. The trends Figure 14: Reaction enthalpies for reaction (18) with M = first transition row (■) and M = second transition row (❏). The dotted line represents ΔHf(H2S) – ΔHf(H2O) = 2.294 ± 0.008 eV. (◆) D0(Pd+–O) is derived assuming IE(PdO) = 9.1 eV (see text).
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for the metals of the first and second transition row are again very similar with palladium as an exception (see below). According to Fig. 14, the transition metals can be divided into three groups: (i) the early transition metals, 4 or fewer valence electrons, where ΔRH < 0, (ii) the metals with 5 to 9 valence electrons, for which reaction 18 is significantly endothermic, and (iii) the group 11 and 12 metals, where ΔRH ~ ΔHf(H2S) – ΔHf(H2O). Thus, the early transition metals will always have a high tendency towards oxide formation independent of the O-providing reagent. In contrast, the oxide formation of the metals summarized under (ii) should be tunable by the difference in the heat of formations of the neutrals in reactions analogous to process 18. Another characteristic quantity for comparison of the transition metal oxides and sulfides are the IEs (Fig. 15). Although the data are incomplete for the 4d metals, it is obvious from Fig. 15 that the value for IE(PdO) is exceptional. This deviation and the ones observed in Figures 12b and 14 can either result from a too low D0(Pd+–O), a too high D0(Pd+–S), or they are caused by some special electronic property of palladium, e.g., (IE)Pd is also high compared with its neighbors. In order to probe the former aspect, the generation of either PdO+ or PdS+ in the FTICR was attempted, but was never successful. Pd+ is found to neither react with N2O and O2 nor with c-C2H4S and COS to form PdO+ and PdS+, respectively, at thermal energies. Even upon excitation of the Pd+ ion, only insignificant amounts of the desired species are formed. B3LYP/3-21G calculations(g) predict too low D0 values for the MO+ ions (M = Zr–Ag) with the exception of D0,calc(Pd+–O) = 1.97 eV compared to D0,exp(Pd+–O) = 1.46 ± 0.11 eV. Similarly, the calculated D0(M+–S) values are too low, but no deviation occurs for the bond energy of PdS+ in this case.(c) These apparent discrepancies suggest that some of the thermochemical data used may be erroneous. In particular, these comparisons suggest that D0(Pd+–O) = 1.46 ± 0.11eV may be questioned. This value was derived in a GIB study from the threshold for formation of PdO+ from bare Pd+ and O2, reaction 19.71 Pd+ + O2 → PdO+ + O
(19)
If oxygen-atom transfer is associated with a barrier in reaction 19, the resulting threshold E0 is too high and the bond energy is too low. While this is possible, no similar barriers are apparent for other second row transition metal ions in the analogous reactions.71 However, a larger D0(Pd+–O) would make palladium match the trends of the other 3d- and 4d-metals, such that it would no longer be exceptional. The possibility of D0(Pd+–O) = 1.46 ± 0.11eV being
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Figure 15: Ionization energies of (a) the first and (b) the second transition-row metal oxides (❍) and sulfides (●). (Ë) D0(Pd+–O) is derived assuming IE(PdO) = 9.1 eV (see text).
too low is further supported by a Born-Haber cycle with the neutral PdO. Appearance-energy measurements72 imply IE(PdO) = 9.1 eV although the unspecified uncertainty of this value is likely to be large (0.5–1.0 eV). Together with D0(Pd–O) = 2.84 ± 0.13 eV and Equation 16, D0(Pd+–O) = 2.08 eV is obtained, which agrees somewhat better with the general trends in Figs 12b, 14, and 15.
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Pd+ + CS2 → PdS+ + CS
387
(20)
Further, note that overestimation of D0(Pd+–S) due to involvement of excited states of Pd+ in reaction 20 seems unlikely because the lowest excited state of Pd+ is the 4F state, which is 3.03 eV above the 2 D ground state. Although the arguments listed above suggest the possibility of an erroneous D0(Pd+–O) value, palladium also has special electronic features that might explain the observed deviations. Neutral Pd is the only metal of group 10 that exhibits a ground state with a d10 configuration. The extraordinary stability of the d10 configuration is nicely displayed by the ionization energies of the first and second transition-row metals (Fig. 16). Further, the periodic trends of the bond energies for the second-row transition-metal oxide cations, as discussed in reference 71, seem sensible. However, for the time being, we cannot further address the peculiar behavior of PdO+ and PdS+ and must await further experimental and theoretical studies. A correlation of the ΔRH(18) values and the IE(M) of the transition metals of the second transition row yields a reasonable correlation coefficient (r = 0.95 when D0(Pd+–O) = 1.46 ± 0.11 eV is used).(h) This correlation implies that, relative to the M–S bonds, the M–O bonds become weaker as the IEs of the neutral metals get higher. Larger IEs in turn imply higher electronegativities of the Figure 16: Ionization energies of the first (■) and the second transition-row metals (❏).
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corresponding metal cations. Because oxygen (ΧO = 3.50)55 is more electronegative than sulfur (ΧS = 2.44),55 an increase in ΧM+ will result in a stronger destabilization of the M–O bond. Another interesting feature of Fig. 15a is that IE(MS) equals IE(MO) for M = Sc, Cr, Co, Ni, and Cu and even exceeds IE(MO) for M = Ti, V, and Zn. These findings are surprising, considering that the ionization of the sulfides is expected to be less energetic because the ionization energy of atomic oxygen, IE(O) = 13.61 eV, is higher than that of sulfur, IE(S) = 10.36 eV. While the opposite trends could evolve from erroneous bond energies for the neutral and/or cationic transition-metal chalcogenides, they may also result from the energetics of the orbitals, i.e., from where the electron is removed upon ionization. The former issue can only be probed by either spectroscopic measurements or high-level calculations, but the second point is addressed in the following. First, we have to recall the different bonding patterns found in the metal chalcogenides. The bonds in the cationic oxides and sulfides of the early transition metals have been compared to those in CO and CS, respectively. The molecular orbital diagrams for CO and CS given in Reference 44 reveal that the orbital gaps are smaller in CS compared to CO. A similar trend is found for the oxides and sulfides of the early transition metals and manifests itself in smaller state splittings for the transition-metal sulfide cations, e.g., VS+: 3Σ− → 3Δ = 0.36 eV, 3 − Σ → 5Π = 1.37 eV vs. VO+: 3Σ− → 3Δ = 1.36 eV, 3Σ− → 5Π = 3.17 eV.10j The bonding in the late transition-metal oxide (sulfide) cations has been compared to that of a triplet O2 (S2) molecule.3,49a,73 For O2 and S2 the state splittings are also smaller for the sulfur species, i.e., O2: 3Σg– → 1Δg = 0.98 eV and S2: 003Σg– → 1Δg = 0.62 eV.70 The same holds true for the cationic chalcogenides of the late transition metals, e.g., FeO+: 6Σ+ → 4Δ = 1.0 eV3 and FeS+: 6Σ+ → 4Π = 0.34 eV.10e From these findings, we can conclude that the orbital gaps are larger in the transition-metal oxides than in the sulfides. Thus, relative to the 1δ orbitals of MO and MS, the antibonding orbitals of the metal oxides lie higher in energy than those of the metal sulfides. From this, it follows that the removal of an electron from the highest occupied orbital is less demanding for the metal oxide compared to the sulfide, thus reversing the general trend that ionization of oxygen compounds is more energetic than ionization of sulfur compounds. VIII. ELECTRONIC GROUND STATES AND THE BONDING IN MX0/+ (X = O, S) Some spectroscopic properties of the neutral and cationic transitionmetal chalcogenides of the 3d and 4d-rows are given in Tables 1–6.
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The data for neutral MO and MS of the first transition-row metals (Table 6, upper part) have been obtained by Bauschlicher et al.5,47 employing the CCSD(T) level of theory. The data for the MX+ species with metals of the first transition row have been obtained at the B3LYP/6-311+G* level of theory. Although, Siegbahn74 has studied the neutral transition-metal oxides of the second transition row at the MCPF level of theory, all data given in Table 5 for the neutral MX with metals from the second transition row refer to results from B3LYP/3-21G calculations for reasons of consistency and completeness. However, the bond lengths and ground states of MO (M = Y–Pd) presented in Table 6 agree with those given in Reference 74. Analysis of the data given in Tables 1, 4, 5, and 6 reveals that there is perfect agreement of the electronic ground states for the neutral and cationic metal oxides and sulfides of the 3d-metals. The same holds true within the second transition row with the exception of the RhO+/ RhS+ couple. B3LYP/3-21G calculations predict a 3Σ− ground state for RhO+ with a 0.12 eV more energetic 5Δ state, whereas a 5Δ ground state is found at this level of theory for RhS+ with the 3Σ− state at 0.4 eV. In contrast, ADF calculations predict a reverse state ordering for RhS+ with a 3Σ−/5Δ splitting of 0.18 eV. Higher levels of theory will be required for the correct assignment of the ground state. Comparison of the ground-state configurations of the first and second transition-row metal compounds shows that the spin multiplicities of the ground states match perfectly with the exceptions of the TiX/ZrX and CoO+/RhO+ couples, while the symmetries differ for MX with M = Ru, Rh, and Pd. A closer inspection of the orbital occupations reveals that the late transition-metal chalcogenides of the second transition row prefer the double occupation of either the 1δ orbitals (Ru, Rh) or the 2π orbitals (Pd) over the double occupation of 3σ orbitals. This finding points to the fact that the 3σ orbital is more energetic for the metal chalcogenides of the second transition row. Table 6 also contains information about the orbitals from which the electrons are removed upon ionization. For the metal oxides and sulfides of the first transition row, the electron stems either from the 3σ or the 2π orbitals (see above). Recalling that the character of the 3σ orbital changes from antibonding in the early to bonding in the late transition metals, we can explain the reverse trends found for the ionization energies (Fig. 15a) of the first-row transition-metal oxides and sulfides. The bonding/antibonding character is further confirmed by the decrease of rMX upon ionization for the early transition metals and the elongation of rMX for the late transition metals. The trend in rMX indicates the removal of bond-weakening contributions for the early transition metals, whereas the bond is weakened for the late transition metals.
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Further, from the discussion in Section VII, we know that the orbital splittings are smaller for the sulfur than for the oxygen-containing species. Combining these two facts, it is clear that the removal of an electron from the 3σ orbital of an early transition-metal oxide is less demanding energetically than ionization of the corresponding sulfide, because the 3σ lies lower in the latter. This results in lower or similar IEs for the early transition-metal oxides and sulfides. The trend reverses to IE(MS) < IE(MO) for Fe, because the character of the 3σ orbitals changes to bonding. IX. CONCLUSIONS The following conclusions can be drawn from the data presented and discussed in this chapter. The bonding situation in the early transition-metal sulfide cations is viewed best as a triple bond comparable to the bond in the CS molecule, whereas the bonding pattern in the late transition metals resembles that of the triplet S2 biradical. The description of the group 11 and 12 metals requires including dative and ionic configurations. The bonding in the metal-sulfide cations of the second transition row resembles that of the first transition row. The character of the 3σ orbital is found to change from antibonding for the early to bonding for the late transition-metal sulfides. This trend is rationalized by the contraction of the d orbitals with increasing nuclear charge of the metal. Further, reasonable correlations of the bond energies of the transition-metal sulfide cations with the charge on the metal, qNBO(M), and the Mulliken electronegativity Χ(M2+) are found. Comparison of cationic transition-metal oxides and sulfides reveals that the bonding situation present in MS+ is comparable to that in MO+ leading to the same ground-state multiplicities and symmetries except for M = Rh. This observation is rationalized by the comparable electronic properties of the O and S ligands. The M–O bond strengths exceed those of the sulfides for almost all metals of the first and second transition row, which is most likely the result of the higher electronegativity of oxygen and the better overlap with the oxygen 2p orbitals. Further, the reaction enthalpies of the S/O exchange reaction for MS+ with H2O (Equation 18), evolve along the 3d series as follows. This reaction is slightly exothermic for the early transition-metal sulfide cations, while it becomes endothermic for the middle and late transition-metal sulfide cations. This helps to rationalize why catalysts consisting of the early transition metal sulfides are sensitive towards water impurities, whereas oxides of the late transition metals are poisoned by sulfur-containing components.
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ACKNOWLEDGMENTS This research was supported by the Deutsche Forschungsgemeinschaft, the Volkswagen-Stiftung, the Fonds der Chemischen Industrie (scholarship for IK), and the National Science Foundation, CHE-9877162. DS thanks the Auswärtiges Amt for travel support. The Konrad-Zuse Zentrum Berlin is acknowledged for a generous allocation of computing time. Chad Rue is thanked for his contributions to the experimental work that forms the basis for the discussion presented here. NOTES (a)
(b)
(c)
(d)
(e)
+
Calculated D0(M –S) values at the B3LYP/6-311+G* level of theory are: D0(Sc+–S) = 4.57 eV, D0(Ti+–S) = 4.11 eV, D0(V+–S) = 3.33 eV, D0(Cr+–S) = 2.34 eV, D0(Mn+–S) = 2.41 eV, D0(Fe+–S) = 3.15 eV, D0(Co+–S) = 2.69 eV, D0(Ni+–S) = 2.39 eV, D0(Cu+–S) = 2.04 eV, D0(Zn+–S) = 2.02 eV. For species containing a metal of the second transition row, the standard allelectron 3-21G basis sets are employed for all atoms, because no other complete set of all-electron basis sets with equal quality for all metals are available for the metals of the second transition row. Calculated D0(M+–S) values at the B3LYP/3-21G level of theory are: D0(Y+–S) = 5.51 eV, D0(Zr+–S) = 4.77 eV, D0(Nb+–S) = 3.97 eV, D0(Mo+–S) = 2.30 eV, D0(Tc+–S) = 2.72 eV, D0(Ru+–S) = 2.02 eV, D0(Rh+–S) = 1.45 eV, D0(Pd+–S) = 1.74 eV, D0(Ag+–S) = 0.91 eV, D0(Cd+–S) = 1.19 eV. A similar deviation of MnS+/q(Mn) and ZnS+/q(Zn) is also observed for the Mulliken-charge distribution. Here, the correlation coefficient increases from r = –0.75 to r = –0.98 when the species are excluded from the regression analysis. Calculated as: sx =
(f) (g)
(h)
å( x i − x i )2 i
n −2
X(M) vs. X(M+): r = 0.96; X(M) vs. X(M2+): r = 0.98; X(M+) vs. X(M2+): r = 0.97. D0(Y+–O) = 7.88 eV, D0(Zr+–O) = 7.40 eV, D0(Nb+–O) = 6.62 eV, D0(Mo+–O) = 3.85 eV, D0(Tc+–O) = 3.79 eV, D0(Ru+–O) = 2.60 eV, D0(Rh+–O) = 2.27 eV, D0(Pd+–O) = 1.97 eV, D0(Ag+–O) = 0.78 eV, D0(Cd+–O) = 1.41 eV. A substantially worse correlation is obtained when D0(Pd+–O) = 2.08 eV is used.
REFERENCES (1)
(2)
See, for example: (a) Stiefel, E.I., Matsumoto, K., (eds.) (1996) Transition Metal Sulfur Chemistry, ACS Symposium Series 653, ACS, Washington D.C. (b) Heinrich, V.E., Cox, P.A. (1994) In: The Surface Science of Metal Oxides, Cambridge University Press, Oxford. Pedley, J.B., Marshall, E.M. (1983) J. Phys. Chem. Ref. Data, 12: p. 967.
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Index
acetone, binding energies with magnesium, calcium and zinc ions 91–105 Al+(C2H4) 288 alkali metal atom-ammonia clusters 3–14 aluminium, ammonia complexes 212–215 ammonia complexes of aluminium, indium and vanadium atoms 212–216 solvation of sodium atoms and aggregates 1–37
water cluster complexes with group 1 metal atoms 42–43 zero electron kinetic energy photoelectron spectra of metal clusters and complexes 193–195 condensed phase 145, 170–175 coordinated divalent transition-metal ions see microsolvation of coordinated divalent transition-metal ions copper ions and exchange equilibria 105–108 [CuII(bpy)(serine - H)]+ • 160–163
binding energies metalloion–ligand 108–115 Mg2+, Ca2+ and Zn2+ with oxygen ligands 91–105
direct charge-transfer dissociation 291 dissociation dynamics 283–286 dissociation equilibria 83–86 dopants non-spherical orbitals 247–251 spherical orbitals 232–233 doubly charged transition metal complexes in the gas phase analysis and interpretation of data 130–142 conclusion and view of the future 142 introduction 121–125 preparation of multiply charged metal complexes 125–130
Ca+(C2H4) 289–290 calcium ion binding energies with oxygen ligands 91–105 carbides 203–207, 209–212 carbonic anhydrase 108–116 charge transfer 167–170 charge-transfer dissociation 291 cluster growth sequences model 234–241 cluster limits 167–170 cluster synthesis 150–155 cluster temperature 156–160 collision complexes solvated metal ions and ion clusters 303–305 stabilization 307–310 computational methods transition-metal monoxide and sulfide binding 354–355
electron–hydrogen bonds in the OH[e]HO structure 39–75 electronic structures of water cluster complexes 39–75 see also water cluster complexes electrospray 82–83, 84 ether complexes of zirconium and yttrium atoms 216–221 397
398
Index
ethylene complexes see photodissociation spectroscopy: metal ion-ethylene interactions exchange equilibria 86, 105–108 Fourier-transform ion cyclotron resonance mass spectrometry (FTICR-MS) 352–353 “freezing” of reaction intermediates 305–307 gas phase equilibria 77–119 geometric structures of water cluster complexes 39–75 see also water cluster complexes group 1 metals 39–75 see also water cluster complexes guided ion beam (GIB) apparatus 350–352 hard sphere geometrical model 234–241 histidine 105–108 hydration of singly and doubly charged ions 87–91 hydrides see transition metal monohydrides hydrochloric acid and reactions with metals 319–320 hydrogen–electron bonds see electron–hydrogen bonds indium, ammonia complexes 215 inert gases 300–302 see also metal ion-doped noble gas clusters instrumentation microsolvation of coordinated divalent transition-metal ions 149–150 transition-metal monoxide and sulfide binding 350–354 intracluster proton transfer 79 ion-equilibria determinations 82–83 ion-ligand equilibria 83 iron(II)-polypyridine complexes 163–175 ligand dissociation equilibria 83–86 ligand exchange equilibria 86
ligand-field excitation of [CuII(bpy)(serine - H)]+ • 160–163 light metal ion-ethylene complexes 271–283 lithium-water clusters 40–42, 46–73 magic numbers 232–233 magnesium ion binding energies with oxygen ligands 91–105 mass spectrometry 149–155, 232–251, 350–353 metal ion-doped noble gas clusters apparatus and experimental methods 229–231 introduction 228–229 mass spectroscopy 232–251 photofragmentation spectroscopy 251–262 summary 262–263 metal-to-ligand charge transfer 163–175 metalloenzymes 108–116 metalloion–ligand binding energies 108–116 metalloporphyrin Q-band excitation 175–180 metastable decomposition 156–160 N-methylacetamide, binding energies with magnesium, calcium and zinc ions 91–105 Mg+(C2H4) 287–288 microsolvation of coordinated divalent transition-metal ions characterization of cluster temperature using metastable decomposition 156–160 concluding remarks 180 experimental approach 148–160 introduction 146–148 ligand-field excitation of [CuII(bpy)(serine - H)]+ • 160–163 metal-to-ligand charge transfer in iron(II)-polypyridine complexes 163–175 metalloporphyrin Q-band excitation 175–180 molecular dynamics photodissociation spectroscopy 267–294 simulations 241–247
Index monohydrides see transition metal monohydrides monoxides 201–203 see also transition-metal monoxide... multiply charged metal complex preparation 125–130 nanodroplets 314–315 neutralization reactions 320–322 niobium oxides, carbides and nitrides 201–212 nitrides 208–212 noble gas clusters see metal ion-doped noble gas clusters nonadiabatic dissociation dynamics 283–286 OH[e]HO structure in water cluster anions 43–46 optical properties of clusters 251–262 oxygen ligands 91–105 pentaniobium dicarbide and dinitride 209–212 photoabsorption 251–252 photodetachment transitions 3–10, 14–23 photodissociation spectroscopy 149–150 photodissociation spectroscopy: metal ion-ethylene interactions discussion 283–291 introduction 267–269 light metal ion-ethylene complexes 271–283 methodology 269–271 summary 292 photoelectron spectroscopy see zero electron kinetic energy photoelectron spectra of metal clusters and complexes photofragmentation spectroscopy 251–262 pick-up techniques 127–130 precipitation reactions 320–322 Q-band excitation 175–180 reduction-oxidation reactions in solution 316–319
399
Schlegel diagrams 238–240 selective cluster synthesis 150–155 sequential ligand dissociation equilibria 83–85 sequential metal ion-ligand binding energy determination by gas phase equilibria and theoretical calculations experimental methodology and theoretical calculations 82–87 introduction 78–82 results and discussion 87–116 sequential solvation 167–170 simulation, molecular dynamics 241–247 sodium dimer-ammonia clusters 14–30 sodium trimer-ammonia clusters 30–34 sodium-water clusters 40–42, 46–73 solvated metal ions and ion clusters clusters solvated by inert gases 300–302 complexes of metal cations with small molecular ligands 310–314 cooling the collision complex 303–305 generation 297–300 hydrated ions as nanodroplets 314–315 hydration of ions and reduction-oxidation reactions in solution 316–319 introduction 296–297 neutralization and precipitation reactions 320–322 reactions of metals with hydrochloric acid 319–320 stabilization of collision complexes 307–310 summary 322–323 temperature control and "freezing" of reaction intermediates 305–307 solvation of sodium atoms and aggregates in ammonia clusters alkali metal atom-ammonia clusters 3–14 introduction 2–3 sodium dimer-ammonia clusters 14–30 sodium trimer-ammonia clusters 30–34
400
Index
spectroscopy mass 149–155, 232–251, 350–353 photodissociation 149–150, 267–294 photoelectron 187–225 photofragmentation 251–262 Sr+Arn 252–262 sulfides see transition-metal monoxide and sulfide... temperature control, solvated metal ions and ion clusters 305–307 transition metal complexes see doubly charged... transition metal monohydrides 325–345 transition-metal monoxide and sulfide binding comparison of the cationic and neutral transition metal-monoxides and sulfides 379–388 comparison of D0(M+-S) with D0(M+-SiH2) and D0(M-S) 365–372 conclusions 390 electronic ground states and the bonding in MX0/+ (X=O, S) 388–390 general bonding 355–358 instrumentation and computational methods 350–355 introduction 348–350 periodic trends in D0(M+-S) of the 3d transition-metal sulfide cations 358–364 periodic trends in (M+-S) of the 4d transition-metal sulfide cations and comparison with their 3d congeners 372–379 triniobium dicarbide 203–207 triniobium dinitride 208–209 triniobium monoxide 201–203 triyttrium dicarbide 207
trizirconium monoxide 201–203 vanadium ammonia complexes 215–216 dimer, trimer and tetramer 195–197 vertical detachment energies 13, 25–27 vibrational analysis 286–290 water cluster complexes with group 1 metal atoms computational details 42–43 conclusion 72–73 electronic and geometric structure of M(H2O)n 46–72 introduction 40–42 OH[e]HO structure in water cluster anions 43–46 yttrium carbide 207 dimer 197–201 dimethyl ether complexes 218–221 zero electron kinetic energy photoelectron spectra of metal clusters and complexes ammonia and ether complexes of metal atoms 212–221 experimental and computational methods 190–195 introduction 188–190 metal cluster oxides, carbides, and nitrides 201–212 small bare metal clusters 195–201 summary 221 zinc ion binding energies with oxygen ligands 91–105 zirconium dimethyl ether complexes 216–218, 220–221 monoxide 201–203
