Theoretical Aspects of Transition Metal Catalysis

12 Topics in Organometallic Chemistry Editorial Board: J.M. Brown · P.H. Dixneuf · A. Fürstner · L.S. Hegedus P. Hofman...

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12 Topics in Organometallic Chemistry

Editorial Board: J.M. Brown · P.H. Dixneuf · A. Fürstner · L.S. Hegedus P. Hofmann · P. Knochel · S. Murai · M. Reetz · G. van Koten

Topics in Organometallic Chemistry Recently Published and Forthcoming Volumes

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Theorectical Aspects of Transition Metal Catalysis Volume Editor : G. Frenking

With contributions by D. V. Deubel · G. Drudis-Sole · G. Frenking · A. Lledos · C. Loschen F. Maseras · A. Michalak · K. Morokuma · G. Musaev S. Sakaki · V. Staemmler · S. Tobisch · G. Ujaque · T. Ziegler

2 3

The series Topics in Organometallic Chemistry presents critical overviews of research results in organometallic chemistry, where new developments are having a significant influence on such diverse areas as organic synthesis, pharmaceutical research, biology, polymer research and materials science. Thus the scope of coverage includes a broad range of topics of pure and applied organometallic chemistry. Coverage is designed for a broad academic and industrial scientific readership starting at the graduate level, who want to be informed about new developments of progress and trends in this increasinly interdisciplinary field. Where appropriate, theoretical and mechanistic aspects are included in order to help the reader understand the underlying principles involved. The individual volumes are thematic and the contributions are invited by the volumes editors. In references Topics in Organometallic Chemistry is abbreviated Top. Organomet. Chem. and is cited as a journal Springer WWW home page: springeronline.com Visit the Top. Organomet. Chem. contents at springerlink.com

Library of Congress Control Number: 2004116518 ISSN 1436-6002 ISBN-10 3-540-23510-8 Springer Berlin Heidelberg New York ISBN-13 978-3-540-23510-8 DOI 10.1007/b94252 Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliographie; detailed bibliographic data is available in the Internet at . This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable to prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springeronline.com © Springer-Verlag Berlin Heidelberg 2005 Printed in Germany The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Fotosatz-Service Köhler GmbH, Würzburg Production editor: Christiane Messerschmidt, Rheinau Cover: design & production GmbH, Heidelberg Printed on acid-free paper 02/3141 me – 5 4 3 2 1 0

Volume Editor Professor Dr. Gernot Frenking Philipps-Universität Marburg Fachbereich Chemie Lahnberge 35032 Marburg, Germany [email protected]

Editorial Board Prof. John M. Brown

Prof. Pierre H. Dixneuf

Dyson Perrins Laboratory South Parks Road Oxford OX1 3QY [email protected]

Campus de Beaulieu Université de Rennes 1 Av. du Gl Leclerc 35042 Rennes Cedex, France [email protected]

Prof. Alois Fürstner

Prof. Louis S. Hegedus

Max-Planck-Institut für Kohlenforschung Kaiser-Wilhelm-Platz 1 45470 Mühlheim an der Ruhr, Germany [email protected]

Department of Chemistry Colorado State University Fort Collins, Colorado 80523-1872, USA hegedus@lamar. colostate.edu

Prof. Peter Hofmann

Prof. Paul Knochel

Organisch-Chemisches Institut Universität Heidelberg Im Neuenheimer Feld 270 69120 Heidelberg, Germany [email protected]

Fachbereich Chemie Ludwig-Maximilians-Universität Butenandstr. 5–13 Gebäude F 81377 München, Germany [email protected]

Prof. Gerard van Koten

Prof. Shinji Murai

Department of Metal-Mediated Synthesis Debye Research Institute Utrecht University Padualaan 8 3584 CA Utrecht, The Netherlands [email protected]

Faculty of Engineering Department of Applied Chemistry Osaka University Yamadaoka 2-1, Suita-shi Osaka 565, Japan [email protected]

Prof. Manfred Reetz Max-Planck-Institut für Kohlenforschung Kaiser-Wilhelm-Platz 1 45470 Mülheim an der Ruhr, Germany [email protected]

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Preface

It has been stated in the past that the search for new catalysts has more the character of an art than a science discipline. This is because there was usually more speculation than true knowledge about the reaction mechanisms of catalytic processes. Even the identity of the catalytically active species was frequently not known, which is the reason that systematic testing of all possibly interesting compounds for catalytic reactions was carried out. This is costly and time consuming. The situation has changed in the last decade because much progress has been made in understanding the mechanisms of many catalytic reactions. Besides sophisticated experimental tools, quantum chemical calculations of transition states and reaction intermediates played a prominent role in gaining much better insight into the fundamentals of transition metal catalysis. Estimating solvent effects and the calculation of spectroscopic data are now routinely included in many theoretical studies. Although the design of new catalytically active species is still largely a trialand-error process, modern research is guided by theoretical calculations in the search for new catalysts, which helps researchers to focus on more promising compounds. The progress in quantum chemical method development has led to the present situation where theory and experiment are synergistically used in an unprecedented manner. In particular, the calculation of transition metal compounds is no longer a too-difficult task for quantum chemistry because efficient methods are available for dealing with many-electron atoms and with relativistic effects. The seven articles in this volume do not provide a comprehensive view of theoretical investigations of catalytic reactions, because the field has expanded already beyond the scope that can be covered in one book. The contributions written by experts in the field exemplarily demonstrate the strength but also the present limitations of quantum chemical methods for giving insights into the mechanism of transition-metal mediated reactions. Because the development of new theoretical methods is still a very active research area, much progress can be expected in the coming years. Marburg, Germany, February 2005

Gernot Frenking

Preface

Contents

Transition Metal Catalyzed s -Bond Activation and Formation Reactions D. G. Musaev · K. Morokuma . . . . . . . . . . . . . . . . . . . . . . . . .

1

Theoretical Studies of C-H s -Bond Activation and Related Reactions by Transition-Metal Complexes S. Sakaki . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Enantioselectivity in the Dihydroxylation of Alkenes by Osmium Complexes G. Drudis-Solé · G. Ujaque · F. Maseras · A. Lledós . . . . . . . . . . . . . 79 Organometallacycles as Intermediates in Oxygen-Transfer Reactions. Reality or Fiction? D. V. Deubel · C.Loschen · G. Frenking . . . . . . . . . . . . . . . . . . . . 109 Late Transition Metals as Homo- and Co-Polymerization Catalysts A. Michalak · T. Ziegler . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Co-Oligomerization of 1,3-Butadiene and Ethylene Promoted by Zerovalent ‘Bare’ Nickel Complexes S. Tobisch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 The Cluster Approach for the Adsorption of Small Molecules on Oxide Surfaces V. Staemmler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 Author Index Volume 1-14 . . . . . . . . . . . . . . . . . . . . . . . . . . 257 Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263

Topics Organomet Chem (2005) 12: 1– 30 DOI 10.1007/b104397 © Springer-Verlag Berlin Heidelberg 2005

Transition Metal Catalyzed s -Bond Activation and Formation Reactions Djamaladdin G. Musaev (

) · Keiji Morokuma

Cherry L. Emerson Center for Scientific Computation and Department of Chemistry, Emory University, 1515 Dickey Dr., Atlanta GA 30322, USA [email protected], [email protected]

1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2

2

The Role of the Lower-Lying Electron States of Transition Metal Cations in Oxidative Addition of the s -Bonds (such as H-H, C-H and C-C) . . . . . . .

2

3 3.1 3.2

Role of Cooperative Effects in the Transition Metal Clusters . . . . . . . . . . Reaction of Pt and Pd Metal Atoms with H2/CH4 Molecules . . . . . . . . . . . Reaction of Pd2 and Pt2 Dimers with H2/CH4 Molecules . . . . . . . . . . . . .

6 7 9

4

s -Bond Activation via Nucleophilic Mechanism: the Role of Redox Activity of the Transition Metal Center – Hydrocarbon Hydroxylation by Methanemonooxygenase (MMO) . . . . . . . . . . . . . . . . . . . . . . .

10

5

Vinyl-Vinyl Coupling on Late Transition Metals Through C-C Reductive Elimination Mechanism . . . . . . . . . . . . . . . 5.1 Reductive Elimination from PtIV Halogen Complexes [Pt(CH=CH2)2X4]2– (X=Cl, Br, I) . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Reductive Elimination from Mixed PtIV Complexes [Pt{cis-/trans-(CH=CH2)2(PH3)2}Cl2] . . . . . . . . . . . . . . . . . . . . . . 5.3 Reductive Elimination from PtII Halogen Complexes [Pt(CH=CH2)2X2]2– (X=Cl, Br, I) . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Reductive Elimination from PtII Complexes with Amine and Phosphine Ligands [Pt(CH=CH2)2X2] (X=NH3, PH3) . . . . . . . . . . . 5.5 Reductive Elimination from PdIV Complexes [Pd(CH=CH2)2X4]2– (X=Cl, Br, I) 5.6 Reductive Elimination from Mixed PdIV Complex [Pd{trans-(CH=CH2)2(PH3)2}Cl2] . . . . . . . . . . . . . . . . . . . . . . . . 5.7 Reductive Elimination from PdII Halogen Complexes [Pd(CH=CH2)2X2]2– (X=Cl, Br, I) . . . . . . . . . . . . . . . . . . . . . . . . 5.8 Reductive Elimination from PdII Complexes with Nitrogen and Phosphine Ligands [Pd(CH=CH2)2X2] (X=NH3, PH3) . . . . . . . . . . . 5.9 Reductive Elimination from RhIII, IrIII, RuII and OsII Complexes . . . . . . . . 5.10 General Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.11 Comparison of the Vinyl-Vinyl (Csp2-Csp2) and Alkyl-Alkyl (Csp3-Csp3) Reductive Elimination . . . . . . . . . . . . . . . 6

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17

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18

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19

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21

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21 23

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23

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23 24 24

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Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

27

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

27

References

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D. G. Musaev · K. Morokuma

Abstract The factors controlling the transition metal catalyzed s-bond (including H-H, C-H and C-C) activation and formation, the fundamental steps of many chemical transformations, were analyzed. It was demonstrated that in the mono-nuclear transition metal systems the (1) availability of the lower lying s1dn–1 and s0dn states of the transition metal atoms, and (2) nature of the ligands facilitating the reduction of the energy gap between the different oxidative states of the transition metal centers are very crucial. Meanwhile, in the transition metal clusters the “cooperative” (or “cluster”) effects play important roles in the catalytic activities of these clusters. Another important factor affecting the catalytic activity of the transition metal systems shown to be their redox activity. Keywords s-Bond activation and formation · Transition metal systems · Catalytic activity

1 Introduction Sigma-bond (including H-H, C-H and C-C) activation and formation are fundamental steps of many chemical transformations and have been subject of numerous review articles [1]. It is well accepted that certain transition metal complexes significantly facilitate the s-bond activation/formation steps, which may occur via various mechanisms, including oxidative addition/reductive elimination, metathesis and nucleophilic attack. However, the factors affecting H-H, C-H and C-C activation/formation still need to be clarified in detail. In this chapter we intend to analyze some factors that control the catalytic activity of transition metal complexes toward H-H, C-H and C-C bond activation/ formation. Namely, we elucidate the role of (a) lower-lying electronic states of transition metal cations/atoms, (b) cooperative effects in transition metal clusters, (c) redox activity of the transition metal centers, and (d) the role of metal and ligand effects in vinyl-vinyl coupling.

2 The Role of the Lower-Lying Electron States of Transition Metal Cations in Oxidative Addition of the s -Bonds (such as H-H, C-H and C-C) The study of gas-phase activation of H-H, C-H and C-C bonds of the hydrogen molecule and saturated hydrocarbons, respectively, by bare transition metal atoms and cations is very attractive for getting insight to the mechanisms and factors (such as nature of metal atoms and their lower-lying electronic states) controlling catalytic activities of transition metal complexes. Such studies, which are free from the ligand and solvent effects, have been subject of many experimental [2] and theoretical [3] papers in the past 10–15 years. Experimental studies indicate that reaction of some transition metal cations (such as Fe+, Co+, and Rh+) with methane exclusively leads to the ion-molecule complex M+(CH4), while others (such as Sc+ and Ir+) pro-

Fig. 1 Potential energy profile of the reaction Ir++CH4 calculated at the MR-SDCI-CASSCF level of theory

Transition Metal Catalyzed s-Bond Activation and Formation Reactions 3

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D. G. Musaev · K. Morokuma

ceed further via oxidative addition mechanism and leads to hydrido-metalmethyl and/or MCH2++H2 products. In order to find some insight to the difference in the reactivity of early and late, as well as first-, second- and thirdrow transition metal cations (TMCs), we have studied the mechanism of the reaction of M+ (M=Sc, Fe, Co, Rh and Ir) with CH4 at the CASSCF and MR-SDCI levels of theory in conjunction with large basis sets. The results of these studies have been published elsewhere [4]. Here we discuss general trends, factors controlling reactivity of the transition metal cations toward s-bonds, and predict the most favorable metal cations that can efficiently insert into s-bonds. As expected, the first step of the reaction M++CH4 is the formation of ion-molecule complex M+(CH4) (see Fig. 1, which, as an example, includes the potential energy surface of the reaction Ir++CH4 at the several lower-lying electronic states of the Ir cation). Our calculations show that these complexes are structurally non-rigid, where M+ can nearly freely rotate around the CH4 molecule by the pathways (C2v)´(C3v, TS)´(C2v)´… and/or (C3v)´(C2v, TS)´(C3v)´…, depending on the nature of metal atom and the electronic state of the complex M+(CH4). These complexes are stable by 21.9 (M=Sc), 15.5 (13.7±0.8) (M=Fe), 21.4 (22.9±0.7) (M=Co), 16.8 (M=Rh), and 20.7 (M=Ir) kcal/mol relative to the ground state dissociation limit M++CH4 (experimental values are given in parentheses). From the resultant M+(CH4) complex the reaction proceeds via the C-H bond activation transition state (TS) to give the hydrido-metal-methyl cation complex, HMCH3+. In this step the C-H s-bond is broken and M-H and M-CH3 bonds are formed.Also, the oxidation number of the M-center increases by two. In order to analyze the reactivity of TMCs toward C-H (as well as H-H and C-C) bond, one has to elucidate the factors controlling thermodynamics and kinetics of the reaction M+(CH4)ÆHMCH3+. Our [4] and other [3] studies have shown that thermodynamics of the reaction M+(CH4)ÆHMCH3+ is controlled by the two factors. The first factor is the availability of the s1dn–1 state of the cation M+, which is expected to be the dominating bonding state in the resultant HMCH3+ complex. The second factor is the loss of exchange energy (the loss of high-spin coupling (exchange energy) between valence electrons on the unsaturated transition-metal ion subsequent to the formation of covalent metal-ligand bonds) upon formation of M-H and M-CH3 bonds [5]. Upon formation of M-H and M-CH3 bonds, which stabilize the system, the loss of exchange energy occurs and counteracts the stabilization. Thus, if the s1dn–1 configuration of the cation M+ is the energetically most favorable one (or easily available, i.e. the promotion energy from the ground state to the excited s1dn–1 state is small) and the loss of exchange energy for formation of two, M-H and M-CH3, bonds in the s1dn–1 state is small, the reaction M+(CH4) ÆHMCH3+ is thermodynamically favorable. Taking into account these factors, one can easily explain the calculated trends in the exothermicity of the reaction M+(CH4)ÆHMCH3+, and predict thermodynamically the most favorable reaction M+(CH4)ÆHMCH3+.

Transition Metal Catalyzed s-Bond Activation and Formation Reactions

5

Our studies show that the reaction M+(CH4)ÆHMCH3+ is endothermic by 20.3, 32.3, 37.7 and 40.3 kcal/mol for M=Sc, Fe, Co, and Rh, respectively, while it is exothermic by 8.7 kcal/mol for M=Ir. This trend in the energy of the reaction M+(CH4)ÆHMCH3+ can be qualitatively explained in terms of the energy gap between the lower lying s0dn and s1dn–1 states of the metal cations and the necessary exchange energy loss for formation of two covalent bonds to the s1dn–1 state. Indeed, the s1dn–1 state is a ground state for Ir+, and thus Ir+ can easily form two M-L s-bonds. While the ground states of the Sc and Fe cations are the s1dn–1 states, these cations need 3.7 and 41.4 kcal/mol energy (exchange energy loss for formation of two covalent bonds to the s1dn–1 state) to form two M-L bonds. Meanwhile the ground electronic configurations of Co and Rh are the s0dn states, and the calculated exchange energy loss for formation of two covalent bonds to the s1dn–1 state plus s0d8Æs1d7 promotion energy are 39.2 and 77.5 kcal/mol for Co+ and Rh+, respectively. Thus, the calculated trend in the energy of the reaction M+(CH4)ÆHMCH3+, Ir (–6.6)<Sc (20.3)Ni+ (41.6)~Fe+ (41.4)>Co+ (39.2) (in kcal/mol) [5],we expect that the thermodynamic stability of insertion product to decrease via M=Sc+>Ti+>V+>Cr+ and increase Mn+
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D. G. Musaev · K. Morokuma

Scheme 1 Schematic presentation of “donation” and “back-donation” contributions on M-(HX) interaction

In contrast, transition metal cations such as Co+ and Rh+, have the s0dn ground state with empty s-orbital as opposed to Sc+, Ir+, and Fe+, and one may expect the strong s(C-H)Æ(s,ds) (M) donation effects for the former cations. Thus, availability of the s0dn state (with doubly occupied dp and empty s-orbitals) for Co+ and Rh+, as well as Fe+, facilitates both “donation” and “back donation” effects and makes the s-bond activation significantly easier for these cations compared to Sc+ and Ir+. This statement is consistent with the calculated trends; the reverse reaction HMCH3+ÆM+(CH4) occurs without barrier and is controlled by thermodynamic factors for M=Fe+, Co+ and Rh+. Meanwhile reaction M+(CH4)ÆHMCH3+ occurs with energetic barrier of 38.5 and 2.1 kcal/mol, for M=Sc and Ir, and is controlled by both thermodynamic and kinetic factors. The reverse reaction HMCH3+ÆM+(CH4) occurs with 18.2 and 10.8 kcal/mol barriers for M=Sc and Ir, respectively. On the basis of these discussions, we conclude that: (1) The s0dn state of the TMC favors the formation of ion-molecule complexes, while the s1dn–1 state leads to formation of oxidative addition product, (2) the availability of both s1dn–1 and s0dn configurations of transition metal cations (and atoms) is absolutely necessary for their reactivity toward s-bonds (such as H-H, C-H, C-C, O-H, and N-H), and (3) all early first-row (Sc+, Ti+ and V+) transition metals cations, having empty s or d orbitals with a1 symmetry, as well as many third-row (Hf +, Ta+, W+, Re+, Os+, Ir+ and Pt+) TMCs, can easily activate s-bonds in the gas phase, and stabilize the oxidative addition product complexes.

3 Role of Cooperative Effects in the Transition Metal Clusters In this section we expand the conclusions of the previous section to bare transition metal clusters in order to test them again and to identify another,“cooperative”(or “cluster”) effect that affects the reactivity of transition metals. In practice, transition metals are important ingredients of heterogeneous and nano-catalysts, therefore clear understanding of their reactivity at electronic level is essential to unravel the secret of their catalytic activities. Diverse classes of experimental and theoretical studies already have provided a wealth of information concerning the electronic structure, spectroscopic as well as dynamic properties of variety types of clusters, including Ptn [6], Pdn [7], Fen+ [8], Con+ [9], and Nbn+ [10].

Transition Metal Catalyzed s-Bond Activation and Formation Reactions

7

In particular, in the experimental work of Cox et al. [6, 7], the measured rate constants of CH4 and H2 activation by unsupported Pt and Pd clusters (n=6~24) show a large variation as functions of the cluster size. In the case of Pt clusters, it was found that dimer through pentamer were the most reactive, while the reactivity dropped significantly starting from Pt6. The single Pt atom was less reactive compared to Pt2–5 by an order of magnitude, and the bulk was less reactive by at least several orders of magnitude. In the case of Pd clusters, it was found that the activation rate constants for both H-H and C-H bonds show significant oscillation in terms of the cluster size. The peak value of the measured rate constant is around n=8 and 10, and the minimum rate constants have been observed for n=3 and n=9. Understanding the size-dependence of reactivity of clusters has become one of the most fascinating and intriguing issues in cluster chemistry [11]. To unravel the reason behind the observed variation of reactivity as a function of cluster size [6, 7], we have chosen to study the detailed mechanism of H2 and CH4 activation on small Ptn and Pdn (n=1–6) clusters. Results of these studies have already been published [12]. Here, we intend to analyze the factors controlling the reactivity of these clusters. 3.1 Reaction of Pt and Pd Metal Atoms with H2/CH4 Molecules First of all, we recall briefly the electronic structure and reactivity of Pd and Pt atoms, shown in the previous section, since they are the fundamental building blocks of the clusters and their characteristics have a major influence on the properties of clusters. According to a large number of theoretical as well as experimental studies, Pd and Pt atoms have very different electronic structures and consequently distinct reactivities. The ground state of Pd atom has a closedshell s0d10 configuration, where the open-shell s1d9(3D) state is 21.9 kcal/mol above [13]. Therefore, based on the conclusions of the previous section, one may expect that the Pd atom cannot break the H-H or C-H bonds in H2 and CH4 and rather forms molecular complexes Pd(H2) and Pd(CH4), respectively. The calculated Pd-H2 bond energy is 16.2 kcal/mol. For the Pt atom, the s1d9(3D) state is the ground electronic state, while the s0d10 configuration is 11.1 kcal/mol higher in energy [13]. Consequently, it has been observed that Pt atom breaks the H-H and C-H bond, in agreement with the conclusions of the previous section. Since the ground state of Pt atom is a triplet but resultant HPtH or HPtCH3 is a singlet, a curve crossing from the triplet to the singlet state is required, and the minimum crossing point can be viewed as the transition state for the activation process starting from the ground electronic state atom (Fig. 2a). The binding energy of H2 and CH4 to the Pt atoms is 47.4 kcal/mol and 34.3 kcal/mol, respectively. Thus, the calculated results for the reactions Pd+H2/CH4 and Pt+H2/CH4 once again confirm our conclusions from the previous section.

Fig. 2a–d Potential energy profile of the reactions: a Pt+H2/CH4; b Pd2+H2; c Pd2+CH4; d Pt2+CH4

8 D. G. Musaev · K. Morokuma

Transition Metal Catalyzed s-Bond Activation and Formation Reactions

9

3.2 Reaction of Pd2 and Pt2 Dimers with H2/CH4 Molecules As seen in the potential energy profile of these reactions, shown in Fig. 2b–d, both Pd2 and Pt2 activate H-H/C-H bonds with very small barrier. In reaction Pt2+H2/CH4, H-H/C-H activation preferentially takes place on a single metal atom.Afterwards, one of the H atoms migrates to the other Pt atom over a negligible isomerization barrier. On both the singlet and the triplet state, H-H activation is expected to be barrierless, while C-H activation has a distinct barrier on the triplet state for reaction starting from the ground triplet state Pt2. Nevertheless, since the barrier for C-H activation on the triplet state is small and lower than the expected minimum of seams of crossing (MSX) between singlet and triplet in the Pt-CH4 system, it is expected that Pt2 activates the C-H bond in CH4 with a faster rate than the Pt atom, which is in accord with the experimental observation of Cox et al. [6, 7]. Calculations show that the ground state of the reactants Pd2+H2/CH4 is a triplet state, while the product complexes have a singlet ground state. Therefore, one may expect that the reaction proceeds either on the excited singlet state surface or through the minimum of triplet-singlet seams of crossing. On the singlet state potential energy surface of Pd2+H2/CH4 (see Fig. 2b,c) the reaction is downhill without activation transition state. Meanwhile, the calculated triplet-singlet MSX lies lower in energy than the triplet state transition state. Therefore, the H2/CH4 activation by Pd2 starting from the triplet ground state dimer is expected to proceed via an intersystem crossing mechanism with very small barrier. Interestingly, the activation of s-bonds occurs only upon perpendicular approach of H-H/C-H bonds to the Pd-Pd bond. Thus, in contrast to the single atom case where Pd and H2/CH4 form only a molecular complex and no H-H/C-H bond cleavage occur, two Pd atoms work “cooperatively” and readily break H2/CH4. This “cooperative” mechanism for H2/CH4 activation on Pd2 is different from the case of Pt2+H2/CH4. In Pt2 dimer H2/CH4 activation takes place preferentially on a single atom, while in Pd2 dimer it occurs on the Pd-Pd bond. Moreover, in the final activation products, H/CH3 groups prefer the bridged sites of Pds, but are localized on metal sites in Pt2. Those results can be rationalized as the following, as illustrated in Scheme 2. The singlet state Pd2 consists of mainly two s0d10 Pd atoms, and the LUMO sg has a correct symmetry to accept electron density effectively from the H2/CH4 s orbital upon perpendicular approach.As a result, the activation takes place preferentially in this approach. In the case of Pt2+H2/CH4 reaction, the metal HOMO and LUMO are of localized metal d character (as established in a number of studies of metal clusters, the s-s contribution in the metal-metal bonding is dominant, while d-d interaction is weak). Therefore, the HOMO and LUMO of triplet Pt2 are all of localized d characters, while the s and s* orbitals that contain large s characters are much lower and higher in energy, respectively, and therefore activation takes place preferentially on a single atom (rather than on the Pt-Pt bond, where the strongest HOMO/LUMO interaction between the metal and H2 is expected.

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D. G. Musaev · K. Morokuma

Scheme 2 Orbital diagram of triplet Pd2 and Pt2, MO energies (in hartree) are calculated at the full valence (20el./12orb.) CASSCF level

In the final singlet products, Pt2(H)2/Pt2(H)(CH3) and Pd2(H)2/Pd2(H)(CH3), the metal dimers actually are in their triplet configurations. In the case of Pt2, the metal-metal s bonding orbital is low in energy, and the Pt-H/CH3 bond has large d character. Therefore, the H/CH3 groups in Pt2(H)2/Pt2(H)(CH3) do not like the bridged sites, but rather localize on each Pt atom. In the case of Pd2, in its triplet electronic state, the metal-metal s bonding orbital is the HOMO. Therefore, both the CH3/H-Pd-Pd bonding and antibonding orbitals have much metal s component. As a result, the H/CH3 ligands prefer the bridged sites rather than the localized metal sites. Thus, our studies of the reactivity of Pd/Pt clusters with H2/CH4 molecules clearly show a “cooperative” effect that could play a significant role in the reactivity of the transition metal clusters. Thus, the catalytically inactive metal atoms could form very active clusters !

4 s -Bond Activation via Nucleophilic Mechanism: the Role of Redox Activity of the Transition Metal Center – Hydrocarbon Hydroxylation by Methanemonooxygenase (MMO) Another important factor controlling the reactivity of transition metal centers toward s-bond is their redox activity. Indeed, it is well established that transition metal centers with low redox potential can be active catalysts [14]. For example, let us discuss the reactivity in hydrocarbon hydroxylation by Methanemonooxygenase (MMO).

Transition Metal Catalyzed s-Bond Activation and Formation Reactions

11

MMO, one of the members of diiron-containing metalloenzyme family, is an enzyme that catalyzes methane oxidation reaction, i.e. conversion of the inert methane molecule to methanol [15]. During this reaction two reducing equivalents from HAD(P)H are utilized to split the O-O bond of O2. One O atom is reduced to water by 2-electron reduction, while the second is incorporated into the substrate to yield methanol: CH4 + O2 + NAD(P)H + H+ Æ CH3OH + NAD(P)+ + H2O Experimental studies [16] show that the best-characterized forms of the soluble MMO (sMMO) contain three protein components: hydroxylase (MMOH), so-called B component (MMOB) and reductase (MMOR), each of which is required for efficient substrate hydroxylation coupled to NADH oxidation. The hydroxylase, MMOH, which binds O2 and substrate and catalyzes the oxidation, is a hydroxyl-bridged binuclear iron cluster. In the resting state of MMOH (MMOHox), the diiron cluster is in the diferric state [FeIII-FeIII], and can accept one or two electrons to generate the mixed-valence [FeIII-FeII] or diferrous state [FeII-FeII], respectively. The diferrous state of hydroxylase (MMOHred) is the only one capable of reacting with dioxygen and initiating the catalytic cycle. X-ray crystallographic studies of the enzyme from Methylococcus capsulatus (Bath) [17] and Methylosinus trichosporium OB3b [18] have unveiled the coordination environment of the Fe centers of MMOHox and MMOHred. According to these studies, in MMOHox each Fe center has six-coordinate octahedral environment (see Scheme 3). Fe ions are bridged by a hydroxy ion, a bidentate Glu g-carboxylate and a water molecule (or another carboxylate). In addition, each Fe ion is coordinated by one His nitrogen ligand and one monodentate Glu carboxylate. The two Fe centers are different from each other in that one of them (Fe2) has an additional monodentate glutamate carboxylate, while the other Fe (Fe1) has one additional water molecule. Upon reduction, one of carboxylate ligands undergoes a so-called “1,2-carboxylate shift” from being a terminal, monodentate ligand bound to Fe2 to a monodentate, bridging ligand between the two irons, with the second oxygen of this carboxylate also coordinated to Fe2. In addition, the hydroxyl bridge is lost, and the other hydroxyl/water bridge shifts from serving as a bridge to being terminally bound to Fe1. Also, the terminal water bound to Fe1 in the oxidized form of MMOH seems to move out upon reduction of the cluster. Thus, in reduced form of MMOHred the ligand environment of Fe ions becomes effectively five coordinated, which is reasonable since this is the form of the cluster that activates dioxygen. It was established that MMOHred reacts very fast with O2 and forms a metastable, so-called compound O, which spontaneously converts to another compound called P (see Scheme 4). Spectroscopic studies [19] indicate that compound P is a peroxide species, where both oxygens are bound symmetrically to the irons. Compound P spontaneously converts to compound Q, which was proposed to contain two antiferromagnetically coupled high-spin Fe(IV)

Scheme 3 Structural representation of the binuclear Fe center of diferric MMOHox and diferrous MMOHred (see [15])

12 D. G. Musaev · K. Morokuma

Transition Metal Catalyzed s-Bond Activation and Formation Reactions

13

Scheme 4 Experimentally proposed catalytic cycle of MMO (see [15])

centers. EXAFS and spectroscopic studies [20, 21] of compound Q, trapped from M. trichosporium OB3b and M. capsulatus, have demonstrated that compound Q has diamond core, (FeIV)2(m-O)2 structure with one short (1.77 Å) and one long (2.05 Å) Fe-O bond per Fe atom and a short Fe-Fe distance of 2.46 Å. Compound Q has been proposed to be the key oxidizing species for MMO. In the literature there have been several computational attempts [22–25] to elucidate mechanism of methane oxidation by intermediate Q. Our results [25] show that reaction proceeds via the mechanism presented in Fig. 3. Later, this mechanism was validated by several times and currently is well accepted. As seen in Fig. 3, reaction of compound Q (modeled as structure I) with methane starts with coordination of CH4. In general, the CH4 molecule could coordinate to I via two distinct pathways: O-side and N-side. The O-side pathway corresponds to the coordination of the methane molecule from the side where the two Glu (carboxylate) located, while the N-side pathway corresponds to the coordination of CH4 from the two His (imidazole) side. Our calculations show that both pathways proceed via very similar transition states and intermediates, and the N-side pathway is thermodynamically and kinetically more favorable than O-side. In spite of this, in this paper we base our discussions only on the O-side mechanism because it is believe to correspond to the process occurring in the protein. The coordination of CH4 to complex I leads to the methane-Q complex, structure II. The interaction between methane and structure I (compound Q) is extremely weak; the complexation energy is calculated (relative to the corresponding reactants) to be 0.7 and 0.3 kcal/mol for the 9A and 11A state, respectively. Because of unfavorable zero point energy and entropy factors, it is most likely that the complex II does not exist in reality, and therefore we will not discuss it.

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D. G. Musaev · K. Morokuma

Fig. 3 The potential energy profile (in kcal/mol) for both the 9A state and the 11A state of the methane activation reaction via O-site pathways: (NH2)(H2O)Fe(m-O)2(h2-COO)2Fe(H2O)(NH2)+CH4Æ(NH2)(H2O)Fe(m-O)(HOCH3)(h2-HCOO)2Fe(H2O)(NH2)

Results in Table 1 show that the 9A state of structure I very qualitatively is the Fe(IV)-Fe(IV) complex. On the other hand, in the 11A state it is the Fe(IV)Fe(III) mixed valence species, where Fe2 is in the Fe(III) state with five spins that are heavily delocalized onto O2. The calculated fact that I_9 (here and below in A_B, A is the structure, while B is the electronic state) is lower in energy than I_11 suggests that Fe(IV)-Fe(IV) is the preferred state for complex I (and compound Q). This is consistent with the experimental conclusions [21]. The activation of the methane C-H bond takes place on the diamond oxygen O1. At the TS1, structure III, the C-H bond to be broken is elongated from 1.089 Å in II to 1.271 Å and 1.296 Å in transition states III_9 and III_11. Furthermore, the O-H bond is nearly formed, with distance of 1.250 Å and 1.241 Å at the TSs, compared to 0.983 Å and 0.978 Å in products IV_9 and IV_11, respectively. These geometrical changes indicate clearly that III_9 and III_11 are the TSs corresponding to the H abstraction process. The H-abstraction barriers are calculated to be 23.2 and 19.0 kcal/mol for the 9A and 11A states, respectively, relative to the corresponding CH4 complexes II_9 and II_11, respectively. These values of the barrier are in reasonable agreement with available experimental estimates, 14–18 kcal/mol [23]. The spin densities for TS1, III, and product IV are found to be similar to each other within their respective 9A and 11A states (see Scheme 5 and Table 1). Furthermore, the spin densities are nearly identical between 9A and 11A, except for those on the O2..H..CH3 frag-

Transition Metal Catalyzed s-Bond Activation and Formation Reactions

15

Scheme 5 The spin recoupling scheme in the intermediates of the reaction Table 1 Relative (in kcal/mol, relative to the 9A reactants) energies, and Mulliken atomic spin densities (in e) of various intermediates and transition states, for 9A and 11A states, for the reaction of the complex I with molecule of methanea. The numbers after slash are relative to the 11A reactants

Structures

DE (in kcal/mol)

Atomic spin densities (in e) LnFe2

LnFe1

O2

O1

Hb

CH3c

9A

state I+CH4 II III IV V VI VII IVd

0.0 –1.5 23.2 11.3 20.6 –41.8 –34.3 23.7

3.44 3.43 4.59 4.64 4.58 4.54 4.49 4.52

3.55 3.52 3.54 3.51 3.23 2.92 2.95 1.69

0.44 0.44 0.40 0.43 0.38 0.35 0.38 0.56

0.30 0.31 –0.37 0.08 0.20 0.00 0.00 0.07

– – 0.06 0.00 0.00 0.00 0.00 0.00

– – –0.55 –0.99 –0.73 0.00 0.00 0.99

11 A state I II III IV V VI VII IVd

5.4/0.0 4.2/–1.2 24.4/19.0 –11.3/5.9 18.6/13.2 –53.9/–59.3 –46.7/–52.1 –15.5/10.1

4.62 4.62 4.63 4.67 4.57 4.48 4.54 4.65

3.47 3.47 3.52 3.58 3.97 4.59 4.54 4.54

1.03 1.03 0.43 0.43 0.50 0.66 0.67 0.42

0.43 0.43 0.55 0.10 0.01 0.00 0.00 0.08

– – –0.07 0.00 0.01 0.00 0.00 0.00

– – 0.59 0.98 0.81 0.00 0.00 0.99

a

Here, LnFe stands for the (H2O)(NH2)Fe-fragment. This table does not include the portion of spin densities located on the bridging carboxylate ligands, each of which may have about 0.10–0.15e spin. b H atom located between O2 and CH fragments. 3 c The number for the entire CH fragment. 3

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D. G. Musaev · K. Morokuma

ment. For the CH3 groupitself, the total Mulliken charge (not given in Table 1) is at most +0.03e for both the 9A and 11A states and the spin densities on this group for 9A and 11A are of same magnitude but of opposite sign. One can interpret all these values in the following way. In both TSs, III_9 and III_11, a radical center begins to develop on the CH3 group, with spin densities of –0.46e and +0.52e, respectively, and in both intermediates, IV_9 and IV_11, the CH3 group is now a real radical with spin densities of –0.98e and 1.00e, respectively. The spin densities on Fe1 and Fe2 in IV_9 and IV_11, which formally can be written as L4Fe(m-O)(m-OH)FeL4 with the methyl radical only weakly interacting via a C...HO interaction, can qualitatively be considered to correspond to Fe(IV) with four spins and Fe(III) with five spins, respectively. In going from II_9 to III_9, the very qualitative formal oxidation state of Fe2 changes from Fe(IV) to Fe(III), while from II_11 (which is already Fe(III)) to III_11, no such change is required. Since the two Fe centers are coupled ferromagnetically in both 9A and 11A states, the spin of the CH3 radical in both III and IV has to couple antiferromagnetically (with negative spin) and ferromagnetically (with position spin) to make the total spin 2S+1 equal to 9 and 11, respectively. In the radical complexes IV_9 and IV_11 the interaction of the CH3 radical with the two iron atoms is very weak and, therefore, their total energies are nearly identical. It is quite interesting that we find that a mixed valence state is responsible for the methane oxidation reaction. The present spin density analysis clearly demonstrates that (1) the methane oxidation proceeds via a bound-radical mechanism, and (2) the first electron transfer from substrate to Fe-centers occurs through the TS1 and is completed at the resultant bound-radical complex IV. The second electron transfer from the substrate to Fe-centers starts with the recombination of methyl radical with the bridging hydroxyl ligand at the transition state, TS2, structure V. Indeed, our results show that in the 11A state upon going from IV_11 to the methanol complex VI_11, Fe1 changes its formal oxidation state from Fe(IV) with four spins to Fe(III) with five spins, while the spin density on the methyl radical is completely annihilated upon forming a covalent bond between CH3 and OH. The transition state V_11 has a spin distribution between that of IV_11 and VI_11. On the other hand, in the 9A state upon going from IV_9 to the methanol complex VI_9, the spin density on Fe1 is reduced by about 0.5, corresponding to the disappearance of roughly one unpaired electron. Since Fe(V) is not a stable species, it is most likely Fe1 changed its formal oxidation state from Fe(IV) with four spins to Fe(III) with five formal d electrons. Because of the restriction 2S+1=9, i.e., the total number of unpaired electrons must be 8 within the Fe(III)-Fe(III) core, Fe1 in VI_9 chose to form one d-lone pair with only three spins remaining. This complex VI_9 is thus higher in energy than the corresponding complex VI_11 in violation of the Hund rule. The barrier heights for the CH3 addition to the hydroxyl ligand calculated relative to the intermediate IV_9 and IV_11 are 9.3 and 7.3 kcal/mol for the 9A and 11A states, respectively. Obviously, this step of the reaction is not rate-determining, and can occur rather fast. Overcoming the barriers at TS2 leads to the complexes methanol-complexes VI, L4Fe(OHCH3)(m-O)FeL4, and completes

Transition Metal Catalyzed s-Bond Activation and Formation Reactions

17

the second electron transfer process. The overall reaction I + CH4ÆVI is calculated to be exothermic by 34.3 and 46.8 kcal/mol for the 9Aand 11A states, respectively. The final step of elimination of the methanol molecule and regeneration of the enzyme could be a complex process, and possibilities of different mechanisms exist but have not yet been studied computationally. Thus, these results clearly show that the Fe-centers are not directly involved in methane C-H bond cleavage. However, they play a crucial role in the methane oxidation process, by accepting two electrons from the substrate. Having low oxidation potential for Fe-centers is definitely an important factor in this process and significantly facilitates it. Thus, during the hydrocarbon hydroxylation by MMO, the Fe centers undergo multiple reduction and oxidation steps; at first, MMOHox [ Fe(III)-Fe(III) state] should be reduced (2-electron reduction) to MMOHred [Fe(II)-Fe(II) state], then it should be oxidized (4-electron oxidation) by O2 molecule to [Fe(IV)-Fe(IV) state], after which it again is reduced by substrate to Fe(IV)-Fe(III) state and Fe(III)-Fe(III) states (see Scheme 6). Thus facile oxidation and reduction of Fe-center plays a crucial role in the hydrocarbon hydroxylation by MMO.

Scheme 6 The redox cycle of Fe-centers during hydrocarbon hydroxylation by MMO

5 Vinyl-Vinyl Coupling on Late Transition Metals Through C-C Reductive Elimination Mechanism Another important s-bond activation/formation process discussed in this article is vinyl-vinyl coupling, shown in Scheme 7. Vinyl-vinyl coupling opens a convenient route to conjugated 1,3-dienes and is widely employed in many catalytic coupling reactions. The great potential of the field is still under continuous development [26, 27] and, therefore, elucidation of the C-C bond formation mechanism and the factors controlling it are very crucial. In literature, numerous mechanistic studies on C-C reductive elimination and reverse process, oxidative addition (C-C bond activation), have been reported for di-

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D. G. Musaev · K. Morokuma

Scheme 7 Vinyl-vinyl coupling reaction on transition metal complexes

alkyl or mixed complexes of Pt [28–34], Pd [31, 35], Rh [33], Ru [32] and Ir [33]. Also, several theoretical investigations on C-C bond activation by Pt [36–39], Pd [36–40], Rh [40–43] and Ir [42, 44] have been performed. However, these studies were made for Csp3-Csp3 and Csp3-Caryl (in most cases methyl-methyl and methyl-aryl, respectively) bonds, and no theoretical study appears to have been carried out for reductive elimination of unsaturated vinyl ligands leading to a conjugated product. Therefore, we have published [45] two theoretical (DFT and ONIOM) papers on the mechanism of vinyl-vinyl C-C reductive elimination reaction on the transition metal complexes, major conclusions of which are summarized here and compared with other C-C coupling processes. We also intend to analyze the factors controlling these reactions. 5.1 Reductive Elimination from PtIV Halogen Complexes [Pt(CH=CH2)2X4]2– (X=Cl, Br, I) As shown in Fig. 4, our calculations showed that the reaction involving vinyl ligands may proceed via two different transition states, 1_TS and 1A_TS, which possess s-cis and s-trans configuration around the central single bond, respectively. Their corresponding energies are given in Table 2. We note here that at the B3LYP level of theory, the calculated relative energies of s-trans, s-gauche and s-cis conformers are 0.0, 3.5 and 4.0 kcal/mol respectively, in agreement with earlier findings. Reductive elimination through the s-trans pathway retains C2 symmetry and has to overcome the activation barrier of 29.4 kcal/mol. On the other hand, initial complex (1A_Init) and transition state (1A_TS) for s-cis pathway belong to Cs point group and the activation energy is 4.9 kcal/mol higher than for the former (Table 2). In the latter process, the product buta-1,3-diene will be released in the s-gauche (C2) form. Reductive elimination reactions are exothermic by 17.0 and 19.9 kcal/mol for s-cis and s-trans pathways, respectively (Table 2). Energy difference between the initial bis-s-vinyl complexes 1_Init and 1A_Init is only 0.6 kcal/mol, with the former being more stable. The relative order of the transition states (1_TS and 1A_TS) reflects the stability of corresponding buta-1,3-diene isomers in a free form. Thus, s-cis transition states are expected to lie higher in energy and we will continue the study following the s-trans pathway only.

Transition Metal Catalyzed s-Bond Activation and Formation Reactions

19

Fig. 4 S-cis and s-trans reductive elimination pathways from octahedral complexes

Upon examination of the C-C reductive elimination reaction from a series of halogen complexes (PtIV: X=Cl, Br, I; Table 2), a clear trend is observed; the heavier the ligand, the smaller the activation barrier, and the larger the exothermicity of the process. Therefore, the easier reductive elimination reaction should be expected from iodide complexes of PtIV with the activation energy of only 25.0 kcal/mol and reaction energy of –30.3 kcal/mol. 5.2 Reductive Elimination from Mixed PtIV Complexes [Pt{cis-/trans(CH=CH2)2(PH3)2}Cl2] Introducing phosphine ligand either in cis or trans position to s-vinyl groups favors C-C bond formation (Table 2). However, in the case trans substitution (4) the influence is much larger, DE≠=18.5 kcal/mol, compared to DE≠=27.6 kcal/mol for cis derivative (5) and DE≠=29.4 kcal/mol for the chloride complex (1). It is found that lower activation barriers are accompanied by higher reaction exothermicity (cf. DEfor 1, 4 and 5 in Table 2).

–19.9 –17.0 –25.3 –30.3 –40.4 –33.2 –3.7/26.1 –8.3/20.6 –12.3/13.0 –8.5/0.9 –27.4/–17.8 –51.3 –55.4 –57.4 –22.2/2.3 –26.9/–4.8 –30.8/–12.0 –25.7/–15.4 –42.3/–33.8 –29.1 –13.8 –44.8/23.2 –42.2/35.0

DE 28.6 34.0 26.4 24.2 17.5 26.5 39.1 34.2 30.0 33.7 18.2 12.5 10.9 6.6 17.8 14.0 11.0 14.3 5.9 16.8 27.3 27.6 33.5

DH≠ –19.4 –16.0 –24.8 –29.9 –39.9 –33.5 –2.9/27.6 –7.3/21.9 –11.3/14.3 –7.8/1.5 –26.4/–17.5 –50.5 –54.6 –56.3 –21.1/4.2 –25.6/–3.1 –29.5/–10.4 –24.8/–14.7 –41.0/–33.3 –28.8 –13.7 –42.8/21.9 –40.1/34.2

DH 29.2 33.2 26.5 24.3 18.0 27.6 39.0 34.0 29.9 32.2 18.5 12.9 11.3 7.2 18.2 14.2 11.0 13.6 6.1 18.2 28.4 29.7 35.5

DG≠ –30.6 –28.0 –35.9 –41.4 –52.2 –46.6 –3.0/17.9 –7.5/12.6 –11.5/5.0 –9.3/–10.0 –26.9/–29.0 –61.2 –65.8 –67.4 –21.2/–5.2 –26.0/–12.2 –29.9/–19.4 –26.0/–25.5 –42.1/–44.4 –41.0 –26.4 –39.0/13.0 –36.2/23.4

DG

DE≠=E(TS)–E(Init); for MIV complexes: DE=E(Prod)–E(Init); for MII complexes: DE=E(p-Comp)–E(Init), while the values after/correspond to DE=E(Prod)–E(Init). The same is applicable also for enthalpies and free energies. b Two vinyl ligands are cis to each other, X1 and X2 are trans to vinyl ligands, and X3 and X4 are trans to each other. c Reductive elimination through the s-cis pathway (see Fig. 4); all the other calculations were done for the s-trans pathway.

29.4 34.3 27.2 25.0 18.5 27.6 40.6 35.4 31.2 35.2 19.3 12.9 11.4 7.3 18.9 15.0 11.9 15.3 6.8 17.8 28.5 28.1 34.1

Pt(IV), X=Cl Pt(IV), X=Cl, s-cisc Pt(IV), X=Br Pt(IV), X=I Pt(IV), X1,X2=PH3; X3,X4=Cl; Pt(IV), X1,X2=Cl; X3,X4=PH3; Pt(II),X=Cl Pt(II), X=Br Pt(II), X=I Pt(II), X=NH3 Pt(II), X=PH3 Pd(IV), X=Br Pd(IV), X=I Pd(IV), X1,X2=PH3; X3,X4=Cl; Pd(II),X=Cl Pd(II),X=Br Pd(II), X=I Pd(II), X=NH3 Pd(II), X=PH3 [RhIII(CH=CH2)2(PH3)3Cl] [IrIII(CH=CH2)2(PH3)3Cl] [RuII(CH=CH2)2(PH3)3Cl] [OsII(CH=CH2)2(PH3)3Cl]

1 1A 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

a

DE≠

Systemb

No.

Table 2 Activation (DE≠, DH≠, DG≠) and reaction energies (DE, DH, DG) of the C-C reductive elimination stage in the gas phase (in kcal/mol)a

20 D. G. Musaev · K. Morokuma

Transition Metal Catalyzed s-Bond Activation and Formation Reactions

21

Reactions of both 4 and 5 lead to the same products, trans-[Pt(PH3)2Cl2] and buta-1,3-diene. Therefore, the difference in reaction energies (DE) reflects the relative stability of initial bis-s-vinyl derivatives; 5_Init is thermodynamically more stable by 7.2 kcal/mol than 4_Init.Very likely, destabilization of 4_Init due to mutual trans orientation of vinyl and phosphine ligands is responsible for Æ 4_TSÆ Æ 4_Prod. facilitating the reductive elimination process 4_InitÆ 5.3 Reductive Elimination from PtII Halogen Complexes [Pt(CH=CH2)2X2]2– (X=Cl, Br, I) C-C bond formation initiated from the square planar bis-s-vinyl complexes (6, 7 and 8) also proceeds through the three-centered transition state (Fig. 5). Upon metal-carbon s-bond breakage and reductive elimination, the coordination vacancy becomes available at the metal center and a p-complex of buta-1,3-diene is formed. Double bond coordination (h2-C=C) to the metal atom is preferred in this case, while the structure with central C-C bond coordination has an imaginary frequency corresponding to h2–C–CÆh2–C=C rearrangement. The same trend as noted above for PtIV is observed for the series of PtII complexes (6 to 8, Table 2); heavier halogen ligands make C-C bond formation easier by decreasing the activation energy and favoring the process thermodynamically. However, comparing the C-C reductive elimination reaction from PtII (6–8, Table 2) complexes with those of PtIV (1–3, Table 2) complexes, one can deduce a clear preference of the higher oxidation state. For the PtIV derivatives the activation barriers are lower by 11.2–6.2 kcal/mol and the processes are more exothermic by 16.2–18.0 kcal/mol than the corresponding PtII species. 5.4 Reductive Elimination from PtII Complexes with Amine and Phosphine Ligands [Pt(CH=CH2)2X2] (X=NH3, PH3) The energetics of the C-C bond formation reaction starting from the amine complex 9 (DE≠=35.2 and DE=–8.5 kcal/mol) are similar to those for the bromide derivatives (DE≠=35.4 and DE=–8.3 kcal/mol, Table 2). However, reductive elimination reaction from phosphine complex 10 is much easier with the activation energy of only 19.3 kcal/mol and reaction exothermicity of –27.4 kcal/mol (Table 2). This barrier is only slightly higher than that for the corresponding PtIV phosphine complex (4, Table 2). In addition, Pt(PH3)2 can be considered as a rather stable product in contrast to Pt(NH3)2 and PtX22– (X=Cl, Br, I). The finding is consistent with the experimental experience that phosphine is often added to reaction mixtures to keep the catalyst from decomposing so that the process can take place under homogeneous conditions [1a, 28, 29, 46]. Obviously, phosphine derivatives are the best candidates for reductive elimination process among the PtII complexes.

Fig. 5 S-trans reductive elimination pathway from square planar complexes

22 D. G. Musaev · K. Morokuma

Transition Metal Catalyzed s-Bond Activation and Formation Reactions

23

5.5 Reductive Elimination from PdIV Complexes [Pd(CH=CH2)2X4]2– (X=Cl, Br, I) In the PdIV complexes, the C-C bond formation takes place rather easily with very low barriers of 12.9 and 11.4 kcal/mol for 11 (X=Br) and 12 (X=I), respectively (Table 2). These are about 14 kcal/mol lower than for the corresponding PtIV complexes, while the exothermicity of the reactions is increased by as much as 26 kcal/mol. The high exothermicity suggests very early transition state structures. The results (see Table 2) show that reductive elimination from PdIV complexes would proceed most easily among the MII and MIV halogen derivatives (M=Pt, Pd). 5.6 Reductive Elimination from Mixed PdIV Complex [Pd{trans-(CH=CH2)2(PH3)2}Cl2] We excluded from consideration the complexes with PH3 ligands located cis to s-bonded carbon atoms, since this type of PtIV derivatives (5, Table 2) showed very small effect of PH3 on reaction energetics. Previous PtIV/PtII results (4 and 10, Table 2) suggest that phosphines trans to carbons should significantly facilitate the reductive elimination process. This trend seems to be rather general and applicable to PdIV complexes as well; the corresponding PdIV complex 13 with phosphines trans to carbons has a low activation barrier for C-C bond formation of only 7.3 kcal/mol. 5.7 Reductive Elimination from PdII Halogen Complexes [Pd(CH=CH2)2X2]2– (X=Cl, Br, I) Within the series of PdII halogen complexes 14 (X=Cl), 15 (X=Br) and 16 (X=I), the expected trends in the energies and geometry changes are again found; the heavier the halogen, the smaller the activation energy and the earlier the transition state. The smallest barrier is calculated for iodide complex DE≠= 11.9 kcal/mol and the largest 18.9 kcal/mol for chloride, with bromide in-between, 15.0 kcal/mol. Increase in activation energies is accompanied by decrease in exothermicity (Table 2).As discussed earlier for the corresponding Pt compounds, reductive elimination reaction from PdII halogen complexes also gives anionic Pd0 species [47]. 5.8 Reductive Elimination from PdII Complexes with Nitrogen and Phosphine Ligands [Pd(CH=CH2)2X2] (X=NH3, PH3) The activation and reaction energies for the complexes with X=NH3 and X=Br (17 and 15 in Table 2) are similar: DE≠=15.0 and 15.3 kcal/mol and DE=–26.9 and –25.7 kcal/mol for X=Br and X=NH3, respectively. Thus, both complexes would show a similar reactivity in the reductive elimination process. However,

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D. G. Musaev · K. Morokuma

the stability of [Pd0Br2]2– and [Pd0(NH3)2] relative to the corresponding p-complex differs significantly, the former being ca. 11 kcal/mol less stable than the latter. For the PdII phosphine complex 18 (X=PH3), vinyl-vinyl coupling reaction is very easy, with the barrier of only 6.8 kcal/mol, the smallest barrier reported in this article. 5.9 Reductive Elimination from RhIII, IrIII, RuII and OsII Complexes We extended the study of C-C reductive elimination reactions to other members of late transition metals in order to find possible alternatives to Pd/Pt complexes for catalytic coupling reactions. The calculations were performed only for the corresponding phosphine complexes, for which experimental precedents for the reaction were reported. In the case of Rh and Ir derivatives, an extra s-bonded ligand has to be added to maintain correct oxidation state, because RhII and IrII compounds are rarely known [48]. The chloride has been chosen for this purpose. Thus the model compounds studied are 19 [RhIII(CH=CH2)2(PH3)3Cl], 20 [IrIII(CH=CH2)2(PH3)3Cl], 21 [RuII(CH=CH2)2(PH3)3], and 22 [OsII(CH=CH2)2(PH3)3]. As in the previous cases (Figs. 4 and 5), vinyl-vinyl coupling for these compounds also occurs through the three-centered transition states. The smallest activation barrier among these four compounds is found for RhIII19 (17.8 kcal/mol), while those for the other complexes are considerably higher (28.1–34.1 kcal/mol). To summarize, the present calculations show that RhIII-based complexes can be considered as possible catalysts for vinyl-vinyl reductive elimination, while IrIII, RuII and OsII analogs are likely to be less active. Once again, our calculations shown that the second raw metals have lower barriers as well as higher exothermicity than the third row metals within each subgroup RhIII>IrIII and RuII>OsII. 5.10 General Discussion Thus, our calculations, in an agreement with the available experiments, have demonstrated that the reactivity of the [M(CH=CH2)2Xn] complexes (for M=Pd and Pt) in C-C bond formation depends on the nature of the ligand X, and decreases in the order: X=PH3>I>Br,NH3>Cl for both MIV and MII oxidation states. In all the cases, phosphine ligands decrease the activation barriers and increase the exothermicity of the reaction. The present results also show that all the second row metals (Ru, Rh and Pd) show the lower barriers and higher exothermicity than the corresponding third raw metals (Os, Ir and Pt) within each subgroup (Table 2), i.e. the reactivity of the studied complexes decreases via PdII>PtII, PdIV>PtIV, RhIII>IrIII, and RuII>OsII. The complexes of PtIV are more reactive than corresponding complexes of PtII. Similar results have been obtained for Pd complexes, while for them this effect is less pronounced. Considering the most reactive phosphine complexes, the following overall relative

Transition Metal Catalyzed s-Bond Activation and Formation Reactions

25

reactivity order in vinyl-vinyl coupling reaction may be suggested for these metals: PdIV, PdII>PtIV, PtII. Thus, Pd complexes are suggested to be the most reactive for this reaction. Furthermore, these results again demonstrate the importance of the electronic configuration of the metal for s–bond activation/formation reaction.As pointed out earlier, the change in the degree of oxidation of metal atoms during the oxidative addition/reductive elimination reactions could be described in terms of the promotion of electronic configuration of metal atoms. In the M0, MII, and MIV complexes, both Pt and Pd atoms possess d10, s1d9 and s2d8 electronic configurations, respectively.13 In M0 no covalent bonds are possible, since all five d orbitals are doubly occupied. In contrast, MII and MIV atoms can make two and four covalent bonds, respectively, through the hybrid s and d orbitals. The energy differences between the lower-lying electronic configurations of Pd and Pt atoms, and the calculated average reaction energies for C-C reductive elimination reactions of the Pd/Pt-complexes are given in Table 3. As seen from Tables 3 and 2, the concept of lower lying electronic configurations provides reliable qualitative description of the systems studied. In particular, (i) MIVÆMII reductive elimination is always more exothermic than MIIÆM0, which is consistent with the calculated s2d8Æs1d9 and s1d9Æd10 promotion energies, and (ii) both PdIVÆPdII and PdIIÆPd0 processes are more exothermic compared to PtIVÆPtII and PtIIÆPt0, which is again agreed with the calculated s2d8Æs1d9 and s1d9Æd10 promotion energies of Pd and Pt atoms. In agreement with the Hammond postulate, (i) the activation energies are lower when the reaction starts from MIV derivatives than from MII, and (ii) C-C bond formation involving palladium complexes requires significantly smaller barriers than with platinum.

Table 3 Promotion and average reaction energies (in kcal/mol) for C-C reductive elimination reactions from platinum and palladium complexesa,b

Reaction

Atomic energy differencec

DEaverage X=PH3, NH3d

X=Cl, Br, I Pd MIVÆMII (s2d8Æs1d9) MIIÆM0 (s1d9Æs0d10) a

Pt

–56.0

–14.8

–21.9

11.1

Pd

Pt

Pd

Pt

–53.4 (11,12) –4.8 (14–16)

–27.8 (2,3) 19.9 (6–8)

–57.4

–40.4

–33.8 [–15.4]

–17.8 [0.9]

The compounds used for averaging are given in parentheses (see Table 2 for energies). For PtII and PdII, DE with respect to the final products (MX2+diene), rather than to p-complexes is used. c Experimentally determined. d Values for X=NH3 are given in brackets. b

26

D. G. Musaev · K. Morokuma

Similar considerations are also applicable for the reductive elimination reactions for the other platinum group metals. Our calculations on reductive elimination reactions have shown an energetic preference of RhIII compounds to IrIII, RuII and OsII compounds. The fact can be rationalized taking into account that the only exothermic promotion energy of –37.6 kcal/mol13 is expected for s2d7Æs1d8 (RhIIIÆRhI). In contrast, s2d7Æs1d8(IrIIIÆIrI) and s1d7Æd8 (RuIIÆRu0) are endothermic by 25.1 and 9.2 kcal/mol respectively [13]. 5.11 Comparison of the Vinyl-Vinyl (Csp2-Csp2) and Alkyl-Alkyl (Csp3-Csp3) Reductive Elimination Comparing Csp2-Csp2 reductive elimination with the similar process involving alkyl groups (Csp3-Csp3), one may clearly note the same qualitative trends. Experimental studies have shown that dimethyl complexes of Pt(II) eliminate ethane much easier than their Pt(II) analogs [30, 35], and reactivity of Pt(IV) methyl complexes is higher than Pt(II) [30]. These results are in line with our findings (Table 2). However, the absolute values of activation energies computed for vinyl-vinyl coupling are significantly lower than that for methyl-methyl coupling. Particularly, DE≠=49.8 kcal/mol (MP4//MP2 level) [39a], DE≠=60.8 kcal/mol (MP4//HF) [39b,c], and DH≠=41.1 kcal/mol (GVB) [37a] were reported for ethane reductive elimination from [PtII(CH3)2(PH3)2]. The values are much higher than DE≠=1 9.3 kcal/mol (DH≠=18.2 kcal/mol) calculated in the present work for vinyl-vinyl coupling from [PtII(CH=CH2)2(PH3)2]. Ethane elimination from [PdII(CH3)2(PH3)2] was found to proceed with DH≠=10 kcal/mol (GVB) [37a] and DE≠=26.3 kcal/mol (MP4//HF) [39c], while our value for [PtII(CH=CH2)2(PH3)2] is again lower DE≠=6.8 kcal/mol (DH≠=5.9 kcal/mol). Similar relationships are found for the ethane reductive elimination from [RhIII(CH3)2(PH3)Cp] DE≠= 65.6 kcal/mol (MP2//HF) [43] and [PtIV(CH3)2(PH3)2Cl2] DH≠=34.2 kcal/mol (GVB) [37a] as compared to [RhIII(CH=CH2)2(PH3)2Cl] DE≠=17.8 kcal/mol and [PtIV(CH=CH2)2(PH3)2Cl2] DH≠=17.5 kcal/mol given in the present work. In addition, vinyl-vinyl coupling is generally much more exothermic than methylmethyl coupling [37a, 39, 43].The differences may come from the relative stability in the products; D(C-C) in buta-1,3-diene, 115.8 kcal/mol, is considerably larger than in ethane, 90.0 kcal/mol [49]. Thus, the vinyl-vinyl coupling is energetically more favored than the methyl-methyl reductive elimination. These theoretical results fairly well agree with experimental findings, which point out that practical implementation of Csp3–Csp3 coupling is rather problematic due to slow reductive elimination [50], in contrast to the processes involving vinyl groups.

Transition Metal Catalyzed s-Bond Activation and Formation Reactions

27

6 Concluding Remarks Above we have presented four different factors that control the catalytic activity of transition metals toward s-bonds. In the mono-nuclear transition metal systems (1) the availability of the lower lying s1dn–1 and s0dn states of the transition metal atoms, and (2) the nature of the ligands facilitating the reduction of the energy gap between the different oxidative states of the transition metal centers are very crucial. Meanwhile, as was demonstrated, in the transition metal clusters the “cooperative” (or “cluster”) effects play important roles in the catalytic activities of these clusters. Another factor, which could be very important for catalytic activity of the transition metal systems is shown to be their redox activity. However, those four factors are definitely not the only ones that play crucial roles in the catalytic activity of transition metal systems with s-bonds. The transition metal catalyzed s-bond activation and formation are very complex processes and need more detailed investigations. Acknowledgment Acknowledgement is made to National Science Foundation for continuous support (presently CHE-0209660) of our homogeneous catalysis project.

References 1. (a) Diederich F, Stang PJ (1998) (eds.) Metal-catalyzed cross-coupling reactions. VCH, Weinheim; (b) Corlins B, Herrman WA (1996) (eds.) Applied homogeneous catalysis with organometallic compounds. VCH, Weinheim; (c) Musaev DG, Morokuma K (1996) In: Prigogine I, Rice SA (eds) Advances in chemical physics, vol XCV. Wiley, New York, p 61 2. (a) Ausloos P, Lias SG (1987) (eds) Structure/reactivity and thermochemistry of ions. Reidel, Dordrecht, The Netherlands; (b) Russell DH (ed) (1989) Gas phase inorganic chemistry. Plenum, New York; (c) Davies JA, Watson PL, Liebman JF, Greenberg A (eds) (1990) Selective hydrocarbon activation: principles and progress. VCH, New York; (d) Eller K, Schwarz H (1991) Chem Rev 91:1121; (e) Fontijn A (ed) (1992) Gas-phase metal reactions. Elsevier, Amsterdam; (f) Weisshaar JC (1992) In: Ng C (ed) Advances in chemal physics, vol 81.Wiley-Interscience, New York; (g) Armentrout PB (1991) Science, 251:175; (h) Weisshaar JC (1993) Acc Chem Res 26:213; (i) Schroder D, Schwarz H (1995) Angew Chem Int Ed Engl 34:1973 and references therein 3. (a) Perry JK, Ohanessian G, Goddard WA III (1993) J Phys Chem 97:5238; (b) Perry JK, Ohanessian G, Goddard WA III (1994) Organometallics 13:1870; (c) Blomberg MRA, Siegbahn PEM, Svensson M (1994) J Phys Chem 98:2062; (d) Siegbahn PEM, Blomberg MRA, Svensson M (1993) J Am Chem Soc 115:4191 4. (a) Musaev DG, Koga N, Morokuma K (1993) J Phys Chem 97:4064; (b) Musaev DG, Morokuma K (1993) Isr J Chem 33:307; (c) Musaev DG, Morokuma K, Koga N, Nguyen KA, Gordon MS, Cundari TR (1993) J Phys Chem 97:11435; (d) Musaev DG, Morokuma K (1994) J Chem Phys 101:10697; (e) Musaev DG, Morokuma K (1996) J Phys Chem 100:11600 5. Carter EA, Goddard WA III (1988) J Phys Chem 92:5679

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D. G. Musaev · K. Morokuma

6. Trevor DJ, Cox DM, Kaldor A (1990) J Am Chem Soc 112:3742 7. Fayet P, Kaldor A, Cox DM (1990) J Chem Phys 92:254 8. (a) Schnabel P, Irion MP (1992) Ber Bunsengers Phys Chem 96:1101; (b) Irion MP, Schnabel P (1992) Ber Bunsengers Phys Chem 96:1091; (c) Lian L, Su CX,Armentrout PB (1992) J Chem Phys 97:4072 9. Guo BC, Kerns KP, Castleman AW Jr (1992) J Phys Chem 96:6931 10. (a) Jiao CQ, Freiser BS (1995) J Phys Chem 99:10723; (b) Berg C, Schindler T, Lammers A, Niedner-Schatteburg G, Bondybey VE (1995) J Phys Chem 99:15497 11. See, for example, Ber Bunsengers Phys Chem (1992) 96(6) 12. (a) Cui Q, Musaev DG, Morokuma K (1998) J Chem Phys 108:8418; (b) Cui Q, Musaev DG, Morokuma K (1998) J Phys Chem A 102:6373; (c) Moc J, Musaev DG, Morokuma K (2000) J Phys Chem A 104:11606; (d) Moc J, Musaev DG, Morokuma K (2003) J Phys Chem A 107:4929 13. Moore CF (1971) Atomic energy levels NSRD-NBS, vol III. U.S. Government Printing Office, Washington DC 14. Parshall GW, Ittel SD (1992) Homogenous catalysis, 2nd edn. Wiley, New York 15. Wallar BJ, Lipscomb JD (1996) Chem Rev 96:2625 and references therein 16. (a) DeRose VJ, Liu KE, Kurtz DM Jr, Hoffman BM, Lippard SJ (1993) J Am Chem Soc 115:6440; (b) Fox BG, Hendrich MP, Surerus KK, Andersson KK, Froland WA, Lipscomb JD (1993) J Am Chem Soc 115:3688; (c) Thomann H, Bernardo M, McCormick JM, Pulver S, Andersson KK, Lipscomb JD, Solomon EI (1993) J Am Chem Soc 115:8881 17. (a) Rosenzweig AC, Fredrick CA, Lippard SJ, Nordlung P (1930) Nature 366:537; (b) Rosenzweig AC, Nordlung P, Takahara PM, Fredrick CA, Lippard SJ (1995) Chem Biol 2:409 18. (a) Elango N, Radhakrishman R, Froland WA, Waller BJ, Earhart CA, Lipscomb JD, Ohlendorf DH (1997) Protein Sci 6:556; (b) Nesheim JC, Lipscomb JD (1996) Biochemistry 35:10240 and references therein 19. (a) Liu KE, Wang D, Huynh BH, Edmondson DE, Salifoglou A, Lippard SJ (1995) J Am Chem Soc 116:7465; (b) Liu KE, Valentine AM, Wang D, Huynh BH, Edmondson DE, Salifoglou A, Lippard SJ (1995) J Am Chem Soc 117:10174; (c) Liu KE,Valentine AM, Qiu D, Edmondson DE, Appelman EH, Spiro TG, Lippard SJ (1995) J Am Chem Soc 117:4997 20. Wilkinson EC, Dong Y, Zang Y, Fujii H, Fraczkiewicz R, Fraczkiewicz G, Czernuszewicz RS, Qui L Jr (1998) J Am Chem Soc 120:955 21. Shu LJ, Nesheim JC, Kauffmann K, Munch E, Lipscomb JD, Que L (1997) Science 275:515 22. (a) Dunietz BD, Beachy MD, Cao Y,Whittington DA, Lippard SJ, Friesner RA (2000) J Am Chem Soc 122:2828; (b) Baik MH, Newcomb M, Friesner RA, Lippard SJ (2003) J Chem Rev 103:2385; (c) Gherman BF, Dunietz BD, Whittington DA, Lippard SJ, Friesner RA (2001) 123:3836; (d) Friesner RA, Baik MH, Guallar V, Gherman BF,Wirstam M, Murphy RB, Lippard SJ (2003) Coord. Chem Rev 238/239:267; (e) Baik MH, Gherman BF, Friesner RA, Lippard SJ (2002) J Am Chem Soc 103:2385 23. (a) Yoshizawa K (2000) J Inorg Biochem 78:23; (b) Yoshizawa K, Suzuki A, Shiota Y, Yamabe T (2000) Bull Chem Soc Jpn 73:815; (c) Yoshizawa K, Ohta T,Yamabe T, Hoffmann R (1997) J Am Chem Soc 119:12311; Yoshizawa K, Ohta T,Yamabe T (1998) Bull Chem Soc Jpn 71:1899; (d) Yoshizawa K, Shiota Y,Yamabe T (1997) Chem Eur J 3:1160; (e) Yoshizawa K, Shiota Y,Yamabe T (1998) J Am Chem Soc 120:564; (f) Yoshizawa K (1998) J Biol Inorg Chem 3:318 24. (a) Siegbahn PEM, Crabtree RH (1997) J Am Chem Soc 119:3103; (b) Siegbahn PEM (1999) Inorg Chem 38:2880; (c) Blomberg MRA, Siegbahn PEM (1999) Mol Phys 96:571; (d) Siegbahn PEM, Crabtree RH, Nordlund P (1998) J Biol Inorg Chem 3:314; (e) Siegbahn PEM, Blomberg MRA (2000) Chem Rev 100:421; (f) Siegbahn PEM (2001) J Biol Inorg Chem 6:27; (g) Siegbahn PEM, Wistram M (2001) J Am Chem Soc 11:820

Transition Metal Catalyzed s-Bond Activation and Formation Reactions

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25. (a) Basch H, Mogi K, Musaev DG, Morokuma K (1999) J Am Chem Soc 121:7249; (b) Morokuma K, Musaev DG, Vreven T, Basch H, Torrent M, Khoroshun DV (2001) IBM J Res Dev 45:367; (c) Torrent M, Musaev DG, Basch H, Morokuma K (2001) J Phys Chem B 105:4453; (d) Basch H, Musaev DG, Mogi K, Morokuma K (2001) J Phys Chem B 105:8452; (e) Torrent M, Mogi K, Basch H, Musaev DG, Morokuma K (2001) J Phys Chem B, 105:8616; (f) Basch H, Musaev DG, Mogi K, Morokuma K (2001) J Phys Chem A 105:3615; (g) Torrent M, Musaev DG, Morokuma K (2001) J Phys Chem B 105:322; (h) Torrent M, Vreven T, Musaev DG, Morokuma K, Farkas O, Schlegel HB (2002) J Am Chem Soc 124:192; (i) Torrent M, Musaev DG, Basch H, Morokuma K (2002) J Comput Chem 23:59 26. For some recent examples of vinyl-vinyl coupling see: (a) Gallagher WP, Terstiege I, Maleczka RE (2001) J Am Chem Soc 123:3194; (b) Maleczka RE, Gallagher WP, Terstiege I (2000) J Am Chem Soc 122:384; (c) Caline C, Pattenden G (2000) Synlett 1661; (d) Kim HO, Ogbu CO, Nelson S, Kahn M (1998) Synlett 1059; (e) Ma Y, Huang X (1997) J Chem Soc Perkin Trans 2953; (f) Panek JS, Hu T (1997) J Org Chem 62:4912; (g) Alcaraz L, Taylor RJK (1997) Synlett 791; (h) Jang SB (1997) Tetrahedron Lett 38:1793; (i) Yang DY, Huang X (1997) J Organomet Chem 543:165; (j) Allred GD, Liebeskind LS (1996) J Am Chem Soc 118:2748 27. C-C cross coupling catalyzed by palladium complexes with nitrogen ligands: (a) van Asselt R, Elsevier CJ (1994) Organometallics 13:1972; (b) van Asselt R, Elsevier CJ (1994) Tetrahedron 50:323 28. Collman JP, Hegedus LS, Norton JR, Finke RG (1987) Principles and application of organotransition metal chemistry. University Science Books, Mill Valley, CA 29. Parshall GW, Ittel SD (1992) Homogeneous catalysis: the applications and chemistry of catalysis by soluble transition metal complexes, 2nd edn. Wiley-Interscience, New York 30. (a) Williams BS, Goldberg KI (2001) J Am Chem Soc 123:2576; (b) Crumpton DM, Goldberg KI (2000) J Am Chem Soc 122:962; (c) Hill GS, Yap GPA, Puddephatt RJ (1999) Organometallics 18:1408; (d) Albrecht M, Gossage RA, Spek AL, van Koten G (1999) J Am Chem Soc 121:11898; (e) Hill GS, Puddephatt RJ (1997) Organometallics 16:4522; (f) Goldberg KI,Yan JY, Breitung EM (1995) J Am Chem Soc 117:6889; (g) Goldberg KI,Yan JY,Winter EL (1994) J Am Chem Soc 116:1573; (h) Brown MP, Puddephatt RJ, Upton CEE (1974) J Chem Soc Dalton Trans 2457; (i) Appleton TG, Clark HC, Manzer LE (1974) J Organomet Chem 65:275; (j) Ruddick JD, Shaw BL (1969) J Chem Soc A 2969; (k) Chatt J, Shaw BL (1959) J Chem Soc 705 31. Baylar A, Canty AJ, Edwards PG, Slelton BW, White AH (2000) J Chem Soc Dalton Trans 3325 32. Van der Boom ME, Kraatz HB, Hassner L, Ben-David Y, Milstein D (1999) Organometallics 18:3873 33. Rybtchinski B, Milstein D (1999) Angew Chem Int Ed 38:870 and references therein 34. Rendina LM, Puddephatt RJ (1997) Chem Rev 97:1735 35. (a) Reid SM, Mague JT, Fink MJ (2001) J Am Chem Soc 123:4081; (b) Moravskiy A, Stille JK (1981) J Am Chem Soc 103:4182; (c) Loar MK, Stille JK (1981) J Am Chem Soc 103:4174; (d) Ozawa F, Ito T, Nakamura Y,Yamamoto A (1981) Bull Chem Soc Jpn 54:1868; (e) Gillie A, Stille JK (1980) J Am Chem Soc 102:4933 36. Tatsumi K, Hoffmann R, Yamamoto A, Stille JK (1981) Bull Chem Soc Jpn 54:1857 37. (a) Low JL, Goddard WA (1986) J Am Chem Soc 108:6115; (b) Low JL, Goddard WA (1986) Organometallics 5:609 38. Hill GS, Puddephatt RJ (1998) Organometallics 17:1478 39. (a) Sakaki S, Mizoe N, Musashi Y, Biswas B, Sugimoto M (1998) J Phys Chem A 102:8027; (b) Sakaki S, Ogawa M, Musashi Y, Arai T (1994) Inorg Chem 33:1660; (c) Sakaki S, Ieki M (1993) J Am Chem Soc 115:2373

30

Transition Metal Catalyzed s-Bond Activation and Formation Reactions

40. (a) Siegbahn PEM, Blomberg MRA (1995) In: van Leeuwen PWNM, van Lenthe JH, Morokuma K (eds.) Theoretical aspects of homogeneous catalysis, applications of ab initio molecular orbital theory. Kluwer Academic Publishers; (b) Siegbahn PEM, Blomberg MRA (1992) J Am Chem Soc 114:10548; (c) Blomberg MRA, Siegbahn PEM, Nagashina U, Wennerberg J (1991) J Am Chem Soc 113:424 41. (a) Sundermann A, Uzan O, Martin JML (2001) Organometallics 20:1783; (b) Sundermann A, Uzan O, Milstein D, Martin JML (2000) J Am Chem Soc 122:7095 42. Cao Z, Hall MB (2000) Organometallics 19:3338 43. Koga N, Morokuma K (1991) Organometallics 10:946 44. Krogh-Jespersen K, Goldman AS (1999) In: Truhlar DG, Morokuma K (eds) Transition state modeling for catalysis. ACS symposium series, ACS, Washington DC, p 151 45. (a) Ananikov VP, Musaev DG, Morokuma K (2001) Organometallics 20:1652; (b) Ananikov VP, Musaev DG, Morokuma K (2002) J Am Chem Soc 124:2839 46. Brandsma L,Vasilevsky SF,Verkruijsse HD (1998) Application of transition metal catalysts in organic synthesis. Springer, Berlin Heidelberg New York 47. (a) Amatore C, Azzabi M, Jutand A (1991) J Am Chem Soc 113:8375; (b) Negishi E, Takahashi T, Akiyoshi, K (1986) J Chem Soc Chem Commun 1338 48. Cotton SA (1997) Chemistry of precious metals. Blackie Academic and Professional (Chapman & Hall), London 49. Lide DR (ed.), (1999) CRC handbook of chemistry and physics 1999–2000, 80th edn. CRC Press, Boca Raton 50. Knochel P (1998) In: Diederich F, Stang PJ (eds) Metal-catalyzed cross-coupling reactions. VCH, Weinheim, p 387

Topics Organomet Chem (2005) 12: 31– 78 DOI 10.1007/b104398 © Springer-Verlag Berlin Heidelberg 2005

Theoretical Studies of C-H s -Bond Activation and Related Reactions by Transition-Metal Complexes Shigeyoshi Sakaki (

)

Department of Molecular Engineering, Graduate School of Engineering, Kyoto University, Nishikyo-ku, Kyoto 615-8510, Japan [email protected]

1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

32

2 2.1 2.2 2.3 2.4 2.5 2.6

s -Bond Activation via Oxidative Addition . . . . . . . Important Orbital Interaction . . . . . . . . . . . . . . Electron Correlation Effects in Oxidative Addition . . . Transition State Structure . . . . . . . . . . . . . . . . . Activation of sp3 and sp2 C-H s-Bonds . . . . . . . . . . s-Bond Activation of Various Substrates . . . . . . . . . Reductive Elimination from the p-Allyl Complex and Oxidative Addition Leading to the p-Allyl Complex

. . . . . .

. . . . . .

33 33 35 38 42 51

. . . . . . . . . . . . .

55

3 3.1 3.2 3.3

s -Bond Activation via Metathesis . . . . . . . . . . Reliability of Computational Methods for Metathesis Metathesis via Heterolytic s-Bond Scission . . . . . Metathesis via Homolytic s-Bond Scission . . . . .

. . . .

. . . .

57 57 58 64

4

Miscellaneous s -Bond Activation . . . . . . . . . . . . . . . . . . . . . . . . .

71

5

Several Examples of Catalytic Reaction via s -Bond Activation

. . . . . . . . .

72

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76

References

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Abstract Many s-bond activation reactions are classified into two main categories, oxidative addition and metathesis, except for several examples. Important orbital interactions and electronic process in the oxidative addition are discussed first.Also, the characteristic features of the transition state are reviewed in several typical oxidative addition reactions of H2, CH4, SiH4, C2H6, and SiH3CH3. The significant differences in reactivity among C-H, Si-H, C-C, and C-B s-bonds are discussed in terms of the orbital interaction in the transition state and the bond energy. Also, theoretical studies of the s-bond activation via metathesis are reviewed, in which the heterolytic C-H s-bond activation of benzene and methane by palladium(II) formate complex and the homolytic Si-H s-bond activation of silane by Cp2Zr(C2H4) and Cp2Zr(R1)(R2) (R1, R2=H, alkyl, or silyl) are mainly discussed to clarify the electronic process and the driving force. At the end of this chapter, several theoretical studies of transitionmetal-catalyzed reactions via s-bond activation are presented as typical examples. Keywords Theoretical approach · C-H s-bond activation · Oxidative addition · Metathesis · Heterolytic s-bond activation

32

S. Sakaki

List of Abbreviations CASPT2; CAS-SCF calculation followed by the second order perturbation theory CAS-SCF Complete active space SCF method CCSD(T) Coupled cluster expansion with single and double excitations, where contribution of triple excitations is non-iteratively incorporated with perturbation MP4(SDQ) Möller-Plesset 4-th order perturbation theory incorporating single, double, and quadruple excitations MPn Möller-Plesset n-th order perturbation theory

1 Introduction C-H s-bond activation of hydrocarbons by transition metal complexes is of considerable importance in modern organometallic chemistry and catalytic chemistry by transition-metal complexes [1], because a functional group can be introduced into alkanes and aromatic compounds through C-H s-bond activation. For instance, Fujiwara and Moritani previously reported synthesis of styrene derivatives from benzene and alkene via C-H s-bond activation of benzene by palladium(II) acetate [2]. Recently, Periana and his collaborators succeeded to activate the C-H s-bond of methane by the platinum(II) complex in sulfuric acid to synthesize methanol [3]. Both are good examples of the reaction including the C-H s-bond activation. In my understanding, the s-bond activation is classified into two main categories, oxidative addition (Eq. 1) and metathesis (Eq. 2), except for several examples. In the product of the oxidative addition, both A and B groups are bound with the metal center. Because the A and B groups are considered anion when they coordinate with the metal center, the oxidation state of the MLn + A-B Æ M(A)(B)Ln

(1)

MXLn + A-B Æ M(B)Ln + A-X

(2a)

M(R2C=CR¢2)Ln + A-B Æ M(B)(CR2-CAR¢2)Ln

(2b)

transition-metal center increases by +2 in a formal sense through the oxidative addition reaction. In the metathesis, on the other hand, the oxidation state of the metal center does not always increase. For instance, the A group is bound with an X ligand and the B group is bound with the metal center in the products of Eq. (2a). In this case, the oxidation state of the metal center does not change. If the X ligand is anion, the A group becomes positively charged in A-X, while the B group becomes negatively charged because it is bound with the transition-metal center in the product. It is likely to say that the s-bond breaking of A-B occurs in a heterolytic manner. In Eq. (2b), however, the metal

Theoretical Studies of C-H s-Bond Activation and Related Reactions

33

oxidation state increases by +2, because the B group and alkene change into the anionic B and alkyl ligands, respectively, in the product. In this case, it is likely to consider that the homolytic s-bond breaking takes place. In this review article, we wish to summarize theoretical studies of s-bond activation reactions through oxidative addition and metathesis, to clarify characteristic features of several important s-bond activation reactions, and to present general and deep understanding of the s-bond activation. In the last section, we will report several recent theoretical studies of catalytic reactions including the s-bond activation.

2 s -Bond Activation via Oxidative Addition 2.1 Important Orbital Interaction Let’s consider the oxidative addition of Eq. (1). Because A and B groups become anion and the d electron number of the metal center decreases by 2 in a formal sense, the charge-transfer should take place from the occupied d orbital of the metal center to the s* anti-bonding orbital of the A-B bond. Actually, Hoffmann and his collaborators previously indicated the importance of the charge-transfer from the occupied d orbital to the s* anti-bonding orbital in the oxidative addition of the C-H bond to a transition-metal complex [4]. As shown in Scheme 1, one doubly occupied dxz orbital becomes unoccupied and the anti-bonding s*-orbital of A-B receives two electrons from the d orbital. As a result, the A-B bond is broken and both A and B groups become anion in a formal sense, and the d electron numbers of the metal center decrease by 2. The other explanation is based on the valence bond picture [5]. Both MLn and A-B take a singlet spin state in general oxidative addition reaction. Approach of A-B to MLn induces energy destabilization if doubly occupied valence orbitals do not change at all. In M(A)(B)Ln, the dnÆdn–1s1 promotion occurs to form the M-A and M-B covalent bonds, as shown in Scheme 2. Because of this promotion, two valence orbitals of the M atom expand toward A and B groups. In A-B, the s2Æs1s*1 promotion should occur to form the M-A and M-B bonds (Scheme 2). This idea indicates that it is not the d orbital energy but the promotion energy from dn to dn–1s1 that is an important factor for the oxidative addition. Though these two explanations are different seemingly, the former becomes essentially the same as the latter if polarizations of MLn and A-B moieties are taken into consideration in the former explanation.

34

Scheme 1

Scheme 2

S. Sakaki

Theoretical Studies of C-H s-Bond Activation and Related Reactions

35

2.2 Electron Correlation Effects in Oxidative Addition The oxidative addition of methane to Pt(PH3)2 has been theoretically investigated with various methods [5–8], since this is a prototype of the C-H s-bond activation and the size of this system is moderate enough to perform detailed calculation. The geometries of precursor complex, transition state, and product were optimized with the MP2 method, as shown in Fig. 1 [8f]. In the precursor complex, little distorted geometries of methane and Pt(PH3)2 moieties clearly show that the interaction between methane and Pt(PH3)2 is weak and that the dispersion interaction is important in this precursor complex. In the transition state, the C-H s-bond is coplanar to the P-Pt-P plane. The product is a planar four-coordinate complex, cis-PtH(CH3)(PH3)2. Binding energy (BE), activation barrier (Ea), and energy of reaction (DE) were evaluated with various methods, as listed in Table 1, where definitions of BE, Ea, and DE are given in captions of Table 1.Apparently, the DFT method provides a much smaller BE value than the others. This is because the DFT method does not incorporate well the dispersion interaction [10] which plays an important role in the interaction between such two closed-shell molecules as CH4 and Pt(PH3)2. The activation barrier (Ea) by the DFT method is somewhat larger than those by MP4(SDQ) and CCSD(T) methods, while MP4(SDQ) and CCSD(T) methods yield a similar Ea value. It is noted that the MP4(SDQ)//DFT and CCSD(T)//DFT calculations present similar BE, Ea, and DE values to those of the MP4(SDQ)//MP2 and CCSD(T)//MP2 calculations. These results suggest that the less time-consuming DFT method is useful for geometry optimization. It is also important to investigate whether the single reference wavefunction is useful or not. The singlet instability of Hartree-Fock wavefunction was not found in the transition state [8f]. As shown in Table 1, the Ea and DE values somewhat fluctuate around the MP2 and MP3 levels but little fluctuate upon going to MP4(SDQ) and CCSD(T) from MP3. These results suggest that the single reference wavefunction is reliable for the oxidative addition of the C-H s-bond to Pt(PH3)2. One reason is that the s-bond breaking which needs multireference wavefunction occurs before or after the transition state, as will be mentioned below. The other reason is that the single reference wavefunction is useful for the distorted methane molecule of which geometry is similar to that in the transition state. For instance, the MP4(SDQ) and CAS-SCF methods provide almost the same potential energy surface of distorted methane [8e]. These results clearly indicate that incorporation of electron correlation effects is indispensable but the single-reference wavefunction is useful for the C-H s-bond activation of methane. The oxidative addition of methane to CpRhCl(CO) was investigated with various computational methods [11–15], and the energy changes were compared with experimental results [16]. This reaction proceeds through a precursor complex and a transition state, to afford a product, CpRh(H)(CH3)(CO), as shown in Fig. 1, where geometries were optimized with the MP2 method [12]. The DFT

36

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Table 1 Binding energy (BE) of precursor complex, activation barrier (Ea), and energy of reaction (DE) by the oxidative addition of the C-H s-bond of methane to Pt(PH3)2 and CpRh(CO)

(A) Pt(PH3)2 MP2//MP2 MP3//MP2 MP4(DQ)//MP2 MP4(SDQ)//MP2 MP4(SDQ)//DFT CCSD(T)//DFT DFT//DFT MP4(SDQ)//HF (B) CpRh(CO) DFT(LDA) MP2 MP2 MCPF//MP2 PCI-80//MP2 MP2//MP2 CASPT2//MP2 DFT(B3LYP)//MP2 DFT(B3P86)//MP2 MP2//DFT MP4(SDTQ)//DFT DFT//DFT Expt. Estimd.

BE

Ea

DE

Ref.

–0.8 –0.7 –0.7 –0.8 –0.7 –0.7 –0.7 –0.6

24.4 30.7 29.2 27.9 28.2 28.5 32.1 28.1

6.5 8.3 9.3 9.4 7.0 5.2 12.0 6.5

[8e]

–6.9 –14.8 –7.7 –10.1 –12.5 –12.3 –11.7 –5.6 –8.0 –13.6 –13.8 –6.37 –10.0

8.8 4.1 5.1 1.7 6.6 6.2 9.6 –3.1 –3.1 23.5 10.4 12.9 4.5

–14.8 –30.6 –16.4 –11.5 –17.2 –18.8 –21.9 –5.8 –5.8 –19.2 –13.3 –4.24 –15.0

[9]

[8b] [11] [12] [13] [14]

[15]

[16]

BE represents the energy difference between the precursor complex and the sum of reactants. Ea is the energy difference between the transition state and the precursor complex. DE is the energy difference between the product and the sum of reactants, where a negative value represents that the reaction is exothermic.

method underestimates the BE value, compared to the other methods, like that of the precursor complex, Pt(PH3)2(CH4) (see Table 1A,B). Siegbahn reported that the DFT calculations with B3LYP or B3P86 functional provided no barrier or too small barrier [14]. Ziegler et al. [11] theoretically investigated the same reaction with the DFT method and reported that Ea and DE values calculated agreed well with the experimental results. Su et al. theoretically investigated this reaction with MP2, MP4(SDTQ), and DFT(B3LYP) methods, where the geometries were optimized with the DFT(B3LYP) method. The activation barrier was overestimated in all their calculations and the reaction energy by the DFT(B3LYP)//DFT(B3LYP) method was considerably underestimated. The differences would come from exchange-correlation functionals and basis sets used; Ziegler et al. used Hartree-Fock-Slater exchange functional with correc-

Fig. 1 MP2-optimized geometry changes in the oxidative addition of methane to Pt(PH3)2 and to CpRh(CO). Bond length in Å and bond angle in degrees. From [8f, 13] with permission of American Chemical Society

Theoretical Studies of C-H s-Bond Activation and Related Reactions 37

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S. Sakaki

tions by Stoll et al. and Vosko et al. and employed STO basis sets. Su et al. employed the B3LYP functional like Siegbahn, but did not add one d-polarization and one p-polarization function on the first row elements and the H atom, respectively, unlike Siegbahn. The very small barrier or no barrier calculated by Siegbahn with the DFT(B3LYP or B3P86) method is understood in terms that the BE value is underestimated by the DFT(B3LYP or B3P86) method and as a result the transition state becomes too stable relative to the precursor complex. It should be noted that the exothermicity is underestimated by all DFT calculations. Two MP2 calculations [12, 13] with different basis sets provide significant differences in Ea and DE values, which indicate the importance of polarization functions in the calculation of transition-metal complexes. The CASPT2 method presents the moderately larger Ea value and moderately smaller exothermicity rather than the MP2 method and experimentally estimated values [14, 16]. Since the differences between these two methods are not large, it is concluded that the single reference wavefunction is useful in this oxidative addition reaction, too. In conclusion, the above discussion suggests that geometry is reliably optimized by the DFT method but it is safe to evaluate the energy changes not only by the DFT method but also by the post-Hartree-Fock methods with sufficiently good basis sets. 2.3 Transition State Structure From the orbital interaction diagram (see above), the A-B molecule had best take a position so as to present the large overlap between the anti-bonding s*-orbital of A-B and the doubly occupied d orbital of the metal center at a high energy. In the bent structure of Pt(PH3)2 that is taken in the transition state, the dxz orbital is at a higher energy than the dyz orbital, as shown in Scheme 3A,B, because the lone pair orbital of PH3 destabilizes the dxz orbital but not the dyz orbital. Thus, the anti-bonding s* orbital of the A-B bond forms a stronger charge-transfer interaction with the dxz orbital than with the dyz orbital. The other feature is that the valence px orbital of the metal center mixes into the dxz orbital to expand the dxz orbital toward the A-B molecule, as shown in Scheme 3C. However, the valence py orbital does not mix into the dyz orbital because of the difference in symmetry. These orbital pictures suggest that the charge-transfer interaction is stronger in the transition state when the A-B s-bond is on the Pt(PH3)2 plane than that when the A-B s-bond is perpendicular to the Pt(PH3)2 plane. Certainly, the oxidative addition of H2 to Pt(PH3)2 takes place through a planar transition state [5–7]. In this transition state, the H-H distance moderately lengthens and the Pt-H distance is still long. Consistent with the reactant-like transition state, the activation barrier is very small. The planar transition state was calculated in the oxidative additions of CH4 and SiH4 to Pt(PH3)2, too [6–8]. The importance of orbital interaction is indicated by the oxidative addition of the C-H s-bond of methane to CpRh(CO), too. In the precursor complex,

Theoretical Studies of C-H s-Bond Activation and Related Reactions

39

Scheme 3 From [8f, 31] with permission of American Chemical Society

methane approaches the Rh center from the direction of LUMO to avoid the exchange repulsion; see Scheme 4 for HOMO and LUMO. In the transition state, the C-H bond approaches the Rh center in a side-on manner, because HOMO of the CpRh(CO) moiety mainly consists of a dp orbital with which the antibonding C-H s*-orbital overlaps well in the side-on approach. These results indicate that the orbital overlap is a key factor to determine the geometry of the transition state.

Scheme 4 From [13] with permission of American Chemical Society

40

S. Sakaki

However, non-planar transition state was reported in the oxidative additions of the Si-C and C-C s-bonds to Pt(PH3)2 [8f], against the above explanation based on the orbital interaction. As shown in Fig. 2, the dihedral angle between the P-Pt-P plane and the C-X bond (X=C or Si) is 70° and 78° in the transition states of the oxidative additions of the Si-C and C-C s-bonds, respectively. The product takes a planar four-coordinate structure, as expected. The intrinsic reaction coordinate (IRC) calculation of the oxidative addition of the Si-C s-bond was carried out to ascertain whether the non-planar transition state leads to the planar product or not.As shown in Fig. 2, the geometries 2 and 3 are still non-planar, in which the dihedral angle between the P-Pt-P plane and the Si-C bond is the same as that of the transition state. In 4, the dihedral angle slightly decreases to 67°.After 4, the dihedral angle gradually decreases and the geometry smoothly becomes planar. The Si-C distance in 4 is considerably longer than the usual SiC covalent bond (1.907 Å), while it is moderately longer than the usual Si-C bond in the transition state. From these results, it is concluded that the Si-C bond is not weakened very much in the transition state but it is considerably weakened in 4, and that the geometry starts to become planar when the Si-C bond becomes considerably weaker. The reason is easily understood, as follows. When the Si-C bond considerably lengthens, the s* orbital of the Si-C bond becomes lower in energy and therefore the charge-transfer from the occupied d orbital of the Pt center to the s* orbital of the Si-C bond becomes stronger, which stabilizes the planar geometry more than the non-planar one. As a result, the geometry starts to become planar when the Si-C bond lengthens considerably. In other words, breaking of the Si-C bond occurs infrequently in the transition state but does occur after the transition state. Because the Si-C bond breaking does not occur much in the transition state, the transition state does not need to become planar and it can be represented well with a single-reference wavefunction (see above). Transition states of oxidative additions of H-SiCl3, H-SiMe3, CH3-SiCl3, and CH3-SiMe3 to Pt(PH3)2 have been compared with each other [8f]. The transition state of the oxidative addition of the Si-H bond is very reactant-like and planar, independent of the substituents of the Si atom. On the other hand, the transition state of oxidative addition of the Si-C bond is non-planar and the dihedral angle between the P-Pt-P plane and the Si-C bond depends on the substituent of CH3-SiX3; it is 84° and 76° in the oxidative additions of CH3-SiCl3 and CH3SiMe3, respectively. From the inspection of the geometry and energy changes in the reaction, it is likely to conclude that the dihedral angle is determined by the balance between the steric repulsion of the substrate with Pt(PH3)2 and the extent of the s-bond breaking in the transition state. The transition state is planar when the s-bond breaking occurs either in the transition state or before the transition state. Also, the transition state is planar when the s-bond breaking occurs after the transition state and the steric repulsion between the substrate and the metal moiety is not significantly large. The examples are the planar transition states of the oxidative addition of the H-H and Si-H s-bonds. On the other hand, the transition state is non-planar, when the s-bond breaking occurs after the transition state and the steric repulsion is large.

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Fig. 2 IRC calculation of the oxidative addition of the Si-C s-bond of CH3-SiH3 to Pt(PH3)2. Bond length in Å and bond angle in degrees. From [8f] with permission of American Chemical Society

42

S. Sakaki

2.4 Activation of sp3 and sp2 C-H s -Bonds The oxidative addition of H2 to Pt(PH3)2 takes place much more easily than that of the C-H bond of methane [5–7]. The lower reactivity of methane compared to that of H2 is observed in the oxidative addition to bare metals [17]. This is reasonably interpreted with two factors, as follows. One of them is the difference in valence orbital between H and CH3; the H atom has a spherical 1s valence orbital, while the CH3 group has a directional sp3 orbital.As a result, the CH3 group must change its direction toward the metal center to form the bonding interaction with the metal center. This direction change gives rise to destabilization energy [4c, 7, 8f, 17, 18]. The other factor is the bond energy. The M-H bond energy is much larger than the M-CH3 bond energy, as shown in Table 2. Thus, the oxidative addition of the H2 molecule produces a more stable product than that of methane. This explanation becomes less effective in the early transition metal element, because the M-H bond energy is smaller than the M-alkyl bond energy in the early transition metal element. Although the oxidative addition of the C-H s-bond to the transition metal complex is difficult, the oxidative addition of methane derivative to a palladium(0) complex was experimentally proposed [19], where a chelate phosphine was employed as a ligand and two electron-withdrawing substituents were introduced to the sp3 C atom. The C-H s-bond activation of methane by palladium(0) and platinum(0) chelate phosphine complexes was theoretically investigated [8e, 20], as shown in Fig. 3. When monodentate phosphine was employed, the C-H bond is lengthened very much in the transition state and the geometry of the transition state is similar to that of the product. When the chelate phosphine was employed, the Pd-C, Pd-H, and C-H distances in the

Table 2 Bond energiesrelated to oxidative addition of methane and benzene to M(PH3)2 (M=Pd or Pt) [9, 20]

CH4 CH3CN CH2(CN)2 Pd(H)2(PH3)2 Pd(H)(CH3)(PH3)2 Pd(H)(CH2CN)(PH3)2 Pd(H)(CH(CN)2)(PH3)2 Pt(H)2(PH3)2 Pt(H)(CH3)(PH3)2 Pd(H)(Ph)(PH3)2 Pt(H)(Ph)(PH3)2 kcal/mol unit.

E(C-H) E(C-H) E(C-H) E(Pd-H) E(Pd-CH3) E(Pd-CH2CN) E(Pd-CH(CN)2) E(Pt-H) E(Pt-CH3) E(Pd-Ph) E(Pt-Ph)

MP4(SDQ)

CCSD(T)

DFT

108.6 106.4 105.7 48.5 28.7 30.9 40.1 60.2 41.0 57.6 73.3

109.0 –

112.5

49.5 30.7

52.8 28.8

60.8 42.9 51.4 63.4

61.8 38.6 41.0 51.2

Fig. 3 MP2-optimized geometry changes in the oxidative addition of methane to Pd(PH3)2 and Pd(dppe) (dppe=H2PCH2CH2PH2). Bond length in Å and bond angle in degrees. From [8e] with permission of Royal Society of Chemistry and from [20] with permission of American Chemical Society

Theoretical Studies of C-H s-Bond Activation and Related Reactions 43

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Table 3 Binding energy of the precursor complex (BE), activation barrier (Ea), and energy of reaction (DE) of the oxidative addition of the sp3 C-H s-bond of methane derivativesa

Pd(PH3)2 Pd(dipe)

Pd(dppe) Pd(PH3)2 Pt(PH3)2 a

Substrate

BE

Ea

CH4 CH3CN CH2(CN)2 CH4 CH3CN CH2(CN)2 CH4 CH2(CN)2

–0.7 –4.7 –5.7 –7.7 –22.3 –22.2 –5.1 –16.7

36.9 31.9 25.1 22.1 23.2 18.0 26.7 19.3

34.1 23.2 10.8 11.7 1.4 –10.8 19.8 –6.0

–3.8 –5.3

26.5 17.1

22.1 –3.9

C6H6 C6H6

DE

Calculated with the MP4(SDQ) method (in kcal/mol) [9, 20].

transition state are similar to those of the monodentate phosphine complex (see Fig. 3A,B). As shown in Table 3, introduction of the chelate phosphine considerably decreases the activation barrier and the endothermicity. These effects of chelate phosphine are interpreted in terms of the distortion energy and the d orbital energy of the Pd and Pt moieties. In the transition state, the P-M-P angle must decrease to push up the d orbital in energy, as discussed above. When chelate phosphine was coordinated with the metal center, the geometry of the reactant is similar to that of the transition state, as shown in Fig. 3. This means that the distortion of the metal moiety does not necessarily occur in the transition state when chelate phosphine coordinates with the metal center. Actually, the activation barrier decreases to a similar extent to the decrease of the distortion energy upon going to the chelate phosphine complex from the monodentate phosphine complex. However, the oxidative addition of the C-H s-bond of methane to the palladium(0) chelate phosphine complexes still needs a considerably large activation barrier and it is endothermic. These results suggest that not only chelate phosphine but also introduction of the electron-withdrawing substituent is necessary to perform easily the oxidative addition.Apparently, the introduction of one CN group substantially decreases the endothermicity by 12 to 16 kcal/mol, as shown in Table 3. This is easily interpreted in terms of the C-H and Pd-alkyl bond energies; though the C-H bond of methane derivatives becomes slightly weak by introduction of the CN group, the Pd-alkyl bond becomes considerably strong by introduction of the CN group.As a result, the oxidative addition of methane derivatives becomes less endothermic (or more exothermic) by introduction of the CN group. Though the endothermicity considerably decreases upon introduction of one CN group, the activation barrier moderately decreases upon introduction of the CN group when PH3 is employed as a ligand and slightly increases when dipe is employed, where dipe represents that

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two PH3 ligands are placed so as to mimic diphosphinoethane. This is interpreted in terms of the coordination of the CN group with the Pd center; the introduction of CN stabilizes the transition state, while CH3CN coordinates with the Pd center to stabilize the precursor complex. Because of the cancellation, the activation barrier does not change very much by introduction of one CN group. However, the transition state is considerably stabilized and the activation barrier decreases when two CN groups are introduced to the sp3 C atom. Thus, the oxidative addition of the C-H s-bond occurs with a moderate activation barrier and considerable exothermicity even in the palladium(0) complex when two electron-withdrawing substituents are introduced on the C atom and the chelate phosphine coordinates with the Pd center. These results are consistent with the experimental proposal mentioned above [19]. The next issue is to elucidate the reasons why the electron-withdrawing substituent increases the exothermicity and decreases the activation barrier. The exothermicity depends on the bond energy. The C-H bond energy moderately decreases in the order CH4>CH3CN>CH2(CN)2, as shown in Table 2, while the Pd-alkyl bond energy considerably increases by about 10 kcal/mol upon introduction of one CN group. It is of considerable importance to clarify the reason why the Pd-alkyl bond becomes stronger with the introduction of electron-withdrawing substituent. This tendency had often been proposed in the experimental field without clear explanation, but it was clearly explained with the simple Hückel MO method here [20]. Let us consider that the covalent bond is formed from A and B. The stabilization energy by the covalent bond formation is represented by Eq. (3) when the jA and jB orbitals are separated well in energy: DEcov = eB – eA + b2/(eB–eA)

(3)

and the absolute value of resonance integral |b| is much smaller than the absolute value of energy difference |eA-eB|. Here, eA and eB are orbital energies of jA and jB , respectively, and we assumed that the jA orbital is at a lower energy than the jB orbital. This equation indicates that the bond energy increases with increase in the energy difference between jA and jB, because the third term of Eq. (3) is negligibly small. Apparently, the sp3 orbital of alkyl group becomes lower in energy by introduction of CN group. Since the d orbital of the Pd moiety is at higher energy than the sp3 orbital of the alkyl group, the introduction of CN group increases the energy difference between the d orbital and the sp3 orbital, to strengthen the Pd-alkyl bond. We wish to discuss the reason why the CN group also decreases the activation barrier. Because the CN group possesses the p* orbital, the charge-transfer (CT) interaction between the doubly occupied d orbital of the Pd center and the p* orbital of CN is formed in addition to the CT interaction between the C-H s* orbital and the occupied d orbital of the Pd center [20], as shown in Scheme 5A. This interaction induces additional stabilization energy, to lower the activation barrier. The oxidative addition of the sp2 C-H s-bond of benzene

46

S. Sakaki

A

B

Scheme 5 From [9, 20] with permission of American Chemical Society

to Pt(0) and Pd(0) complexes was recently investigated [9]. As shown in Fig. 4, the transition state is very product-like in the oxidative addition to the Pd(0) complex, while the transition state is less product-like in the oxidative addition to the Pt(0) complex. Consistent with these geometries of transition states, the oxidative addition to Pd(PH3)2 takes place with very large activation barrier and considerably large endothermicity, as shown in Table 3. On the other hand, the oxidative addition to Pt(PH3)2 occurs with much smaller activation barrier and endothermicity than those of the Pd analogue. This difference between palladium(0) and platinum(0) complexes was discussed above in terms of the energy of d orbital. The difference in reaction energy between methane and benzene is interpreted in terms of the M-Ph and M-CH3 bond energies; the C-H bond of benzene is much stronger than that of methane by about 10 kcal/mol but the M-Ph bond is much stronger than the M-CH3 bond by about 20 kcal/mol, as shown in Table 2. As a result, the C-H s-bond activation of benzene is more exothermic than that of methane. The lower activation barrier of the oxidative addition of benzene is interpreted in terms that the p* orbital of benzene participates in the CT interaction with the occupied d orbital of M(PH3)2, as shown in Scheme 5B. This is similar to the CT interaction between the p* orbital of CN and the doubly occupied d orbital of M(PH3)2. The reductive elimination of methane from the platinum(IV) complex is the reverse of the oxidative addition of methane to the platinum(II) complex. Puddephatt et al. [21] theoretically investigated the reductive elimination of methane and ethane from five-coordinate platinum(IV) complexes, [PtHMe2L2]+ and [PtMe3L2]+, to afford the alkane complexes, [PtMe(CH4)L2]+ and [PtMe(C2H6)L2]+, where the DFT(B3LYP) method was employed. The structure of [PtHMe2L2]+ is square pyramidal, because the Pt center takes a d6 electron configuration. In the transition state, the Pt-H and Pt-CH3 distances are similar to those of the platinum(IV) complex and the C-H distance is very long like the transition state of the oxidative addition of methane to Pt(PH3)2. The activation barrier is calculated to be 12 and 19 kcal/mol, and the endothermicity is 9 and 15 kcal/mol for L=NH3 and PH3, respectively, as shown in Fig. 5. The reductive elimination of methane from the platinum(IV) complexes more easily occurs than that from the platinum(II) complexes, as expected. The oxidative addition of methane to the platinum(II) complex occurs with an activation barrier of 12

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Fig. 4 DFT-optimized geometry changes in the oxidative addition of benzene to M(PH3)2 (M=Pd or Pt). Bond length in Å and bond angle in degrees. From [9] with permission of American Chemical Society

and 19 kcal/mol for L=NH3 and PH3, respectively. Unexpectedly, these activation barriers are smaller than that (30 kcal/mol) of the oxidative addition of methane to Pt(PH3)2, while the oxidative addition to the platinum(II) complexes is much more endothermic than that to Pt(PH3)2, expectedly.Also, the oxidative addition of the C-C s-bond to a Pt(II) complex, [Pt(PH3)2Me]+, occurs with activation barrier of about 40 kcal/mol which is similar to that of the oxidative addition of ethane to Pt(PH3)2, while the endothermicity is much larger than the latter reaction (see Fig. 5). This higher reactivity of [Pt(CH3)L2]+ than that of Pt(PH3)2 has not been discussed yet, to our knowledge. Goldberg et al. [22] theoretically investigated the reductive elimination of methane from PtCl2(H)(CH3)(PR3)2, where R is either H or Me, and discussed the fact that the reaction course depends on the kind of phosphine; the reductive elimination occurs with phosphine dissociation (see 5Æ6 in Scheme 6) when PH3 was employed as a

48

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Fig. 5 Energy changes of the oxidative additions of the C-H s-bond of methane and the C-C s-bond of ethane to [PtMe(L)2]+ (L=NH3 or PH3). Calculated with the DFT method. From [21] with permission of American Chemical Society

Scheme 6 From [21] with permission of American Chemical Society

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Table 4 Reductive elimination of CH4 from PtCl2L2(H)(CH3)a

L

PH3

PMe3

Ea

DE

Without dissociation of L (5Æ6)b

15–16

–31.9

16.8

–39.1

With dissociation of L (5Æ7Æ8)b

3.0 (13.2)c

–17.6 (–7.4)

0.7 (18.8)

–24.2 (–6.1)

a b c

Ea

DE

Calculated with the DFT method (in kcal/mol) [22]. See Scheme 6. Out of parentheses are energies change relative to PtCl2L(H)(CH3). In parentheses are those relative to PtCl2L2(H)(CH3).

ligand and without phosphine dissociation (see 5Æ7Æ8 in Scheme 6) when PMe3 was employed, as shown in Table 4. The oxidative addition of methane to PtCl2(PR3)2 needs activation barriers of 47 and 56 kcal/mol for L=PH3 and PMe3, respectively, when phosphine dissociation does not occur. These values are much larger than the activation barrier of the oxidative addition of methane to Pt(PH3)2, as expected. If phosphine dissociates from the Pt center, the oxidative addition of methane to the Pt(II) center occurs with much smaller activation barriers of 20.6 and 24.9 kcal/mol for L=PH3 and PMe3, respectively. Thus, it is likely to conclude that dissociation of phosphine facilitates the oxidative addition of methane to the platinum(II) center. Though the clear reason was not discussed about the effects of phosphine dissociation, one of plausible reasons is the steric repulsion; the oxidative addition to four-coordinate platinum(II) complex leads to a six-coordinate platinum(IV) complex but the oxidative addition to the three-coordinate platinum(II) complex yields a less congested five-coordinate platinum(IV) complex. The similar oxidative addition of methane to the platinum(II) diimine complex was theoretically investigated with the DFT method by Tilset et al. [23]. In their work, it is concluded that the oxidative addition occurs much more easily than the metathesis of methane with the Pt-CH3 bond, as shown in the left-hand side of Fig. 6. The other important result is that water molecule accelerates the oxidative addition because water coordinates with the Pt(IV) center to stabilize the platinum(IV) complex to a greater extent than the platinum(II) complex (see the right hand side of Fig. 6). H/D exchange in TpPt(H)2(CH3) (Tp=hydrido-tris(pyrazolyl)borate) was investigated with the DFT method [24], where various functionals were used. The reaction takes place through the reductive elimination of methane, methane rotation, and the oxidative addition. Important in this reaction is that the platinum(II) methane complex is very stable; the binding energy of methane with the Pt(II) center was evaluated to be 6.0 kcal/mol and the activation barrier for methane loss was 11.9 kcal/mol, where mPW1k functional was

50

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Fig. 6 Energy changes of the oxidative addition of the C-H s-bond of methane to the platinum(II) complexes. Calculated with the DFT method. From [23a] with permission of American Chemical Society

employed. Because the dispersion interaction plays a key role in the complex of methane with the metal center, post Hartree-Fock methods such as MP2 to MP4(SDQ) methods should be also applied to this kind of reaction. The oxidative addition of the C-H bond of methane to d6 metal complexes, [CpM(PH3)(CH3)]+ (M=Rh or Ir), was theoretically investigated, where geometries were optimized with the MP2 method and energy changes were evaluated with MP2 and QCISD methods [25]. The MP2 method presents a considerably smaller activation barrier than the QCISD method. This difference between MP2 and QCISD methods suggests that the MP2 method is not sufficiently good for the oxidative addition reaction, as discussed above. It is noted that the Ir complex undergoes the oxidative addition with much smaller activation barrier than the Rh complex. This result is interpreted in terms of the singlet-triplet energy difference in [CpM(PH3)(CH3)]+. This explanation is based on the valence bond picture [26, 27]. However, the singlet excitation energy should be compared with the reactivity, in my understanding, because the promotion energy corresponds to the singlet excitation energy, as discussed above. The successful explanation based on the singlet-triplet excitation energy is due to the fact that

Theoretical Studies of C-H s-Bond Activation and Related Reactions

51

the promotion energy is parallel to the singlet-triplet excitation energy in many cases. The explanation is essentially the same as that proposed by Goddard et al. [7]. 2.5 s -Bond Activation of Various Substrates Besides the C-H s-bond, the oxidative addition of various s-bonds such as Si-H, Si-C, C-C, B-B, and B-X (X=C, Si, Ge, or Sn) bonds to Pt(0) and Pd(0) complexes were theoretically investigated and interesting differences in reactivity among them were reported [8a,b,f, 13, 28, 29–31]. Apparently, the oxidative addition of the Si-H s-bond to Pt(PH3)2 and RhCl(PH3)2 (Eqs 4 and 5) Pt(PH3)2 + SiH4 Æ cis-Pt(H)(SiH3)(PH3)2

(4)

RhCl(PH3)2 + SiH4 Æ cis-RhCl(H)(SiH3)(PH3)2

(5)

easily occurs with almost no barrier and significantly large exothermicity, while that of the C-H bond to the Pt(0) and Rh(I) complexes needs a considerably large activation barrier with moderate endothermicity, as shown in Table 5 [8a,b, 28]. These significant differences between them are reasonably interpreted, as follows. The Si-H bond energy (84.6 kcal/mol) is much smaller than the C-H bond energy (100.0 kcal/mol), while the Pt-SiH3 bond energy (61.5 kcal/mol) is much larger than the Pt-CH3 bond energy (39.7 kcal/mol), where these bond energies were evaluated with the MP4(SDQ)//Hartree-Fock calculations.Also, the s* orbital of the Si-H bond is at a lower energy than that of the C-H bond. As a result, the oxidative addition of the Si-H s-bond occurs with lower activation barrier and larger exothermicity than those of the C-H s-bond. It is noted that the oxidative addition of the C-C s-bond to Pt(PH3)2 needs much larger activation barrier than that of the C-H s-bond [8f], while these two oxidative addition reactions take place with the similar energy of reaction, as shown in Table 5. Similarly, the oxidative addition of the Si-C s-bond to Pt(PH3)2 Table 5 Oxidative addition of C-H, C-C, Si-H, Si-Si bonds to RhCl(PH3)2, Pt(PH3)2, and Pt(CH3)(PH3)2

RhCl(PH3)2 Pt(PH3)2

Pt(CH3)(PH3)2

C-H of CH4 Si-H of SiH4 C-H of CH4 Si-H of SiH4 C-C of C2H6 Si-C of SiH3CH3 C-C of C2H6

QCISD(T) QCISD(T) MP4(SDQ) MP4(SDQ) MP4(SDQ) MP4(SDQ) DFT

BE

Ea

DE

Ref.

–12.8 –21.4 – – – – –

7.7 No 27.9 2.9 57.4 19.5 41.0

–10.0 –44.6 9.4 –19.3 7.6 –7.1 34.0

[25] [8e]

[21]

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requires a larger activation barrier than that of the Si-H s-bond. The larger activation barriers of the oxidative additions of the C-C and Si-C s-bonds are easily interpreted in terms of the directional sp3 valence orbital of the CH3 group; because the valence orbital of the CH3 group is a directional sp3 orbital, the CH3 group must change its direction to the metal center to form a M-CH3 bond, as shown in Scheme 3(A). The direction change induces the energy destabilization of CH3-CH3 and SiH3-CH3. On the other hand, the H atom can form a new M-H bonding interaction without such energy destabilization, because the valence orbital of the H atom is a spherical 1s orbital. The larger activation barrier of the oxidative addition of the Si-C bond than that of the Si-H s-bond is interpreted in the same way. Interestingly, the platinum(II) complex, [Pt(CH3)(PH3)2]+, undergoes the oxidative addition of the C-C s-bond of ethane with considerably smaller activation barrier than does the platinum(0) complex, Pt(PH3)2, while the oxidative addition to the former complex is much more endothermic than that to the latter one [21], as shown in Table 5 and Fig. 6. The larger endothermicity of the oxidative addition to the palladium(II) complex is consistent with our understanding that the transition-metal complex with lower oxidation state is more reactive than that with higher oxidation state. However, the smaller activation barrier of the oxidative addition to the platinum(II) complex is against our understanding. This suggests that the d orbital energy is not only one key factor for the activation barrier. Detailed analysis should be performed to clarify what factors determine the activation barrier. Interestingly, the oxidative addition of CH3-B(OH)2 to M(PH3)2 (M=Pd or Pt; Eq. 6) takes place with a much smaller activation barrier than that of CH3-CH3 [31]: Pt(PH3)2 + CH3B(OH)2 Æ cis-Pt(CH3)[B(OH)2](PH3)2

(6)

as shown in Table 6, where geometries were optimized with the MP2 method and energy changes were evaluated with the MP4(SDQ) method. The transition state is non-planar like those of the oxidative addition of CH3-CH3 and SiH3Table 6 Oxidative addition of s-bond including the boryl group, H3X-B(OH)2, to Pd(PH3)2 and Pt(PH3)2a

XH3

CH3

SiH3

GeH3

SnH3

(a) Pd(PH3)2 Ea DE

No reaction

1.2 –13.7

1.1 –14.1

No –22.4

21.5 3.0

No –33.0

2.2 –33.9

No –39.4

(b) Pt(PH3)2 Ea DE a

Calculated with the MP4(SDQ) method (in kcal/mol) [31].

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Table 7 Bond energies related to oxidative addition reactions and energy of valence orbital of ·XH3 and ·B(OH)2a

(A) H3X-B(OH)2 bond energy (kcal/mol unit; MP4(SDQ) method) XH3=CH3 109.7

SiH3 86.8

GeH3 83.5

SnH3 72.8

(B) M-B(OH)2 and M-XH3 bond energies M=Pd M=Pt

B(OH)2 52.8 64.4

CH3 29.4 42.4

SiH3 44.1 54.2

GeH3 42.3 50.7

SnH3 40.3 46.3

(C) Orbital energies (eV unit) ·B(OH)2 –9.6 a

·CH3 –10.4

·SiH3 –9.0

·GeH3 –8.9

·SnH3 –8.6

[31].

CH3 (see above). The endothermicity is similar in these two reactions, because the B-C bond is stronger than the C-C bond but the Pt-B(OH)2 bond is stronger than the Pt-CH3 bond, as shown in Table 7. This means that the reasons of the smaller activation barrier of the C-B s-bond activation should be found in the transition state.As is well known, the boryl group, B(OH)2, has an sp2 lone pair orbital and an empty p orbital perpendicular to the boryl plane, as shown in Scheme 7A. This empty p orbital of B(OH)2 can participate in the bonding interaction with the doubly occupied d orbital of Pt(PH3)2, in addition to the B-C s*-orbital, in the transition state, as shown in Scheme 7B. This bonding interaction yields additional stabilization of the transition state, to decrease the activation barrier of Eq. (6).

Scheme 7 From [31] with permission of American Chemical Society

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Reactivity of the H3X-B(OH)2 bonds (X=C, Si, Ge, or Sn) in the oxidative addition to Pt(PH3)2 is compared in Table 6. Although the oxidative addition of the B-C s-bond takes place with a substantially large activation barrier and moderate endothermicity, the oxidative addition of the other B-X s-bond occurs with significantly large exothermicity and either no barrier or very small barrier. The differences in reactivity were interpreted in terms of bond energy. The B-C bond energy is much larger than the B-Si, B-Ge, and B-Sn bond energies, while the Pt-XH3 bond becomes stronger in the order Pt-CH3H3Si-B(OH)2>H3Ge-B(OH)2> H3Sn-B(OH)2. In addition to the s-bonding interaction, the p-type interaction is the strongest in H3C-B(OH)2 and becomes weaker in the order H3Si-B(OH)2> H3Ge-B(OH)2>H3Sn-B(OH)2. However, the Pt-XH3 bond energy cannot be interpreted in a simple way. The valence orbital of ·MH(PH3)2 is at somewhat higher energy (–6.8 eV) than the sp3 orbital of all ·XH3 groups. From Eq. (3), the Pt-CH3 bond is expected to be the strongest, since the sp3 orbital of CH3 is the lowest in these ·XH3 groups. This expectation is against the smallest Pt-CH3 bond energy. The overlap between the sp3 orbital of XH3 and the valence orbital of the Pt center is the other important factor to determine the bond energy. The overlap is the smallest for CH3 and the largest for GeH3 [31]. It is likely to conclude that the Pt-XH3 bond energy depends on both orbital energy and orbital overlap. The oxidative addition of the B-B s-bond of diboron to the Pt(0) complex was believed to be involved in the platinum-catalyzed diborylation of alkyne. This reaction takes place through non-planar transition state with moderate activation barrier of 12.5 kcal/mol and the exothermicity of 10.9 kcal/mol, where the DFT(B3LYP) method was employed [29]. Though the B-B bond of (HO)2BB(OH)2 is as strong as the C-C bond of ethane [32], the oxidative addition of the B-B bond much more easily occurs than that of the C-C bond, interestingly. One reason is that the Pt-B(OH)2 bond is much stronger than the Pt-CH3 bond [32]. The other reason is that the CT interaction from the metal d orbital to the empty p orbital of the boryl group participates in stabilization of the transition state, as discussed above and Scheme 7(B). The oxidative addition of the B-B bond to the Pd analogue needs moderate activation barrier of 8.6 kcal/mol, while the reductive elimination easily occurs with nearly no barrier like the oxidative addition of methane to Pd(PH3)2. It was theoretically proposed that the diborylation of alkyne could not be catalyzed by the palladium(0) complex because of this difficulty of the oxidative addition of the B-B bond to Pd(PH3)2 [29].

Theoretical Studies of C-H s-Bond Activation and Related Reactions

55

2.6 Reductive Elimination from the p -Allyl Complex and Oxidative Addition Leading to the p -Allyl Complex The p-allyl complex plays important roles in organometallic chemistry. In this regards, the oxidative addition leading to the p-allyl complex and the reductive elimination from the p-allyl complex are worthy of investigation. The reductive elimination of CH2=CHCH2XH3 (X=C, Si, Ge, or Sn) from p-allyl palladium(II) complexes, Pd(p-C3H5)(XH3)(PH3), was theoretically investigated, where the geometries were optimized with the MP2 method and the energy changes were evaluated with MP2–MP4(SDQ) methods [33]. As shown in Fig. 7, the transition state is substantially different between the reductive elimination of CH2=CHCH2CH3 and those of the others; in the reductive elimination of CH2=CHCH2CH3, the C-C distance between methyl and p-allyl groups is still very long (2.112 Å) but the distance between C of p-allyl and Pd considerably lengthens to 2.408 Å. The geometry of the p-allyl moiety slightly changes from that of the reactant, Pd(p-C3H5)(CH3)(PH3). These geometrical features indicate that the Pd-CH3 bond becomes considerably weak but the C-C bond is not sufficiently formed in the transition state. In the transition state of the reductive elimination of CH2=CHCH2SiH3, the Si-C distance between p-allyl and SiH3 groups is moderately longer than that of the product, while the Pd-SiH3 distance becomes slightly longer than that of the reactant. In other words, the SiH3 group interacts with the C atom of p-allyl, keeping the Pd-SiH3 bond. The similar geometrical features of the transition state are observed in the other reductive eliminations of CH2=CHCH2GeH3 and CH2=CHCH2SnH3. This means that the hypervalency of Si, Ge, and Sn participates in the stabilization of the transition state. Consistent with these geometrical features, the reductive elimination of CH2=CHCH2CH3 needs much larger activation barrier (23.3 kcal/mol) than the other reductive eliminations, whereas its exothermicity (27.7 kcal/mol) is the largest in these reductive eliminations, where the energy changes were evaluated with the CCSD(T) method. The other reductive eliminations occur with moderate activation barrier of 11 to 12 kcal/mol, while the exothermicity is much smaller than that of the reductive elimination of CH2=CHCH2CH3; the exothermicity is 6.0 kcal/mol for SiH3, 1.6 kcal/mol for GeH3, and the endothermicity is 5.9 kcal/mol for SnH3. It is noted that the oxidative addition of the Sn-C s-bond of CH2=CHCH2SnH3 to the Pd(0) center can take place with moderate activation barrier, to afford the Pd(II) p-allyl stanyl complex. This result arises from the fact that the Sn-C bond is much weaker than the Si-C bond by 17.8 kcal/mol but the Pd-SnH3 bond is moderately weaker than the Pd-SiH3 bond by 7.0 kcal/mol. The other interesting feature of these reactions is observed in population changes. In the reductive elimination of CH2=CHCH2CH3, both electron populations of CH3 and CH2=CHCH2 moieties decrease and the Pd atomic population increases, as expected (Fig. 8). These features are consistent with our understanding that this is a reductive elimination reaction. In the reductive elimination of CH2= CHCH2SiH3, however, the electron population of the CH2=CHCH2 moiety mod-

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Fig. 7 MP2-optimized geometry changes of the reductive eliminations of CH2=CHCH2CH3 and CH2=CHCH2SiH3 from Pd(h3-C3H5)(XH3)(PH3) (X=C or Si). Bond length in Å and bond angle in degrees. From [33] with permission of American Chemical Society

erately increases but that of the SiH3 moiety considerably decreases. These results suggest that the Pd-SiH3 bond is covalent and the allyl-SiH3 bond is highly polarized due to the large difference in electronegativity between C and Si atoms. This is not surprising because both Pd and Si atoms are electropositive but the C atom is electronegative. The similar population changes are observed in the reductive eliminations of CH2=CHCH2GeH3 and CH2=CHCH2SnH3.

Theoretical Studies of C-H s-Bond Activation and Related Reactions

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Fig. 8 Population changes in the reductive eliminations of CH2=CHCH2CH3 and CH2= CHCH2SiH3 from Pd(h3-C3H5)(XH3)(PH3) (X=C or Si). Positive value represents the increase in electron population and vice versa. From [33] with permission of American Chemical Society

The reductive elimination of CH2=CHCH3 from Pd(p-C3H5)(H)(PH3) was also investigated theoretically [34]. This reaction very easily takes place with moderate barrier (5.6 kcal/mol) and significantly large exothermicity (27.9 kcal/mol). The much smaller activation barrier than those of the reductive eliminations of CH2=CHCH2XH3 (X=C, Si, Ge, or Sn) is interpreted in terms of the spherical 1s valence orbital of the H ligand. The reductive elimination from the Pt analogue occurs with larger activation barrier and smaller exothermicity than those of Pd(p-C3H5)(H)(PH3).Also, the reductive elimination from Pd(p-C3H5)(H)(PH3) occurs with larger activation barrier and smaller exothermicity than those of Pd(H)(CH3)(PH3)2. These results suggest that the s-bond activation leading to the p-allyl complex occurs more easily than that leading to the s-alkyl complex.

3 s -Bond Activation via Metathesis 3.1 Reliability of Computational Methods for Metathesis A comparison of various computational methods is made in the C-H s-bond activation of methane by palladium(II) formate complex, Pd(h2-O2CH)2 [9]. As shown in Table 8, the DFT(B3LYP) method provides considerably smaller activation barrier and exothermicity than the other methods such as MP2 to MP4(SDQ) and CCSD(T) methods. Although the activation barrier and the exothermicity moderately fluctuate around MP2 and MP3 levels, they converge to about 20 and 6–7 kcal/mol, respectively, upon going to CCSD(T) from MP3.

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Table 8 Binding energy (BE), activation barrier (Ea), and energy of reaction (DE) of the C-H s-bond activation of methane and benzene by Pd(h2-O2CH)2a

MP2 MP3 MP4(DQ) MP4(SDQ) CCSD(T) DFT a

BE

Ea

DE

–1.3 –1.2 –1.2 –1.3 –1.5 –0.6

17.5 19.8 21.1 21.5 20.5 13.9

–12.8 –12.8 –12.0 –8.3 –6.1 –4.9

[9].

The similar results were presented for the C-H s-bond activation of benzene by Pd(h2-O2CH)2. These results suggest that the MP4(SDQ) and CCSD(T) methods with proper basis sets provide reliable results in this reaction but we had better apply carefully the DFT(B3LYP) method to this kind of reaction. Because this reaction takes place in a heterolytic C-H s-bond scission, as will be described below, it is considered likely that the weak point of the DFT(B3LYP) method here results from the polarized electron distribution of this reaction system. 3.2 Metathesis via Heterolytic s -Bond Scission The s-bond activation via metathesis has received considerable attention recently because of its important role in the catalytic reaction. Nevertheless, the metathesis has not been well investigated theoretically except for several pioneering works. Siegbahn and Crabtree theoretically investigated the Shilov reaction in which the C-H s-bond activation of methane was achieved with a platinum(II) chloride complex [35]. They optimized geometries with the DFT method and evaluated energy changes with the DFT and PCI methods, where the micro-solvation and the bulk solvation effects were taken into consideration by adding several water molecules and the Onsarger model, respectively. As shown in Fig. 9, the Pt-H distance is 1.82 Å and the C-H distance that interacts with the Pt center is somewhat lengthened to 1.16 Å in the precursor complex. The first step is the substitution of methane for water, which gives rise to free energy increase of 10.5 kcal/mol, where the energy changes are evaluated with the DFT method. In the transition state, the C-H distance of methane considerably lengthens to 1.81 Å which is about 0.8 Å longer than that of free methane, and the H-Cl distance is 1.46 Å which is 0.14 Å longer than that of the product. These geometrical features indicate that the transition state is product-like. The activation free energy change (DG0‡ ) was evaluated to be 16.5 kcal/mol relative to the precursor complex and 27.0 kcal/mol relative to the reactant for both

Fig. 9 DFT-optimized geometry changes in the C-H s-bond activation of methane by platinum(II) chloride. Bond length in Å. From [35] with permission of American Chemical Society

Theoretical Studies of C-H s-Bond Activation and Related Reactions 59

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S. Sakaki

platinum and palladium complexes, where all substrates were treated as ideal gas in evaluation of free energy change. Mulliken population analysis shows that, although the H atom of methane becomes protonic in the product, it is not very protonic in the transition state. The oxidative addition of methane to the platinum(II) dichloride is competitive to the metathesis, while the oxidative addition is much more difficult than the metathesis in the palladium(II) analogue. The difference between the platinum and palladium complexes is interpreted in terms of either the d orbital energy or the dnÆdn–1s promotion energy. The similar C-H s-bond activation of methane and benzene by palladium(II)-formate was theoretically investigated [9] as a model of the FujiwaraMoritani reaction [2]. Geometries were optimized with the DFT method and the energy changes were evaluated with the MP2 to MP4(SDQ) and CCSD(T) methods.As shown in Fig. 10, this reaction proceeds through a precursor complex, the first transition state, an intermediate, and the second transition state, to afford a palladium(II)-phenyl complex. In the first transition state, substitution of one of the O atoms of formate for benzene takes place, to afford the palladium(II)-benzene complex. In this complex, the benzene plane is almost perpendicular to the coordinate bond, which indicates that the p-orbital of benzene interacts with the Pd center. In the second transition state, the C-H bond breaking takes place. The C-H distance considerably lengthens to 1.378 Å and the O-H distance is 1.279 Å; in other words, the H atom is at an almost intermediate position between C and O atoms. In the reaction of the platinum analogue, essentially the same geometry changes are observed. The C-H sbond activation of methane proceeds through the similar geometry changes, while the intermediate palladium(II)-methane complex is a little bit different from the benzene complex. In the methane complex, the C-H bond somewhat lengthens to 1.139 Å and the Pd-H distance is much shorter than the Pd-C distance. These geometrical features are similar to those of the agostic interaction of the C-H s-bond. The energy changes were evaluated with the MP4(SDQ) method (see previous section). In the C-H s-bond activation of benzene by the palladium(II)-formate complex, the palladium(II)-benzene complex is more stable than the reactant by 9.8 kcal/mol, and the second transition state is above this intermediate by 16.1 kcal/mol. Thus, the C-H s-bond activation of benzene easily takes place with a moderate barrier of 16.1 kcal/mol and considerably large exothermicity of 16.5 kcal/mol. In the C-H s-bond activation of methane by the palladium(II)-formate complex, the situation becomes somewhat different, as follows. The intermediate palladium(II)-methane complex is only slightly more stable than the first transition state, and the forward reaction from the methane complex to the methyl complex needs a larger activation barrier than the back reaction from the methane complex to the precursor complex. This means that the activation barrier corresponds to the energy difference between the second transition state and the precursor complex. The barrier is quite large (21.5 kcal/mol). Thus, the palladium(II)-formate complex is useful to the activation of the C-H s-bond of benzene but less useful to the activation of the C-H s-bond of methane. In the platinum(II)-formate complex, the activation

Fig. 10 DFT-optimized geometry changes in the C-H s-bond activation of benzene by Pd(h2-O2CH)2. Bond length in Å and bond angle in degrees. From [9] with permission of American Chemical Society

Theoretical Studies of C-H s-Bond Activation and Related Reactions 61

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of the C-H s-bond of benzene needs a considerably large activation barrier of 21.3 kcal/mol. This is because the intermediate platinum(II)-benzene complex is too stable. On the other hand, the activation of the C-H s-bond of methane by the platinum(II)-formate complex occurs with smaller activation barrier of 17.3 kcal/mol, because of the stronger Pt-H and Pt-CH3 bonds than the Pd-H and Pd-CH3 bonds. Note that the platinum(II)-methane complex is not very stable unlike the platinum(II)-benzene complex. A comparison between the metathesis and the oxidative addition is interesting. Apparently, the oxidative addition of the C-H s-bonds of benzene and methane to Pd(PH3)2 needs considerably larger activation barrier than the metatheses of these C-H s-bonds with Pd(h2–O2CH)2. More important is that the reductive elimination from Pd(H)(CH3)(PH3)2 and Pd(H)(C6H5)(PH3)2 easily occurs with nearly no barrier. Thus, the palladium(0) complex is not useful for the C-H s-bond activation via oxidative addition. It is of considerable interest to clarify the reason that the palladium(II) complex is reactive to the C-H s-bond activation via metathesis. This is interpreted in terms of the bond energy. As shown in Scheme 8, the C-H bond of benzene and one coordinate bond of formate are broken but the Pd-Ph and O-H bonds are formed in the metathesis. On the other hand, only the C-H bond of benzene is broken, while the Pd-Ph and Pd-H bonds are formed in the oxidative addition.Although one coordinate bond of formate is broken in addition to the C-H bond of benzene in the metathesis, the very strong O-H bond is formed in the metathesis. Because of this strong O-H bond, the C-H s-bond activation of benzene by the palladium(II)-formate complex easily takes place; in other words, the formation of this strong O-H bond is one of the important driving forces of the metathesis.

Scheme 8

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63

Fig. 11 Population changes by the C-H s-bond activation of benzene by Pd(h2-O2CH)2 and Pd(PH3)2. Positive value represents the increase in electron population and vice versa. From [9] with permission of American Chemical Society

The electron population changes are shown in Fig. 11 [9]. Apparently, the H atomic population decreases very much in the reaction, which clearly indicates that the H atom becomes protonic. On the other hand, the electron population of the phenyl group somewhat increases. In the transition state, the H atom is more positively charged than that in the reactant, while the phenyl group is more negatively charged than that in the reactant. From these electron populations, it should be concluded that the C-H s-bond activation via the metathesis occurs in a heterolytic bond scission. The similar C-H s-bond activation by platinum(II) sulfonate complex was theoretically investigated [36–38]. This is a model of the methane-to-methanol conversion by the platinum(II) complex in dry sulfuric acid experimentally reported [3]. There are two possible reaction courses in the C-H s-bond activation; one is the oxidative addition of the C-H s-bond to the platinum(II) complex and the other is the metathesis of the C-H s-bond with the Pt-OSO3H moiety. Hush et al. proposed that the C-H s-bond activation took place through the oxidative addition to the platinum(II) complex [36]. This is not surprising because the oxidative addition of methane to the coordinatively unsaturated platinum(II) complex is not very difficult, as discussed above. However, Ziegler et al. reported that the metathesis could take place with the similar activation barrier to that of the oxidative addition [37]. Recently, Goddard et al. clearly concluded that the metathesis more easily proceeded than the oxidative addition in sulfuric acid [38]. They investigated this reac-

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tion with the DFT method incorporating the solvent effects. Important is that protonation of the bi-pyrimidine ligand accelerates the metathesis and solvation effects also facilitate the metathesis. This is because the C-H bond breaking occurs in a heterolytic manner, like that of the C-H s-bond activation by Pd(h2-O2CH)2. 3.3 Metathesis via Homolytic s -Bond Scission If the X ligand is not negatively charged, the metathesis takes place via homolytic bond scission with increase in the metal oxidation state. One of such examples is the palladium-catalyzed thioborylation of alkyne: Pd(PH3)2 + C2H2 + (RO)2B-SR¢ Æ Pd(PH3)2 + (RO)2B-CH=CH-SR¢

(7)

This catalytic cycle was theoretically investigated with the DFT(B3LYP) method [39]. In this reaction, the oxidative addition of thioborane to Pd(PH3)2 does not occur like the oxidative addition of the C-H s-bond to Pd(PH3)2. This is not surprising because the Pd atom has d-orbitals at low energy. The first step is the alkyne coordination followed by the dissociation of PH3, to afford a coordinatively unsaturated species, Pd(PH3)(C2H2). This complex undergoes the metathesis with thioborane, R¢S-B(OR)2, to yield Pd(SR¢)[CH=CHB(OR¢)2] (PH3) (XV in Fig. 12). In the transition state (TSXIII in Fig. 12), the Pd-SR bond has been almost formed and the boryl group is approaching the C atom of acetylene, while the B-C distance (1.863 Å) is much longer than that of the product by 0.34 Å. The acetylene moiety considerably changes its position, while acetylene still coordinates with the Pd center. Thus, this transition state involves five-center interaction. In the intermediate (XV in Fig. 12), the Pd-O and B-C bonds are completely formed. In this intermediate, the Pd-O bond breaking takes place, to afford a three-coordinate intermediate. The activation barrier for the first transition state was evaluated to be 18.6 kcal/mol by the DFT method. The oxidation state of Pd increases by 2 in this elementary process, because two anionic ligands, SR– and vinyl groups, coordinate with the Pd center in the product. This means that the metathesis takes place with increase in the oxidation state of the metal center. It is interesting to investigate the reason why it is not the simple oxidative addition to the metal center but this type of metathesis that takes place in the Pd(0) complex. In the simple oxidative addition, the d10Æd9s1 promotion necessarily occurs to form the Pd-S and Pd-C bonds, as discussed above, which gives rise to destabilization energy. In the metathesis, however, the product is very stable because of the formation of a strong C-B bond. In other words, the formation of this C-B bond is a thermodynamic driving force, which is the same as that of the heterolytic C-H s-bond activation of benzene by Pd(h2-O2CH)2. The similar metathesis of Pd(PH3)(C2H2) with diboron, B2[(OR)2]2, was investigated by the same authors [39]. This reaction needs a considerably large activation barrier of 34.1 kcal/mol, which is much larger than that of the metathesis with thioborane. The significant

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Fig. 12 DFT-optimized geometry changes in the reaction of thioborane with Pt(PH3)(C2H2). Bond length in Å and bond angle in degrees. From [39] with permission of American Chemical Society

difference between diboron and thioborane was interpreted in terms of the hypervalency of the S atom in the thioborane. Recently, Cp2Zr-catalyzed hydrosilylation of ethylene was theoretically investigated [40]. In this reaction, two types of metatheses are proposed as an important elementary process. One is the reaction between SiH4 and Cp2Zr(C2H4), to afford Cp2Zr(H)(CH2CH2SiH3) and Cp2Zr(SiH3)(CH2CH3).As shown in Fig. 13, this reaction proceeds through a five-center transition state. In the transition state leading to Cp2Zr(SiH3)(CH2CH3), the Si-H bond moderately lengthens to 1.600 Å, but the Zr-H distance is 1.980 Å which is slightly longer than the usual Zr-H bond by about 0.13 Å. The C-H distance is still long (2.190 Å). These geometrical features indicate that the C-H bond is not formed yet in the transition state but the Zr-H bonding interaction is formed. In other words, the Si atom takes five coordinate bonds with four H and Zr atoms. This means that the hypervalency of the Si atom plays an important role in this reaction. In the other metathesis leading to Cp2Zr(H)(CH2CH2SiH3), the Si atom forms five coordinate bonds with the C atom of ethylene and four H atoms, too. It is also noted that the Si atom takes a trigonal bipyramidal structure, which is observed in a typical hypervalent system. The contour map of HOMO (Fig. 14) clearly shows that the p* orbital of ethylene overlaps with the dp orbital of Zr in a bonding manner, to form a p-back-donation interaction. The p-back-donation orbital overlaps well with the Si-H s* orbital in a bonding way. Thus, the Zr-SiH3 bond formation and the C-H bond formation occur with concomitant breaking of the Si-H bond in the transition state leading to Cp2Zr(SiH3)(CH2CH3). The similar overlap is observed in the other transition state leading to Cp2Zr(H)(CH2CH2SiH3). From

Fig. 13 DFT-optimized geometry changes in the coupling reaction of Cp2Zr(C2H4) with SiH4. Bond length in Å and bond angle in degrees. From [40b] with permission of American Chemical Society

66 S. Sakaki

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these results, it is concluded that this new type of metathesis can occur easily in Cp2Zr(C2H4) because of the strong p-back-donation interaction in the Zr(C2H4) moiety. In the reaction leading to Cp2Zr(H)(CH2CH2SiH3), the activation barrier and the exothermicity were evaluated with various computational methods, as listed in Table 9.Apparently, the DFT(B3LYP) method underestimates the binding energy of SiH4 with Cp2Zr(C2H4) and the energy of reaction. The activation barrier and exothermicity converge to 21 and 26 kcal/mol, respectively, upon going to MP4(SDQ) from MP2. Thus, the MP4(SDQ) method is considered more reliable than the DFT(B3LYP) method here. In the reaction leading to Cp2Zr(CH2CH3)(SiH3), the similar differences between the DFT(B3LYP) and the MP4(SDQ) methods are observed. The Zr center is considered to take +4 oxidation state in Cp2Zr(C2H4) in the experimental field. In this case, the oxidation state of Zr does not change at all in this metathesis. However, it is also likely to consider that the Zr center takes +2 oxidation state, because ethylene is understood to form a strong p-back donation interaction with the Zr center. In this case, the oxidation state of Zr increases by +2 by this metathesis like that of Pd in the thioboration of alkyne. Maybe, the oxidation state of Zr in Cp2Zr(C2H4) is considered to be intermediate between +2 and +4 and this metathesis is similar to the metathesis of a Pd(0) alkyne complex with thioborane. After the metathesis, either ethylene-assisted C-H and Si-C reductive eliminations or metatheses of Cp2Zr(H)(CH2CH2SiH3) and Cp2Zr(SiH3)(CH2CH3) with silane take place to afford CH3CH2SiH3, whereas the direct C-H and Si-C reductive elimination reactions do not occur [40]. Also, metathesis with silane more easily occurs with lower activation barrier and larger exothermicity than Table 9 Binding energy (BE), activation barrier (Ea), and energy of reaction (DE) of the coupling reaction of SiH4 with Cp2Zr(C2H4)a

BE

Ea

DE

(A) Leading to Cp2Zr(C2H5)(SiH3) DFT –8.2 MP2 –19.9 MP3 –15.3 MP4(DQ) –15.8 MP4(SDQ) –16.6

0.3 1.8 1.4 1.2 0.8

–24.9 –36.4 –32.5 –33.3 –35.9

(–16.7) b) (–16.5) (–17.2) (–17.8) (–19.3)

(B) Leading to Cp2Zr(H)(CH2CH2SiH3) DFT –12.4 MP2 –25.4 MP3 –19.4 MP4(DQ) –20.0 MP4(SDQ) –21.2

5.0 5.3 6.5 6.3 4.9

–17.8 –24.2 –24.4 –24.4 –26.0

(–5.4)b (1.2) (–5.0) (–4.4) (–4.8)

a b

Ref. [40]. Relative to aprecursor complex, Cp2Zr(C2H4)(SiH4).

Fig. 14 Contour maps of the HOMO of the transition state in the coupling reaction of Cp2Zr(C2H4) with SiH4. From [40b] with permission of American Chemical Society

68 S. Sakaki

Fig. 15 DFT-optimized geometry changes in the direct Si-C reductive elimination (top) and ethylene-assisted reductive elimination (middle) of C2H5-SiH3 from Cp2Zr(SiH3)(C2H5) and metathesis of Cp2Zr(SiH3)(C2H5) with SiH4 (bottom). Bond length in Å. In parentheses are relative energy (in kcal/mol; DFT) to 2A

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the direct Si-C and C-H reductive eliminations from these compounds, as shown in Fig. 15. In the transition state TSA2B-1, the Si atom forms five coordinate bonds with four H atoms and one C atom of C2H5, and the H atom forms two-electron three-center interaction with the Zr center and the silyl group. In the other transition state TSA4B-1, the Si atom forms five coordinate bonds, too, in which the Si atom takes a typical trigonal bipyramidal structure. In both transition states, the hypervalency of the Si atom plays important roles. The similar hypervalency of the Si atom was theoretically reported in the non-classical silane s-complex with transition metal element [41]. The reason why these metatheses occur more easily than the direct reductive elimination is reasonably interpreted in terms of the bond energy, as follows. In the direct Si-C reductive elimination, both Zr-CH3 and Zr-SiH3 bonds are broken and the Si-C bond is formed. In the metathesis of Cp2Zr(SiH3)(CH2CH3) with SiH4, the Zr-C2H5 and Si-H bonds are broken, while not only the Si-C bond but also the Zr-H bond is formed. Because of the formation of the Zr-H bond, the products of metathesis are more stable than those of the direct reductive elimination. The same situation is observed in the metathesis of Cp2Zr(H)(CH2CH2SiH3) with SiH4. Thus, it is concluded that the metatheses of Cp2Zr(H)(CH2CH2SiH3) and Cp2Zr(SiH3)(CH2CH3) with SiH4 occur much more easily than the direct Si-C and C-H reductive eliminations. The titanium-catalyzed hydroboration of alkenes is similar to Cp2Zr-catalyzed hydrosilylation of alkene in some cases. In the theoretical study of this reaction [42], the starting complex is not a Ti(II)-olefin complex but a Ti(II)-borane s-complex, Cp2Ti(H-Bcat), as shown in Fig. 16. This non-classical borane s-complex, Cp2Ti(H-Bcat), is not surprising, because H-Bcat coordinates well with the Ti center, as experimentally [43] and theoretically reported [44]. In my understanding, this coordination bond is essentially the same as that of agostic interaction of C-H and Si-H bonds investigated theoretically [45, 46]. The metathesis of Cp2Ti(H-Bcat) with ethylene occurs easily to afford Cp2Ti(H)(CH2CH2Bcat) with activation barrier of 5.8 kcal/mol, while the metathesis

Fig. 16 DFT-optimized geometry changes of the reaction between Cp2Ti[H-B(OH)2] and C2H4. Bond length in Å. In parentheses are relative energy (in kcal/mol; DFT) to 1a. From [42] with permission of American Chemical Society

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leading to the other possible product Cp2Ti(Bcat)(CH2CH3) needs a considerably large activation barrier of 21.0 kcal/mol. This is different from the metathesis of Cp2Zr(C2H4) with SiH4 in which two kinds of product are easily produced with very small or moderate activation barrier [40]. Although detailed analysis was not made, it is likely to consider that the empty p orbital of the boryl group participates in five-member transition state. It is noted that not only the borane s-complex but also the Ti(II)-olefin complex is a plausible candidate for the active species.

4 Miscellaneous s -Bond Activation The C-C s-bond activation that is different from oxidative addition and metathesis was experimentally [47] and theoretically [48] proposed in the ruthenium-catalyzed reaction. The p-allyl ruthenium(II) complex, Ru(CO)3(p-C3H5)L (L=H2CO or Br), undergoes coupling reaction with a carbonyl compound to afford Ru(CO)3(OCH2CH2CH=CH2)L, where geometries were optimized with Hartree-Fock, MP2, and DFT methods and energy changes were evaluated with MP2-MP4(SDQ) methods. In the theoretical study, H2CO was employed as a model of the carbonyl compound. The reverse reaction corresponds to the C-C bond activation. Typical geometry changes are shown in Fig. 17. In the transition state, the h3-allyl moiety becomes similar to the h1-allyl geometry and the C-C bond is formed between the electron-rich C atom of the h1-allyl moiety and the electron-deficient C atom of the carbonyl compound. This means that the charge-transfer interaction plays important roles in the C-C bond formation; in the reverse reaction, the C-C bond breaking occurs in a heterolytic manner. If L is absent, the coupling reaction is considerably endothermic; about

Fig. 17 DFT-optimized geometry changes in the reaction between Ru(h3-C3H5)(CO)3 and H2CO. Bond length in Å. From [48] with permission of American Chemical Society

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20 kcal/mol for Ru(h3-C3H5)(CO)3+H2CO and about 30 kcal/mol for Ru(h3C3H5)Br(CO)2+H2CO. On the other hand, the coupling reaction is almost thermo-neutral in RuBr(h3-C3H5)(CO)3 and Ru(h3-C3H5)(CO)3(H2CO); the energies of reaction is 3.6 and 3.4 kcal/mol for RuBr(h3-C3H5)(CO)3 and Ru(h3C3H5)(CO)3(H2CO), respectively. These results suggest that the C-C bond activation of CH2=CHCH2CH2OH would be achieved with the coordinatively unsaturated ruthenium(II) complex. The driving force of this reaction is considered to be the great stability of the p-allyl coordinate bond with the Ru center.

5 Several Examples of Catalytic Reaction via s -Bond Activation s-Bond activation is involved in various catalytic reactions by transitionmetal complexes. Many theoretical works of such catalytic reactions have been reported so far [49]. In this section, we wish to report recent theoretical works of catalytic reactions including s-bond activation via oxidative addition and/or metathesis. Recently, rhodium-catalyzed direct borylation of alkane with diboron was reported [50], where Cp*Rh(h4-C6Me6) (Cp*=C5Me5) was used as a catalyst. This reaction has drawn considerable interest because the C-H s-bond activation and the introduction of some functional group into alkane were achieved in one pot. The similar reaction (Eq. 8) was theoretically investigated with the DFT method [51]: CpM(CO)2[B(OR)2] + R¢-H Æ CpM(CO)2(H) + R-B(OR)2]

(8)

This reaction is considered as a model of the catalytic reaction. In this work, CpM(CO)2[B(OR)2] (M=Fe, Ru, or W) was employed as a catalyst. Interestingly, the reaction proceeds through the oxidative addition and the reductive elimination for both methane and benzene in the W complex, where the W(V) complex is involved as an intermediate. On the other hand, the Fe-catalyzed reaction proceeds in one step for both methane and benzene, where the Fe(V) species is not involved as an intermediate but the Fe center takes +V oxidation state in the transition state. Thus, the reaction is considered to be metathesis. In the Ru complex, the reaction proceeds through the Ru(V) intermediate for the C-H s-bond activation of benzene, while it proceeds in one step for the C-H s-bond activation of methane like that of the Fe complex. The differences among three metals can be interpreted in terms of the d orbital energy and/or the dnÆdn–1s1 promotion energy, as discussed above. The similar Ir-catalyzed direct borylation of benzene with diboron was recently reported experimentally [52] and its full catalytic cycle was theoretically investigated with the DFT(B3LYP) method [53]. In this reaction, the iridium(III) complex, Ir(bpy)(Beg)3 (bpy=2,2¢-bipyridine; eg=ethyleneglycolate), is an active

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species, and this species undergoes the oxidative addition of the C-H s-bond of benzene to afford an unusual Ir(V) intermediate, Ir(bpy)(Beg)3(H)(Ph), as shown in Fig. 18. From this intermediate, the reductive elimination of phenylborane easily takes place with concomitant formation of Ir(bpy)(H)(Beg)2. The rate-determining step is the oxidative addition of the C-H s-bond of benzene to the Ir(III) complex. Ir(bpy)(H)(Beg)2 undergoes the oxidative addition of the B-B s-bond of diboron to afford the Ir(V) intermediate, Ir(bpy)(H)(Beg)4, again. From this intermediate, the reductive elimination of borane easily occurs to regenerate the active species.After diboron is consumed, Ir(bpy)(H)(Beg)2 starts to react with borane to afford the other Ir(V) intermediate, Ir(bpy)(H)2(Beg)3, from which the reductive elimination of dihydrogen molecule takes place to regenerate the active species. It is clearly described that the presence of the intermediate Ir(V) complex is origin of the successful results of this interesting catalytic reaction, because the reductive elimination of dihydrogen molecule cannot occur easily from the Ir(III) complex but can easily occur from the Ir(V) complex. Also, I wish to mention the catalytic reaction which proceeds via metathesis with heterolytic s-bond activation. Hydrogenation of carbon dioxide to formic acid is one of attractive transition-metal catalyzed CO2 fixation reactions. Rh(I), Rh(III), and Ru(II) complexes were used as a catalyst [54–56]. Of those catalysts, the Ru(II)-catalyzed hydrogenation of CO2 has drawn considerable interest because of its very high efficiency. Its catalytic cycle was theoretically investigated [57]. In this catalytic reaction, the first step is the insertion of CO2 into the RuH bond, to afford the ruthenium(II) formate complex, RuH(h1-OCOH)(PH3)3,

Fig. 18 Catalytic cycle of the Ir-catalyzed borylation of benzene with diboron. Values represent Ea value calculated with the DFT method (in kcal/mol)

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as shown in Scheme 9. The second step is the metathesis of the ruthenium(II)formate complex with the dihydrogen molecule. In the metathesis, the sixcenter transition state needs a smaller activation barrier than the four-center transition state, as shown in Fig. 19. This is because the lone pair orbital of formate interacts more strongly with the H atom in the six-center transition state than in the four-center transition state, as shown in Scheme 10. In this transition state, the H atom is moving to the O atom of formate from the other H atom and it is at an almost intermediate position between the other H atom and the O atom of formate. This transition state is essentially the same as that of the heterolytic C-H s-bond activation of benzene by Pd(h2-O2CH)2 [9]. The similar metathesis was proposed in the rhodium(I)-catalyzed hydrogenation of CO2 into formic acid [58]. Although the reductive elimination of formic acid from Ru(H)(h1-OCOH)(PH3)3 does not occur, the reductive elimination of formic acid takes place from [RhH(h1-OCOH)(PH3)2(H2O)]+ in the Rh(III)-catalyzed hydrogenation of CO2 [59]. The differences among Ru(I), Rh(III), and Ru(II)

Scheme 9

Scheme 10

Fig. 19 DFT-optimized geometry changes of the s-bond metathesis of ruthenium(II)-formate complex with dihydrogen molecule. In parentheses are relative energies (in kcal/mol; DFT) to 3b

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complexes are discussed in terms of the M-H bond energy; because the Rh(I)H and Ru(II)-H bonds are strong, it is not the reductive elimination but the metathesis that takes place in the product release step. On the other hand, the reductive elimination takes place in the Rh(III)-catalyzed hydrogenation, because the Rh(III)-H bond is weak. In conclusion, the theoretical studies of the s-bond activations via oxidative addition and metathesis are reviewed here.Although the detailed knowledge of the s-bond activation reactions have been presented theoretically in the last decade, I wish to mention that there are still several weak points, such as neglect of solvation effects, use of simple and small ligand as a model of a real ligand, substitution of a large substituent for H and/or small substituent, and difficulty of incorporation of non-dynamical correlation effects. I hope that theoretical study will solve these weak points in the next decade and will present useful proposals as to what transition-metal complexes are useful for the s-bond activation to construct catalytic reactions.

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Topics Organomet Chem (2005) 12: 79– 107 DOI 10.1007/b104399 © Springer-Verlag Berlin Heidelberg 2005

Enantioselectivity in the Dihydroxylation of Alkenes by Osmium Complexes Galí Drudis-Solé · Gregori Ujaque (

) · Feliu Maseras (

) · Agustí Lledós

Unitat de Química Física, Departament de Química, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain [email protected], [email protected]

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4 MM Studies on the Enantioselectivity . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract The asymmetric dihydroxylation of olefins by osmium tetroxide is one of the most useful reactions in organic synthesis. Apart from the enormous experimental work, an extensive theoretical effort has been applied to study this reaction. A vast number of computational methods like QM, MM, Q2MM, QM/MM, and those commonly applied to enzymatic studies like docking, Molecular Dynamics (MD) and Genetic Algorithms (GA) have been employed. The computational studies performed to date in order to understand the mechanism of this reaction are reviewed here, with special focus on those directed to study the origin of the high enantioselectivity. Keywords Catalysis · Asymmetric dihydroxylation · QM/MM · Computational chemistry · Enantioselectivity

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1 Introduction The osmium-catalysed dihydroxylation of olefins is a powerful method for the enantioselective introduction of chiral centres in organic substrates [1]. Its importance is remarkable because of its common use in organic and natural product synthesis, due to its capability of introducing two vicinal functional groups in hydrocarbons with no functional groups [2]. In 2001, Prof. Sharpless was awarded the Nobel Prize in chemistry for his development of asymmetric catalytic oxidation reaction of alkenes, including his outstanding achievements in the osmium asymmetric dihydroxylation of olefins. The initial work on the reaction of osmium tetroxide with olefins was carried out by Hofmann early in the last century [3, 4]. In the 1930s, Criegee [5] showed that the addition of a base, such as pyridine, accelerates the reaction rate. Later on, catalytic variations of the reaction were developed employing relatively inexpensive reagents for the reoxidation of the osmate species [6]. More recently, several advances were achieved to immobilize the catalyst and to improve the catalytic oxidation chain. In particular, recent work couples the oxidation of the osmium(VI) compound to a green terminal oxidant such as air or hydrogen peroxide [7–9]. It was in the 1980s when the effort carried out in the Sharpless group led them to introduce stereoselectivity on this reaction [10]. Using quinuclidine derivatives (like acetate ester of cinchona alkaloids) as chiral ligands, they were able to obtain moderate enantiomeric excesses. Other ligands were developed in other laboratories, and good results were obtained from those based on chiral diamine ligands. Nevertheless, a breakthrough in the stereoselectivity of this reaction was not achieved until the discovery of the so called second generation ligands [11, 12]. They have two cinchona ligands linked by an heterocyclic spacer, and in fact, most of the theoretical work here reviewed deals with this type of ligands. Theoretical chemistry methods are very helpful in determining reaction mechanisms [13–16]. In the following sections there is an overview of the theoretical and computational studies performed on this reaction. We will first review the theoretical work made to help establishing the reaction mechanism, that had remained controversial for a long time.A description of the mnemonic device proposed largely from experimental data to predict the major enantiomeric product of the reaction is also presented. After that, the application of different methods to explain the origin of the enantioselectivity is discussed. The next two sections are devoted to reviewing the semiquantitative studies based on pure Molecular Mechanics (MM) calculations, and on the application of enzyme-based techniques like docking (using Genetic Algorithms (GA)) and Molecular Dynamics (MD) methods. The last two sections are dedicated to theoretical methods providing more quantitative results, reviewing thus the application of Quantum Mechanics to Molecular Mechanics (Q2MM) methods first, and the application of the hybrid Quantum Mechanics/Molecular Mechanics (QM/MM) methods later on. The chapter ends with some concluding remarks.

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2 Reaction Mechanism The asymmetric dihydroxylation of olefins is a unique reaction due to its outstanding selectivity and broad scope. Nevertheless, despite the large amount of experimental work carried out on the reaction, it was not since the synergistic experimental-theoretical work was done that an answer for the reaction mechanism was generally accepted. Two were the major mechanistic proposals for the reaction: the [3+2] mechanism where the five-membered ring is directly formed through a concerted cycloaddition, and the stepwise [2+2] mechanism where the initial cycloaddition leads to a four-membered ring osmaoxetane, following a rearrangement to give the five-membered ring (see Fig. 1). The first theoretical study on the proposed reaction mechanisms of the dihydroxylation of alkenes by osmium tetroxide was performed in 1986 by Jorgensen and Hoffmann [17]. In that work, the authors carried out a theoretical study from a frontier orbital point of view. They used symmetry arguments and extended Hückel [18] calculations to perform their analysis. The authors claimed in their work that it is not possible from a qualitative orbital argument to discard any of the two proposed mechanisms. Nevertheless, the authors favoured the [3+2] mechanism over the [2+2]. They based their choice on several factors: the frontier orbitals in osmium tetroxide are set up for a [3+2] cycloaddition reaction, whereas a geometric distortion of osmium tetroxide would have to take place for the [2+2] cycloaddition, followed by a second deformation back to the symmetric osmium ester intermediate. This might be expected to be unfavourable due to the principle of least motion. The addition of a base (generally amines) has been proved to increase markedly the reaction rate. To evaluate this effect, the authors studied how the addition of two base molecules to OsO4 changes the frontier orbitals of the catalyst. Two different geometries, one with both amines occupying cis positions, and the other with both amines in trans positions were evaluated. The energies of the frontier orbitals after distortions are quite similar for both geometries,

Fig. 1 Schematic representation of both mechanistic proposals: the concerted [3+2] and the stepwise [2+2] mechanisms

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suggesting that both ligand dispositions could be equally probable. Using a frontier orbital analysis, the authors stated that the increased reactivity by adding amine to the system comes mainly from a decrease in the energy difference between the HOMO and the LUMO. They also investigated the catalyst when it was formed by one osmium tetroxide molecule and one amine molecule. The structure is trigonal-bipyramidal with an oxygen and the amine in apical positions, and the remaining three oxygens occupying the equatorial positions. The calculations indicated a pattern of the frontier orbitals similar to the previous case. Latter studies using ab initio [19] or DFT [20] calculations were not able to discern between the two proposed mechanisms. In the first case, the theoretical study on different model systems showed that the [2+2] mechanism was a plausible mechanism based on thermodynamics of the studied reactions. The DFT calculations were carried out on related species, using as oxidant a ReO4, and were not able either to discern between both mechanisms. The controversy about the reaction mechanism was finally solved after the thorough work of several experimental [21–24] and theoretical [25–30] research groups. All the theoretical works presented basically the same results: the energy barrier is ca. 50 kcal/mol for the stepwise [2+2] mechanism, whereas the energy barrier found for the concerted one was lower than 10 kcal/mol. Hence, a scientific consensus emerged considering the concerted [3+2] as the reaction mechanism [31]. Despite this general consensus, several questions still remained open. For instance, how does the ligand influence the free energy profile relative to the reaction of olefins with OsO4 and OsO4(NR3), or how can one explain the experimentally observed variation of the reaction constant over the temperature? The latter, for the case of the second generation catalysts, was explained by the theoretical characterization of the required intermediate [32]. Further investigations on related species were able to show that in some special cases, and using other metal oxides, the activation barrier for the stepwise mechanism is lower in energy than for the concerted one [33, 34]. Other mechanisms, such as a diradical mechanism, have also been discussed [35] and, interestingly, it has been shown that in those cases where a stepwise mechanism may be feasible, it would proceed through the diradical instead of the [2+2] mechanism.

3 Mnemonic Device for Enantioselectivity Given the importance of this reaction to generate enantioselectively diols oxidising a double bond, it is very useful to be able to predict the stereochemical outcome of the asymmetric dihydroxylation. With this aim, and based on the experimental results, the Sharpless group developed a mnemonic device capable of predicting the enantiomeric product [36] for a given olefin.

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Fig. 2 Mnemonic device for prediction of the asymmetric dihydroxylation selectivity

This mnemonic device, that was developed for the second generation catalysts, has been updated several times [11, 36–38]. As shown in Fig. 2, they proposed that the southeast quadrant (SE) and the northwest (NW) quadrant of this device presented steric barriers. In the southeast quadrant the crowding is severe, strongly disfavouring all substituents larger than hydrogen, whereas in the northwest quadrant small substituents are allowed (though not phenyl groups). The southwest (SW) quadrant is the major attractive area, where the aromatic substituents are usually attracted, whereas the northeast (NE) quadrant is a relatively open area. Another important feature of this reaction is its enzyme-like behaviour. The kinetic studies on the reaction mechanism of the second generation catalysts support the idea of the existence of a binding pocket. This binding pocket is believed to be formed by the osmium tetroxide and the aromatic moieties of the catalyst. Depending on the orientation of the olefin inside the binding pocket, two different pockets, usually labelled as Corey’s and Sharpless’ pockets, have been defined. The main differences between both pockets are the orientation adopted by the olefin having the terminal carbon atom of the double bond bonded to an equatorial or to the axial oxygen, and the role of the quinoline B, being involved or not the in binding pocket of the catalyst (see Fig. 3). The use of computational techniques is very helpful in order to give an explanation at the molecular level of the controversies raised in the explanations of the experimental results, as will be shown in the following sections.

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b

Fig. 3a, b Schematic representation of: a the Corey; b the Sharpless binding pockets

4 MM Studies on the Enantioselectivity In 1994 Sharpless and coworkers carried out a molecular mechanics (MM) study on this reaction [39]. The amine ligands employed in their calculations were those developed in their own laboratory, cinchona alkaloids. They carried out the theoretical studies supposing that the mechanism was [2+2], since at that time, the mechanism was not completely understood, and their experimental work suggested that the mechanism was the [2+2]. The calculations were done using the MM2 force field, including new parameters developed for this type of complexes. A new set of parameters were developed for the metal catalyst, concretely for an osmium tetroxide with a tertiary amine coordinated. They developed these parameters based on X-ray structures and DFT calculations on related systems.As they pointed out in their paper,“the scarcity of data makes quantitative predictions from these models unreliable. The purpose of this paper is to qualitatively identify the factors responsible for the observed face selectivities and rates in the AD reaction”. In their work, the authors initially presented the study of dihydroxylation of styrene by osmium tetroxide using dihydroquinidine 4-chlorobenzoate (DHQD-CLB) as the amine ligand. This ligand belongs to the so-called first generation of ligands, where simple esters or ethers of the parent alkaloids were used; the second generation ligands are made by two alkaloid units linked by an heterocyclic spacer (Fig. 4). In order to study the reaction, they defined all the different pathways for approaching the olefin to the catalyst. They are depicted in Fig. 5a. There are three ways of approaching the olefin to the osmium tetroxide, each one directed to one of the equatorial oxygens. Thus, the different isomers of the oxetane complex can be created from the osmium tetraoxide-cinchona ligand complex by adding the olefin in a [2+2] fashion, therefore distorting an equatorial oxo

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Fig. 4 Representation of the first and second generation ligands

group ~30° either clockwise of counterclockwise around the N-Os-O axis (Fig. 5b). Hence, depending on the region of entry of the olefin A, B or C, three rotameric forms of the four diastereomers are created. Moreover, depending on the orientation of styrene it can be in four different positions yielding a total of 12 main isomers of the intermediate in this reaction. For a chiral ligand, there are 12 additional diastereomers with the olefin attacking the other side of the equatorial meta-oxo bond; in Fig. 5b the olefin approaches from the side of the R¢ substituent, but it could also approach from the side of the R substituent. These diastereoisomers were not considered because apparently the difference with the previous are not large enough to explain the observed enantioselec-

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a

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Fig. 5a, b Definition of the possible approaching pathways of the olefin to the catalyst within the [2+2] mechanism: a top view along the O-Os-N axis showing the three different “regions” of entry of the olefin (A, B, C); b side view perpendicular to the O-Os-N axis showing the four possible “orientations” of the olefin substituent (I, II, III, IV)

tivity. The point where the selectivity is actually decided is the transition state, and therefore this would be the most interesting point to study. Nevertheless, in this work the authors studied the 12 selected diastereoisomers (intermediates) of the reaction, because the method used did not allow the location of transition structures. The obtained results were in good agreement with experiment, where the major observed product is the R product, with an ee of 71% [40]. Calculations showed that the most stable diastereomer corresponds to an isomer leading to the R product. The second lowest energetic isomer, with a relative energy of 1 kcal/mol, also gives the R product. The most stable isomer giving the S product is slightly higher than 1 kcal/mol with respect to the best R isomer. To clarify the origin of the differences among the diastereomers the authors analysed the main interactions between the olefin and the catalyst. The calculations revealed that there is a stabilization by the interaction of the styrene phenyl ring with the chlorobenzoate moiety of the ligand; this stabilization is only available for those conformations approaching by region B. In the approach from the two other regions, A and C, the quinoline moiety cannot significantly stabilize the intermediate through stacking interactions with the phenyl substituent. These results are also in concordance with previous kinetic studies [38] where the same group showed that the reaction rate was highest when large aromatic groups, which can experience strong stacking stabilization, were present in both the ligand and the substrate. The enantioselectivity of the dihydroxylation reaction improved dramatically when the second generation ligands (dimeric ligands) were developed [11, 12]. The best known examples, shown in Fig. 4, are the bis(dihydroquinidinyl)phthalazine [(DHQD)2PHAL] and the bis(dihydroquinidine)pyridazine

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[(DHQD)2PYDZ] ligands, developed at the research laboratories of Sharpless and Corey, respectively. Experimental investigations show that when one of the dihydroquinidine groups is replaced by another non-basic group, thus not being able to bind to OsO4, the effectiveness of the ligand is retained, and sometimes the results are even improved [41]. Therefore, although these ligands present an apparent C2 symmetry, these results indicate that only one of the alkaloids units of the ligand is needed to accomplish the asymmetric dihydroxylation reaction. One of the most interesting features of this type of ligands is that they present a binding cleft. In the conformational analysis of the OsO4(DHQD)2PHAL system, Norrby et al. observed that despite the large number of conformations a priori possible for this system, only a few variations of this U-shape conformation were found [39]. This U-shape conformation is formed by one quinoline in one side, the heterocyclic spacer at the bottom, and the OsO4 unit and sometimes the other quinoline at the other side (see Fig. 3). In the computational MM study of the dihydroxylation of styrene by OsO4(DHQD)2PHAL, Norrby et al. show that in their postulated intermediate, the binding cleft is formed by the OsO4 unit, one of the quinoline units and the phthalazine ring (Fig. 6). The particular shape adopted by the second generation ligands allows the interactions between the olefin substituents and the alkaloid ligands to become much more efficient. Thus, for the case of styrene, it experiences attractive face-to-face interactions with the phthalazine group, and edgeto-face interactions with one of the methoxyquinoline groups. They compared both conformations, those proposed by Sharpless and Corey, finding that the

Fig. 6 The intermediate in the asymmetric dihydroxylation of styrene adopting the [2+2] mechanism, highlighting the function of each of the parts of the catalyst

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Sharpless one is lower in energy. Subsequent calculations using more elaborated methods by the same authors and others (see below) show that both conformations are generally quite close in energy, especially in the case of styrene. Hence, despite assuming the [2+2] mechanism for the reaction, the application of molecular mechanics methods was able to rationalize qualitatively the origin of enantioselectivity. Following their reasoning, it is governed mainly by the combination of the stabilizing stacking interactions between the substituents of the olefin and the aromatic moieties of the catalyst, and the repulsive interactions between the oxetane ring and the group where the chirality of the ligand is defined. For the second-generation ligands, the stacking interactions are more favourable due to its enzyme-like binding pocket structure. MM studies were also carried out by Corey and co-workers [42] in order to support their mechanistic proposals according to the [3+2] mechanism. The asymmetric dihydroxylation of a set of allylic 4-methoxybenzoates by OsO4· (DHQD)2PYDZ was analysed. In their calculations the catalyst adopted a U-shape conformation. They performed the analysis on a series of allylic 4methoxybenzoates representative of different olefin classes like allylic amides, esters, thioesters and ketones, homoallylic 4-methoxyphenyl substituted ethers, and others. They performed an analysis using CPK models based on MM results. The main conclusions can be summarized as follows: the substrate has a suitable binding group (an aromatic group) to favourably interact with the U-shape binding pocket of the catalyst, and all the allylic studied families have an accessible s-cis conformation of the substrate that places the suitable binding group in the proper spatial orientation to interact with the catalyst.

5 Docking, Genetic Algorithm and MD Studies With the intention of developing a new computational tool to predict the stereochemical outcome of asymmetric reactions, Chapleur and co-workers decided to study the Sharpless asymmetric dihydroxylation of olefins [43]. With this aim, the authors made use of techniques that were principally developed for drug-design studies. These techniques are able to predict the position of a ligand in the active site of a protein and to evaluate its binding affinity [44, 45]. Hence, since many catalyst-substrate complexes can be formally viewed as ligand-receptor complexes, the same procedures used for enzymes as flexible docking methods, could be, in principle, applicable to these systems. Consequently, the authors designed a protocol based on genetic algorithms [46] and molecular mechanics to study and explain the observed enantioselectivity of asymmetric reactions. Due to the enzyme-like behaviour presented by the olefin-catalyst system in the asymmetric dihydroxylation of olefins using the second generation catalysts, this reaction was an adequate candidate to be studied by this procedure. Hence, this protocol was applied to the study of a set of mono-, di-, and tri-sub-

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Fig. 7 Olefins studied using the procedure developed by Chapleur and co-workers

stituted olefins, with different kinds of substituents. The studied olefins are shown in Fig. 7. In some particular cases, the product of the asymmetric dihydroxylation does not follow the prediction of the mnemonic device. They also tried to rationalize the mnemonic device, and why some olefins do not follow its predictions. In the protocol developed by Chapleur and coworkers the selected function to calculate the free energy was similar to that used in docking programs: G = Gsolvation + EMM – TSsolute In such a way, they were somehow including the solvent and entropic effects. The authors took the [3+2] mechanism as the reaction mechanism. The geometry of the transition state of the core of the systems was kept frozen during all the calculations (similarly to the transition state force field calculations on this

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reaction previously performed in Houk’s group (see below)). The authors also assumed that the complex formation was reversible and the facial selectivity was controlled at the binding stage. The ratio of products formed should be determined by the difference between the free activation energies, DDG. This double difference would cancel the inherent errors associated with the approximations and with the force field parameterisation. With these conditions, a genetic algorithm was developed in order to obtain the most stable conformations for each of the four approaching geometries of the olefin to the catalyst. The energy function was the one described above, and the genes were made from the rotatable torsion angles. In Fig. 8 there is a schematic representation of the genetic algorithm as implemented by the authors. To check the quality of the method, two different olefins were initially tested. Both selected olefins had been previously studied by other research groups

Fig. 8 Flow chart of the Genetic Algorithm developed by Chapleur and co-workers

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using different methodologies. The results from the genetic algorithm were in agreement with the previous results, giving one of the olefins in the Corey’s pocket, and the other in the Sharpless’ pocket, therefore validating the developed protocol. Moreover, the quality of the protocol was corroborated by its reproducibility since the same minima were located regardless of the initial population. In all cases, the major predicted enantiomer matches the experimentally observed one. Throughout the study, only two main conformations were found to be energetically accessible. They correspond to the so-called Corey’s and Sharpless’ pockets. In both, the conformation of the catalyst is essentially the same, though the orientation of the olefin inside the binding pocket changes dramatically. In some particular cases, a different conformational mode is found, which roughly corresponds to a combination of both; the catalyst adopts a conformation similar to the Sharpless pocket, whereas the olefin is found in a conformation similar to that of the Corey’s pocket. The fact that depending on the olefin the conformational mode adopted can be one or the other had been already suggested by Norrby et al. in their Q2MM studies (see below). On the basis of this work, Chapleur and co-workers tried to rationalize the mnemonic device initially proposed by Sharpless based on experimental work [36]. The authors identified the role of each part of the catalyst as shown in Fig. 9. One of the attractive areas can be related to the hydrophobic or stacking interactions with one of the quinolines of the catalyst, whereas the other corresponds to the same kind of interactions with the phthalazine ring. In addition, a second role is attributed to the phthalazine: it has an attractive interaction with one of the substituents but it clashes with the other substituent bonded to the same carbon atom. Depending on the olefin, the lowest energy conformation gives rise to one model or the other (Corey’s and Sharpless’ pockets), and in some cases the energetic difference is smaller than 1 kcal/mol. In most cases, the predicted enantiomer by calculation is the same as that predicted by the mnemonic device, and that found experimentally. Nevertheless, in the case of D-xylose the asymmetric dihydroxylation led to the opposite diol to that predicted by the a

b

Fig. 9a, b Rationalization of the Sharpless mnemonic device

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mnemonic device. In this case, the lowest energetic conformation was that with the olefin in the Sharpless pocket, but with the terminal olefin carbon atom reacting with an equatorial oxygen. The tribenzylated xylopyranoside core was found to be too large to fit into the binding site. The olefin substituent interacts with both quinolines and the phthalazine ring. In another case where the mnemonic device does not work, the dihydroxylation of the (E)- and (Z)- methyl enol ethers of benzoin, the R-a-hydroxyketone enantiomer was found as the major product in both cases, though both olefins cannot match the mnemonic device at the same time. The calculations show that the most stable conformation for each of the olefins had a different orientation inside the binding pocket, one resembling the Sharpless pocket and the other the Corey’s pocket, but both giving rise to the same R enantiomer. In order to give some quantitative predictions using this procedure, the authors made some assumptions such as, for instance, that the reaction takes place only in the presence of the ligand, and that no reaction happens in solution. Nevertheless, the most significant assumption was to compute the ee only from the energy of two conformations, one leading to the R product and the other leading to the S product. All other computed conformations were neglected in the calculation of the ee. Despite these significant approximations (especially the last one) the calculated ee agree reasonably well with the experimental values (see Table 1). In order to check the convergence criterion of the developed protocol, two separate runs were performed following the same protocol for each of the Table 1 Experimental and computed ee using the procedure developed by Chapleur

Olefin

Observed ee

Mnemonic device

Predicted ee

1 2 4 6 7 8 5 9 10 11 12 13 14 15 16 17 18

98–R 98–R 78–S 97–R 57–R 53–S 98–R 98–2R,3S 60–2S,3S 97–S,S 79–R 72–R,R 90–R,R 69–R 98–R 90–R 99–R

R R R R R S,R R 2S,3R S,S–R,R S,S R R,R R,R R R R–S R–S

49–R 74–R 66–S 90–R 53–R 59–S 99–R 98–2S,3R 48–2S,3R 99–S,S 99–R 99–R,R 95–R,R 9–R 99–R 83–R 99–R

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olefins. The results were mostly the same, finding slightly more energetically favoured conformations for two olefins. These results, compared to those obtained using a Q2MM method, give comparable results (see below); the authors presented this fact as an indication that keeping the reacting centre frozen may not be a severe approximation. Decomposition of the total free energy difference into the molecular mechanics and solvation energies also suggests that the latter are playing a role in the catalytic process. In previous work by the same group [47], and using a different computational protocol, the authors were interested in explaining the reversal of enantioselectivity observed for some D-xylose olefins (4 in Fig. 7), according to the mnemonic device. In this preliminary work, the authors used techniques based on the MD methods. The authors performed MD simulations assuming the [3+2] mechanism as the operative one. In order to check the different possible orientations of the olefin in the binding pocket of the catalyst, a docking analysis was first performed [48]. The authors utilised a flexible docking procedure, allowing flexibility on both, the ligand (the olefin) and the catalyst (the alkaloid), choosing the simulated annealing as a search algorithm. The authors studied the asymmetric dihydroxylation of three olefins, two that had been already studied in order to validate their method, and a D-xylose to investigate the origin of its reversal enantioselectivity. In the case of allyl 4-methoxybenzoate, the results obtained from these calculations showed that the olefin fits well in the Corey’s pocket [42, 49–51]. The aromatic ring is located in the U-shape cavity formed by the catalyst interacting with both of the quinoline rings of the catalyst. Moreover, the allyl has the s-cis conformation also proposed by Corey based on MM2 calculations [49] (see above). In the other test case, in contrast, the phenyl ring of styrene is placed parallel to one of the quinoline rings of the catalyst. This result is explained by the authors by the fact that for allyl 4-methoxybenzoate the ring and the double bond are more separated in distance compared to styrene, allowing therefore an interaction with the quinoline ring in the same side of the osmium tetroxide. The model here obtained is in full agreement with that of Maseras and coworkers using a QM/MM method [52] (see below). The reaction of D-xylose, where the OH have been protected by OR groups (R=Bzl), using (DQDH)2-PHAL as the catalyst ligand was also investigated using the same procedure described above. In this case, and in contrast to the two other olefins studied, the U-shape of the catalyst is not retained. The main stabilizing interactions are between the aromatic rings of the benzyl protecting groups of the sugar and the methoxyquinoline rings of the catalyst. This could also explain the role of aromatic protecting groups for a good diastereoselectivity in the dihydroxylation of these allyl compounds containing aromatic rings as protecting groups. In contrast, the efficiency of using cyclohexanoyl protecting groups should be because of simple hydrophobic interactions. The use of docking procedures and molecular dynamics simulations, despite the severe assumptions made to accomplish the results, is able to predict the

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right enantiomer. Nevertheless, no quantitative approximation about the enantiomeric excess can be given, even though a fast prediction of the major enantiomer as well as a semiquantitative estimation of the ee can be achieved by using genetic algorithms as a conformational tool. The mnemonic device was rationalized by means of the two binding pockets resembling those proposed by Corey and Sharpless, respectively.

6 Q2MM Studies Theoretical studies using transition state molecular mechanics force fields were initially carried out in the group of Prof. Houk [53]. In that work, they studied the stereoselectivities of the dihydroxylation of alkenes by chiral diamine complexes of osmium tetroxide. In order to provide enantioselectivity to the reaction, in the late 1980s several groups developed their respective diamine ligands, obtaining excellent results. Houk and co-workers performed a computational evaluation on the mechanism using the diamine ligands developed by Tomioka [54], Hirama [55] and Corey [56], respectively. These amine ligands are shown in Fig. 10. In their work, Houk and coworkers applied the so-called “MM2 transition structure modelling”, a method originally developed in the same group [57]. At the time this work was performed, the reaction mechanism was not yet established. Nevertheless, envisioning the future, the authors assumed that the transition state was the symmetrical five-membered ring. The MM2 transition structure model developed to study this reaction, was constructed based on geometrical information from X-ray data and ab initio calculations of osmates and other OsO4-amine complexes. The parameters for the alkene moiety were adapted from the transition structure of the ethylenefulminic acid reaction [58]. The geometry around the Os centre was taken from the X-ray structure of an osmate ester [59]. The Os centre, the two axial oxygens, the two nitrogens from the amines, and the two equatorial oxygens along with the incoming carbon atoms from the double bond were kept frozen during the optimisations.

Fig. 10 Schematic representation of the chiral diamine ligands developed for the enantioselective dihydroxylation of olefins by Tomioka, Hiyama and Corey

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The dihydroxylation of several olefins by each of the chiral diamines developed by the groups of Tomioka, Hirama and Corey was evaluated. The DE obtained by the theoretical calculations were directly compared to the experimental DG between the R and S enantiomers. The theoretical predictions reasonably agree with the experimental values. For the calculation on the Tomioka diamine ligand, the calculated stereoselectivities are nearly additive, with transdisubstituted alkenes giving double stereoselectivity compared to the monosubstituted alkenes. In general, the energetic differences between one or the other enantiomer adducts are explained by the non-equal steric interactions between the olefin substituents and the diamine ligand. Calculations modelling the Hirama and the Corey chiral diamines were also performed, giving also a reasonable agreement between the calculated and experimental values. In 1999, Norrby, Houk and co-workers used a more elaborated Q2MM method [60] to broaden their previous studies on the asymmetric dihydroxylation reaction [61]. They used QM calculations on several similar reactants to find the transition state, and used these parameters to build up an unbiased molecular mechanics force field. The most important improvement is that with this method they were able to calculate transition states using the developed force field. A large set of QM transition structures and energies were used to develop the parameters for the transition states. Several were the approximations carried out during the MM parameter development. First of all, the true transition states present an opposite variation of the C-O forming bonds than that expected for a minimum: these bonds have shortened their lengths in the transition states for substituted alkenes compared to the unsubstituted ones. The tentative solution of the authors was to introduce a large artificial eigenvalue for the normal mode corresponding to the reaction coordinate [39, 62].Another important structural parameter is the rotation about the Os-N bond, the bond between the osmium tetroxide and the cinchona alkaloid. For the amine complexes, the N-H bonds are eclipsed with the Os=O bonds [25–28], whereas for the tertiary amine complexes these bonds are staggered [63, 64]. The authors overcame this issue by including data with the correct orientation in the reference date set. Hence, by introducing the proper parameters for a correct description of the van der Waals and electrostatic interactions, the conformational preferences for each of the complexes were well described. The selectivities were calculated using the Boltzmann distribution, based on the energies of the most stable conformations. The authors performed a conformational analysis for each of the 12 different pathways of approaching of the olefin to the osmium tetroxide. They combined two techniques, the pseudo-systematic Monte Carlo [65] to explore the entire conformational space, and the Low Mode [66] searching to explore exhaustively a local region of the potential energy surface (Table 2). The enantioselectivities obtained by this procedure correlate very well with the experimental values (Table 2). For all the presented cases the enantiomer predicted corresponds to the experimentally observed one. In addition, the pre-

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Table 2 Experimental and calculated ee using a Q2MM method

Olefin

DHQD ligand

Calculated ee

Observed ee

1-Phenyl-cyclohexene Styrene b,b-Dimethyl styrene B-Vinyl naphthalene trans-Stilbene tert-Butyl ethene a-Methyl styrene cis-b-Methyl styrene Styrene Styrene tert-Butyl ethene b-Vinyl naphthalene Styrene a-Methyl styrene trans-Stilbene

CLB CLB CLB CLB CLB CLB CLB CLB MEQ PHN PHN PHAL PHAL PHAL PHAL

91 70 72 94 98 70 65 78 94 98 89 100 97 99 100

91 74 74 88 99 44 62 35 87 78 79 98 97 94 100

dicted enantioselectivity is within a few percentage points of the experimentally observed values. Looking at the origin of the enantioselectivity, the authors analysed the two pathways proposed by Corey [21] and Sharpless [2] for each of the studied substrates to explain the enantioselectivity (Fig. 3). Depending on its substituents, the substrate orientates following one given path, though sometimes they are quite close in energy (<1 kcal/mol). For the case of styrene, the authors arrive to the same conclusions as those obtained on the same substrate in QM/MM studies (see below [52]). In the case of trans-disubstituted alkenes they use both pockets for binding, having one of the substituents interacting with one of the quinolines, and the other with the heterocyclic spacer (PHAL for Sharpless cinchona alkaloid). These results are in very good agreement with the experimental observation that trans-disubstituted alkenes are the best substrates for the asymmetric dihydroxylation reaction, both in terms of reaction rate [67] and enantioselectivity [2]. The authors extended the analysis to the first generation ligands. They showed that, for these ligands, both pockets are used in the interactions with the substrates. Only very small preferences are found for one over the other. In this case, however, the preference for one or the other pocket also depends on the amine ligand itself. In a subsequent work by Norrby et al. [68], the kinetics of the asymmetric dihydroxylation of a set of trisubstituted alkenes was studied experimentally and computationally using the same Q2MM procedure. The authors used in their work a second generation catalyst, the OsO4·(DHQD)2PHAL species. This work also allowed them to introduce some refinement to the mnemonic device previously proposed by Sharpless [11, 36–38].

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Fig. 11 The updated mnemonic device describing the moieties of the catalyst involved

In this new analysis the authors were able to assign which parts of the catalyst are involved in each of the regions of the mnemonic device (Fig. 11). The most sterically demanding region, the SE corner, remains the same in the updated mnemonic device. The NE corner now becomes an attractive region. These attractive interactions are provided by the spacer of the catalyst and corresponds to the previously described Sharpless’ pocket. The SW corner is also an attractive region. In this case, the attractive interactions are made available by one of the quinolines of the catalyst, and correspond to the previously described Corey’s pocket. The last region, the NW corner, was originally proposed to provide moderate steric repulsion. The authors, however, proposed that this region is a free region and can accommodate any substituent from the alkene. Indeed, the authors propose that if the substituent is long and flexible, it can wrap around the catalyst and experience moderate steric stabilization. In order to show the quality of the updated mnemonic device, the authors compared the experimental results with those obtained computationally for a set of tri-substituted olefins with one large substituent and two methyl groups. By comparing the reactivity of these olefins, the interactions in each of the positions of the mnemonic device can be elucidated. The obtained results agree with the computational predictions; therefore, the new mnemonic device can rationalize the experimental results from all alkene classes, and improves the predictivity for tri-substituted alkenes.

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7 QM/MM Studies As has been already shown in the previous studies, in order to introduce the asymmetry of the reaction in the calculations, it is necessary to introduce a chiral amine ligand (e.g. cinchona alkaloid) coordinated to the osmium centre. The application of QM/MM methods, concretely the IMOMM(B3LYP:MM3) method [69] to study the asymmetric dihydroxylation of olefins, was carried out by Maseras and co-workers. Using this method, and following their previous studies on this reaction [32, 70], the authors performed a quantitative theoretical characterization of the origin of the enantioselectivity for this reaction. In these investigations, they analysed the dihydroxylation of olefins having aromatic or n-aliphatic groups as substituents using OsO4·(DHQD)2PYDZ as catalyst. The partitioning of the system into QM and MM regions, was done as shown in Fig. 12. As far as the catalyst is concerned, the OsO4·NH3 moiety was described at B3LYP level, whereas the rest of the amine ligand was described at MM3 level. For the olefins, different QM regions were adopted depending on the olefin class. In the study of olefins with aromatic substituents, CH2=CH2

a

b Fig. 12a, b Partitioning scheme for IMOMM calculations of the dihydroxylation of: a styrene; b 1-decene by OsO4·(DHQD)2PYDZ. Alkenes highlighted in black

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was described at B3LYP level, whereas the Ph substituent was described at MM3 level. In the case of olefins with aliphatic substituents, the CH2=CH-CH3 moiety was described at B3LYP level, whereas the rest of the n-aliphatic chain was described at MM3 level. In their investigations the authors took the [3+2] mechanism, since it was already accepted by the scientific community. Using this method, the authors were capable of characterizing true transition states. Hence, for this reaction, to investigate the transition states associated with the formation of the osmate ester in a chiral system, one must take into account all the different ways in which an olefin can approach to the catalyst. These different paths were classified according to the criteria depicted in Fig. 13. The olefin binds to an axial and an equatorial oxygen providing three different families of reaction paths labelled as “regions” A, B and C. When the olefin has one substituent, it can be placed in four different “orientations”, which are labelled as I, II, III, IV. The joint consideration of the three regions and the four possible positions of the olefin substituent yield a total of twelve different pathways. These are the same pathways analysed by other authors using other methodologies (see above). The styrene was chosen as a representative example of the asymmetric dihydroxylation of alkenes having an aromatic substituent [52]. The twelve transition states corresponding to all of the possible regions and orientations of entry of the styrene were characterized. As far as the region of entry is concerned, the three lower energy saddle points correspond to region B: B-I, B-III and B-IV, with relative energies of 0.0, 0.1 and 2.6 kcal/mol, respectively (Fig. 14). Thus, there is no doubt that B is the computed preferred region of entry of the olefin, in complete agreement with experimental observations obtained from kinetic studies [37] and previous calculations [39, 53]. The fact that region B is preferred over the other regions is given by the nature of the

a

b

Fig. 13a, b Definition of the possible approaching pathways of the olefin to the catalyst within the [3+2] mechanism: a top view along the O-Os-N axis showing the three different “regions” of entry of the olefin (A, B, C); b side view perpendicular to the O-Os-N axis showing the four possible “orientations” of the olefin substituent (I, II, III, IV)

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Fig. 14 IMOMM(B3LYP:MM3) optimised transition state B-I. The styrene and the OsO4 unit are highlighted in black

steric interactions between the substrate and the catalyst. Region A is the least hindered region; therefore, the magnitude of steric interactions should be smaller in this region than in region B. The fact that the energy of the saddle points is lower in region B can only mean that the steric interactions are of an attractive nature. This is fully consistent with the existence of a binding pocket in the catalyst. After showing that the reaction goes through region B, the authors analysed the different orientations of the olefin within this region, since the enantioselectivity is decided by the orientation of the olefin with respect to the catalyst. Isomers I and III lead to the R product, whereas isomers II and IV lead to the S product. B-I and B-III are the lowest energy saddle points leading to the R product, with relative energies of 0.0 and 0.1 kcal/mol, respectively. The lowest energy saddle point leading to S product is B-IV, with a relative energy of 2.6 kcal/mol. The computed enantiomeric excess using these energetic values is 99.9%, in good agreement with the experimental value of 96% [21, 22]. B-I and B-III transition states can be associated to the Corey and Sharpless pockets, respectively. Thus, when the olefin is styrene both orientations have practically the same energy. The properties of these transition states were analysed in some detail, since this is the point where the selectivity is decided. Comparing the relative QM and MM energies it was found that the major differences are in the MM part, with QM energies remaining very similar. The MM interaction energies between the catalyst and the substrate were evaluated for each of the transition states. The results obtained allowed the identification of the role played by the different parts of the catalyst, and the quantification of their relative importance. The catalyst was divided in five parts: quinoline A, quinoline B, PYDZ, OsO4, and the rest, including both of the remaining quinuclidines (see Fig. 12). Both quinolines and the PYDZ account for more than 75% of the interaction energy between the catalyst and the substrate, detached as follows: quinoline A 53%, quinoline B 20% and PYDZ 12%. Thus, albeit quinoline B and PYDZ are

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significant, quinoline A is playing the key role in deciding the stereochemistry in this reaction. The main interactions between the substrate and the catalyst are the stacking interactions, face-to-face with the quinolines, and face-to-edge with the PYDZ. The study was broadened by the same authors to the investigation of the origin of the enantioselectivity in the dihydroxylation of terminal aliphatic n-alkenes. The dihydroxylation of the series from propene to 1-decene was studied by means of the IMOMM method [71]. Experimental studies on propene, 1-butene, 1-pentene, 1-hexene and 1-decene showed that the reaction was enantioselective in all cases, leading to the R product. Moreover, the results show a dependence of the enantioselectivity with the chain length. It sharply increases when going from propene to 1-pentene, and after that the enantioselectivity remains practically constant for 1-hexene and 1-decene. The explanation for this dependence of the enantioselectivity with the chain length remained elusive. On the other hand, the p–stacking interactions that were found to be critical for styrene cannot be responsible for the observed enantioselectivity for these terminal aliphatic n-alkenes because they do not have aromatic rings. The computational study of the osmium dihydroxylation of aliphatic alkenes is much more complicated than the case of aromatic alkenes due to the large number of conformations that the former could adopt. To overcome this issue, the authors considered the system as composed of two different parts: the catalyst and the olefin. For the catalyst, the considered conformation is that from the X-ray structure.As already shown in the study of styrene, and by some experimental works [72], the catalyst is a quite rigid molecule. For the aliphatic alkenes under study, there is a large number of possible conformations; in addition, the stability of an olefin conformation is also affected by the interactions between the olefin substituent and the catalyst. Hence, the catalyst has to be necessarily included in the conformational search. The conformational analysis was done using a scheme based on the “systematic search” approach [73]. Their strategy consisted of two parts: first they developed a method to identify all the possible conformations; afterwards, they screened all the possible conformations at the MM level to select the most stable and carry out the relatively expensive QM/MM calculations only on them. The “catalyst+aliphatic n-alkene” system, for all the olefins from propene to 1-decene, gives almost 40,000 possible conformations. The most stable conformations for each of the olefins, around 1700, were selected and their transition states were optimised at IMOMM level. The results of the calculated enantiomeric excesses are in Fig. 15. Calculations are able to reproduce the observed increase of ee for short chains, and the presence of a ceiling value after which the increase in enantioselectivity is much smaller, in excellent agreement with experiment. Once the experimental trends were properly reproduced by the calculations, the authors analysed the main differences between the R and S enantiomers trying to identify the origin of the enantioselectivity for these olefins and its dependence on the chain length. As in the case of styrene, the major differences

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Fig. 15 Experimental and computed enantiomeric excesses as a function of the chain length of the aliphatic n-alkene

comparing the energy of the transition states for each of the olefins are in the MM term. The analysis of the MM term for all of the transition states is unpractical, due to the large number and variety of relevant conformations; instead, the authors decided to examine in detail some of the most stable conformations. Analysing the different contributions to the MM energy for the R and S selected transition states for the complete series of olefins, the major difference was in the van der Waals term. These dissimilarities in the van der Waals term were caused by the difference in the substrate-catalyst interactions between the R and S transition states. The interaction energies for the R enantiomer increase for the complete series of olefins, though the augment is larger on going from propene to 1-hexene than for the rest of the olefins of the series. For the S enantiomer, in contrast, the interaction energy increases slowly and constantly for all the olefins studied. This difference explains the particular behaviour of the enantioselectivity as a function of the chain length (see Fig. 15). Hence, for the first part of the series (propene to 1-hexene), the enantioselectivity of the reaction increases with the chain length because the attractive interactions between the olefin and the catalyst increase more rapidly for the R enantiomer than for the S enantiomer in their respective transition states. The interaction energies between the different parts of the catalyst and the substrates were also evaluated in the case of aliphatic n-alkenes. The part of the catalyst having a larger interaction with the olefins is quinoline A. It accounts for more than 40% of the total interaction for the R enantiomer, and ca. 60% for S enantiomer. Nevertheless, its behaviour is very similar for both enantiomers, therefore, even though quinoline A is decisive for catalytic purposes, it is responsible neither for enantioselectivity nor for its dependence on the chain

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length. Hence, a significant difference appears in the way the catalyst interacts with aromatic and aliphatic alkenes. The second largest contribution to the interaction energy corresponds to the spacer PYDZ. This interaction highly increases when going from propene to 1-hexene, and after that it remains approximately constant for the rest of the olefins of the series. In the case of S enantiomers, however, the interaction energy with PYDZ is not so relevant. This is noteworthy because it means that the PYDZ region is one of the key factors that differentiates the interaction between the olefins and the catalyst for the R and S transition states, deciding the enantioselectivity. The interaction energies of quinuclidine B with the substrate have a similar behaviour to that of PYDZ for the R and S enantiomers, though their absolute values are smaller. Thus, quinuclidine B is also helping in deciding the stereochemistry for the aliphatic n-alkenes, but was not relevant for aromatic alkenes. The interactions between the olefins and the remaining parts of the catalyst, quinoline B, OsO4 and quinuclidine A are quite small in all cases compared to those just commented on.As a result, the enantioselectivity in the dihydroxylations of aliphatic n-alkenes is determined by the interactions of the olefin with two regions of the catalyst: PYDZ and quinuclidine B. Figure 16 shows the structures for the most stable transition states leading to the R products for propene, 1-hexene and 1-decene. Looking at these structures the authors claim that one can see how the elongation of the olefin chain from propene to 1-hexene increases the interactions between the olefin and the three most important parts of the catalysts, Quinoline A, PYDZ and Quinuclidine B. From propene to 1-hexene, the carbon atoms added to the aliphatic chain are close to these three parts of the catalyst, and can have a strong interaction. In contrast, once the aliphatic n-alkene has six carbon atoms, all the carbon atoms subsequently added to the chain are far from the catalyst, and they cannot be expected to make strong direct interactions with the catalyst. These interactions between the aliphatic chain of the alkene and the aromatic rings of the catalyst (PYDZ and Quinoline A) can be described as CH…p interactions [74], whereas the interactions with Quinuclidine B can be described as hydrophobic-hydrophobic interactions [75].

Fig. 16 A view of the selected transition states giving the R product for: propene, 1-hexene and 1-decene. The olefin is highlighted in black

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The origin of enantioselectivity in the asymmetric dihydroxylation of alkenes with aromatic and aliphatic substituents catalysed by OsO4·(DHQD)2PYDZ has been analysed by means of QM/MM methods. The enantiomeric excesses computed for both types of olefins are in excellent agreement with experiment. Moreover, the origin of the enantioselectivity was also identified, being of p-stacking nature for aromatic olefins, and CH-p plus hydrophobic interactions for aliphatic terminal n-alkenes. The most relevant parts of the catalyst responsible for enantiomeric differentiation have been also recognized; they are in agreement with other studies (see above), though their stabilizing contributions were here quantified.

8 Concluding Remarks The asymmetric dihydroxylation of olefins by OsO4·NR3 catalysts is an extremely useful reaction in organic synthesis. It is able to introduce two vicinal functional groups simultaneously on olefins not functionalised. The application of theoretical methods to study this reaction has proven to be critical in order to determine the reaction mechanism, and to identify the origin of the enantioselectivity. The application of ab initio methods has allowed to discern between the stepwise [2+2] mechanism and the concerted [3+2] mechanism, supporting the latter. Nevertheless, in order to study the enantioselectivity computationally, the size of the system to be considered increases significantly.At this point, the number of atoms to be included in theoretical calculations is too large to be described at QM level, and the use of other computational methods is required. Several quantitative or semiquantitative methodologies have been developed and applied to study the origin of the enantioselectivity of this reaction. The application of MM methods was successful in explaining the origin of the enantioselectivity, though no quantitative predictions were possible. This is mainly due to the difficulty of obtaining reliable force field parameters for transition metal atoms. The development of a Genetic Algorithm employing enzyme-based methods to study asymmetric reactions, was satisfactorily applied for this particular reaction. The use of this procedure, apart from qualitative in explaining the origin of the enantioselectivity, allowed the authors to perform semiquantitative predictions of the enantiomeric excess. Transition state force fields based on quantum mechanics calculations were also developed to study this reaction. The initial applications were successful explaining the enantioselectivity, though in those calculations the geometries of the transition states were kept frozen. The later development of force field parameters for transition states based on quantum mechanics calculations allowed the authors to perform full optimisation of the transition states. Hence, the application of this Q2MM method gave excellent results in predicting the

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enantioselectivity and explaining its origin, and allowed to make quantitative predictions of the enantiomeric excess. The parameter development can be somehow laborious, but once the parameters have been obtained the transition state optimisations are quite fast. The application of QM/MM methods, concretely the IMOMM method, has also been proven to be successful to determine the origin of the enantioselectivity, and to predict quantitatively the origin of the enantioselectivity. In addition, the contribution of each part of the catalyst to the enantioselectivity was also quantified. In this case, all the transition states were fully optimised. The advantage of this method is that it can be directly applied to study any reaction, because no parameterisation is needed, albeit the single calculations are more expensive. The application of these theoretical methods has allowed us to explain and understand the reaction mechanism, and to determine how the different parts of the reactants (the olefin and the catalyst) are involved in the reaction. The U-shape conformation of the second generation catalyst has been confirmed by all the methods used. The three aromatic regions of the catalyst (two quinolines and the heterocyclic spacer) are attractively interacting with the olefin inside the binding pocket. The orientation of the olefin giving rise to the Corey and Sharpless pockets are, for most of the studied olefins, quite similar in energy; therefore, to know the orientation for a particular olefin, theoretical calculations are needed. The asymmetric dihydroxylation of olefins constitutes an excellent example of how computational chemistry, in close collaboration with experiment, can substantially improve the understanding of catalytic reactions of practical interest.

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Top Organomet Chem (2005) 12: 109– 144 DOI 10.1007/b104400 © Springer-Verlag Berlin Heidelberg 2005

Organometallacycles as Intermediates in Oxygen-Transfer Reactions. Reality or Fiction? Dirk V. Deubel 1 ( 1

2

) · Christoph Loschen · Gernot Frenking 2 (

)

Department of Chemistry and Applied Biosciences, ETH Zürich, Computational Science Laboratory, USI Campus, 6900 Lugano, Switzerland [email protected] Department of Chemistry, Philipps Universität Marburg, 35032 Marburg, Germany [email protected]

1

Introduction and Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

2

Computational Methods

3 3.1 3.2 3.3

Metalla-2,3-Dioxolanes in the Olefin Epoxidation with Peroxo Complexes . . Experimental Pioneering Work . . . . . . . . . . . . . . . . . . . . . . . . . . Quantum Chemical Studies of the Reaction Mechanism . . . . . . . . . . . . Quantum Chemical Predictions of Organometallacycles . . . . . . . . . . . .

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Metalla-2-Oxetanes in [2+2] Addition Reactions of Metal Oxides to Olefins . . Experimental Pioneering Work . . . . . . . . . . . . . . . . . . . . . . . . . . . Quantum Chemical Studies of the Reaction Mechanism . . . . . . . . . . . . . Quantum Chemical Predictions of Metalla-2-Oxetanes . . . . . . . . . . . . . .

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References

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Abstract Organometallacyclic compounds have been suggested as intermediates in several transition metal mediated oxidation reactions without direct experimental evidence for such species. In this work, we review theoretical studies of the last decade aiming to clarify whether the reactions proceed via formation of organometallacyclic species. Keywords Organometallacycles · DFT calculations · Oxidation reactions · Reaction mechanism

List of Abbreviations and Symbols CDM Continuum dielectric model DFT Density functional theory hmpa Hexamethylphoshoramide HSAB principle Hard and soft acid and base principle MTO Methyltrioxorhenium(VII)

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OT Oxygen transfer TOP Thermodynamic oxygen transfer potential, according to: J Am Chem Soc 2004 126:996 TS Transition state

1 Introduction and Scope The suggestion of organometallacycles as intermediates in metal-mediated oxygen-transfer reactions challenges chemical intuition. Why would reactions involving an oxygen transfer from metal oxo or peroxo complexes to hydrocarbons proceed via intermediate organometallacycles, cyclic compounds containing a metal-carbon bond? Metal-complex-mediated oxygen transfer processes often involve a metal in a high oxidation state. The hard and soft acid and base (HSAB) principle [1] would predict metal-carbon bonds to be much weaker than the metal-oxygen bonds of the reactants. Small cyclic hydrocarbons such as cyclopropane and cyclobutane show a considerable ring strain energy in the region of ~27 kcal/mol relative to that in cyclohexane [2], and a similar magnitude of ring strain may be anticipated for their metalla-analogues. On the other hand, the prediction of thermodynamic oxygen-transfer potentials (TOP) [3] demonstrated a large gain of free energy in the reaction of typical organic and inorganic oxidants with olefins, e.g., of ~–50 kcal/mol in ethylene epoxidation. The free energy profiles of reactions like olefin epoxidation or cis-dihydroxylation may easily accommodate an intermediate organometallacycle with a free energy between those of reactants and products, if the formation of the intermediate is kinetically preferred to a direct oxygen transfer. However, a relation between the thermodynamics and kinetics of similar reactions is predicted qualitatively by the Bell-Evans-Polanyi principle [4] and quantitatively by Marcus theory [5]: The more exergonic reaction typically proceeds via a lower free energy barrier. Hence, the question remains, which factors would render a stepwise mechanism via an organometallacycle kinetically more favorable than the concerted oxygen-transfer event. The question whether prominent oxygen-transfer reactions such as Sharpless dihydroxylation [6] or Herrmann epoxidation [7] (Fig. 1) do proceed via organometallacycles is of direct practical relevance to the search for new transition metal catalysts, because the molecular understanding of a reaction may open up new strategies for a rational control of reactivity. Oxygen transfer reactions are of considerable importance both in the laboratory and in the chemical industry [8–11]. Industrial syntheses often start from simple hydrocarbons. The products of an oxygen-transfer process may serve as activated intermediates like oxiranes, molecules bearing oxygen-containing leaving groups or final 1,2-bifunctional groups like vicinal diols. Asymmetric oxidations play an important role in stereoselective synthesis [12].

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Fig. 1 Catalytic cycles of the Sharpless dihydroxylation (top) and Herrmann epoxidation (bottom), simplified

Quantum chemical calculations, in particular those based on density functional theory (DFT) [13–15], are an essential part of the research into transition metal mediated oxygen transfer reactions. The increasing computational performance and methodological developments allow accurate studies of relatively large molecules and transition states containing more than 50 atoms. There are many reasons to choose quantum chemistry for the clarification of reaction mechanisms in homogeneous catalysis. (i) Each step of a mechanistic proposal rather than only the rate-determining step is accessible in detail. (ii) Competing mechanistic proposals can be studied. (iii) The geometric structure of transition states can be predicted. (iv) The electronic structure of transition states can be predicted to elucidate the consequences of a modification of the metal, ligands, and substituents in the substrate. In this chapter, we review the results from quantum chemical studies on the mechanism of selected oxygen-transfer reactions of d0-transition-metal complexes for which the organometallacycles shown in Fig. 2 have been postulated to be intermediates. It covers the literature of the last decade, ranging from the pioneering density functional studies of potential intermediates (1994) [16] to an advanced mechanistic design (2003) [17]. Because of the fact that O, NH, and CH2 are isoelectronic, current computational studies on the nitrene and carbene-analogue chemistry are included as well. Experimental work is discussed herein if it is a pioneering work, a response to quantum chemical calculations, or a recent development that calls for quantum chemical investigation in the future. Other book chapters and review articles on computational studies of

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Fig. 2 Organometallacycles suggested as intermediates in oxygen-transfer reactions

oxidation reactions have been published in the last five years focused on the reactions of metal oxides and peroxides with alkenes and other hydrocarbons [18–22]. Possible organometallacyclic intermediates in Jacobsen-Katsuki-type epoxidations of olefins with oxo complexes were covered elsewhere [22] and are beyond the scope of the present chapter. Another chapter of the present book illuminates the origin of the stereoselectivity in the Sharpless dihydroxylation of olefins [23, 24]. Two recent Accounts of Chemical Research describe the end of the debate on the [3+2] vs [2+2] addition of metal oxides across C=C bonds [25] and the solution of four controversies on the oxygen-transfer mechanism in the olefin epoxidation with inorganic peroxides [26]. This chapter is organized as follows: In the next section we briefly summarize the quantum chemical methods that have been employed for the calculated results presented in the subsequent sections. The following section deals with five-membered organometallacycles, metalla-2,3-dioxolanes, as potential intermediates in the olefin epoxidation with transition metal peroxo complexes. The section after that deals with four-membered metalla-2-oxetanes as potential intermediates in the Sharpless dihydroxylation of olefins with oligooxo complexes and in related reactions. The section following that considers threemembered metallaoxiranes. The order has been chosen for historical reasons, because the five-membered organometallacycles were suggested earliest (1970) [27] and the three-membered rings were suggested latest (1996) [28]. The title of this chapter alludes to the review of Jørgensen and Schiøtt in 1990 [29] which was entitled: Metallaoxetanes as Intermediate in Oxygen Transfer Reactions – Reality or Fiction? Fifteen years later, we can answer this question and assess whether these and other organometallacycles are likely intermediates. We demonstrate that Computational Chemistry should not be considered simply a new service to experimentalists for a quantitative evaluation of mechanistic proposals. Creative chemists with quantum chemical methods can discover novel compounds, design mechanisms that appeared formerly to be utopian, and define future directions of chemistry.

2 Computational Methods Accurate calculations on reactions of transition metal complexes typically require the use of modern quantum chemistry [30]. Whereas early quantum chemical studies based on semi-empirical methods gave some qualitative in-

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sights into the stereoelectronic requirements of the reactions, the relative energies were only rough estimates. In the last decade, density functional theory (DFT) methods have been used extensively [13–15], because they presently provide the best compromise between accuracy and computational efficiency. The DFT-Hartree-Fock hybrid method B3LYP was shown to be particularly useful; it consists of the three-parameter fit of Becke [31] of exchange and correlation functionals including the correlation functional of Lee,Yang, and Parr [32]. In fact, most of the results of this chapter are based on DFT calculations at the B3LYP level, while some of them are based on the exchange and correlation functionals of Becke [33] and Perdew [34] (BP86) and some of them are based on the post-Hartree-Fock-method Möller-Plesset perturbation theory [35] (MP2). Calculated structures agree well with X-ray crystal structures and B3LYP relative energies agree well with those calculated using the highly correlated coupled cluster singles doubles method with perturbative triple excitations (CCSD(T) method) [36, 37]. Quantum chemical studies on the reactions of complexes of second and third row transition metal compounds are often performed using an effective core potential (ECP) at the metal. The LANL2DZ ECP of Hay and Wadt [38] has been used most frequently in the studies summarized in this chapter. Effective core potentials improve the efficiency of quantum chemical calculations. First, core electrons, which do not participate in chemical bonding, are not considered explicitly but is only their effect on the valence electrons. Second, ECPs allow the implicit treatment of relativistic effects [39–41], which must not be neglected in calculations involving second and third row transition metals. To assess the quality of the ECP, we frequently used the zeroth order relativistic approximation (ZORA) [42] as an all-electron reference method. Relative structures and energies calculated using the LANL2DZ ECP were found to be in good agreement with those at the ZORA method. The consideration of scalarrelativistic effects, i.e., of mass-velocity and Darwin terms, and the neglect of spin-orbit terms is a reliable approach for closed-shell molecules involved in the reactions of considered in this work. We would like to emphasize that very large basis sets are required to obtain accurate relative energies. For geometry optimization, we typically utilized a partly decontracted version of the LANL2DZ basis at the metal together with the 6–31G(d) basis set at the other atoms. This basis set combination is denoted II [30]. For subsequent improved energy calculations, we have fully decontracted the basis set at the metal and augmented it with a set of f functions [43]. The 6–311+G(d,p) basis set was preferably used on H, C, N, and O and the 6–311+G(3d,p) basis set was preferably used on the third-row main group elements, P, S, and Cl [44]. This basis set combination is denoted III+ [45]. Large basis sets were found to be particularly important in the calculation of energies using the B3LYP and CCSD(T) methods. Relative free energies (also denoted Gibbs free energies or free enthalpies, DG) are typically more meaningful with respect to the experiment than are relative energies (DE). DG is calculated using standard methods of statistical

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thermodynamics for zero-point vibrational energy, thermal energy, work term, and entropy. Zero-point-energy corrections of approximately 5 kcal/mol to relative energies of the metallacycles considered in this work were not uncommon.Additional corrections arise from thermal corrections, work, and entropy. Entropic corrections are particularly important upon changes in the number of molecules. For instance, in the formation of a metallacycle from ethylene and a metal oxide in a bimolecular reaction, there is a loss of translational, rotational, and vibrational entropy which increases the activation free energy and the reaction free energy by ~12 kcal/mol at room temperature in vacuo relative to the activation energy and reaction energy, respectively. Most of the results reported in this work are based on DFT calculations of reactions in vacuo. Unless otherwise mentioned, the results reported in this work refer to free energy calculations in vacuo at the B3LYP level using large basis sets. Relative energies in solution are very similar if the reactants are neutral and no charged molecule is generated during the reaction. Solvation free energies may be estimated by using a continuum dielectric model (CDM). The definition of the molecular cavity may have a large influence on calculated relative energies and should be properly calibrated to experimental data [46]. The quantum chemical analysis of the electronic structure and bonding interactions in molecules and transition states provides an important method for understanding chemistry.A first trend in the electronic effects in a reaction becomes evident from atomic charges. Natural population analysis (NPA) [47] was used, because they do not depend strongly on the basis set. Fragment-based energy- and charge decomposition schemes provide a particularly meaningful tool [48]. Prominent examples are the approaches of Morokuma [49], Ziegler and Rauk [50–52], and Dapprich and Frenking [53]. The methods have in common that the wave function of AB, which can be either a molecule or the transition state of a bimolecular reaction is expressed as a linear combination of the wave functions of the fragments A and B as basis. In the analysis of a metal complex AB, A is the ligand and B is the remaining metal fragment. In the analysis of a transition state, A and B are the reactants. The Charge Decomposition Analysis (CDA) [53] is a quantum chemical interpretation of the DewarChatt-Duncanson model [54, 55] and describes the relative importance of donation and backdonation either in a metal complex or in a transition state [56].A key feature of the Ziegler-Rauk analysis is a decomposition of the interaction energy into electrostatics, Pauli repulsion, and stabilizing orbital interactions [51]. The latter term can be decomposed further into the contributions from symmetry orbitals [57]. The decomposition analyses refer to molecules in vacuo. Due to the dependence of the coulomb interaction on the reciprocal of the dielectric constant e, one may anticipate electrostatic interactions between charged species in solution to be less important than those in vacuum. When interpreting the results, it is also important to know about the strong distance dependence of the energy components [58]. The distance dependence is particularly significant in transition states, and the analysis of several structures along the reaction coordinate of the two reactions that are compared with each

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other may be more meaningful than the analysis of the transition states themselves [46]. Although charge and energy decomposition methods have been a valuable part of our research into the understanding of reaction mechanisms, the results of these analyses shall be less emphasized in the present book chapter due to space limitations.

3 Metalla-2,3-Dioxolanes in the Olefin Epoxidation with Peroxo Complexes 3.1 Experimental Pioneering Work The epoxidation of olefins is one of the key reactions in organic synthesis. Oxiranes are valuable intermediates in the laboratory and industry, because the opening of the three-membered ring with various nucleophiles gives 1,2-bifunctional hydrocarbons with a well-defined stereochemistry [59]. Methods for olefin epoxidation that employ hydrogen peroxide for the terminal oxidant are of particular interest for several reasons. First, H2O2 is relatively inexpensive with a cost of less than $0.7 per kg (100% H2O2). 2.4 million tons are produced annually, mainly for use as bleach [60]. Second, it is environmentally benign, because water is the only theoretical co-product. This aspect is relevant to the desirable replacement of (i) the chlorohydrin process for the production of alkyl-substituted oxiranes, which uses large amounts chlorine, or (ii) the HalconArco route, which requires high temperature and pressure [10].Various metalcatalyzed olefin epoxidation methods that employ hydrogen peroxide as the terminal oxidant have been developed, and they may be divided into three categories with respect to their catalyst precursors [61]: (i) heterogeneous, (ii) soluble metal oxides including polyoxotungstates [62, 63], and (iii) homogeneous coordination compounds. An important class of homogeneous catalysts was derived from the pioneering work of Mimoun and co-workers [27, 64] on the stoichiometric epoxidation of olefins with molybdenum(VI) h2-diperoxo complexes [65] bearing one or two additional ligands such as hexamethylphoshoramide (hmpa) and water (Fig. 3). Sundermeyer and co-workers [66] designed a biphasic method with for catalytic olefin epoxidation with Mo diperoxo complexes and hydrogen peroxide as the terminal oxidant.Amphipatic trialkylamine, -phosphine, or -arsine oxides coordinate with the metal of the diperoxo complex generated in the aqueous phase and transfer the catalyst into the organic phase, where epoxidation takes place. The discovery of the methyltrioxorhenium (MTO)-catalyzed olefin epoxidation with H2O2 by Herrmann and co-workers [7] was a major breakthrough [67–69]. MTO activates H2O2 (30% H2O2) via an equilibrium with the rhenium(VII) mono- and diperoxo species (Fig. 3) [70]. Sharpless and co-workers [71], Kühn and co-workers [72], and others investigated nitrogencontaining aromatic heterocycles like pyridine and pyrazole as co-ligands in

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Fig. 3 Four and five-coordinated trioxo, monoperoxo, and diperoxo complexes of molybdenum(VI) and rhenium(VII). R=NMe2

the catalytic process and achieved ligand-accelerated catalysis as well as suppression of undesirable oxirane hydrolysis. The formation of an intermediate organometallacycle, a metalla-2,3-dioxolane, is a central part of the mechanism proposed in the pioneering work of Mimoun and co-workers (1970) for the olefin epoxidation with Mo diperoxo complexes (Fig. 4). The initial step of the suggested mechanism is the coordination of the olefin with the d0 metal. The second step is the formation of the organometallacycle upon cycloinsertion of the coordinated olefin into a metaloxygen bond of the metal diperoxo complex. Note that metalla-2,3-dioxolanes of late transition metals are known [73, 74]. The final step is the cycloreversion of the organometallacycle, yielding the oxirane. Two years later (1972), the mechanistic proposal of Mimoun was challenged by Sharpless and co-workers [75]. They divided various olefin oxidation reactions in two categories based on the relative reactivity of norbornene vs cyclohexene towards oxidants like organic peracids and osmium tetraoxide (Fig. 5). Whereas the former substrate is oxidized by OsO4 much more rapidly than is the latter, the reaction rates for the oxidation of both substrates by organic peracids are very similar. This interesting observation implied a different “size of the transition state” [76], with the TS involving either three atoms or five atoms. Because [MoO(O2)2(hmpa)] was found to react with norbornene approximately as fast as with cyclohexene, the transition state of the reaction was

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Fig. 4 Concerted (top) vs stepwise (bottom) mechanism in the olefin epoxidation with Mo diperoxo complexes. R=NMe2 or alkyl

Fig. 5 Reactivity ratio of the oxidation of norbornene vs cyclohexene by various oxidants. Postulated structure and “size” of transition state (TS) with respect to the olefin moiety. R=NMe2, R=p-chlorophenyl

assigned to the three-atom category. Additional substrates like trans- vs ciscyclododecene and additional oxidants were considered to support this conclusion, leading to a new mechanistic proposal: The olefin epoxidation with [MoO(O2)2(hmpa)] does not proceed via a five-membered transition state and a five-membered organometallacycle, but via a three-membered transition state with no intermediate being involved [75] (Fig. 4, concerted OT). A con-

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Fig. 6 Extension of the controversy on the reaction mechanism to the olefin epoxidation with alkylhydroperoxides

certed oxygen-transfer mechanism [77] is generally accepted in the olefin epoxidation with dioxiranes and peroxy acids, as was demonstrated by transition states predicted by Bach, Houk, and others [78–81] with the help of quantum chemical calculations. The two seminal contributions of Mimoun and Sharpless laboratories led to a controversy on the reaction mechanism that was lasting longer than for two decades [82] and expanded to the olefin epoxidation with other metal peroxo complexes, in particular those of rhenium. Kinetic studies of Al-Ajlouni and Espenson [83, 84] on the MTO-catalyzed olefin epoxidation with H2O2 revealed the importance of both mono- and diperoxo species in the catalytic process as well as substituent effects on reaction rates, but the molecular mechanism remained uncertain. The mechanistic debate was further extended to the olefin epoxidation with alkylhydroperoxides catalyzed by d0 transition metal complexes of V or Mo (Fig. 6). In the Halcon-Arco process, the alkylhydroperoxide is generated from the alcohol and molecular oxygen at high temperature and pressure [10]. A major difference to the metal-mediated olefin epoxidation with hydrogen peroxide is the fact that the oxygen-carbon bond in the alkylhydroperoxide remains intact, so the formation of peroxo species is unlikely and a putative organometallacyclic intermediate would contain a dative bond from the alkyl-substituted oxygen of the alkylhydroperoxide to the metal center (Fig. 6). Again, Mimoun et al. [85] favored the stepwise pathway, whereas Chong and Sharpless [86] and others [87, 88] supported concerted oxygen transfer pathways, in particular the transfer of the metal-bound oxygen of the alkylhydroperoxo complex to the olefin and simultaneous coordination of the remaining alcoholato moiety with the metal.

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3.2 Quantum Chemical Studies of the Reaction Mechanism In early quantum chemical studies that aimed to elucidate the reaction mechanism [89, 90], semi-empirical methods were employed, which did not allow a quantitative prediction of activation barriers. A major breakthrough was achieved in 1998, when Rösch and co-workers [91] reported a density functional theory (DFT) study on the mechanism of the ethylene epoxidation with mono- and diperoxo complexes, [ReO2(O2)Me] and [ReO(O2)2Me], derived from methyltrioxorhenium(VII) (MTO). Figures 7, 8 and 9 display the theoretically predicted structures of the competing mechanisms for the reaction of [ReO2(O2)Me] with ethylene. The calculations show that ethylene does not coordinate to the MTO derivatives. However, several transition states (TS) were predicted which correspond to a formation of the organometallacycles upon direct insertion of the free olefin into a metal-oxygen bond of the metalladioxirane moiety. Theory predicts high activation free energies of 46 kcal/mol or larger for these [2+2]-like pathways; the TS lowest in free energy is given in Fig. 7. Various transition structures for a concerted oxygen transfer from diperoxo complexes [ReO(O2)2MeL] and monoperoxo complexes [ReO2(O2)MeL] (L=no ligand or H2O) to ethylene were also predicted.All of them have a spiro geometry, i.e., a tetrahedral environment at the oxygen atom that is transferred to the olefin, as demonstrated first by Wun and Sun [92]. The calculated activation free energy for the concerted mechanism is considerably smaller than that for the formation of the organo-

Fig. 7 Calculated structure of the reactants (left), transition state (middle), and organometallacyclic intermediate (right) in the stepwise mechanism of the reaction of ethylene with [ReO2(O2)Me]

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Fig. 8 Calculated structure of the transition state (left) and products (right) in the concerted mechanism of the ethylene epoxidation with [ReO2(O2)Me]

metallacycle. The TS shown in Fig. 8 is 29 kcal/mol higher in free energy than are the reactants. The quantum chemical investigation on the decomposition of the hypothetical organometallacycle turned out to be particularly informative [17, 93]. The calculations reveal a favorable pathway for the decomposition of the organometallacycle with a relatively small activation barrier. The reaction proceeds via the transition state shown in Fig. 9 and leads to wrong product. The cycloreversion of the hypothetical organometallacycle is coupled to a sigmatropic shift of one of the hydrogens from 4 to 5-position of the metalla-2,3-dioxolane upon cleavage of the metal-carbon and oxygen-oxygen bonds. Therefore, the intermediate formation of the organometallacycle would give aldehydes rather than epoxides. Figure 10 compares the calculated free energy profile for the reaction of ethylene with the rhenium monoperoxo complex [ReO2(O2)Me]. The concerted Sharpless mechanism is shown at the left-hand side, and the stepwise Mimoun mechanism via the organometallacycle is at the right-hand side. The reaction of the related molybdenum(VI) Mimoun-type complexes, [MoO(O2)2(OPR3)] with olefins, was also studied using DFT methods. A surprising difference to the Re analogues was the quantum chemical characterization of the ethylene complexes of the d0 metal [94] (Fig. 11). However, both the addition of ethylene to [MoO(O2)2(OPH3)] and the substitution of the neutral phosphine oxide by ethylene was predicted to be exergonic by more than 15 kcal/mol, respectively. The calculations indicate that there is no subsequent reaction channel from the ethylene adduct [MoO(O2)2(OPH3)(ethylene)], neither to the organometallacycle, nor to the product.As in the rhenium-analogue

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Fig. 9 Calculated structure of the transition state (left) for the sigmatropic cycloreversion of the hypothetical organometallacyclic intermediate in the stepwise mechanism. This mechanism gives aldehydes (right) rather than epoxides

Fig. 10 Theoretically predicted free energy profile for the concerted and stepwise mechanism of the reaction of ethylene with [ReO2(O2)Me]

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Fig. 11 Calculated structure of the ethylene complexes formed upon addition of ethylene to [MoO(O2)2(OPH3)] (left) and upon substitution of the phosphine oxide by ethylene (right)

chemistry, several transition states may lead directly to the organometallacycle, but the activation energies are again much higher than that for the direct oxygen transfer mechanism [93]. Several additional studies on the reactions of other metal peroxo complexes with olefins were performed, which also did not support intermediate organometallacycles. For instance, Rösch and co-workers [95] compared the ethylene epoxidation with group 6 peroxo complexes of the type [MO3–n(O2)nLm] of (M=Cr, Mo, W; L=NH3; n=1, 2; m=1, 2). In each case, the activation barrier for the concerted oxygen transfer mechanism is predicted to be smaller than that of the formation of the organometallacycle. The calculations predict the following trend in the activation barriers for olefin epoxidation. (i) Cr>Mo>W. The lower barrier for the complex of the heavier metal was attributed to the indirect destabilization of the O-O bond due to the relativistic stabilization of the W-O(peroxo) bonds [96]. (ii) Monoperoxo (n=1)>diperoxo complexes (n=2). In the reaction of the diperoxo complexes, the transfer of the peroxo oxygen distal to the equatorial L ligand is clearly preferred to the transfer of the proximal peroxo oxygen. (iii) Five ligands (m=2)>four ligands (m=1). The presence of two additional donor ligands (here represented by an ammine model ligand) increases the barrier, because the diamine complex is less electrophilic than the monoamine complex. The electrophilic character [97–100] of the oxidant has been a valuable concept for the elucidation of barrier heights in various metalcomplex mediated olefin epoxidations [101–107]. The effect of substituents on the olefinic C=C bonds are in line with this finding, i.e., the reactivity strongly increases with the number of alkyl substituents [72]. Bühl and co-workers [108] employed Car-Parrinello molecular dynamics simulations [109] at the BP86 level for investigating the reaction of ethylene with [VO(O2)2(imidazole)]– and derivatives in aqueous solution. These compounds may represent a model of the active site of vanadium-dependent haloperoxidases. The authors [108] also

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showed that the epoxidation follows the concerted mechanism.Although a DFT study on organometallacyclic derivatives of alkyl hydroperoxides has not been reported yet, the formation of such metalla-2,3-dioxolanes with an alkyl substituent in 2-position does not appear to be likely. 3.3 Quantum Chemical Predictions of Organometallacycles Because modern quantum chemistry sounded the death knell for metalla-2,3dioxolanes in the olefin epoxidation with peroxo complexes of early transition metals, the design of related five-membered organometallacycles species of d0 metals has been a particular challenge. In a recent DFT study [17], one of us explored the reaction of ethylene with [Re(O)2(O-NH)Me], a formal hydroxylamine derivative of the peroxo species [Re(O)2(O-O)Me]. These investigations were based on the idea that N-O bonds are significantly stronger than O-O bonds, as indicated by a reaction free energy of –24 kcal/mol of the isodesmic reaction, H2O2+NH3ÆNH2OH+H2O. Note that the formation of the five-membered organometallacycles, rhena-2,3- or 3,2-oxazolidine, leaves the N-O bond of [Re(O)2(O-NH)Me] intact, whereas a concerted epoxidation or aziridination with [Re(O)2(O-NH)Me] requires the cleavage of this bond. Hence, the thermodynamic prerequisites may result in a significant free energy penalty on the activation barrier for the concerted Sharpless mechanism in the nitrogenanalogue chemistry of the reaction of Re peroxides with olefins. DFT predicts the formation of [Re(O)2(O-NH)Me] from MTO and hydroxylamine to be 9 kcal/mol endergonic, while the corresponding perhydrolysis reaction of MTO is predicted to be 2 kcal/mol endergonic. Figure 12 shows the calculated free energy profile for multiple reactions of [Re(O)2(O-NH)Me] with ethylene. Pathways involving cleavage of the metal-N bond are displayed with black solid lines, pathways involving cleavage of the metal-O bond are displayed with gray solid lines. The latter pathways will not be discussed in this work because they are less favored than the former. Several isomers of transition states and intermediates exist which lie higher in energy. As expected from the initial considerations, the activation barrier for the ethylene aziridination with [Re(O)2(O-NH)Me] (41 kcal/mol) is much higher than that of the ethylene epoxidation with [Re(O)2(O2)Me] (29 kcal/mol). In contrast, the barriers for the formation of the organometallacycle are approximately equal: 42 kcal/mol for the addition of ethylene across the Re-N bond of [Re(O)2(O-NH)Me] and 45 kcal/mol for the addition of ethylene across a Re-O(peroxo) bond of [Re(O)2(O2)Me]. The calculations reveal an additional pathway that leads to the formation of organometallacycles in the reaction of [Re(O)2(O-NH)Me] with ethylene. Figure 12 displays the free energy profile of this pathway with gray dashed lines; structural drawings of the species involved are given in Figs. 13 and 14. The metallaoxaziridine moiety is predicted to open upon metal-O bond cleavage (Fig. 13). [3+2] addition of this metalla-analogue nitrosonium ylide,

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Fig. 12 Theoretically predicted free energy profile for multiple mechanisms in the reaction of ethylene with [ReO2(O-NH)Me]

Fig. 13 Calculated structures of the ring opening mechanism of [ReO2(O-NH)Me]: reactants (left), transition state (middle), and [ReO2(h1-O-NH)Me] intermediate (right)

[Re(O)2(h1-O-NH)Me], across the C=C bonds occurs with a relatively moderate barrier and yields the metalla-3,2-oxazolidine (Fig. 14). Although this species is predicted to be 11 kcal/mol less stable than the reactants, as-yet-unpublished results indicate that there is a huge potential of controlling the free energies of transition states, intermediates, and products by substituents. Present work also aims to characterize the intermediates and products of these fascinating reactions experimentally.

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Fig. 14 Calculated structure of the [3+2] transition state (left) for the reaction of [ReO2(h1-O-NH)Me] with ethylene, which gives the metalla-3,2-oxazolidine (right)

4 Metalla-2-Oxetanes in [2+2] Addition Reactions of Metal Oxides to Olefins 4.1 Experimental Pioneering Work The discussion about the possible formation of metalla-2-oxetanes in transition metal-mediated oxidation reactions began with the ground breaking work of Sharpless in the field of enantioselective dihydroxylation of olefins with osmium tetraoxide using cinchona alkaloids as ligands [6]. The transfer of the stereochemical information of the chiral ligand to the substrate was explained by Sharpless with a two-step mechanism for the addition reaction, which should occur rather than a concerted [3+2] addition as originally proposed [110] (Fig. 15).

Fig. 15 Schematic representation of the two reaction paths suggested for OsO4 addition to olefins

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It was suggested that the initial step of the reaction course is a [2+2] addition yielding the osma-2-oxetane, which then rearranges to the cyclic ester. There was no direct experimental observation of the osma-2-oxetane, however. Support for a two-step mechanism of the osmylation reaction came from kinetic studies, which revealed a nonlinear correlation between the reciprocal of temperature and the enantioselectivity of the reaction [111]. However, experimental tests of the [3+2] and [2+2] pathways by means of 12C/13C kinetic isotope effects which were carried out by Corey et al. showed that the [3+2] mechanism is in accord with experimental results, while the [2+2] mechanism is not [112].A kinetic study of Heller et al. showed that a nonlinear temperature behavior of product ratios in selection processes may be due to a distortion of the reactant equilibrium [113]. The experimental results did not give conclusive evidence about the alternative reaction mechanisms of the dihydroxylation

Fig. 16 Schematic representation of the p-stacking model for the [3+2] transition state and the proposed stepwise sequence for the equimolar formation of the diastereomers 6 and 7. R*OH=(-)-8-phenylmenthol. Reproduced with permission from [114]

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reaction shown in Fig. 15. A definitive answer in favor of the [3+2] mechanism came from quantum chemical calculations which are described below. A similar scenario as for the dihydroxylation has recently been opened for the diamination: Muñiz et al. reported experimental studies on the asymmetric diamination of olefins with osmium(VIII) imido complexes using (–)-8-phenylmenthyl esters as chiral auxiliaries [114–116]. The reaction of (Nt-Bu)3OsO with enantiopure acrylates and methacrylates yielded only two out of four possible stereoisomers, whose absolute configurations are inconsistent with a concerted [3+2] mechanism of olefin face differentiation. The authors considered a stepwise mechanism via an osma-2-azetidine intermediate as reasonable pathway (Fig. 16). Metalla-2-oxetanes have been suggested by experimentalists as intermediates in oxidation reactions for other metals than osmium. Gable and coworkers reported about kinetic studies on alkene extrusion from rhenium(V) dioxylates, which is the inverse of the oxidation reaction [117]. The results were interpreted in favor of a stepwise mechanism yielding a rhena-2-oxetane as intermediate, but a positive evidence for the structure of the intermediate could not be given. Strong evidence for the intermediacy of rhena-2-oxetanes in the dissociation reaction of rhenium(V) dioxylates came from recent mass spectrometric studies of Chen et al. [118, 119] using electrospray ionization techniques.

Fig. 17 Proposed reaction mechanism for the olefination of aldehydes catalyzed with (h2-alkyne)methyl(dioxo)rhenium complexes. Reproduced with permission from [120]

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Fig. 18 Reaction of norbornene with the platinum oxo complex 1 yielding the platina-2oxetane 2. Reproduced with permission from [121]

The latter work, concerns the reaction course of cations which can be quite different to the reaction mechanism of neutral compounds. The formation of a rhena-2-oxetane in a metal catalyzed aldehyde olefination reaction has recently been suggested by Kühn et al. [120]. These workers reported about the reaction of PPh3 with 4-nitrobezaldehyde and ethyldiazoacetate in the presence of CH3ReO2(alkyne) as catalyst. On the basis of chemical observations using labeled compounds and NMR spectroscopic results it was proposed that the reaction cycle follows the mechanism shown in Fig. 17. The authors suggested that the rhena-2-oxetane C is the precursor of the olefin which is formed during the reaction, but there is again no direct proof for its formation. Direct evidence for the formation of a metalla-2-oxetane in a metal mediated oxidation reaction was recently reported by Sharp and coworkers [121]. The oxidation of norbornylene by the tetranuclear platinum(II) m-oxo complex 1 yielded nearly quantitative formation of the platina-2-oxetane 2 shown in Fig. 18. The compound 2 could be isolated and the structure was identified with X-ray structure analysis. However, it is unclear if the reaction of this late transition metal complex takes place via [2+2] addition of a metal-oxo moiety across the C=C double bond. The authors write that the formation of the C-O bond allows considerable speculation on this process. DFT calculations are underway to help differentiate the various possibilities [121]. 4.2 Quantum Chemical Studies of the Reaction Mechanism The first quantum chemical calculations which provided quantitative data about the mechanism of the cis-dihydroxylation of olefins with OsO4 were reported in 1994 by Sharpless et al. [122] and by Veldkamp and Frenking [123]. Previous work by Jorgensen and Hoffmann [124] focused on a qualitative orbital analysis using EHT calculations. In the first paper by Sharpless [122a] the authors took RuO4 instead of OsO4 because of limited computational resources. The authors suggested that the

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results may be used as a model for the OsO4 addition reaction, because RuO4 can also be employed for the cis-dihydroxylation of olefins. The results of the DFT calculations showed that the [2+2] addition of RuO4 to ethylene yielding the ruthena-2-oxetane 1Ru (see Fig. 15 for the OsO4 reaction) is slightly exothermic by ~3 kcal/mol, but the formation of the ruthenium dioxylate 2Ru via [3+2] addition is much more exothermic by ~52 kcal/mol. The calculations were also carried out using NH3 as a model base which is bonded to the metal. The [2+2] and [3+2] reactions become more exothermic in the presence of NH3 with the latter reaction becoming even more thermodynamically favored than the [2+2] addition. Nevertheless, the authors advocated the two-step mechanism via initial formation of 1Os (Fig. 15) in the presence of a base because they could explain the enantioselectivity of the reaction in the presence of chiral bases using a mnemonic device as a model for the chiral transition states. It was assumed that the thermodynamically less favored [2+2] addition has a lower activation barrier than the [3+2] addition and therefore, 1Os could be formed in a kinetically controlled reaction [122a]. This view was substantiated by molecular mechanics calculations for the osmium-catalyzed asymmetric dihydroxylation (AD) of trisubstituted olefins using large chiral bases as ligands [122b]. The authors calculated several isomers of the osma-2-oxetanes using osmium parameters which were derived from DFT calculations of 1Os(NH)3. The results showed that many features of the reaction, such as ligand acceleration, stabilizing stacking interactions, the enantioface selectivity, and the trends of different classes of olefins, can be rationalized by the calculated relative energies of the intermediates. The paper by Veldkamp and Frenking also reported only about possible intermediates of the [2+2] and [3+2] addition but the ab initio calculations were carried out for osmium compounds rather than ruthenium compounds [123]. The theoretically predicted energies at QCISD(T) using HF optimized geometries gave similar results as the RuO4 work by Sharpless et al. [122a]. The [2+2] addition yielding osma-2-oxetane 1Os (see Fig. 15) was even calculated to be endothermic by 18.3 kcal/mol while the formation of the osmium dioxylate 2Os via [3+2] addition was predicted to be exothermic by 12.2 kcal/mol. The reaction profiles for the [2+2] and [3+2] reaction in the presence of one or two molecules NH3 become thermodynamically more favored but the reaction energy of the [3+2] addition is clearly lower than that of the [2+2] reaction. Veldkamp and Frenking calculated also model intermediates of the osmylation reaction which had been suggested by Corey [125] They are shown in Fig. 19. The authors also investigated theoretically the product of the oxidation of 2Os followed by a second [3+2] addition of ethylene which may then become further oxidized (Fig. 20). The latter reaction course had been suggested by Sharpless to be a competing reaction cycle of the stereoselective reaction [126]. The results by Veldkamp and Frenking showed that the alternative mechanism suggested by Corey [125] was energetically feasible which meant that the calculation of the activation barriers was crucial for addressing the question about the validity of the reaction mechanism.

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Fig. 19 Reaction mechanism for the enantioselective dihydroxylation of olefins with OsO4 in the presence of chiral ligands L via [3+2] addition suggested by Corey

Fig. 20 Reaction mechanism for the two-cycle dihydroxylation of olefins with OsO4 in the presence of chiral ligands L via [3+2] addition suggested by Sharpless

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Fig. 21 Calculated reaction profiles for the [3+2] addition of OsO4 to ethylene (bottom) and for the two-step reaction (top) with initial [2+2] addition yielding the osma-2-oxetane and subsequent rearrangement. Reproduced with permission from [127]

The answer to the pivotal question came in two simultaneously published papers from the groups of Frenking [127] and Morokuma [128] which were published in 1996. Quantum chemical ab initio calculations showed clearly that the two-step reaction of OsO4 to ethylene via initial [2+2] addition has much higher activation barriers than the [3+2] addition which was predicted to proceed with little activation energy (Fig. 21). The same result was obtained using DFT calculation which were later reported by Torrent et al. [129]. The final proof for the [3+2] mechanism came from a theoretical paper by Houk, Sharpless and coworkers [130] who showed that the kinetic isotope effects of the asymmetric dihydroxylation which were calculated using the transition state structure for the [3+2] addition agree nicely with experimental data. The cis-dihydroxylation of olefins with OsO4 is an example of how a long-standing controversy about the mechanism of a transition metal mediated reaction was settled with the help of quantum chemical calculation. The competing formation of metalla-2-oxetane via [2+2] addition vs metalladioxylate formation through [3+2] addition has been theoretically studied for

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Table 1 Relative energies (kcal/mol) of the rhena-2-oxetanes and rhenadioxylate intermediates of the[2+2] and [3+2] addition reactions of LReO3 to ethylene calculated at B3LYP. Reproduced with permission from [131]. The energies are given relative to LReO3+ethylene

Ligand L

Dioxylate

Oxetane

DDE

Cp* Cp Cl Me OH OMe O–

– 4 – 8 +16 +31 +19 +17 +33

+15 + 5 +10 +10 +11 +12 +27

+19 +13 – 6 –21 – 9 – 7 – 6

metals other than osmium. An important contribution to the topic was made by Rappé and coworkers [131] who calculated the relative energies of the two isomers for the addition of LReO3 to ethylene (L=Cp*, Cp, Cl, Me, OH, OCH3, O–) using DFT at the B3LYP level. The calculations showed that the rhenadioxylate is energetically lower-lying than the rhena-2-oxetane when L=Cp*, Cp, but the [2+2] reaction is thermodynamically favored over the [3+2] addition when L=Cl, Me, OH, OCH3, O– (Table 1). The authors reported the calculated activation energy for the [3+2] rhenadioxylate extrusion yielding ethylene and CpReO3 (27.2 kcal/mol) to be in excellent agreement with the experimental result of 28.0 kcal/mol with L=Cp* reported by Gable [117a]. Because the calculated reaction energy of ~0 kcal/mol and the per deuterium kinetic isotope effect were also in agreement with experimental values, the authors concluded [131] that the reaction of Cp*ReO3 with ethylene proceeds via [3+2] addition and not via [2+2] addition as previously suggested [117]. The reaction mechanism of the addition of rhenium trioxo compounds LReO3 to ethylene with L=O–, Cl, Cp, Cp* was also theoretically studied by Deubel and Frenking [45]. The authors calculated the reaction energies and activation barriers for the [2+2] and [3+2] addition at the B3LYP level. They found in agreement with the work of Rappé [131] that the rhena-2-oxetanes with L=Cl, O– are lower in energy than the rhenadioxylates. However, the calculated activation barriers for the former [2+2] addition were higher than for the latter [3+2] reaction [45]. A lower activation energy for the [3+2] addition was also calculated for L=Cp. Computational studies of pericyclic reactions of other metal oxides like permanganate and chromyl chloride with olefins were reported by Houk and Strassner [132], Torrent et al. [133], and Limberg [134]. In each case, the activation barrier for the thermal [3+2] mechanism was predicted to be lower than that for the thermal [2+2] mechanism. Drees and Strassner [135] considered the reaction of ethylene with RuO4 in different electronic states and concluded that the [3+2] addition on the singlet potential energy surface is strongly preferred to [2+2] pathways.

Fig. 22 Calculated overall reaction profile at B3LYP for the reaction of OsO4 with ethylene. The energy values are given in kcal/mol, the ZPE corrected values are given in parentheses. Reproduced with permission from [136]

Organometallacycles as Intermediates in Oxygen-Transfer Reactions 133

Fig. 23 Calculated overall reaction profile at B3LYP for the reaction of RuO4 with ethylene. The energy values are given in kcal/mol, the ZPE corrected values are given in parentheses. Reproduced with permission from [136]

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The complete reaction mechanism of the OsO4 addition to ethylene yielding the cis-diol was recently calculated and compared with the analogous reaction of RuO4 by Frunzke et al. [136]. The focus of the work was the question why the oxidation of olefins with RuO4 usually proceeds under cleavage of the carboncarbon bond whereas oxidation by OsO4 yields cis-diols. The theoretically predicted overall reaction profiles for the two reactions at B3LYP are given in Figs. 22 and 23. The calculations suggest that the first step of the OsO4 and RuO4 addition to ethylene proceeds via a concerted [3+2] reaction which has for both metal oxides very low activation barriers. The calculations also indicate that the first step should be followed by a cascade of further oxidation reactions and addition of ethylene which eventually leads to the ruthenium(VI)bisdioxylate 6(Ru) or, in case of osmium, to the osma(VIII)bisdioxylate 7(Os). The crucial step which explains the cleavage of the C-C bond upon oxidation by RuO4 is the very small barrier for carbon-carbon bond breaking of the ruthenium(VIII)bisdioxylate 7(Ru) (Fig. 23). The analogous reaction of the osmium intermediate 7(Os) has a much higher barrier (Fig. 22). It was suggested that the latter species undergoes hydrolysis yielding the cis-diol whereas 7(Ru) reacts via C-C cleavage. The calculated reaction profile shown in Fig. 23 explains also why the oxidation of olefins with RuO4 under mild conditions may be tuned towards formation of cis-diols. The oxidation of ruthenium(VI)bisdioxylate 6(Ru) to ruthenium(VIII)bisdioxylate 7(Ru) with hydrogen peroxide as a representative oxidant [3] is endothermic and the former intermediate may become hydrolyzed instead of oxidized [136]. 4.3 Quantum Chemical Predictions of Metalla-2-Oxetanes All theoretical studies which analyzed the reaction course of the addition of metal oxides to olefins which were claimed by experimentalists [111, 117] to yield metalla-2-oxetanes via [2+2] addition showed that the [3+2] pathway has a lower activation barrier than the [2+2] addition [127–136]. This made some theoreticians search for oxidation reactions where the [2+2] addition of an oxide to an olefin has a lower barrier than the [3+2] addition. The first success albeit nor for a metal oxide was reported by Houk et al. [137]. They reported about ab initio and DFT calculations which show that the [3+2] addition of SO3 to ethylene yielding ethylensulfite has a higher barrier than the [2+2] addition giving the four-membered cyclic sulfone. It follows that the formally symmetryforbidden [2+2] addition can become more favorable than the [3+2] addition. An explanation for the reversal of the activation barriers was given in terms of the strongly polarized frontier orbitals of SO3, which has the LUMO essentially localized at sulfur and the HOMO localized at the oxygen atoms. They idea of searching for species which have highly polarized frontier orbitals was picked up by Frenking and co-workers who first investigated the

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Fig. 24 Reaction pathways for the addition of OsO4 and LReO3 (L=O–, H3PN, Me, Cp, Cp*) which have been considered in [140]

effect of substituents on the mechanism of OsO4 addition to substituted ethylenes RHCCH2 (R=F, CHO, Me, NH2) [138]. The substituents had only a weak influence on the activation barrier for the [3+2] addition which was calculated to be <10 kcal/mol for all species. Ujaque et al. [139] gave theoretical evidence for a possible involvement of a diradical intermediate in the reaction of osmium tetraoxide with protoanemonin (5-methylene-2-(5H)-furanone). This substrate reacts as a dienophile in Diels-Alder reactions via a diradical mechanism as well. In a density functional study of Deubel, Schlecht and Frenking (DSF), the authors investigated the regio- and stereoselectivity of the addition of OsO4 and LReO3 (L=O–, H3PN, Me, Cp, Cp*) to ketene [140]. Figure 24 shows schematically the transition states investigated in this work. The calculations of the transition states led to the following predictions concerning the kinetically most favorable reactions pathways [140]. The reaction of ketene with OsO4 should proceed via [3+2] addition across the C=C bond. The [2+2] addition reactions of all LReO3 species to ketene have lower activation energies than the [3+2] addition. These were the first examples where calculations showed that the [2+2] addition of a metal oxide to a C=C bond has a lower barrier than the [3+2] addition. For ReO–4 and (H3PN)ReO3 it was found that the [2+2] addition to the C=O bond is kinetically even more favorable than the addition to the C=C bond. However, the calculation predicted that the [2+2] addition of MeReO3, CpReO3 and Cp*ReO3 should proceed via [2+2] addition across the C=C bond yielding the metalla-2-oxetane. The theoretical result did not agree with the experimental finding that Cp*ReO3 reacts cleanly with diphenylketene yielding the metalla-2,5-dioxolane-one, which is the product of a formal [3+2] addition across the C=C bond [141]. The product was characterized via X-ray structure analysis which leaves no doubt about its structure. DSF searched for other reaction pathways which may yield the metalla-2,5-dioxolane-one as product. They found for the addition of diphenylketene an energetically low-lying zwitterionic intermediate which can be formed via nucleophilic attack of Cp*ReO3. The latter reaction

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Table 2 Calculated activation energies DEA and reaction energies DER [kcal/mol] for the [2+2] addition of ethylene to metal-ligand double bonds M=X and for the [3+2] addition to X=M=X¢ (X, X¢=O, NH, CH2). The calculations were carried at the B3LYP level. The values are taken from [140, 142, 143]

Reaction

Metal bonds

DEA

DER

[2+2] [3+2]

OsO4 Os=O O=Os=O

47.9 11.8

+12.7 –19.1

[2+2] [2+2] [3+2] [3+2] [3+2]

Os=O Os=NH O=Os=O O=Os=NH HN=Os=NH

46.5 42.5 8.3 6.1 0.4

+ 7.1 – 8.4 –23.9 –46.4 –67.2

[2+2] a [2+2] a [3+2] [3+2] [3+2]

Os=O Os=CH2 O=Os=O O=Os=CH2 H2C=Os=CH2

41.3 34.8 27.5 8.1 13.0

+ 8.1 – 8.9 – 7.0 –42.4 –72.7

OsO2(NH)2

OsO2(CH2)2

a

The formal [2+2] reaction takes place as a two-step process with initial formation of a metalla oxirane.

may become additionally stabilized by solvent effects. Thus, it was suggested that the metalla-2,5-dioxolane-one was not formed via a concerted [3+2] addition but in a two-step process with prior formation of a zwitterionic intermediate [140]. The scope of the theoretical studies about the competition of [2+2] vs [3+2] addition of OsO4 to ethylene has recently been extended to isoelectronic bisoxo and biscarbene compounds OsO2(NH)2 and OsO2(CH2)2. Deubel and Muñiz [142] calculated the reaction pathways for the [2+2] and [3+2] addition of ethylene to OsO2(NH)2. Five different reaction products may be envisaged. They are the [2+2] addition to the Os=O and Os=NH bonds and the [3+2] addition across the O=Os=O, O=Os=NH and HN=Os=NH moieties. Table 2 gives the calculated energies for the transition states. The calculations by Hölscher et al. [143] revealed substantial differences between the reactions courses of the ethylene addition to OsO2(NH)2 and OsO2(CH2)2. The [2+2] addition is in both cases energetically unfavorable compared to the [3+2] addition, but the former reaction of OsO2(CH2)2 takes place as a two-step process with initial rearrangement of the reactant through oxygen-carbon bond formation which yields a metallaoxirane as intermediate. The rearrangement reaction has a high activation barrier of 40.9 kcal/mol for formation of the metallaoxirane which then adds to the olefin [143]. The [3+2] addition of ethylene to OsO2(CH2)2 exhibits also peculiar features. The thermo-

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dynamics of the reaction shows the same pattern as for the OsO2(NH)2 addition, i.e. the reaction becomes more exothermic with the trend O=Os=O < O=Os=CH2 < H2C=Os=CH2. However, the calculated activation barriers indicate that the kinetically most favorable reaction is the [3+2] addition of ethylene to O=Os=CH2, i.e. the activation barriers increase with O=Os=CH2 < H2C=Os=CH2 < O=Os=O (Table 2). The calculations also showed that hydrogen migration reactions and rearrangements may compete with the [2+2] and [3+2] addition reactions of ethylene to OsO2(CH2)2 [143]. It should be pointed out that most theoretical studies cited herein did not only report about the calculated data making predictions about the reaction pathways. They gave also the results of an analysis of the electronic structure which explains the reason for the observed trends of the reaction and activation energies.

5 Metallaoxiranes Metallaoxiranes, the smallest organometallaoxacycles, are interesting compounds because they are isoelectronic to metal diperoxo complexes and metallaoxaziridines (Fig. 25). Zhu and Espenson [28] reported in 1996 the catalysis of the carbene transfer from ethyldiazoacetate (eda) to olefins by methyltrioxorhenium(VII) (MTO), which gives cyclopropanes. Similar reactions include the synthesis of aziridines from arylimides and that of oxiranes from aldehydes or ketones. Metallaoxiranes play a key role in the mechanism proposed by the authors (Fig. 26). The suggested initial reaction is a [3+2] cycloaddition of eda across a Re=O bond of MTO, yielding a metalla-2,4,5-oxadiazoline. Cycloreversion of this intermediate is anticipated to liberate dinitrogen and the metallaoxirane. The subsequent carbene transfer from the metallaoxirane is thought to be analogue to the concerted oxene transfer from diperoxo complexes to olefins (see above). Although neither the metalla-2,4,5-oxadiazoline nor the metallaoxirane of the carbene transfer reaction were isolated and characterized, the suggested mechanism is chemically intuitive and may explain similar carbene transfer reactions catalyzed by MTO. An open question is whether oxygen transfer reactions from these metallaoxiranes, if they exist, may also be achieved. The potential role of rhenaoxiranes in the rhenium-catalyzed carbene transfer may be supported by the characterization of related vanadium(IV)

Fig. 25 Oxenoid (peroxo complex), nitrenoid (metallaoxaziridine), and carbenoid (metallaoxirane) derivatives of methyltrioxorhenium(VII) (MTO)

Fig. 26 Postulated reaction mechanism of the MTO-catalyzed cyclopropanation of olefins with ethyl diazoacetate (eda)

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metallaoxiranes [144]. Current experimental and quantum chemical work on the reaction mechanisms in the fascinating carbene-analogue chemistry of the MTO-catalyzed olefin epoxidation is in progress.

6 Conclusion The results of quantum chemical DFT and ab initio calculations of the reaction mechanism of the olefin epoxidation with diperoxo complexes and cisdihydroxylation with oxo complexes show clearly that the organometallacyclic compounds which were previously suggested as intermediates in the reaction are not formed. The epoxidation reactions do not proceed via formation of metalla-2,3-dioxolanes as intermediate but rather via direct attack of the metal peroxo moiety to the olefin. Likewise the reaction of neutral metal oxides in high oxidation states with olefins occurs not as a [2+2] addition via metalla2-oxetanes but through [3+2] addition yielding directly metalla-2,5-dioxolanes. Acknowledgement This work was supported by the Fonds der Chemischen Industrie, the Deutsche Forschungsgemeinschaft and the Bundesministerium für Bildung und Forschung, Germany. Excellent service has been provided by the computing centers HRZ Marburg, HLRZ Stuttgart, and CSCS Manno.

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Top Organomet Chem (2005) 12: 145 –186 DOI 10.1007/b104401 © Springer-Verlag Berlin Heidelberg 2005

Late Transition Metals as Homo- and Co-Polymerization Catalysts Artur Michalak 1, 2 · Tom Ziegler 2 ( 1

2

)

Department of Chemistry, University of Calgary, Calgary Alberta Canada T2N 1N4 [email protected] Department of Theoretical Chemistry, Jagiellonian University, Cracow, Poland [email protected]

1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

2

Steric Control of Molecular Weight . . . . . . . . . . . . . . . . . . . . . . . . 150

3 3.1 3.2 3.2.1 3.2.2 3.2.3 3.3 3.3.1 3.3.2 3.3.3 3.3.4

Control of the Polymer Topology . . . . . . . . . . . . . . . . . . . . . . . Modelling the Polyolefin Branching . . . . . . . . . . . . . . . . . . . . . . Energetics of Elementary Reactions and Relative Stability of Isomers . . . Relative Stability of Isomeric Alkyl Complexes and the Olefin p-Complexes Olefin Insertion Barriers, 1,2- vs 2,1-Propylene Insertion . . . . . . . . . . Chain Isomerisation Barriers . . . . . . . . . . . . . . . . . . . . . . . . . Stochastic Simulations of the Polyolefin Growth . . . . . . . . . . . . . . . Ethylene Polymerization Catalysed by Pd-Diimine Catalyst . . . . . . . . . Propylene Polymerization Catalysed by the Pd-Diimine Catalysts . . . . . Ethylene Polymerization Catalysed by the Ni-Anilinotropone Catalyst . . . Model Simulations – Effect of Catalyst Variation . . . . . . . . . . . . . . .

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155 156 158 159 159 160 160 163 165 166 167

4 Co-Polymerization Between Ethylene and Polar Monomers . . . . . . . . . . 4.1 Co-Polymerization of CO and Ethylene . . . . . . . . . . . . . . . . . . . . . . 4.1.1 Experimental and Calculated Rates for the Insertion Processes of Importance for Alternating Ethylene/CO Copolymerization . . . . . . . . . . . . . . . . . 4.1.2 Experimental and Calculated Rates for the Insertion Processes of Importance for Alternating Ethylene/CO Copolymerization Catalysed by Nickel Complexes

169 170

5 5.1 5.2 5.3

Co-Polymerization of Olefin with Other Polar Monomers . Preferred Binding Mode of Oxygen Containing Monomers . Preferred Binding Mode of Nitrogen Containing Monomers Methyl Acrylate Insertion and the Chelate Opening . . . . .

6

Concluding Remarks

References

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Abstract In the present account we address two aspects of the polymerization processes catalyzed by the late-transition-metal complexes: (i) influence of the catalyst structure and the reaction conditions (temperature and olefin pressure) on the polyolefin microstructure; (ii) co-polymerization of a-olefins with oxygen-containing monomers. Gradient corrected DFT has been used to determine the energetics and the activation barriers of the elementary

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reactions in these processes. A stochastic model has been developed and used to simulate the polymer growth under different T, p conditions. Keywords Density functional theory · Olefin polymerization · b-Hydride elimination · Stochastic approach · Branching List of Abbreviations DFT Density functional theory MD Molecular dynamics MM Molecular mechanics NMR Nuclear Magnetic Resonance QM Quantum Mechanics

1 Introduction Brookhart and coworkers [1] have recently developed Ni(II) and Pd(II) diimine based catalysts of the type (ArN=C(R)-C(R)=NAr)M-CH3+ (1a of Fig. 1) that are promising alternatives to both Ziegler-Natta systems and metallocene catalysts for olefin polymerization. Not only can these catalysts convert ethylene into high molecular weight polyethylene, but the polymers also exhibit a controlled level of short chain branching. Traditionally, such late metal catalysts are found to produce dimers or extremely low molecular weight oligomers due to a facile chain termination processes [2]. It should be pointed out that cationic Pd(II) complexes containing bidentate tertiary phosphine ligands already were developed in the early 1980s by Sen [2a] and Drent [2b] as catalysts for the co-polymerization of CO and ethylene. Brookhart’s group has studied the mechanistic details of the polymerization including the role of the bulky substituents on the diimine ligands [1, 2]. Three main processes are thought to dominate the polymerization chemistry of these

Fig. 1 Late transition metal catalysts for olefin polymerization of current interest

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Fig. 2a–c Proposed reaction mechanism for: a insertion; b chain termination; c chain branching in the case of the Brookhart Ni-bis-imine polymerization catalyst. Large bulky substituents have been removed for clarity

catalyst systems, namely propagation, chain branching and chain termination (Fig. 2). Following co-catalyst activation of the pre-catalyst, a diimine methyl cation is formed. The first insertion of ethylene yields a diimine alkyl cation which upon uptake of another ethylene molecule produces a metal alkyl olefin p-complex. This p-complex has been established by NMR studies [1] to be the catalytic resting state of the system. The chain propagation cycle is depicted in Fig. 2a. The first step involves the insertion of the coordinated olefin moiety to form a metal alkyl cationic species. Rapid uptake of monomer returns the system to the initial resting state p-complex. Chain termination occurs via monomer assisted b-hydrogen elimination, either in a fully concerted fashion as illustrated in Fig. 2b or in a multi-step associative mechanism as implicated by Johnson et al. [1]. The unique short chain branching observed with these catalysts is proposed to occur via an alkyl chain isomerisation process as sketched in Fig. 2c. In this proposed process, b-hydride elimination first yields a putative hydride olefin p-complex. Rotation of the p-coordinated olefin moiety about its co-ordination axis, followed by reinsertion, produces a secondary carbon unit and therefore a branching point. Consecutive repetitions of this process allows the metal center to migrate down the polymer chain, thus producing longer chain branches. Similar Ni and Pd catalysts developed by Keim [4] and others [5, 6] which do not posses the bulky ligand systems have been used to produce dimers or extremely low molecular weight oligomers. Brookhart has suggested [1] that the bulky aryl ligands act to preferentially block the axial sites of the metal center as illustrated by Fig. 3. This feature in the catalyst system must in some

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Fig. 3 Axial (Ax) and equatorial (Eq) coordination sites of the metal center and their potential steric interactions with the bulky substituents

way act to retard the chain termination process relative to the propagation process, thereby allowing these catalysts to produce high molecular weight polymers. More recently the groups of Brookhart [7] and Gibson [8] have investigated the catalytic potential of iron(II) and cobalt(II) complexes with tridentate pyridine diimine ligands (1c of Fig. 1). They find that especially the iron(II) system can produce high-density polyethylene in good yields when bulky ortho-substituted aryl groups are attached to the imine-nitrogens. The new catalysts have polymerization activities comparable to, or even higher than, those of metallocenes under similar conditions. They exhibit further great potential for controlling polymer properties by external parameters such as pressure and temperature. Most recently, Grubbs’ group demonstrated that some neutral salicylaldiminato nickel(II) complexes, whose skeleton structure appears as 1b in Fig. 1, show catalytic activities rivaling those of the diimine complexes [9]. This potentially opens the door to a new class of catalysts as the active sites derived from these nickel complexes are neutral, thus reducing the ion-pairing problems encountered in the current catalysts. Theoretical studies have been carried out on all the late transition metal catalysts 1a [10–13], 1b [14] and 1c [15] in Fig. 1. It is not the objective here to review all the computational results.We shall instead discuss the general mechanistic insight that has been gained from the theoretical studies with the main emphasis on Brookhart’s diimine catalysts. The experimental work on late transition metal olefin polymerization catalysts has been reviewed recently by Ittel et al. [16]. Similarly to the early-metal-based systems, the late-metal-complexes can yield high molecular-weight polymers. Moreover, they can lead to poly-olefins with different microstructures, depending on the catalysts and the reaction conditions (temperature, olefin pressure) [16, 21]. Unlike the heterogeneous catalysts and the early-metal-complexes, the late-metal-based systems exhibit substantial tolerance toward polar groups, and as such they may be useful for the co-polymerization of a-olefins with polar monomers [1b, 16, 17, 22]. In the present account we address two aspects of the polymerization processes catalyzed by the late-transition-metal complexes:

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1. Influence of the catalyst structure and the reaction conditions (temperature and olefin pressure) on the polyolefin microstructure (topology) 2. Co-polymerization of a-olefins with the oxygen-containing monomers Recently, hyper-branched polymers were obtained [16–23] in the polymerizations of simple monomers such as ethylene and linear a-olefins, catalyzed by Ni- and Pd-diimine catalysts [1a, 1c, 16]. Branches in these poly-olefins form as a result of fast chain isomerisation reactions. The topology of the polymers is strongly affected by the olefin pressure: under low pressure highly-branched structures are obtained, whereas high pressure gives rise to structures with linear side-chains. Interestingly, in the polymerization catalyzed by Pd-diimine complexes the average number of branches is pressure independent, while for the Ni-based system it is strongly affected by the pressure. Branching in olefin polymerization catalyzed by diimine complexes can also be controlled to some extent by the polymerization temperature and the substituents on the catalyst. Recently, another late transition metal catalyst has been shown to exhibit similar branching features: in the polymerization processes catalyzed by a neutral Ni-anilinotropone complex polymer branching can be controlled by a variation in temperature and pressure [24]. Quantum chemistry has established itself as a valuable tool in the studies of polymerization processes [25, 26]. However, direct quantum chemical studies on the relationship between the catalyst structure and the topology of the resulting polymer, as well as on the influence of the reaction conditions, are not practical without the aid of statistical methods. We have to this end proposed a combined approach in which quantum chemical methods are used to provide information on the microscopic energetics of elementary reactions in the catalytic cycle, that is required for a ‘mesoscopic’ stochastic simulations of polymer growth [25].A stochastic approach makes it possible to discuss the effects of temperature and olefin pressure. The major goal of this study was to understand the factors controlling polyolefin branching and the relationship between the catalyst structure, temperature, pressure and the polyolefin topology. The DFT calculations were carried out for the elementary reactions in the polymerization of ethylene and propylene catalyzed by Pd-based diimine catalysts [13c,d] and the ethylene polymerization catalyzed by the Ni-anilinotropone catalyst [28]. The polymer growth in these processes was modeled by a stochastic approach [27–29]. Further, the model simulations were performed by systematically changing insertion barriers to model the influence of catalyst, beyond the diimine systems [29]. The design of an efficient catalyst for the co-polymerization of olefins with polar group containing monomers is one of the challenges for the catalytic polymerization research [1b, 16, 22, 23]. The studies in 2. have been focused on understanding the factors responsible for the differences between the Pd(active catalyst for CO/ethylene and acrylate/ethylene co-polymerization) and Ni-diimine (inactive) catalyst [1b, 16, 22, 23]. The full mechanistic DFT studies,

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involving static calculations and molecular dynamic (MD) simulations, have been performed for both Ni- and Pd-based systems [30, 32]. The results of this study reveal the factors that inhibit the polar co-polymerization in the case of the Ni-diimine catalyst.

2 Steric Control of Molecular Weight We discuss in this section how steric bulk can be used to increase molecular weight by enhancing the rate of insertion (Fig. 2b) and decrease the rate of termination. We shall demonstrate this point by first discussing the barriers of insertion/termination for the generic diimine system (HN=C(H)-C(H)= NH)M-R+ in which we have replaced the aryl rings of 1a in Fig. 1 with hydrogens. These barriers will be compared to those obtained from calculations on the full system in order to gauge the influence of steric bulk. The uptake of an ethylene molecule by (HN=C(H)-C(H)=NH)NiC3H7+, 2a, is exothermic [13a] by 19.9 kcal/mol and results in the formation of a p-complex in which the ethylene molecule is situated in an axial position above the N-Ni-N coordination plane, 3a of Fig. 4. The p-complexation energy is higher than for early d° transition metal complexes because of the additional metal-to-olefin back donation. In fact, the p-complex is so stable that according to experimental studies [16] it becomes the resting state for the catalytic system. For (HN=C(H)-C(H)= NH)PdC3H7+, 2b, one finds [13c]a similar ethylene complexation energy of 18.8 kcal/mol. Insertion of ethylene into the Ni-C bond in 3a leads to the alkyl complex 4a via the transition state TS[3a–4a] with a barrier [13a] of 17.5 kcal/mol relative to 3a. It is worth to note that in TS[3a–4a] both ethylene and the a-carbon of the growing (propyl) chain are situated in the N-Ni-N plane. For the corresponding palladium complex the insertion barrier [13c] is somewhat higher at 19.9 kcal/mol. The termination process of Fig. 2b takes place from 3a by transfer of a b-hydrogen on the growing chain to a carbon on the incoming ethylene monomer. The result (5a of Fig. 4) is a new (ethyl) growing chain and a complexed olefinic (propylene) unit made up of the old (propyl) growing chain. The olefinic unit might subsequently dissociate, thus giving rise to chain termination. The transition state for this process TS[4a–5a] has a barrier [13a] of 9.7 kcal/mol. It is important to note that in TS[4a–5a] (Fig. 4) we have two groups in the axial position over and below the N-Ni-N coordination plane, see also Fig. 3. One group is the incoming ethylene and the other the a-carbon of the growing (propyl) chain. It follows from our discussion so far [13a] that for the generic catalyst, termination has a much lower barrier than insertion. Thus (HN=C(H)-C(H)= NH)NiC3H7+ is not going to be an efficient olefin polymerization catalyst. Rather, 2a, will at best be able to produce small oligomers of ethylene. This is

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Fig. 4 Structures resulting from ethylene insertion and chain termination due to the generic catalyst (HN=C(H)-C(H)=NH)PdC3H7+. Ethylene complex (3a), insertion transition state (TS[ 3a–4a]), termination transition state (TS[3a–5a), new olefin product from termination process (5a)

in line with the experimental observation [16] that only diimines with bulky substituents are able to function as polymerization catalysts whereas less encumbered systems works as oligomerization catalysts. We shall now discuss how the introduction of steric bulk influences both insertion and termination. Our discussion will be based on calculations [13b] involving 1a of Fig. 1 in which M=Ni, R=i-Pr, and R¢=H. We shall label the different species involved by Roman numerals to distinguish them from the corresponding generic systems labeled by Arabic numerals. In the actual calculations on Ia ( or IIa) use was made of a combined quantum mechanical

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Fig. 5 QM/MM representation of structure IIa

(QM) and molecular mechanical (MM) scheme [13b] in which the core ((HN= C(H)-C(H)=NH)NiC3H7+) was represented by QM and the remaining part by MM. Quite similar calculations have been carried out by Morokuma et al. [11e]. The uptake of olefin by IIa (Fig. 5) leads to the ethylene complex IIIa of Fig. 5 with a complexation energy [13b] of 14.7 kcal/mol. The ethylene complexation energy is reduced compared to the generic system 3a by 5.2 kcal/mol. This is understandable since the ethylene molecule in IIIa is sitting in one of the axial positions and thus is encumbered sterically by the bulky phenyl groups, Figs. 3 and 5. Further studies have shown that the uptake energy can be influenced by a few kcal/mol by changing the substituents R and R¢ on 1a of Fig. 1. It has also been demonstrated that the steric bulk on the diimine nitrogens gives rise to a free energy of activation barrier for the uptake due to entropic effects as the ethylene monomer has to approach a narrow channel in order to bind to the metal [13e]. The subsequent insertion of ethylene into the Ni-C bond transforms IIIa into the pentyl complex IVa via the insertion transition state TS[IIIa–Va] of Fig. 6. However it is interesting to note that the barrier of insertion has been reduced from 17.5 kcal/mol for the generic system (TS[3a–4a]) to 13.2 kcal/mol for the real system [13b] (TS[IIIa–IVa]). The reduction is not so much due to a change in the relative energies of the transition states since both the monomer and the a-carbon of the growing chain are situated in the N-Ni-N coordination plane (Fig. 6) where they are relatively unencumbered by the bulky phenyl groups. Instead it is the steric destabilization of the IIIa resting-state

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Fig. 6 Ethylene complex (IIIa) and insertion transition state TS[IIIa–IVa] for the polymerization process involving 1a (or IIa)

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Fig. 7 Transition state TS(IVa–Va) and product Va process involving hydride transfer process from original ethylene complex IVa

relatively to 3a that is responsible for the reduction in the insertion barrier for the real system. Thus, by introducing steric bulk one is able to enhance the polymerization activity of the Brookhart based Ni(II)-diimine complexes. Similar conclusion have been reached for the homologous Pd(II) systems [1]. However, the effect is not as pronounced as the steric congestion around the palladium center is less pronounced due to the longer Pd-N bonds. It is worth to note that the calculated insertion barrier [13b] of 13.2 kcal/mol recently has been confirmed by Brookhart et al. [16] with an experimental estimate of 12.0 kcal/mol. A similar good agreement between theory and ex-

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periment has also been obtained for the palladium [13f] system. The termination process leading from IIIa over TS[IIIa–Va] to Va by the transfer of a b-hydrogen on the growing chain to a carbon on the incoming ethylene monomer is calculated to have a barrier of 18.6 kcal/mol. This is a substantial increase compared to the generic system with a barrier (TS[4a–5a]) of 9.7 kcal/mol. The increase can be understood by observing in Fig. 7 that the transition state TS[IIIa–Va] has the ethylene molecule in one axial position and the a-carbon of the growing chain in the other. It is thus understandable that introducing bulky aryl groups considerably destabilizes TS[IIIa–Va] compared to TS[4a–5a] with the result that termination becomes less feasible that propagation for the real system. The discussion here illustrates that it should be possible by gradually increasing the size of the substituents on the diimine nitrogen atoms to proceed from catalysts for oligomerization to polymerization catalysts. For the recent Grubbs catalyst [9] (1b of Fig. 1) steric bulk is also required [14] to obtain high molecular weight polymers. For the Fe(II) and Co(II) catalysts [7, 8] with tridentate pyridine diimine ligands (1c of Fig. 1), steric bulk is required to destabilize the resting state in the form of a olefin complex and lower [15a,b] the barrier of insertion sufficiently. The Fe(II) system seems further to carry out insertion and termination on energy surfaces with different [15a,d] spinmultiplicity.

3 Control of the Polymer Topology The third process in Fig. 2 involves the possible isomerisation (branching) of a growing chain. The isomerisation is mediated first by the migration of a bhydrogen on the alkyl chain of IIa to the metal center, thus producing a hydrido olefin complex. The b-hydrogen elimination is followed by a 180° rotation of the olefin unit and a subsequent insertion of the olefin into the M-H bond resulting in an isomerisation (branching) of the growing chain. The principle is illustrated by the isomerisation of the n-propyl chain in IIa via the transition state TS[IIa–VIa] of Fig. 8 to produce the iso-propyl complex VI. The internal barrier (relative to IIa) for the process is 15.3 kcal/mol [13b]. For the generic C(H)=NH)Ni(n-C3H7)+ system the isomerisation barrier is [13a] somewhat lower at 12.8 kcal/mol. This is understandable since the olefin unit has more space for its rotation. In the case of the Pd-diimine catalyst the isomerisation process has a barrier of 5.8 kcal/mol [13c] for the generic system and 6.1 kcal/mol [16] for the real catalyst. The lower barrier is a result of the longer Pd-N distance (compared to the Ni-N bond length) which provides space for rotation of the olefin unit, even when the diimine nitrogens are attached to bulky substituents. The fact that the internal barrier of isomerisation is much lower for the palladium than for the nickel system makes the former a more likely candidates

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Fig. 8 Transition state TS[IIa–VIa] and product VIa from the isomerization of IIa

for producing branched polymers. We shall in the following illustrate how palladium catalysts can be used to produce different branched structures by changing the steric bulk around the metal center. The principle will be illustrated in connection with the polymerization of propylene and ethylene. 3.1 Modelling the Polyolefin Branching Scheme 1 presents the mechanism of propylene polymerization catalyzed by late-metal catalysts. In this process, the resting state of the catalyst is an olefin p-complex, A, from which the polymer chain may grow via 1,2- (RA) or 2,1-

Scheme 1 Chain growth and isomerization reactions in the a-olefin polymerization catalyzed by Pd-diimine catalyst

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insertion (RB). Both insertion paths introduce one methyl branch. The “chain straightening” isomerisation reaction (RC) is responsible for a removal of a branch; this isomerisation reaction may follow the 2,1-insertion. However, the isomerisation reactions may also elongate branches, when they proceed in the opposite direction (RD, RE, etc.). Another isomerisation reaction which may follow the 1,2-insertion introduces an additional methyl branch, and also may proceed further (RF, RG, etc.). Thus, in the polymerization cycle, many different alkyl species are present (B–F), in which the metal atom forms a bond with primary, secondary, or tertiary carbon atoms; each of them can capture a new monomer and give rise to a subsequent insertion. Thus, in order to understand the influence of the catalyst and reaction conditions on the polymer microstructure, one must consider all these elementary reactions. 3.2 Energetics of Elementary Reactions and Relative Stability of Isomers In two recent papers [13c,d] we reported the results of computational studies on the elementary reactions in the ethylene and propylene polymerization catalyzed by Pd-based diimine catalysts with different substituents (Scheme 2). Comparison of the results for the model catalysts (1) and the real systems (2–7)

Scheme 2 Model and ‘real’ Pd(II)-based diimine catalysts

Fig. 9 Energetics (in kcal/mol) of the chain growth and chain isomerization reactions in the ethylene polymerization catalyzed by the Pd-diimine complex 7 (see Scheme 2). The experimental and theoretical (in parentheses) values are presented. The calculated energies for the chain isomerization reactions (marked with *) were obtained from the model catalyst 1

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of Scheme 2 makes it possible to separate the electronic and steric effects. Energetics of the elementary reactions in the catalytic cycle obtained from the calculations for 7 of Scheme 2 is summarized and compared with experimental data [33–35] in Fig. 9. Similar studies were performed [18] for the ethylene polymerization with the Ni-anilinotropone complex. 3.2.1 Relative Stability of Isomeric Alkyl Complexes and the Olefin p-Complexes The calculations were performed for the isomeric propyl and butyl complexes. Two general trends can be observed [13c,d, 28] for both diimine and anilinotropone complexes: (i) the more branched the alkyl is, the more stable the corresponding b-agostic complex is; (iii) the steric bulk on the catalyst has little effect on the relative stability of the alkyl complexes. There are two opposing factors determining the stability of alkyl complexes: (i) the stability of free alkyl radicals, increasing for more branched systems; (ii) the energy of binding of the radicals, decreasing for more branched alkyls [13d]. As a result, the energy order of isomeric alkyl complexes resembles the energy order of the alkyl radicals, with smaller energy differences between them than between the free radicals. For the model catalysts 1 of Scheme 2 the olefin p-complexes with branched alkyls are more stable than with the linear ones [13d]. This electronic preference is strongly affected by the steric bulk on the catalyst due to an interaction between the alkyl group and the catalyst substituents [13d]. Thus, for the most bulky real catalysts the p-complexes with linear alkyl have lower energy. This is true for both ethylene and propylene complexes. A similar effect was observed for both, the diimine and anilinotropone systems [13c,d, 28]. The presence of the steric bulk also affects the olefin complexation energies, and the relative stability of ethylene and propylene complexes. This has been discussed in details in [13d]. 3.2.2 Olefin Insertion Barriers, 1,2- vs 2,1-Propylene Insertion Comparing the systems with isomeric alkyls, the olefin insertion barriers increase from the systems with primary alkyl to those with tertiary alkyl [13c]. As a result, the insertion from the ‘tertiary’ p-complexes practically does not happen. In the case of the ‘real’ Pd-diimine systems the TS for the ‘secondary’ ethylene insertion has slightly higher energy than the ‘primary’ TS. The computed value of 0.5 kcal/mol is slightly lower then the experimental result (1 kcal/mol, Fig. 9). For the generic catalyst the 2,1-insertion of propylene is preferred by. ca. 2 kcal/mol over the 1,2-insertion. The origin of this preference was discussed in details in [13c]. The propylene 1,2-insertion TS are hardly affected by the steric bulk [13d]. However, the TS for the propylene 2,1-insertion is strongly

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destabilized due to a repulsion between the methyl group of propylene and the catalyst substituents [13d]. As a result, in the real systems the 1,2-insertion becomes preferred. As we will discuss later, this is of great importance for the branching control in the propylene polymerization. 3.2.3 Chain Isomerisation Barriers In the case of Pd-diimine catalyst, the isomerisation barriers (5.5–8.0 kcal /mol) are substantially lower than the insertion barriers (17.5–18.5 kcal/mol) [13c,d, 17, 33–35]. The difference between the isomerisation and insertion barriers is substantially larger than for the corresponding Ni-complexes, for which the isomerisation barriers are higher by ca. 5–8 kcal/mol and the insertion barriers are lower by 4–5 kcal/mol [11d,e, 13a–c]. As we will show later, this is responsible for a difference in the pressure effect on the branching numbers observed for Ni- and Pd-based systems [29]. The energetics of the isomerisation reactions is determined by the stability of the alkyl complexes discussed earlier. We would like to point out only that, as a result, the isomerisation going from primary to secondary carbon is always energetically favored. Also, the secondary CÆsecondary C¢ isomerisation reactions have usually lower barriers than the secondary CÆprimary C¢ isomerisations. This implies a fast ‘walking’ along the polymer chain. 3.3 Stochastic Simulations of the Polyolefin Growth The outcome of the complex polymer growth and branching in Scheme 1 is best modeled by the kind of stochastic simulations [27] described in the following. The outcome of such simulations are predictions about the polymer structures. A few initial steps in a typical simulation are presented in Fig. 10. Initially, one carbon atom (a methyl group) is attached to the metal of the catalyst (A in Scheme 1). In the first step, it will capture and insert a propylene molecule via either 1,2- or 2,1-insertion route. Thus, one of these insertion events is stochastically chosen; this choice, however, is not totally random but weighted by the probabilities of the two reactions. Here the relative probabilities are proportional to the relative rates. Now, one assumes that the 1,2-insertion has happened in the first step, i.e. the iso-butyl group is attached to the catalyst (B) after insertion. At this stage four different elementary events are possible: two alternative insertion routes (1,2- and 2,1-) proceeded by the capture of olefin, the termination reaction, and the isomerisation reaction that would lead to a tert-butyl group attached to the metal center. If, for instance, the 2,1-insertion happened, a heptyl group would be attached to the catalyst by its secondary carbon atom (C); thus, five reactive events would be possible (two insertions, a termination, and two isomerisations), one of them would be stochastically chosen in a next step, etc.

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Fig. 10 Stochastic simulations. In the starting structure (A) one C atom is attached to the catalyst, only two events are possible: propylene capture followed by the 1,2- or 2,1-insertion. For the structure B four events are taken into account: isomerization to the tertiary carbon, 1,2- and 2,1-insertions, and a termination. For the structures C, D and E five events are considered: two isomerizations, two insertions and a termination. The probabilities of these events are equal for the structures C and E (in both cases two different isomerizations lead to a primary or secondary carbon at the metal), and different for the structure D (for which both isomerizations lead to the structure with a secondary carbon attached to the metal). For clarity, the numbers ((1), (2), and (3)) labeling different atom types (primary, secondary, and tertiary, respectively) are shown

In the stochastic model one assigns different probabilities for similar events starting from or/and leading to structures with a carbon atom of different character being attached to a metal. For example, the 1,2-insertion starting from a primary carbon is not equivalent to the 1,2-insertion starting from the secondary carbon. Similarly, the isomerisations starting from a primary, secondary, and tertiary carbon are not equivalent in general, and also the two isomerisations starting from a secondary carbon may be inequivalent, e.g. if one of them leads to a primary and another – to a secondary or tertiary carbon at the metal (as at stage C and E). In other words, one takes into account in this model: three different 1,2-insertions, three different 2,1-insertion, three different terminations (each starting from 1°-, 2°-, and 3°-carbon), and nine different isomerisations (starting from and leading to 1°-, 2°-, and 3°-carbon).

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It should be emphasized here as well, that at different stages the absolute probabilities of equivalent events may be different, since they depend on the probabilities of all the other events (because of the probability normalization). For example, at the stages C and D in Fig. 10, the secondary carbon is attached to the metal, and five reactive events are possible. However, at the stage C the isomerisation reactions are inequivalent (one leads to the primary carbon and another – to the secondary carbon), while at the stage D they are equivalent.As a result, the absolute probabilities of all the events at the stage C will differ from those at the stage D. Scheme 3 summarizes the way in which the stochastic probabilities are generated from the rates of the different reactions. The basic assumption here is that the relative probabilities of elementary reactions at the microscopic level, pi/pj, are equal to their relative reaction rates (macroscopic), ri/rj. Thus, the relative reaction rates (Eq. 1 of Scheme 3) for all pairs of the considered reactive events together with the probability normalization condition (Eq. 2 of Scheme 3) constitute the system of equations that can be solved for the absolute probabilities of all the events at a given stage.With this assumption, one can use the experimentally determined reaction rates or the theoretically calculated relative rate constants, obtained from the energetics of the elementary reactions with the standard Eyring exponential equation. The Eyring equation introduces as well a temperature dependence of all the relative probabilities (as in Eq. 3 of Scheme 3).

Scheme 3 Basic equations used in the stochastic model

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Let us now have a closer look at three basic types of the relative probabilities appearing in the model: for an isomerisation vs another isomerisation, the 1,2-insertion vs 2,1-insertion, and an isomerisation vs an insertion. The right-hand part of Scheme 3 summarizes the equations for the macroscopic reaction rates for the alternative reactive events starting from an alkyl complex b0; let us assume that the secondary carbon atom is attached to the metal, so that two isomerisation reactions have to be considered. The isomerisation reactions are first-order in concentration of the initial alkyl complex, [b0] (Eq. 6, Eq. 7 of Scheme 3). Thus, the relative probability for the two isomerisations (Eq. 3) is given by the ratio of their rate constants, kiso,1/kiso,2 (as equal to the relative rate, riso,1/riso,2), and at given temperature it can be calculated from the isomerisation barriers DG#iso,1 and DG#iso,1, as in Eq. (3). From alkyl complex b0, the olefin can be captured to form the p-complex p0, and inserted via 1,2- or 2,1-insertion route. In the model applied here we consider the olefin capture and its insertion as one reactive event, i.e., we assume a pre-equilibrium between the alkyl and olefin complexes, described by an equilibrium constant Kcompl.=[p0]/[b0]=exp (DGcompl./RT). This corresponds to neglecting the barrier for the monomer capture. Such an approach is valid for the late-transition metal complexes, e.g., the diimine catalysts studied in the present work, where the resting state of the catalyst is a very stable olefin p-complex [16] and the olefin capture barrier and the related p-complex dissociation barrier is much lower than the insertion barriers. This assumption allows one to speed up the simulation: otherwise many olefin capture/dissociation steps, not important for the final result of the simulation, would be happening before insertion takes place. It follows from the above considerations that the insertion rate is given by Eq. (8), and the equation for the isomerisation vs insertion relative probability (Eq. 4) includes the isomerisation and insertion rate constants, the equilibrium constant, Kcompl., and the olefin pressure, polefin,. Finally, the relative probability for the two alternative insertions is given by Eq. (4); it depends on the two rate constants ratio only. It is important to emphasize here that the model in such a form allows one to simulate the influence of the reaction conditions. The temperature dependence of all the relative probabilities appears in the exponential expressions for the rate constants and the equilibrium constants. The olefin pressure influences the isomerisation-insertion relative probabilities.As a result, both, temperature and olefin pressure influence the values of the absolute probabilities for all the reactive events considered. In the following use has been made of calculated reaction rates [13f] to evaluate all stochastic probabilities, unless otherwise stated. 3.3.1 Ethylene Polymerization Catalysed by Pd-Diimine Catalyst The simulations [29] performed for the ethylene polymerization catalyzed by the Pd-based diimine catalyst 7 (Scheme 2) with the theoretically determined

Fig. 11 The pressure and temperature dependence of the average number of branches in the ethylene polymerization catalyzed by the Pd-based diimine catalyst 7 obtained from the stochastic simulations based on experimental energetics (left).An influence of pressure on the polymer topology (right); in each case a chain of 1000 carbon atoms is shown and the main chain of the polymer is projected along the horizontal axis

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energetics (16, 17) of elementary reactions gave the average branching number of 131 branches/100 °C. This is in a reasonable agreement with the experimental value of 122 br./100 °C [19] obtained for a closely related system 6 of Scheme 2. To validate our model further, we performed the simulations with the experimental values [33–35] of the reaction barriers and stabilities of intermediates (see Fig. 9). The value of 121 br./100 °C was obtained, in a very good agreement with experiment. Figure 11 presents the temperature and pressure effects on the average number of branches. The results indicate an increase in the number of branches with an increase in temperature, in agreement with experimental observations [18–21]. This trend can be understood from the energetics of the catalytic cycle (see Fig. 10). The TS for secondary insertion is higher in energy (by 1 kcal/mol) than the TS for the primary insertion. Thus, in the limit of T=0 K only primary insertions may happen, and with an increase in temperature the fraction of the secondary insertions increases. Figure 11 shows that within the wide range of pressures the simulations give a constant average number of branches. The microstructure of the polymer, however, is strongly affected by the pressure. Examples of the polymer structures obtained from the simulations are shown in Fig. 11. The polymers obtained at high pressures are mostly ‘linear’ with a large fraction of atoms located in the main chain, and with relatively short and mostly linear sidechains. With a decrease in pressure the hyperbranched structures are formed. Both, the pressure independence of the branching number and the pressure influence on the polymer topology are in agreement with experimental data for Pd-catalysts [16, 18–21]. 3.3.2 Propylene Polymerization Catalysed by the Pd-Diimine Catalysts For the propylene polymerization catalyzed by the complexes 1–7 (Scheme 2) the simulations were performed [27] based on the calculated energetics of the elementary reactions [13c–d]. For system 6 of Scheme 2, the calculated average number of branches is 238 br./100 °C, which is slightly larger than the experimental value of 213 br./100 °C. However, the temperature and pressure dependence of the number of branches and the polymer microstructure are in-line with experimental observations [21]: 1) an increase in polymerization temperature leads to a decrease in the number of branches; 2) olefin pressure does not affect the branching number, but affects the topology, leading to hyperbranched structures at low p. Further, the simulations confirm the experimental interpretation of the mechanistic details of the process with the catalyst 6 of Scheme 2 [21]: 1) both 1,2- and 2,1-insertion happen with the ratio of ca. 7:3; 2) there are no insertions at the secondary carbons; 3) most of the 2,1-insertion are followed by a chain straightening isomerisation. Thus, for this catalyst the total number of branches is controlled exclusively by the 1,2-/2,1-insertion ratio [27].

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We would like to emphasize here that the branching of polypropylene is controlled by different factors to that of polyethylene [29]. In the case of ethylene the primary/secondary insertion ratio is crucial, whereas in the propylene polymerization catalyzed by diimine catalysts, the ratio between the two alternative insertion pathways (1,2- and 2,1-) is more important [27]. As a result, an opposite temperature effect has been observed for ethylene (increase in branching number with T) and propylene (decrease in branching number with T). 3.3.3 Ethylene Polymerization Catalysed by the Ni-Anilinotropone Catalyst The results of the simulations based on the DFT-calculated energetics [18] for the Ni-anilinotropone catalyst are presented in Fig. 12. The simulations reproduced [28] with a reasonable agreement the experimental pressure and tem-

Fig. 12a, b The calculated and experimental: a temperature; b pressure dependence of the average number of branches 1000/C

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perature dependence of the average number of branches [24]. The temperature dependence (increase in branching number with an increase in temperature) can be rationalized in a similar way as for diimine catalysts. In addition, the stochastic simulations provided detailed information about the topology of the polyethylenes produced in these processes [28]. The results indicate that a variation in pressure affects the polymer topology more than a variation in temperature.At the low pressure regime the length of the branches increases and the branch-on-branch structures are formed more often. 3.3.4 Model Simulations – Effect of Catalyst Variation To model branching features of the ethylene polymerization processes catalyzed by different single-site catalysts we performed a set of model simulations [29] in which the barriers for the primary and secondary insertions were systematically changed, DE1, DE2=1–9 kcal/mol (see Fig. 9). A change of the two insertion barriers corresponds to a change of the catalyst, as the processes catalyzed by different systems are characterized by different free energy profiles. Figure 13 presents the pressure dependence of the average number of branches for different sets of the insertion barriers. The curves of Fig. 13 can be understood when one notices that (i) in the limit of pÆ• (cf. Eq. 1 of Scheme 3) the number of branches must be zero for each catalyst, as ethylene p-complexes would be formed immediately after the insertion and there would be no isomerisation; (ii) in the limit of pÆ0 chain walking would be infinitely fast compared to insertions (cf. Eq. 1), and then the number of branches would be controlled exclusively by the ratio of primary vs secondary insertions (i.e. the insertion /isomerisation ratio would not play a role). Thus, in the low pressure range, the curves of Fig. 13 converge to the average number of branches characteristic for a given pair of [DE1, DE2], while in the high pressure regime they decay to zero. Consequently, for each catalyst there exist a range of (low) pressure values, for which the average number of branches is pressure independent. With an increase of the insertion barriers this range extends towards high pressure values (see Fig. 13). It may be concluded from the results of Fig. 13 that the faster chain walking is compared to insertions, the more extended is the range of pressures for which the average number of branches is constant. This allows us to explain qualitatively the difference between the Pd- and Ni-based diimine catalysts. It is known that for the Pd-diimine systems the isomerisation is much faster compared to insertion than for Ni-complexes [11d,e, 13a–c, 16]. As a result, for the Pd-systems the number of branches is constant in the experimental range of pressure values, while for the Ni complexes the number of branches depends on the pressure in this range (and would be pressure independent for much lower pressures). It should be pointed out that the above discussion is consistent with the kinetic arguments given by Guan et al. [18] for the Pd-diimine catalyst.

Fig. 13 The pressure dependence of the average number of branches obtained from the model stochastic simulations with different primary and secondary insertion barriers, DE1, DE2 (left) and examples of polymer topologies (right). Different atom shadings are used to mark different types of branches (primary, secondary, etc.)

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Finally, let us now discuss the influence of the pressure on the polymer topology. Figure 13 displays examples of the polymer structures obtained for different combinations of DE1, DE2, for p=0.0001.Although all the structures of Fig. 13 are practically hyperbranched, the topology varies to a large extent. As we discussed earlier, in the low pressure regime the branching is controlled by the ratio of primary and secondary insertions. Thus, the difference between the barriers for the primary and secondary insertions controls the polymer topology. For small values of DE2,1=DE2–DE1 branches are formed as a result of both, the primary and secondary insertions with comparable probabilities. With an increase in DE2,1, the probability of secondary insertions decreases and insertions at the ends of branches happen more often; as a result an increase in the length of linear segments can be observed.

4 Co-Polymerization Between Ethylene and Polar Monomers Synthesis of alkene/carbon monoxide co-oligomers and copolymers by transition metal catalysts was pioneered more than 50 years ago by Reppe using nickel based complexes. The Reppe [37] catalyst produced only low-melting oligomers and was not used on an industrial scale. A further development of the nickel based catalyst by Klabunde [38] and Keim [39] led to the synthesis of low molecular weight copolymers. A major advancement of the field came in the early 1980s with the introduction by Sen [29] and Drent [26] of cationic palladium complexes with bidentate tertiary phosphine ligands and weakly coordinating anions. The new generation of catalyst was over the course of one decade optimized by Drent [40] and co-workers at Shell to produce high molecular weight polyketones with high rates at mild conditions (90 °C and 45 bar).At the same time Sen [41] and co-workers have developed cationic Pd(II) catalysts based on the bidentate tertiary phosphine ligand Me-DUPHOS (Scheme 4c) that has the potential to induce chirality into the growing chain. Both Drent [40] and Sen [41] have in addition contributed to a mechanistic understanding of the polyketone polymerization process that is characterized by a remarkably precise alternating ethene/CO copolymerization. More recently Brookhart has contributed to the field by introducing bidentate nitrogen based ligands such as 1,10-phenanthroline (Scheme 4a) and determined rate constants and equilibrium constants for many of the elementary reaction steps involved in the polyketone polymerization process catalyzed by bidentate nitrogen [42] and phosphorus [43] ligands. It is important to note that similar cationic Ni(II) complexes [44] have found little success. Theoretical studies on the polyketone polymerization process have been pioneered by Morokuma et al. [45b]. In a 1996 study [45b] the Morokuma group investigated cationic catalysts of both Ni(II) and Pd(II) with the bidentate nitrogen ligand ethenediimine (Scheme 4b) as a model for 1,10-phenan-

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Scheme 4 Experimental catalysts (a,c) and their computational models (b, d)

throline. At the same time Margl and Ziegler [46] have investigated a cationic Pd(II) system with H2PCH=CHPH2 (Scheme 4d) as a model for Me-DUPHOS (Scheme 4c). We shall in the first part review the theoretical studies and contrast their findings with experimental results including those published after 1996. The synthesis of polyketones from CO and ethylene by transition metal catalysts represents the most successful example of copolymerization between ethylene and a monomer with a polar group. However, it would be highly desirable to develop catalysts that could copolymerize readily available polarfunctionalized monomers H2C=CHX (X=CN,NH2, halogen, C(O)OR and OC(O)R ) with a-olefins at mild conditions to produce a wide range of new polymers. In fact, the design of insertion catalysts for polar copolymerization is currently a very active research area [22, 23], and we shall in the second part review results from theoretical studies in this field [30, 31, 36]. 4.1 Co-Polymerization of CO and Ethylene 4.1.1 Experimental and Calculated Rates for the Insertion Processes of Importance for Alternating Ethylene/CO Copolymerization The co-polymerization of ethylene (olefins) with CO to produce polyketones (9) involves the insertion of CO into a metal-alkyl bond M-CH2-CH2-C(O)-R + CO Æ M-C(O)-CH2-CH2-C(O)-R

(10)

alternating with the insertion of an olefin into the metal-acyl bond M-C(O)-CH2-CH2-C(O)-R + C2H4 Æ M-CH2-CH2-C(O)-CH2-CH2-C(O)-R (11)

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Thus, the CO insertion process (Eq. 10) must be highly competitive with the insertion of ethylene into the metal-alkyl bond representing a “double ethylene insertion”: M-CH2-CH2-C(O)-R + C2H4 Æ M-CH2-CH2-CH2-CH2-C(O)-R

(12)

whereas Eq. (11) will have to be favored over insertion of CO into a metal-acyl bond: M-C(O)-CH2-CH2-C(O)-R + CO Æ M-C(O)-C(O)-CH2-CH2-C(O)-R

(13)

representing a “double CO insertion” . We present in Fig. 14 a chart for the he productive section of the catalytic cycle leading to an alternating CO/olefin co-polymer. Brookhart et al. have in a number of elegant experimental studies [42, 43] determined activation parameters for some of the processes (Eqs, 10–13) and their findings are compared with computational results [45b, 46] in Table 1. It follows from Table 1 that the insertion of CO into a metal-acyl bond (Eq. 13) have calculated activation barriers that are 28.2 kcal mol–1 for (N-N)Pd(acyl)(CO)+ (entry 5) and 26.6 kcal mol–1 for (P-P)Pd(acyl)(CO)+ (entry 11), respectively, whereas the corresponding experimental values are unavailable. These barriers are much higher than for the corresponding insertion

Fig. 14 Flow chart of the productive section of the catalytic cycle leading to an alternating CO/olefin copolymer. Stages of the reaction are identified with numbers. Species in square brackets refer to transition states, structures in curved brackets refer to unstable (not observable) species. All species referred in this section carry a single positive charge

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Table 1 Comparison of calculated and experimental activation barriers for insertions

Entry

Complexa

DH# (calc)b

1 2 3 4 5 6 7 8 9 10 11

(N-N)Pd(CH3)(CH2=CH2)+ (N-N)Pd(C2H5)(CH2=CH2)+ (N-N)Pd(acyl)(CH2=CH2)+ (N-N)Pd(CH3)(CO)+ (N-N)Pd(acyl)(CO)+ (P-P)Pd(CH3)(CH2=CH2)+ (P-P)Pd(C2H5)(CH2=CH2)+ (P-P)Pd(acyl)(CH2=CH2)+ (P-P)Pd(CH3)(CO)+ (P-P)Pd(C2H5)(CO)+ (P-P)Pd(acyl)(CO)+

16.2

a

b c

DH# (expl)b

18.5 18.2 14.9 28.2 15.6 13.9

15.2 15.9 14.8

11.5 26.6

DG# (expl)b 18.5 19.4 16.6 15.4 16.6 16.3 12.3 14.8 13.4

DS# (expl)c

–3.72

–6.2 –1.6 0.1

N-N isb of Scheme 5 for calculated values by Morokuma et al. [45a] anda of Scheme 5 for experimental values by Rix et al. [42], P-P isd of Scheme 5 for calculated values by Margl and Ziegler [46a]and c of Scheme 5 for the experimental valuesby Shultz et al. [43]. kcal mol–1. cal mol–1 K–1.

of ethylene into an acyl bond (11) with calculated activation enthalpies of 18.2 kcal mol–1 (entry 3), 13.9 kcal mol–1 (entry 8) and observed free energies of activation given by 16.6 kcal mol–1 (entry 3) and 12.3 kcal mol–1 (entry 8), respectively. The kinetic data for the processes at Eqs. (11) and (13) clearly seem to indicate that ethylene insertion into the metal-acyl bond is strongly favored over CO insertion as it must for polyketone polymers to be formed. The insertion of CO into the metal-acyl bond is calculated to be endothermic by 15.5 kcal mol–1 for (N-N)Pd(acyl)(CO)+ [46a] and 19.5 kcal mol–1 for (P-P)Pd(acyl)(CO)+ [46a], respectively.A detailed computational analysis [12a] revealed that both the high barrier and unfavorable energetics for CO insertion into the metal-acyl bond can be attributed to the weakness of the resulting carbon-carbon bond. On the other hand the insertion of ethylene into the metal-acyl bond has not only a lower barrier it is also exothermic by 22.3 kcal mol–1 for (N-N)Pd(acyl)(CO)+ [45a] and 17.7 kcal mol–1 for (P-P)Pd(acyl)(CO)+ [46a]. The more favorable kinetics and energetics for the insertion of ethylene into the metal-acyl bond can be attributed to the formation of a strong carbon-carbon bond [46a]. The formation of polyketones according to Eq. (9) requires in addition that CO insertion into the metal-alkyl bond is favored over ethylene insertion. That is, the path IbÆId of Scheme 5 should be preferred over IaÆIc. It is readily shown [8] that [CO] K $ %$ 01 [C H ]%

rate of Ib Æ Id kCO 005 = 6 rate of Ia Æ Ic ke

1

2

4

(14)

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Scheme 5 Ethylene and CO insertion into a metal-alkyl bond

This relation is derived under the assumption that ethylene insertion (1aÆ1c.) and CO insertion (IbÆId) are both sufficiently exothermic to be virtually irreversible. This assumption is justified by the calculated [46b] heats of reaction given by 16.5 kcal mol–1 (IaÆIc.) and 15.3 5 kcal mol–1 (IbÆId), respectively. Kinetically, one finds from experiment that the barriers of ethylene insertion are 3.1 kcal mol–1 and 1.8 kcal mol–1 higher than CO insertion for the (N-N) and (P-P) systems, respectively; see Table 1. The corresponding calculated values are 1.3 kcal mol–1 and 4.1 kcal mol–1 higher, respectively. Thus the ratio of relative rates (kCO/ke) in Eq. (14) would appear to favor CO insertion. However, with the barrier differences given above (ke/kCO) would at most amount to 103 . Thus the difference in rate between the two insertion processes could not alone explain the strict alternation CO and ethylene insertion. This is especially the case since the concentration ratio [CO]/[C2H4] of Eq. (14) under normal experimental conditions [8] is [CO]/[C2H4]~10–3, such that (kCO/ke) [CO]/[C2H4] of Eq. (14) is close to 1. The last factor left is the equilibrium constant K1 = ([Ia][CO]/[Ib][C2H4])

(15)

It has been estimated experimentally to be ~104 for both the N-N [42] and P-P [43] systems. This corresponds to a preference of 5 kcal mol–1 for CO coordination over C2H4 attachment to the alkyl complex in Scheme 5. The corresponding theoretical values are in the range of 7–10 kcal kcal mol–1 depending to the nature of the alkyl complex. It is thus clear, as first pointed out by Rix et al. [42], that the preference for CO insertion in Scheme 1 is due to the larger affinity of CO to the metal-alkyl complex, and to a lesser degree to the faster rate of CO insertion over ethylene insertion. It is finally worth to point out that the two theoretical studies by Morokuma et al. [45] and Margl and Ziegler et al. [46] agree remarkably well with experi-

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ment [42, 43], Table 1. This is so much more gratifying since the computational studies based on density functional theory [37] in some instances were published prior to the experimental investigations. 4.1.2 Experimental and Calculated Rates for the Insertion Processes of Importance for Alternating Ethylene/CO Copolymerization Catalysed by Nickel Complexes Cationic Ni(II) complexes of bidentate nitrogen and phosphorus ligands are not nearly as good catalysts for alternating CO and ethylene co-polymerization as their Pd(II) homologues [44]. The Ni(II) systems have much lower activity and produces at best low molecular weight polyketones [44]. The Ni(II) based CO/ethylene co-polymerization has been studied computationally by Morokuma et al. [45b] with the bidentate nitrogen ‘phen’ ligand of Scheme 4. The calculated enthalpies for complexation of ethylene and CO to methyl and acyl complexes of Ni(II) and Pd(II) are shown in Table 2. The same table displays in addition energy barrier for the insertion of ethylene and CO into the metal-methyl and metal-acyl bonds. It follows from Table 2 that CO insertion (entry 4) has nearly as high a barrier for Ni(II) as for Pd(II). Thus, it would appear that double CO insertion should be just as unlikely for the lighter metal as it was found to be for the 4d congener in the last section. Further, in considering again Eq. (14) for the nickel system one would have to conclude that double ethylene insertions are unlikely. This is so since CO also binds much stronger to Ni(II) than ethylene (K1 (1) whereas the barrier of CO insertion into the Ni-methyl bond is slightly lower than the barrier for ethylene insertion (kCO/ke≥1). Thus, the above consideration would indicate that the pattern of alternating insertions should be just as prevalent for Ni(II) as for Pd(II). Table 2 Comparison of calculated binding energiesb and insertion barriers for nickel and palladium complexes

Entry

1 2 3 4 a c d e f

Complexa c(N-N)M(CH )(CH =CH )+ 3 2 2 d(N-N)M(acyl)(CH =CH )+ 2 2 c(N-N)M(CH )(CO)+ 3 c(N-N)M(acyl)(CO)+

eDHo M=Pd

eDHo

fDH# M=Pd

fDH#

M=Ni

–31.7 –19.1 –41.1 –28.3

–27.9 – 7.6 –39.6 –19.4

16.2 18.2 14.9 28.2

9.9 6.3 9.8 24.9

M=Ni

N-N isb of Scheme 4 for calculated values by Morokuma et al. [45a] bkcal mol–1. Binding and insertion of ethylene. Binding and insertion of CO. Binding energy. Insertion barriers.

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It follows from Table 2 that the CO insertion into a metal-methyl bond (as a representative of a CO insertion into a metal-alkyl bond) and an ethylene insertion into a methyl-acyl bond both are much more facile for Ni(II) than for Pd(II). One might thus be lead to predict that the Ni(II) catalyst should have a higher activity than the Pd(II) system, in direct disagreement with experimental findings [44]. A first clue as to why the Ni(II) system might be a poorer co-polymerization catalyst comes from the binding energies presented in Table 2. The binding of CO or ethylene to the methyl complex in Eq. (16)

(16) is the coordination of the two ligands to a coordinatively unsaturated species and the complexation energy is thus a direct measure of the M-X bond strengths.We note further that the complexation energies for the nickel systems only are a few kcal mol–1 smaller than for the palladium complexes. On the other hand, complexation of X to the acyl complex requires not only the formation of a M-X bond but also the breakage of the M-O link in the h2 acyl complex. Thus, the complexation energy according to Eq. (17) should be

(17) which is much lower than the M-X bond. This is readily seen from Table 2 where the M-X complexation energies for the process at Eq. (16) are much larger than for Eq. (17). In fact, one might estimate the M-O bond energy in the h2 acyl complex as the difference in complexation energy between Eqs. (16) and (17). Such an estimate afford a value of 13 kcal mol–1 for the Pd-O bond compared to 20 kcal mol–1 for the Ni-O bond. The higher oxygen affinity of nickel compared to palladium is not surprising and in good agreement with experimental and computational findings [30, 31]. We shall now revisit the productive cycle in Fig. 14 for alternate CO/ethylene insertion in order to find possible explanations for why Ni(II) systems have such a low activity with respect to CO/ethylene co-polymerization. Our analysis will make use of recent studies of cationic nickel complexes with bidentate phosphine ligands due to Brookhart et al. [44] as well as the observation that nickel is more oxo-philic than palladium. The uptake of CO by (1) to produce (3) (see Fig. 14) is exothermic by 7.7 kcal mol–1 for palladium. Thus, in this case (3) will be present in sufficient concentrations as a precursor for CO insertion into an alkyl bond, although the reaction (1)+COÆ(3) is endergonic by some 2–3 kcal mol–1 assuming an

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entropic contribution of 10 kcal mol–1 to the free energy. The reason that the CO uptake is less favorable than expected is of course the conversion of a strong equatorial chelating Pd-O bond in (1) to a weaker axial chelating Pd-O bond in (3); see Fig. 14. Turning next to the nickel system, we might estimate that the process (1)+COÆ(3) is some 10 kcal mol–1 less favorable since nickel is more oxo-philic and forms weaker Ni-CO bonds. Thus the low concentration of the precursor complex (3) for CO insertion into the nickel-alkyl bond would substantially slow down the CO/ethylene

(18)

co-polymerization process. However the nickel system seems to be able to overcome this hurdle (see Eq. 18) [44] by taking up one additional CO ligand and producing the five coordinated bis-carbonyl complex 3a from which CO insertion is facile leading to (after uptake of one more CO ligand) the five coordinated bis-carbonyl acyl complex 5a that has been characterised by Brookhart et al. [44]. The second insertion in the productive cycle of Fig. 14 would involve the chelated acyl complex (5). Again it might have been difficult to convert this to the olefin complex (6) in the nickel case as the strong chelate Ni-oxygen bond has to be weakened. However, for nickel it seems that (5) is replaced with the five-coordinated acyl complex 5a by uptake of one additional CO. However, 5a is not amenable for ethylene uptake as a first step in the insertion of ethylene into the metal-acyl bond since ethylene will have to replace the more strongly bound CO (>10 kcal mol–1 ). It is thus likely that the CO/ethylene polymerization cycle is blocked by a species such as 5a or the four-coordinated chelate (5) of Fig. 14. We conclude that the inability of cationic Ni(II) complexes to act as CO/ethylene co-polymerization catalysts stems from the strong chelating Ni-O bond as well as the tendency of the nickel system to form five-coordinated bis-carbonyl complexes. However, the nickel systems are not yet as well studied as their palladium homologues, and much more theoretical and experimental work has to be carried out before the Ni(II) system is fully understood.

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5 Co-Polymerization of Olefin with Other Polar Monomers A new emerging frontier in olefin polymerization is the controlled copolymerization of a-olefins with monomers bearing a polar functional group [22, 38]. An incorporation of even small amounts of polar monomers dramatically modifies the polymer properties compared to regular polyolefins in terms of toughness, adhesion, barrier properties, surface properties, solvent resistance, miscibility with other polymers, and rheology [22, 38]. Of particular interest are the copolymers of monomers with oxygen-and nitrogen-containing polar groups, such as vinyl alcohols, acids, esters, amines and acrylonitriles. Presently, available polar copolymers are produced in a radical polymerization processes under high-temperature and high-pressure conditions [39].A design of the single-site copolymerization catalyst would open new, less expensive routes to commercially available copolymers, but it could also lead to the synthesis of new materials, potentially possessing new properties. In order to incorporate polar monomers into a polymer chain in random copolymerization process, it is required that its insertion follows the same reaction mechanism as that of a-olefin Ziegler-Natta polymerization. Thus, the polar monomer must also be bound to the metal center by its double C=C bond rather than by the oxygen (or nitrogen) atom of the polar group. The initial steps in the copolymerization processes involve the competition between the p-complexes of olefin and polar monomer, and the complexes with the latter being bound by its polar group (Fig. 15). Thus, it seems reasonable to assume that potential catalysts can initially be screened by determining the preferred bonding mode: the model systems with a strong preference of the O-bound or N-bound coordination mode can be excluded as less promising catalysts.

Fig. 15 Initial steps in the copolymerization of a-olefins with polar monomers. Here, methyl acrylate and Brookhart Pd-diimine catalyst are used as an example

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We shall next in turn discuss the bonding preference of oxygen and nitrogen containing polar monomers. 5.1 Preferred Binding Mode of Oxygen Containing Monomers Michalak and Ziegler [30] have computationally investigated the binding mode of the oxygen-containing monomers (methyl acrylate and vinyl acetate) in the complexes involving cationic and neutral Ni- and Pd-based catalysts with the Brookhart [1] and Grubbs ligands [9]; see Fig. 16. The main purpose of this study was to understand the origin of the difference in the behavior of the Brookhart systems based on Pd (active copolymerization catalyst for ethylene and acrylate) and Ni (inactive). The role of the electronic and steric factors was discussed, on the basis of the DFT calculations for simplified model systems as well as a selection of real catalysts. Also discussed were the effects of the reduced basicity of the carbonyl oxygen on the monomer (in the fluorinated compounds) as well as of the reduced oxophilicity of the catalyst (in the neutral Grubbs system). The molecular systems discussed are shown in Fig. 16. Consideration was give to complexes in which the polar monomer is bound to the metal by either its olefinic functionality (p-complexes) or by the oxygen atom of the polar group (O-complexes). Both, the Pd- and Ni-based catalysts with Brookhart and Grubbs ligands were considered. With methyl acrylate (MA) and vinyl acetate (VA) as comonomers, the calculations were performed for the generic catalyst models (1a,b and 3a,b of Fig. 16), in which the bulky substituents of the real systems have been replaced by hydrogen atoms; Table 3. In addition, in the generic Brookhart Pd- and Ni-based catalysts, the complexes with fluorinated monomers (FMA and FVA) were also studied in order to obtain insight into the influence of the basicity of the carbonyl oxygen on the complexation energies and the preference of the bonding mode, Table 3. Finally, calculations were also performed on the complexes involving methyl acrylate and the larger models for Ni- and Pd-based Brookhart (2a,b of Fig. 16) and Ni-based Grubbs (4a, 5a, 6a of Fig. 16) systems, with the bulky substituents corresponding to the real catalysts, Table 4. This set of complexes made it possible to discuss the role of both, the electronic and the steric factors, as well as to compare the results with the previous studies [11,13–15] on the ethylene and propylene homopolymerizations with Brookhart and Grubbs catalysts. The results (Table 3) clearly indicate that in the case of the Ni-based Brookhart catalyst the polar monomers are bound by the carbonyl oxygen atom, while in the Pd-systems the p-complexes are preferred, Tables 3 and 4. The difference between the Ni- and Pd-systems has mainly a steric origin with larger repulsive interaction between the occupied d-orbitals on palladium and the oxygen lone-pair orbitals. On the other hand, there is practically no difference in the orbital-interaction contribution (between occupied and virtual orbitals ) to the binding energy between Ni- and Pd-based systems, as far as a

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Table 3 The monomer binding energies for the generic models for the Ni- and Pd-based Brookhart and Grubbs catalysts

Catalysta

Monomera

DE (C=C)b

DE (O)c

E(C=C)–E(O)d

1a. Brookhart/Ni 1b. Brokhart/Pd 1a. Brookhart/Ni 1b. Brokhart/Pd 1a. Brookhart/Ni 1b. Brokhart/Pd 1a. Brookhart/Ni 1b. Brokhart/Pd 3a. Grubbs/Ni 3b. Grubbs/Pd 3a. Grubbs/Ni 3b. Grubbs/Pd

MA MA VA VA FMA FMA FVA FVA MA MA VA VA

–17.10 –20.70 –17.07 –20.12 –13.93 –17.95 –11.41 –14.76 –17.74 –24.34 –16.09 –21.72

–21.10 –17.30 –17.75 –14.96 –16.25 –12.92 – 9.99 – 8.10 –10.18 –10.17 – 9.72 – 9.56

+ 4.00 – 3.40 + 0.68 – 5.16 + 2.32 – 5.03 – 1.42 – 6.66 – 7.56 –14.17 – 7.18 –12.16

a b c d

See Fig. 16. p-Complex stabilization energy, in kcal/mol. Stabilization energy of the O-complex, in kcal/mol. The difference in the energies of the p-complex and O-complex.

Table 4 The binding energies for methyl acrylate complexes with the real Brookhart and Grubbs catalysts

Catalysta

DE (C=C)b

DE (O)c

E(C=C)–E(O)d

2a. 2b. 4a. 5a. 6a.

–10.10 –13.65 –12.82 –12.50 –13.15

–13.09 –10.64 – 6.49 – 7.51 – 7.31

+2.99 – 3.01 – 6.33 – 4.99 – 5.84

a b c d

Brookhart/Ni Brokhart/Pd Grubbs/Ni Grubbs/Ni Grubbs/Ni

See Fig. 16. p-Complex stabilization energy, in kcal/mol. Stabilization energy of the O-complex, in kcal/mol. The difference in the energies of the p-complex and O-complex, in kcal/mol.

comparison between the two binding modes is concerned. In the case of the fluorinated polar monomers (FMA and FVA), the complexation energies of both, the p- and O-complexes are decreased in comparison to methyl acrylate and vinyl acetate. Thus, in a prospective copolymerization with fluorinated compounds, the incorporation of the polar monomer into a polyolefin chain would be relatively modest. The use of neutral catalysts seems to be more promising. The results for Ni- and Pd-based systems with Grubbs ligands show that for both metals the p-complexes are strongly preferred over the O-complexes; the binding energies of the p-complexes are comparable with the corresponding systems involving the Brookhart catalysts.

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Fig. 16 Complexes studied in the work by Michalak and Ziegler [30]

Further, the results show that an introduction of the steric bulk in the real catalysts (Table 4) does not affect the preference of the comonomer binding mode; the absolute values for the binding energies of the p- and O-complexes are decreased, while the differences between them remain qualitatively similar. Also, the relative binding energies of acrylate, propylene, and ethylene, calculated for the real catalyst 2b of Fig. 16, are in qualitative agreement with the experimental data obtained for a similar system [48]; both the calculations and experimental data show the strongest stabilization for the ethylene p-complexes, and the weakest for acrylate. A comparison of Ni- and Pd-based Brookhart systems leads to the conclusion that the analysis of the polar comonomer binding mode can be used as a screening test to select the best prospective catalytic candidates for the copolymerization; the complexes with preference of the O-complexes can be excluded from further studies. Here, the use of theoretical methods can be very useful. Obviously, the monomer binding is only an initial step in the complex mechanism of the copolymerization processes. Therefore, the studies on the polar comonomer binding mode can be used only for a negative selection. To get more definitive answers about the catalyst activities, a full mechanistic study is needed, involving evaluation of the barriers of all the elementary reactions and the relative stabilities of the reaction intermediates.

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5.2 Preferred Binding Mode of Nitrogen Containing Monomers Deubel and Ziegler [36] have studied the coordination of several olefins with a N-containing polar group to Brookharts nickel (1a) and palladium (1b) complexes as well as Grubbs nickel (3a) and palladium (3b) compounds, see Fig. 16. The stabilization energies for the nickel N complexes are given in Table 5. The calculations show that the cationic Brookhart model catalyst (1a) forms very strong bonds to the polar sites. The smallest and largest stabilization energies, respectively, have been predicted for vinylamine (–23.1 kcal/mol) and methylamine (–31.2 kcal/mol) while the calculated coordination energies for nitrile binding are in between (–28.4 kcal/mol). Trimethylamine forms a slightly weaker bond (–28.3 kcal/mol) to the metal than methylamine (–31.2 kcal/mol). The metal-N bonds in the Grubbs system (3a) are much weaker than in the Brookhart system; stabilization energies not larger than –23.2 kcal/mol (methylamine) have been calculated for the N complexes with the Grubbs catalyst. The differences in the energies of p and N coordination are of particular importance. These data are listed in Table 6 for the target monomers. The coordination of the polar site of nitriles and amines with the Brookhart nickel catalyst 1a of Fig. 16 is favored over the p mode by at least 10.0 kcal/mol. There is one exception: vinylamine prefers p coordination by 3.9 kcal/mol. The Grubbs nickel system 3a of Fig. 16 is much more promising than the Brookhart catalyst 1a of Fig. 16. The nitriles favor N coordination only slightly (1.2 kcal/mol), while vinylamine again prefers p binding by more than 3 kcal/mol. Surprisingly, trimethylamine (as a model for monomers of the type CH2=CH(CH2)nN(CH3)2) forms a weaker bond to the metal than methylamine, indicating that steric effects are already present in the generic systems to a Table 5 Calculated stabilization energies (kcal/mol) for the coordination modes a–i of the polar monomers with the modela catalysts 1a–b, 3a–b

a b c d e f g h i a

Monomer

Binding mode

1a

3a

1b

3b

CH2=CH2 CH2=CHCH3 CH2=CH2CN CH2=CH2CN CH2=CH2NH2 CH2=CH2NH2 CH3CN CH3NH2 N(CH3)3

p p p N p N N N N

–16.2 –18.3 –11.5 –28.4 –27.0 –23.1 –28.3 –31.2 –28.3

–18.0 –16.8 –19.0 –20.2 –21.0 –17.5 –17.5 –23.2 –16.1

–20.0 –22.4 –14.6 –27.4 –30.2 –23.9 –27.5 –31.8 –28.9

–24.7 –24.2 –24.8 –21.9 –27.4 –20.8 –20.0 –26.6 –23.7

See Fig. 16.

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Table 6 Calculated differences in the stabilization energies (kcal/mol) for p coordination and N coordination of the polar monomers with the modela catalysts 1a–b, 3a–b. Negative values indicate that the p complexes are favored while positive values indicate that N binding is preferred

Target monomer

Model monomers

1a

3a

1b

3b

CH2=CH2CN CH2=CH(CH2)nCN CH2=CH2NH2 CH2=CH(CH2)nNH2 CH2=CH(CH2)nN(CH3)2

CH2=CH2CN CH2=CHCH3 and CH3CN CH2=CH2NH2 CH2=CHCH3 and CH3NH2 CH2=CHCH3 and CH3N(CH3)2

16.9 10.0 –3.9 12.9 10.0

1.2 1.1 –3.5 6.4 –0.7

12.9 5.2 –6.3 9.5 6.0

–3.2 –4.0 –6.6 2.6 –0.9

a

See Fig. 16.

certain extent. These effects are stronger in 3a than in 1a, since the former catalyst has a larger bite angle. A comparison between the nickel and palladium systems can also be deduced from Tables 5 and 6. The calculations reveal that the Brookhart palladium catalyst 1b and the target monomers form p complexes which are in general more stable than their nickel counterparts 1a by approximately 3 kcal/mol (Table 5). The same systematic trend is present in the complexes with the Grubbs catalysts; the p complexes of the palladium compound 3b are stabilized by about 6 kcal/mol in comparison with the corresponding nickel systems 1b. There are slight differences in the energies for the coordination of the polar site to the Ni and Pd Brookhart catalysts 1a and 1b of Fig. 16. The Pd Grubbs catalyst 3b forms slightly more stable N complexes than the corresponding Ni catalyst 3a of Fig. 16; the energy difference has been predicted to be about 3 kcal/mol (Table 5). A detailed rational for the calculated trends can be found in [36]. 5.3 Methyl Acrylate Insertion and the Chelate Opening The co-polymerization of polar monomers other than CO with a-olefins is a field under development and theoretical calculations are just emerging [30, 49]. We shall here just review some of the findings of a recent study on the co-polymerization of acrylate with ethylene [30]. Figure 17 presents the energy profiles for the methyl acrylate insertion into the Pd-alkyl and Ni-alkyl bond in the generic diimine systems [31, 32]. The results clearly indicate that it is not the insertion barrier which makes the Ni-system inactive in polar copolymerization. The acrylate insertion barrier is substantially lower for the Ni-catalyst then for the Pd-complex. This, in fact, should not be surprising, as the ethylene insertion barriers are also lower for the Ni-system.

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Fig. 17 Energy profile for 2,1-insertion of methyl acrylate into a Pd(II)-alkyl bond (black) or a Ni(II)-alkyl bond (gray)

The results of Fig. 17 also show that the chelate complexes are more stable for the Ni-catalyst then for the Pd-complexes. This larger stability is again a manifestation of the stronger oxophilicity of the Ni-systems. The static and dynamic DFT studies [31, 32] on the chelate opening reactions reveal that the two-step mechanism of the chelate opening must be assumed in order to explain the difference between the Ni- and Pd-based systems. Namely, in the most stable ethylene complexes resulting from the chelates, the chelating metal-oxygen bond is still present in the axial position. The ethylene insertions starting from such structures have very high barriers (ca. 30 kcal/mol for the six-membered chelate with the generic Pd-catalyst). Much lower barriers, comparable to those of ethylene homo-polymerization (ca. 18 kcal/mol for a generic Pd-catalyst) have been obtained for the insertions starting from the higher energy isomers in which the chelating bond has been broken. In both cases the insertion barriers computed for the Ni-catalyst are lower than for the Pd-system. However, the opening of the chelate prior to ethylene insertion has substantially lower barrier for Pd- (ca. 9 kcal/mol) than for Ni-catalyst (ca 15–19 kcal/mol).

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6 Concluding Remarks We have presented a comprehensive review of our recent theoretical studies on the polymerization and copolymerization processes catalyzed by the late transition metal complexes. The results of these studies show that a combined DFT/stochastic approach can be successfully used to model the elementary reactions in the polymerization processes and the influence of the reaction conditions on the polyolefin branching. Such an approach makes it possible to understand the microscopic factors controlling the branching of polyolefins and explain the differences between the Pd- and Ni-catalysts. The results also demonstrate that a wide range of microstructures can be potentially obtained from the ethylene polymerization. Thus, a rational design of the catalyst producing the desired polymer topology should be possible. The results of the static and dynamic DFT calculations for the methyl acrylate copolymerization suggest that there are two factors inhibiting the polar co-polymerization in the Ni-catalyst case: (1) the initial O-complex formation; (2) a difficult chelate opening prior to insertion of the next monomer. Both of those factors may be overcome by the use of the complexes with reduced oxophilicity of the metal on the catalyst. Acknowledgement This work has been supported by the National Sciences and Engineering Research Council of Canada (NSERC) and the Petroleum Research Fund, administered by the American Chemical Society (ACS-PRF No. 36543-AC3). A.M. acknowledges a NATO Postdoctoral Fellowship. T. Z. thanks the Canadian government for a Canada Research Chair.

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11. Musaev DG, Froese RDJ, Morokuma K (1997) J Am Chem Soc 119:367; (b) Musaev DG, Svensson M, Morokuma K, Strömberg S, Zetterberg K, Siegbahn P(1997) Organometallics 16:1933; (c) Musaev DG, Froese RDJ, Morokuma K (1997) New J Chem 22:1265; (d) Froese RDJ, Musaev DG, Morokuma K (1998)J Am Chem Soc 120:1581; (e) Musaev DG, Froese RDJ, Morokuma K (1998) Organometallics 17:1850; (f) Musaev DG, Morokuma K (1999) Top Catal 7:107 12. Von Schenck H, Strömberg S, Zetterberg K, Ludwig M, Åkermark B, Svensson M (2001) Organometallics 20:2813 13. Deng L, Margl P, Ziegler T (1997) J Am Chem Soc 119:1094; (b) Deng L, Woo TK, Cavallo L, Margl P, Ziegler T (1997) J Am Chem Soc 119:6177; (c) Michalak A, Ziegler T (1999) Organometallics 18:3998; (d) Woo TK, Ziegler T (1999) J Organomet Chem 591:204; (e) Woo TK, Blöchl PE, Ziegler T (2000) J Phys Chem A 104:121; (f) Michalak A, Ziegler T (2000) Organometallics 19:1850 14. Chan MSW, Deng L, Ziegler T (2000) Organometallics 19:2741 15. Deng L, Margl P, Ziegler T (1999) J Am Chem Soc 121:6479; (b) Margl P, Deng L, Ziegler T (1999) Organometallics 18:5701; (c) Griffiths EAH, Britovsek GJP, Gibson V, Gould IR (1999) Chem Commun 1333; (d) Khoroshun DV, Musaev DG, Vreven T, Morokuma K (2001) Organometallics 20:2007 16. Ittel SD, Johnson LK, Brookhart M (2000) Chem Rev 100:1169 17. Britovsek GJP, Gibson VC, Wass DF (1999) Angew Chem Int Ed 38:428 and references cited therein 18. Guan Z, Cotts PM, McCord EF, McLain SJ (1999) Science 283:2059 19. Cotts PM, Guan Z, McCord EF, McLain SJ (2000) Macromolecules 33:6945 20. Gates SJ et al. (2000) Macromolecules 33:2320 21. McCord SJ et al. (2001) Macromolecules 34:362 22. Boffa LS, Novak BM (2000) Chem Rev 100:1479 and references cited therein 23. Mecking S, Johnson LK, Wang L, Brookhart M (1998) J Am Chem Soc 120:888 24. Hicks FA, Brookhart M (2001) Organometallics 20:3217 25. Rappe AK, Skiff WM, Casewit CJ (2000) Chem Rev 100:1435 and references cited therein 26. Angermund K, Fink G, Jensen VR, Kleinschmidt R (2000) Chem Rev 100:1457 and references cited therein 27. Michalak A, Ziegler T (2002) J Am Chem Soc 124:7519 28. Michalak A, Ziegler T (2003) Macromolecules 36:928 29. Michalak A, Ziegler T (2003) Organometallics 22:2069 30. Michalak A, Ziegler T (2001) Organometallics 20:1521 31. Michalak A, Ziegler T (2001) J Am Chem Soc 123:12266 32. Michalak A, Ziegler T (2003) Organometallics 22:2660 33. Tempel DJ, Johnson LK, Huff RL, White PS, Brookhart M (2000) J Am Chem Soc 122: 6686 34. Shultz LH, Brookhart M (2001) Organometallics 20:3975 35. Shultz LH, Tempel DJ, Brookhart M (2001)J Am Chem Soc 123:11539 36. Deubel D, Ziegler T (2002) Organometallics 21 37. Reppe W, Magin A (1951) US Pat 2,577,208; Chem Abs (1952) 46,6143 38. Klabunde U, Tulip TH, Roe DC, Ittle SD (1987) J Organometal Chem 41:123 39. Keim W, Maas H, Mecking S (1995) Z Naturforsch 50b:430 40. Drent E, Budzelaar PHM (1996) Chem Rev 96:663 41. Sen A (1993) Acc Chem Res 26:303 42. Rix FC, Brookhart M, White PS (1996) J Am Chem Soc 118:4746 43. Shultz CS, Ledford J, DeSimone JM, Brookhart M (2000) J Am Chem Soc 122:6351 44. Shultz CS, DeSimone JM, Brookhart M (2001) J Am Chem Soc Organometallics 20:16

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45. (a) Koga M, Morokuma K (1986) J Am Chem Soc 108:6136; (b) Svensson M, Matsubara T, Morokuma K (1996) Organometallics 15:5568 46. (a) Margl P, Ziegler T(1996) J Am Chem Soc 118:7337; (b) Margl P, Ziegler T (1996) Organometallics 15:551 47. Angermund K, Fink G, Jensen VR, Kleinschmidt R (2000) Chem Rev 100:1457 and references cited therein 48. Mecking S, Johnson LK, Wang L, Brookhart M (1998) J Am Chem Soc 120:888 49. Philipp DM, Muller RP, Goddard WA III, Storer J, McAdon M, Mullins M (2002) J Am Chem Soc 124:10198

Top Organomet Chem (2005) 12: 187 – 218 DOI 10.1007/b104403 © Springer-Verlag Berlin Heidelberg 2005

Co-Oligomerization of 1,3-Butadiene and Ethylene Promoted by Zerovalent ‘Bare’ Nickel Complexes Sven Tobisch (

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Institut für Anorganische Chemie der Martin-Luther-Universität Halle-Wittenberg, Fachbereich Chemie, Kurt-Mothes-Straße 2, 06120 Halle, Germany [email protected]

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Co-Oligomerization of 1,3-Butadiene and Ethylene vs Cyclooligomerization of 1,3-Butadiene Promoted by Zerovalent ‘Bare’ Nickel Complexes: A Mechanistic Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213

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Abstract The transition-metal-catalyzed cyclooligomerization of 1,3-dienes and the cooligomerization of 1,3-dienes and alkenes, that involve the stereoselective formation of carbon-carbon bonds, are of great interest from both a scientific as well as an industrial point of view. In this account a theoretical well founded, comprehensive mechanistic view of the [Ni0]-catalyzed co-oligomerization of 1,3-butadiene and ethylene is presented. The

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first suggested mechanism of Wilke and co-workers has been confirmed in essential details but supplemented by novel insights into how the catalytic co-oligomerization reaction operates. Furthermore, crucial aspects of important elementary steps of the [Ni0]-catalyzed generation of C10- and C12-olefins via butadiene/ethylene co-oligomerization and butadiene cyclooligomerization are compared. Keywords Structure-reactivity relationships · Reaction mechanism · Density functional calculations · Oligomerization · Homogeneous catalysis

List of Abbreviations and Symbols CDD Cyclodeca-1,5-diene CDT Cyclododeca-1,5,9-triene COD Cycloocta-1,5-diene DFT Density Functional Theory DT Deca-1,4,9-triene VCH 4-Vinylcyclohexene

1 Introduction Zerovalent nickel complexes have been demonstrated by the comprehensive and systematic investigations of Wilke and co-workers as versatile and useful catalysts for the cyclooligomerization of 1,3-butadiene [1, 2]. Depending on the actual structure of the active catalyst species, nickel complexes support the generation of C8-cycloolefins (with 4-vinylcyclohexene, VCH, and cis,ciscycloocta-1,5-diene, cis,cis-COD, as major products) and of C12-cycloolefins (with trans,trans,trans-cyclododeca-1,5,9-triene, all-t-CDT, as the predominant product) along different reaction channels that involve the linkage of two or three butadiene moieties, respectively [3]. Much of the mechanistic understanding of this intriguing reaction is largely due to the fundamental work of Wilke and co-workers [1–3]. Their first proposed mechanism has been recently confirmed in essential details, but supplemented, in a series of theoreticalmechanistic investigations [4], by novel insights into how the catalytic 1,3-butadiene cyclooligomerization reaction operates. The nickel complexes used for 1,3-butadiene cyclooligomerization are also known to catalyze the formation of co-oligomers between 1,3-dienes and olefins. For the zerovalent ‘bare’ nickel complex (for instance [Ni0(COD)2]) the 1,3-butadiene cyclooligomerization affording C12-cycloolefins is largely impeded in the presence of ethylene and instead C10-olefins (viz. 2:1 butadiene/ ethylene co-oligomers) are formed [5]. The product mixture contains both cyclic, namely cyclodeca-1,5-diene (CDD), and linear, namely deca-1,4,9-triene (DT), C10-olefins as the principal products. The co-oligomerization occurs in a highly stereoselective fashion, such that cyclodeca-cis-1,trans-5-diene (cis,

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trans-CDD) and deca-1,trans-4,9-triene (trans-DT) are the exclusively generated C10-olefins among the several possible isomers. The reaction temperature as well as the butadiene-to-ethylene ratio have been found to influence decisively the product distribution. For a 1:1 reactant ratio, low temperatures favor the generation of cis,trans-CDD (CDD:DT ~7:3 at 40 °C), while at elevated temperatures trans-DT is prevalent (CDD:DT ~3:7 at 80 °C). The C10-olefin proportion enlarges with the relative increase of the ethylene concentration, which serves to almost entirely suppress the generation of C12-cycloolefins as side products.

Although the experimental studies of Wilke and co-workers [5] has led to a fundamental understanding of the [Ni0]-catalyzed co-oligomerization of 1,3-butadiene and ethylene, there are still some essential mechanistic details that are not yet firmly established (see below). In the following account, we summarize the recent achievements in the theoretical-mechanistic exploration of the co-oligomerization of 1,3-butadiene and ethylene mediated by zerovalent ‘bare’ nickel complexes. On the basis of the original proposal of Wilke and co-workers, we shall present a theoretically well-founded, refined mechanistic view of the co-oligomerization process as the result of a comprehensive computational exploration of all the critical elementary steps involved in the whole catalytic reaction course. The theoretical-mechanistic analysis provides novel insights into the catalytic structure-reactivity relationships of the co-oligomerization reaction and contributes to a deeper understanding of the decisive factors that control the C10-olefin product selectivity. This chapter is organized as follows. In the following section the tentative catalytic cycle proposed by Wilke and co-workers is outlined, followed, in the next section, by a short description of the computational approach employed and the catalyst model chosen. The structural and energetic aspects of all critical elementary steps of the complete catalytic cycle are presented after that. Then we propose a theoretically verified, refined catalytic reaction cycle, and follow that with the elucidation of the product distribution between linear and cyclic C10-olefins. Finally, the catalytic reaction courses of the [Ni0]-catalyzed co-oligomerization of 1,3-butadiene and ethylene and of the cyclooligomerization of 1,3-butadiene are compared.

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2 Tentative Catalytic Cycle of the [Ni0]-Catalyzed Co-Oligomerization of 1,3-Butadiene and Ethylene Similar to the nickel-catalyzed 1,3-butadiene cyclooligomerization [3], the cooligomerization of 1,3-butadiene and ethylene proceeds in a multistep fashion [5]. The nickel atom template undergoes a repeated change in its formal oxidation state by two, namely [Ni0aNiII], during the multistep addition-elimination mechanism. The reaction course of the co-oligomerization, however, is, to date, not completely understood. Scheme 1 displays a tentative catalytic cycle of the [Ni0]-catalyzed process, which is based on the experimental studies of Wilke and co-workers [5]. The zerovalent olefin-Ni0 complex is the active catalyst. This complex can exist in several forms of either the [Ni0(olefin)2] compound 1a or the [Ni0(olefin)3] compound 1b, where the catalytically active species possesses two coordinated butadienes. The first step involves the oxidative coupling of two butadiene moieties giving rise to the octadienediyl-NiII complex, which may be coordinatively saturated by complexation of further olefins. This complex occurs in various configurations, which are distinguished by the coordination mode of the octadienediyl framework, viz. the h3,h1(C1) species 2, the h3,h1(C3) species 3, and the bis(h3) species 4, all of which can be assumed to be in equilibrium. Ethylene insertion into the allyl-NiII bond in either of the octadienediyl-NiII species, with 4 suggested to be the active precursor [5], leads to the decatrienyl-NiII complex. Similar to the octadienediyl-NiII complex, the decatrienyl-NiII complex is present as species 5, 6, and 7, with the allylic group in the h3-p, h1(C1)-s and h1(C3)-s modes. Either one of these species can be considered as the precursor for production of both CDD and DT, respectively. The [Ni0(CDD)] product 8 is formed by reductive elimination under ring closure via formation of a C-C s-bond between the h1-alkyl group and the terminal allylic carbon, with 5 suggested to be the precursor [5]. The generation of DT, however, requires the transfer of a hydrogen atom. This is likely to proceed by b-H abstraction from the alkyl group, which was envisaged to involve the h1(C3)-s-allyl species 7, giving rise to a hydrido-NiII intermediate 9, and subsequent reductive CH elimination to afford the [Ni0(DT)] product 10. The several isomers of CDD and DT are formed through competing pathways along 5Æ8 and 5Æ10, respectively, that involve different stereoisomers of the decatrienyl-NiII precursor. Displacement of the C10-olefin products in subsequent consecutive kinetically facile substitution steps with butadiene and ethylene regenerates the active catalyst, thereby completing the catalytic cycle. The plausibility of this tentative reaction cycle is supported by stoichiometric reactions and is underlined because of its great similarity to the wellestablished catalytic course of butadiene cyclooligomerization [1–4]. Formal 16e– or 18e– forms of 1a and 1b, respectively, can be envisioned as likely candidates for the active catalyst, although it has been never experimentally characterized. A [Ni0(h4-cis-2,3-dimethyl-butadiene)2] complex [6], with two tetrahedrally coordinated cis-butadienes, and also the [Ni0(ethylene)3] complex [7],

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Scheme 1 Tentative catalytic cycle of the [Ni0]-catalyzed co-oligomerization of 1,3-butadiene and ethylene affording linear and cyclic C10-olefins. Based on experimental studies of Wilke and co-workers [5]. Please note that only the favorable forms of 1a and 1b are displayed

are well established Ni0–olefin compounds. The various octadienediyl-NiII configurations, as well as their facile mutual rearrangement [3e], have been firmly established for the PR3/P(OR)3-stabilized complex [3e, 6a, 8]. Bis(h1)-octadienediyl-NiII species, however, although conceivable as reactive intermediates for allylic conversion and ethylene insertion processes, are not likely to be involved in any of these steps. They have been demonstrated to be highly unfavorable energetically and seen to not participate along viable reaction paths of any of the crucial elementary processes of the cyclooligomerization reaction [4]. Indirect evidence for the intermediacy of the octadienediyl-NiII complex comes from the stereochemistry of the products generated by the co-oligomerization of piperylene (1,3-pentadiene) with ethylene and by piperylene cyclodimerization. The configuration of the methyl groups in the ten-membered ring of the co-oligomer was found to be identical to that observed in the methyl-substituted divinylcyclobutane cyclodimerization product [1a, 9]. Accordingly, the octadienediyl-NiII complex, which is a well-established intermediate of the 1,3-butadiene cyclooligomerization [1–4], is likely to be involved in the co-oligomerization reaction course as well. Although not directly observed for alkenes, insertion of analogous alkynes into the allyl-Ni bond of the octadienediyl-NiII complex has been observed in stoichiometric reactions,

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leading to the isolation of the related insertion product as well as of the corresponding cyclic co-oligomer [10]. Further evidence comes from the experimental observation that the generation of linear co-oligomers is entirely suppressed for the process involving substituted alkenes or alkynes, in which b-hydrogen atoms are absent [1a]. The pioneering investigations of Wilke and co-workers [5] led to a first fundamental understanding of how the [Ni0]-catalyzed co-oligomerization of 1,3-butadiene and ethylene operates. However, there are some important and intriguing, and yet to be firmly resolved, mechanistic aspects that have been the objectives of a recent theoretical-mechanistic investigation [11]: 1. What is the thermodynamically favorable and the catalytically active form of the catalyst complex? 2. In what fashion does the oxidative coupling preferably take place and which of the various octadienediyl-NiII forms is generated initially? 3. Which of the various configurations of the octadienediyl-NiII and the decatrienyl-NiII complexes are the thermodynamically preferred ones, respectively, and which of them act as the precursor for the ethylene insertion and for C10-co-oligomer formation following the CDD- and DT-generating routes? 4. Which of the isomeric syn or anti forms of the allyl-NiII bond of the octadienediyl-NiII intermediate display a higher aptitude to undergo ethylene insertion, and does the insertion preferably occur into the h3- or the h1allyl-NiII bond? 5. Does the competitive production routes for CDD and DT commence from identical or different configurations of the decatrienyl-NiII complex as the precursor? 6. Does the hydrogen transfer along the DT-generating route take place in a stepwise or a concerted fashion; i.e. is an intervening hydrido-NiII intermediate encountered along the most feasible pathway? 7. Is the hydrogen transferred to the unsubstituted C1 or to the substituted C3 allylic terminus along the route for generation of linear C10-olefins? 8. Which of the crucial elementary steps is rate-determining? 9. Which factors control the selective formation of only one of the several possible stereoisomers of the principal CDD and DT products, viz. cis,trans-CDD and trans-DT, respectively? 10. What are the critical factors that regulate the selectivity for generation of linear and cyclic C10-olefins? The following sections summarize recent theoretical results [11] aimed at addressing these questions and therefore contributing to an enhanced mechanistic understanding of the co-oligomerization reaction.

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3 Computational Model and Method 3.1 Model The complete catalytic cycle of the [Ni0]-catalyzed co-oligomerization of 1,3butadiene and ethylene consisting of the critical elementary steps displayed in Scheme 1 has been computationally investigated. The several forms of the [Ni0(olefin)2] and [Ni0(olefin)3] compounds 1a and 1b, respectively, were explicitly considered as possible active catalyst species. These critical elementary steps are oxidative coupling of two butadienes; allylic conversion processes occurring in the octadienediyl-NiII and decatrienyl-NiII complexes, respectively; ethylene insertion into the allyl-NiII bond of the octadienediyl-NiII complex; and reductive CC elimination under ring closure, as well as transition-metalassisted H-transfer commencing from the decatrienyl-NiII complex, respectively, were investigated. Various conceivable paths for individual elementary steps have been explored. Furthermore, the several possible stereochemical pathways, which originate from the enantioface and the configuration (s-trans or s-cis) of the prochiral butadiene moieties involved, have been carefully examined for the favorable route for each of the critical elementary steps (see below). 3.2 Method Currently, the density functional theory (DFT) method has become the method of choice for the study of mechanism of transition-metal-assisted processes. Gradient-corrected DFT methods are of particular value for the computational modeling of catalytic cycles. They have been demonstrated to be able to provide quantitative information of high accuracy concerning structural and energetic properties of the involved key species in numerous applications for a variety of different elementary processes. Furthermore, these methods are capable of treating large, and thereby chemical realistic, models of the real catalysts [12]. For all atoms a standard all electron basis set of triple-z quality for the valence electrons augmented with polarization functions was used in the computations [13a]. The local exchange-correlation potential by Slater [14a,b] and Vosko et al. [14c] was augmented with gradient-corrected functionals for electron exchange according to Becke [14d] and correlation according to Perdew [14e,f] in a self-consistent fashion. This gradient-corrected density functional is usually termed BP86 in the literature. In recent benchmark computational studies it was shown that the BP86 functional gives results in excellent agreement with the best wave function-based methods available today, for the class of reactions investigated here [15]. The applied computational methodology has furthermore been demonstrated to reproduce the total activa-

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‡ tion barrier (DG tot ) for nickel-catalyzed 1,3-butadiene cyclooligomerization reactions with an accuracy of ~1–2 kcal mol–1 when compared with experiment [4b,c]. Due to the similar structure of key species involved along competing stereochemical pathways for oxidative coupling, ethylene insertion, allylic conversion, H-transfer and reductive elimination steps of the co-oligomerization process investigated here, a higher accuracy could be expected for the relative barriers calculated. The reaction and activation free energies (DG, DG‡ at 298 K and 1 atm) were evaluated for standard conditions using computed harmonic frequencies. In the study of monomer association and displacement events of the co-oligomerization reaction, a process that occurs in the liquid phase [5b], the solvation entropy for monomer complexation was approximated as being half of its gasphase value. This is considered as a reliable estimate of the entropy contribution in condensed phase [13a].

3.3 Stereoisomers of the Key Species The enantioface and also the configuration (s-trans, s-cis) of the prochiral butadienes involved in the several elementary steps are of crucial importance for the

Fig. 1 Stereoisomers of the [Ni0(h2-butadiene)2(ethylene)] form of catalyst complex 1b, together with the related stereoisomers of the h3,h1(C1)-, and bis(h3)-octadienediyl-NiII species 2 and 4, respectively. For notation see the text

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stereocontrol of the co-oligomer formation. The several stereoisomeric pathways possible for each of the individual steps were classified according to the kind of butadiene coupling to which the stereoisomeric form of the precursor corresponded. The butadiene coupling, for instance, can occur between identical configurations, viz. two cis-butadienes (c/c) or two trans-butadienes (t/t), or between two butadienes of different configurations (t/c) with either the same (denoted SF; i.e., same face) or the opposite (denoted OF; i.e., opposite face) enantioface of the two butadienes involved. The respective stereoisomers of the active catalyst complex are schematically depicted in Fig. 1 for the [Ni0(h2butadiene)2(ethylene)] form of 1b, as an example, together with the related octadienediyl-NiII species 2 and 4, respectively. In the account given here, the focus is on the most feasible of the several stereochemical pathways for individual elementary processes [13b].

4 Theoretical Exploration of Crucial Elementary Reaction Steps The theoretical-mechanistic investigation of the catalytic co-oligomerization reaction course starts with the careful step-by-step exploration of the elementary processes outlined in Scheme 1. The objective of this examination is to reveal the crucial structural and energetic features of each of the individual steps and to propose the most feasible of the various conceivable paths. 4.1 Oxidative Coupling of Two Butadienes First, the several possible forms of the active catalyst complex are investigated in order to infer the thermodynamically favorable one, which is followed by the investigation of their propensity to undergo oxidative coupling. Based on the precedence to known olefin-Ni0 complexes [6, 7], the two butadienes can be coordinated in bis(h4) and h4,h2 mode for 1a, while tris-(ethylene)-Ni0, tris(h2butadiene)-Ni0, bis(h2-butadiene)(ethylene)-Ni0, bis(ethylene)(h2-butadiene)Ni0 and bis(h2-butadiene)(h4-butadiene)-Ni0, bis(ethylene)(h4-butadiene)-Ni0, (h2-butadiene)(ethylene)(h4-butadiene)-Ni0 compounds are possible 16e– and 18e– species, respectively, of 1b. In general, ethylene complexation is found to have a higher stability relative to the coordination of butadiene, which, for example, amounts to 6.6 kcal mol–1 (DG) for tris(ethylene)-Ni0 vs tris(h2-transbutadiene)-Ni0 species [11]. This is essentially attributed to unfavorable steric interactions, which act to prevent the preferred trigonal planar conformation for the latter species. Among the several forms of 1a and 1b, all being assumed to be in equilibrium, the tris(ethylene)-Ni0 species is predicted to be thermodynamically the most favorable. This, however, is a dormant species. Concerning the catalytically active forms with two (or three) coordinated butadienes, the formal 16e–

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trigonal planar [Ni0(h2-butadiene)2(ethylene)] compound, with butadiene preferably coordinated in the h2-trans mode, is predicted to be prevalent. The related [Ni0(h2-butadiene)3] compound, which is energetically unfavored by 2.0 kcal mol–1 (DG, for the [Ni0(h2-trans-butadiene)3] relative to the [Ni0(h2trans-butadiene)2(ethylene)] species), is pointed out to be present in an appreciable thermodynamic population as well. The other active forms of 1a and 1b, respectively, however, should occur in smaller concentrations, as they are ~2.8–5.8 kcal mol–1 higher in free energy [11]. The examination of various paths for oxidative coupling that commence from different active forms of 1a and 1b, respectively, revealed two feasible coupling routes. The bis(h4)-butadiene form of 1a is the precursor for the first 1aÆ4 route, giving rise to the bis(h3)-octadienediyl-NiII species 4 as the directly generated coupling product (cf. Fig. 2). The formation of a new C-C s-bond between two bidentate coordinated butadienes occurs via the product-like transition state TS[1a–4], where the two allylic moieties are almost completely preformed. The coupling that takes place between two h4-butadienes along 1aÆ4 is found to be favorable for all forms of 1a [11]. The second coupling route is assisted by ethylene. Commencing from the [Ni0(h2-butadiene)2(ethylene)] form of 1b, the oxidative coupling proceeds via establishment of a new C-C bond between the terminal noncoordinated carbons C4 and C5 of two h2-butadienes (cf. Fig. 3), that occurs at a distance of ~2.2–2.3 Å in the eductlike transition state TS[1b–2]. The h3,h1(C1)-octadienediyl-NiII species 2 is generated as the initial coupling product. This route is seen to be energetically preferred for all active forms of 1b [11].

Fig. 2 Selected geometric parameters (Å) of the optimized structures of key species for oxidative coupling via the most feasible pathway for cis-h4/cis-h4-butadiene coupling along 1aÆ4, commencing from the [Ni0(h4-butadiene)2] precursor 1a. Activation and reaction free energies (kcal mol–1) are given relative to the [Ni0(h2-trans-butadiene)2(ethylene)] isomer of 1b

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Fig. 3 Selected geometric parameters (Å) of the optimized structures of key species for oxidative coupling via the most feasible pathway for trans-h2/cis-h2-butadiene coupling along 1bÆ2, commencing from the [Ni0(h2-butadiene)2(ethylene)] precursor 1b. Activation and reaction free energies (kcal mol–1) are given relative to the [Ni0(h2-trans-butadiene)2(ethylene)] isomer of 1b

The activation energy as well as the thermodynamic driving force for oxidative coupling is primarily determined by the configuration and the enantioface of the two reacting butadiene moieties involved in the process. Identical stereochemical pathways are found to be kinetically preferred along 1aÆ4 and 1bÆ2 for coupling of c/c-butadiene (SF coupling), t/t-butadiene (SF coupling) and t/c-butadiene (OF coupling). For the 1aÆ4 route, the thermodynamically most stable bis(h4-cis) isomer is also seen to be kinetically preferred by the overall ‡ , relative to favorable isomer of 1b). lowest total barrier of 22.6 kcal mol–1 (DG tot Coupling of t/c- and t/t-butadiene, however, requires prohibitively higher barriers (DDG‡>14 kcal mol–1; [11]), which indicates that these stereochemical pathways are almost entirely precluded. Accordingly, the bis(h3-anti) isomer of 4 would be exclusively formed along this route. The coupling of t/c-h2-butadiene of opposite enantiofaces is favorable along 1bÆ2 among the several stereochemical pathways, both kinetically by the overall lowest free-energy barrier of 12.8 kcal mol–1 and also thermodynamically by the formation of the most stable h3-syn,h1(C1),D-cis isomer of 2. The competitive stereochemical 1bÆ2 pathways are indicated to be almost entirely suppressed. On the one hand, the coupling of two trans-butadienes, which requires a slightly higher activation barrier (DG‡=15.5 kcal mol–1), however, is a less likely process, since the highly strained, energetically disfavored h3,h1(C1),D-trans coupling species would immediately undergo the more facile reverse reductive decoupling 2Æ1b process (DG‡=3.1 kcal mol–1). On the other hand, formation of the h3anti,h1(C1),D-cis isomer of 2 (c/c-butadiene coupling) is seen to be kinetically impeded by an activation free-energy that is 4.9 kcal mol–1 higher, compared to the favorable t/c-butadiene coupling [11].

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Comparison of the kinetics for the most feasible stereochemical pathways of the alternative 1aÆ4 and 1bÆ2 routes clearly shows that the octadienediyl-NiII complex is preferably generated via the ethylene-assisted coupling of two h2-butadienes along 1bÆ2. Thus, the thermodynamically favorable [Ni0(h2butadiene)2(ethylene)] form of 1b also represents the catalytically active species for oxidative coupling. The [NiII(h3-syn,h1(C1),D-cis,-octadienediyl)(ethylene)] species 2 is almost exclusively formed in a thermoneutral process (DG= –0.1 kcal mol–1) that requires a moderate activation free-energy of 12.8 kcal mol–1. This indicates the oxidative coupling as a facile, reversible step. This leads to the following conclusion for the oxidative coupling elementary step. The [Ni0(h2-butadiene)2(ethylene)] form of 1b is shown to be the predominant species of the active catalyst complex under catalytic reaction conditions with the related [Ni0(h2-butadiene)3] species occurring in appreciable, but smaller concentrations. The first prevalent catalyst compound also represents the catalytically active species for oxidative coupling of two butadiene moieties. The coupling preferably takes place between t/c-butadiene of opposite enantiofaces along the olefin-assisted 1bÆ2 route. This process, when assisted by ethylene or alternatively by h2-butadiene, requires an almost identical ‡ = 0.2 kcal mol–1). The ethylene-assisted intrinsic free-energy barrier (DDG int path, however, is indicated to be the most feasible, since the corresponding precursor is thermodynamically favorable. 4.2 Allylic Conversion Processes Occurring in the Octadienediyl-NiII Complex The interconversion between the various configurations, viz. the h3,h1 species 2, 3 and the bis(h3) species 4, as well as between the several stereoisomers of the octadienediyl-NiII complex may have a distinct influence on the catalytic reaction course. With the initially generated h3-syn,h1(C1),D-cis species 2 as a starting point, the subsequent generation of the decatrienyl-NiII complex can proceed with 2, 3 or 4 acting as the precursor. Furthermore, a stereoisomer different from the initial t/c-butadiene OF coupling species can be involved along the most feasible pathway of this process. This would make allylic conversion steps indispensable. Moreover, the relative rates for allylic interconversion and for formation of the decatrienyl-NiII complex might have a pronounced influence on the stereocontrol of the co-oligomerization process. In the case of a kinetically impeded allylic conversion, as one of the possible mechanistic scenarios, several of the stereochemical pathways for formation of the decatrienyl-NiII complex would be disabled due to the negligible population of the corresponding precursor species. The various octadienediyl-NiII configurations 2–4 are likely to readily undergo mutual conversion for identical stereoisomers [16]. Syn-anti isomerization as well as enantioface conversion of the terminal allylic groups of the octadienediyl-NiII complex are the most likely processes for interconverting different stereoisomeric forms (Fig. 4). Isomerization of the allylic group in-

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Fig. 4 Allylic enantioface conversion in h3,h1(C1)-octadienediyl-NiII species (top), and allylic isomerization occurring through an h3,h1(C3)-allylic intermediate (below)

volves the interconversion of its syn and anti configuration and also the interconversion of its enantioface [17]. On the other hand, the process of enantioface conversion is not accompanied by alternation of the allylic configuration. The conversion of the allylic enantioface is most likely to proceed via the h3,h1(C1)-octadienediyl-NiII transition state TSEFC[2] (Fig. 5). In accordance with evidence provided from both experimental [17, 18] and theoretical [19] studies, allylic isomerization is most likely to occur via the h3,h1(C3)-octadienediyl-NiII transition state TSISO[3], which constitutes the internal rotation of the vinyl group around the formal C2-C3 single bond (Fig. 5). The explicit investigation of monomer-assisted reaction paths revealed that additional ethylene or butadiene does not accelerate either allylic isomerization or enantioface conversion by coordinative stabilization of the corresponding transition state.

Fig. 5 Selected geometric parameters (Å) of the optimized h3-syn,h1(C1) transition-state structure TSEFC[2] for allylic enantioface conversion and of the optimized rotational h3syn,h1(C3) transition-state structure TSISO[3] for allylic isomerization occurring in the [NiII(octadienediyl)(ethylene)] complex. Activation free energies (kcal mol–1) are given relative to the [NiII(h3-syn,h1(C1),D-cis,-octadienediyl)(ethylene)] isomer of 2

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This leads to the conclusion that additional monomers are not likely to participate in the conversion of the terminal allylic groups of the octadienediyl-NiII complex. The conversion of the allylic enantioface is indicated to be a facile process that is connected with similar free-energy barriers of 10.7 and 12.6 kcal mol–1 for t/c-butadiene and c/c-butadiene coupling stereoisomers, respectively. For allylic isomerization, however, the kinetics are found to be quite different for pathways that involve h3-syn,h1(C3) isomers (i.e. conversion between t/cbutadiene and t/t-butadiene coupling products) and h3-anti,h1(C3) isomers (i.e. conversion between c/t-butadiene and c/c-butadiene coupling products). ‡ , relative to the almost Moderate total barriers of 9.8–11.8 kcal mol–1 (DG tot 3 1 1 exclusively generated h -syn,h (C ),D-cis,-octadienediyl-NiII species 2 along 1bÆ2) have to be overcome for conversion between t/c- and t/t-butadiene coupling products. In contrast, the interconversion of c/t- and c/c-butadiene coupling species [20] is predicted to be significantly slower, as it requires a ‡ ). This different behavior is lowest barrier that is 4.9 kcal mol–1 higher (DDG tot almost entirely attributed to the lower thermodynamic stability of h3anti,h1(C3) relative to h3-syn,h1(C3) isomers of the direct precursor 3. Notably, both forms display comparable intrinsic reactivities, as indicated by similar ‡ , relative to the corresponding stereointrinsic barriers of ~7.5 kcal mol–1 (DG int isomer of 3). Overall, commencing from the initially generated h3-syn,h1(C1),D-cis,-octadienediyl-NiII species 2, where the two SF/OF stereoisomers are readily interconverted via the facile allylic enantioface conversion, a smooth conversion ‡ = 9.8 kcal mol–1). takes place into the t/t-butadiene coupling isomers (DG tot These species, however, are not likely to occur in significant stationary concentrations, as they undergo reductive decoupling 2Æ1b readily. The allylic isomerization into c/c-butadiene coupling species, however, is seen to be ‡ = kinetically more difficult, requiring a distinctly higher total barrier (DG tot –1). This may have a decisive influence on the accessible stereo14.7 kcal mol chemical pathways for the generation of the decatrienyl-NiII complex. The favorable path for this elementary step will be clarified next. 4.3 Ethylene Insertion Into the Allyl-NiII Bond of the Octadienediyl-NiII Complex Different paths are conceivable for the generation of the decatrienyl-NiII complex occurring by ethylene insertion into the Ni-C bond of one of the terminal allylic groups of the octadienediyl-NiII complex. The h3,h1 configurations 2, 3 and the bis(h3) configuration 4 are imaginable as precursors. In general, the most favorable transition-state structure that is encountered along the different conceivable insertion paths is characterized by a quasi-planar four-membered cis arrangement of the Ni-C bond, the ethylene, and the nickel atom. The careful inspection of the several possible insertion paths revealed that both the bis(h3) species with an axial coordinated ethylene, 4E, and the h3,h1(C3) species 3 are

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precluded from the energetically most favorable ethylene insertion path. The initially generated h3,h1(C1) oxidative coupling product species 2 is the precursor for the most feasible insertion path. Commencing from 2, ethylene can be inserted into either the h3- or the h1(C1)-allyl-NiII bond. For both paths, a square-planar transition-state structure is encountered along the minimum energy pathway, in which ethylene resides in a square-planar conformation together with the h3- and h1(C1)-allylic groups. Between these two alternative paths, the h3-allyl-NiII bond displays a higher propensity for ethylene insertion when compared with the h1(C1)-allyl-NiII bond. For identical stereoisomers, as an example, the barrier for insertion into the h3-allyl-NiII bond is predicted to always be lower than for insertion into the h1(C1)-allyl-NiII bond [11]. The decatrienyl-NiII complex is seen to be preferably generated through ethylene insertion into the h3-allyl-NiII bond of 2 via a square-planar transition state TS[2–5] that occurs at a distance of ~1.8–1.9 Å for the emerging C-C s-bond (Fig. 6). This leads to the [NiII(h3,h1,D,-decatrienyl)] species 5 as the kinetic insertion product, which represents the thermodynamically favorable form of the decatrienyl-NiII configurations 5–7. Furthermore, additional ethylene or butadiene monomers are indicated to not accelerate the insertion via coordinative stabilization of any of the involved key species and are therefore Æ 5. not likely to assist the decatrienyl-NiII formation along 2Æ Among the several stereoisomers of 2, the predominantly generated h3Æ 2) is also seen to syn,h1(C1),D-cis species (t/c-butadiene OF coupling along 1Æ exhibit the highest aptitude for ethylene insertion (cf. Scheme 2). Pathways with both OF and SF coupling stereoisomers, which are readily interconverted through smooth allylic enantioface conversion (see previous section) are indicated to be feasible. A moderate free-energy barrier of 13.3 and 15.8 kcal mol–1 has to be overcome, affording the h3-anti,h1,D-trans isomer of 5, in a thermo-

Fig. 6 Selected geometric parameters (Å) of the optimized structures of key species for the feasible ethylene insertion into the syn-h3-allyl-NiII bond along 2Æ5, commencing from the [NiII(h3,h1(C1)-octadienediyl)(ethylene)] precursor 2. Activation and reaction free energies (kcal mol–1) are given relative to the [NiII(h3-syn,h1(C1),D-cis,-octadienediyl)(ethylene)] isomer of 2

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Scheme 2 Competing pathways for formation of the decatrienyl-NiII complex along the dominant 2Æ5 route for ethylene insertion into the h3-allyl-NiII bond, together with the various decatrienyl-NiII decomposition pathways along the alternative 5Æ8 and 5Æ10 paths affording cyclic and linear C10-olefins, respectively (NB Only one of the two possible stereoisomers is shown for each of the given species 2 and 5, respectively)

dynamically favorable process that is exergonic by –10.5 and –7.0 kcal mol–1, respectively. The pathway with t/c-butadiene OF coupling stereoisomers is preferable on both kinetic and thermodynamic grounds. The alternative stereochemical insertion pathways are, however, indicated to be inaccessible [11]. Ethylene insertion into the syn-h3-allyl-NiII bond of the t/t-butadiene coupling species is seen to be almost completely precluded, first due to unfavorable kinetics (DDG‡>10 kcal mol–1, relative to the most feasible insertion pathway) and second due to the negligible thermodynamic population of the corresponding precursor stereoisomer of 2 (see above). Moreover, ethylene insertion into the anti-h3-allyl-NiII bond of the h3-anti,h1(C1),D-cis isomer of 2 (c/cbutadiene coupling species) to afford h3-anti,1h,D-cis,-decatrienyl-NiII species is less likely to occur as well. Both unfavorable kinetics (DDG‡>7 kcal mol–1, relative to the most feasible insertion pathway) and also thermodynamic factors are seen to prevent occurrence of h3,h1,D-cis,-decatrienyl-NiII species. The corresponding h3-anti,h1(C1),D-cis precursor stereoisomers 2 are likely ‡ = to be sparsely populated, since the compulsory allylic isomerization (DG tot –1, see previous section) is indicated to be slower than the com14.7 kcal mol petitive ethylene insertion (DG‡=13.3 kcal mol–1). As a consequence, the h3anti,h1,D-trans isomer of the decatrienyl-NiII complex is generated almost

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exclusively along 2Æ5, while the pathways for generation h3,h1,D-cis,-decatrienyl-NiII isomers are completely suppressed (cf. Scheme 2). Identical stereoisomers (t/c-butadiene OF coupling) participate along the most feasible pathways for oxidative coupling 1bÆ2 and ethylene insertion 2Æ5.Accordingly, allylic conversion taking place in the octadienediyl-NiII complex is not required along the catalytic reaction course. Furthermore, the octadienediyl-NiII complex is indicated as a highly reactive intermediate occurring in low stationary concentrations, since the generating oxidative coupling and the consuming ethylene insertion processes are connected with similar moderate activation barriers. This leads to the conclusion that octadienediyl-NiII species are less likely to be isolable in the catalytic co-oligomerization reaction. 4.4 Allylic Isomerization Processes Occurring in the Decatrienyl-NiII Complex Similar to the octadienediyl-NiII complex, the various decatrienyl-NiII configurations 5–7 are likely to be in a dynamic equilibrium. The h3-p-allyl form 5, which is stabilized by the coordinated olefinic double bond, is prevalent, while 6 and 7, with a h1-s-allyl group, are found to be thermodynamically disfavored [11]. The investigation of the interconversion between the initially formed antih3-decatrienyl-NiII form and its syn-h3-allyl counterpart will be focused only on the decatrienyl-NiII isomers with an inner trans double bond that have been shown to be formed almost exclusively along 2Æ5 (see previous section). For allylic isomerization to occur in the decatrienyl-NiII complex, the assistance of an additional monomer moiety has been found to be necessary. The monomer acts to compensate for the decrease of the coordination number of the nickel atom that accompanies the h3Æh1(C3) allylic rearrangement. Antisyn isomerization of the predominantly generated h3-anti,h1,D-trans,-decatrienyl-NiII species via a h1(C3)-allyl rotational transition state is connected ‡ , with a significant lowest total free-energy barrier of 27.0 kcal mol–1 (DG tot 3 1 II relative to the prevalent h -anti,h ,D-trans,-decatrienyl-Ni isomer of 5), for the process that is assisted by ethylene [11]. This indicates that the isomerization of the terminal allylic group of the decatrienyl-NiII complex is a kinetically difficult process. Furthermore, this process is likely to be kinetically retarded relative to the decomposition of the decatrienyl-NiII complex affording linear and cyclic C10-olefins. The implications for the accessibility of the various stereochemical pathways for decomposition will be clarified in the next section, which starts first with the elucidation the most feasible path for generation of linear and cyclic C10-olefins. 4.5 Formation of the C10Co-Oligomers The decomposition of the decatrienyl-NiII complex along the competing routes for reductive CC elimination and for transition-metal-assisted H-transfer leads

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to formation of cyclic and linear C10-olefins products, respectively. The various configurations 5–7 could be the respective precursor species for these processes. The careful exploration of several possible paths for each of the two routes clearly revealed that the h3-allyl,h1,-trans form 5 is involved along the most feasible paths for the CDD and DT generating routes, while the h1allyl,h1,D-trans forms 6 and 7 do not participate along any viable path (cf. Scheme 2) [11]. 4.5.1 Formation of CDD Formation of CDD proceeds, along the most feasible path, by establishing of a C-C s-bond between the terminal unsubstituted carbons of the h3-allylic (C1) and the alkyl group (C10) in 5 that affords the [Ni0(CDD)] product complex 8 (Fig. 7). The transition state TS[5–8], which occurs at a distance of ~1.9–2.1 Å of the newly formed bond, is characterized by a substantial h3-allylÆh2-vinyl transformation. Thus, TS[5–8] appears product-like with an already essentially preformed CDD product that decays into the formal 14e– product species 8 where CDD is coordinated to Ni0 by its two double bonds. Inspection of the several stereochemical pathways revealed the pathway with the h3-anti,h1,D-cis,-decatrienyl-NiII isomer (c/c-butadiene OF coupling) involved as the most feasible one that requires a free-energy barrier of 24.3 kcal mol–1 [11]. This would give rise to the cis,cis-CDD-Ni0 isomer of 8 (cf. Scheme 2). This pathway, however, although kinetically most feasible, is rendered inoperable, since the formation of the h3,h1,D-cis isomer of precursor 5 has been shown to be almost entirely precluded and is therefore likely to occur only in a negligible thermodynamic population (see above). Among the accessible pathways with h3,h1,D-trans,-decatrienyl-NiII isomers of 5 participating, the pathway with the prevalent h3-anti,h1,D-trans species is predicted to be favorable, both on kinetic and thermodynamic grounds. This gives rise to cis,trans-CDD (cf. Scheme 2) as the preferable C10-olefin along 5Æ8 that is generated in an endergonic process (DG=16.1 kcal mol–1) with a free-energy barrier of 26.6 kcal mol–1 (cf. Fig. 7). The kinetic barrier for this process is seen to be in the same range as that predicted for allylic isomerization of the prevalent h3-anti,h1,D-trans species 5 into the h3-syn,h1,D-trans congener (see above), thereby suggesting that the probability of the two processes occurring should be quite similar. Accordingly, the trans,trans-CDD generating pathway with the h3-syn,h1,D-trans isomer of precursor 5 becomes accessible (cf. Scheme 2). Formation of trans,trans-CDD, however, is clearly indicated to be kinetically unfeasible due to a distinctly higher barrier (DDG‡>8 kcal mol–1, relative to the cis,trans-CDD generating pathway). This leads to the following mechanistic conclusions (cf. Scheme 2): (first) cis,trans-CDD is the preferably generated cyclic C10-olefin along the 5Æ8 path that is (second) nearly exclusively formed among the different isomers, since all the other competing stereo-

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Fig. 7 Top: Selected geometric parameters (Å) of the optimized structures of key species for reductive CC elimination affording cis,trans-CDD via the most feasible of the accessible stereochemical pathways along 5Æ8, commencing from the [NiII(h3,h1,D,-decatrienyl)] precursor 5. Activation and reaction free energies (kcal mol–1) are given relative to the [NiII(h3-anti,h1,D-trans,-decatrienyl)] isomer of 5. Bottom: Corresponding key species for the ethylene-assisted process with the [NiII(h3,h1,D,-decatrienyl)(ethylene)] adduct 5E as the precursor. Activation and reaction free energies (kcal mol–1) are given relative to {[NiII(h3anti,h1,D-trans,-decatrienyl)] isomer of 5+C2H4}

chemical pathways are almost entirely precluded due to kinetic and/or thermodynamic considerations. Furthermore, (third) isomerization of the terminal allylic group of the decatrienyl-NiII complex is not necessary along the catalytic reaction course, since identical stereoisomers participate along the most feasible 2Æ5 and 5Æ8 pathways. As anticipated, the reductive elimination, a process that formally occurs with a reduction of the coordination number on nickel, was found to be facilitated by the presence of additional monomer moieties. Notably, the relative kinetics of the various stereochemical pathways are predicted to be very similar for both

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the monomer-assisted path and the path that is not assisted by additional monomers [11]. For the formally 16e– square-planar h3-anti,h1,D-trans species 5, the enthalpic stabilization of axial ethylene coordination in the squarepyramidal adducts 5E was not found to be large enough to compensate for the decrease in entropy associated with the complexation [11]. In contrast, both TS[5–8] and 8 are seen to be stabilized to a considerable extent by monomer coordination, which thereby acts to accelerate the reductive elimination. The total free-energy barrier (relative to the separated prevalent h3-anti,h1,D-trans isomer of 5 and the olefin) becomes reduced to 20.1 and 21.3 kcal mol–1 for the favorable cis,trans-CDD generating pathway, which is now predicted to be exergonic, driven by a thermodynamic force of –10.3 and –8.9 kcal mol–1 (DG) for the process assisted by ethylene and h2-trans-butadiene, respectively. Hence, this points out that ethylene serves preferably to facilitate the cis,trans-CDD generating pathway both kinetically as well as thermodynamically. Cis,transCDD is liberated from the ethylene product adduct 8E through subsequent, consecutive facile substitution steps with butadiene in an overall exergonic process (DH/DG=–9.2/–3.9 kcal mol–1), which regenerates the active catalyst 1b. 4.5.2 Formation of DT Starting from the decatrienyl-NiII complex, the formation of cis- and trans-DT requires the transfer of a hydrogen atom from the alkyl end (b-H of the C9 carbon) to the allylic group (substituted C3 carbon) of the C10 chain (cf. Fig. 8). The probing of several reaction paths revealed that the favorable path, analogous to the findings in the previous section, starts from the h3-allyl,h1,D-trans species 5, which represents the precursor for production of both cyclic and linear C10-co-oligomers, respectively [11]. On the other hand, for the originally suggested, coordinatively unsaturated, h1(C3)-allyl,h1,D species 7 as the active precursor [5], a smooth h1(C3)Æh3 conversion takes place, giving rise to the same key species that appear for the process commencing from 5. Coordinative stabilization of 7 by ethylene complexation, however, leads to an alternative but energetically disfavored reaction path [21]. From this it can be concluded that 6 and 7 are precluded from the energetically most favorable DT generating path. Furthermore, a detailed search gave no indication of the existence of a viable concerted reaction path that excludes the intermediacy of the hydridoNiII species 9. Hence, the 5Æ9Æ10 sequence of steps represents the preferred path for DT generation that comprises of the consecutive b-H abstraction 5Æ9 and reductive CH elimination 9Æ10 steps, with the intervening hydrido-NiII species 9. The hydrogen transfer preferably takes place coplanar to the h3-allyl and the alkyl groups of the C10 chain, with the shifted hydrogen atom residing in square-planar conformation together with the two groups. The process occurs with the displacement of the inner olefinic double bond, which is coordinated in 5, from the immediate proximity of the nickel atom by the shifted hydrogen

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Fig. 8 Selected geometric parameters (Å) of the optimized structures of key species for the b-H abstraction 5Æ9 and reductive CH elimination 9Æ10 steps affording trans-DT via the most feasible of the accessible stereochemical pathways along the overall 5Æ10 process, commencing from the [NiII(h3,h1,D,-decatrienyl)] precursor 5. Activation and reaction free energies (kcal mol–1) are given relative to the [NiII(h3-anti,h1,D-trans,-decatrienyl)] isomer of 5

atom (Fig. 8). The square-planar transition state TS[5–9] for the first b-H abstraction step is reached at the distance of ~1.65–1.75 Å of the vanishing C9-Hb bond and exhibits a hydridonickel bond (1.49 Å) that is almost completely established already, together with an emerging olefinic double bond on the alkyl terminus of the C10 chain. TS[5–9] decays into the stable square-planar hydrido-NiII intermediate 9, which is confirmed to be a minimum structure. Both TS[5–9] and 9 display a great structural similarity. Going further along the reaction path, TS[9–10] for reductive CH elimination is encountered at a distance of ~1.8–1.9 Å of the new C-H bond, giving rise to the [Ni0(DT)] complex 10. After the hydrogen transfer along 5Æ10 succeeded with the establishment of two new double bonds, the inner double bond becomes recoordinated

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to the nickel atom; thus DT is coordinated by all its three double bonds to the nickel atom in the formal 16e– product 10. The 5Æ10 route for DT production, which occurs in two consecutive steps, exhibits a double valley profile. Very similar activation barriers are connected with the first b-H abstraction and the second reductive CH elimination. For the most feasible of the accessible stereochemical pathways, with the prevalent h3-anti,h1,D-trans isomer of 5 (t/c-butadiene OF coupling) participating, the free-energy of activation amounts to 20.0 and 18.7 kcal mol–1, respectively. This affords trans-DT in an overall process that is exergonic by –7.4 kcal mol–1. The intervening hydrido-NiII species 9 is separated by a free-energy barrier of 2.7 and 1.4 kcal mol–1 from the educt and product sides. This indicates 9 as a highly reactive metastable intermediate that should occur only in negligible stationary concentrations. The alternative trans-DT generating pathway with the h3-syn,h1,D-trans isomer of 5 as the precursor, however, is not reachable. This can be concluded from the comparison of the moderate barriers for the preferred trans-DT pathway (see above) with the kinetically difficult (which has a 7.0 kcal mol–1 higher free-energy barrier, see above) but necessary anti-syn isomerization of the h3-anti,h1,D-trans precursor 5. Among the two product isomers, trans-DT is the linear C10-olefin that is exclusively formed along 5Æ10 with the prevalent h3-anti,h1,D-trans (t/c-butadiene OF coupling) isomer of 5 involved (cf. Scheme 2). Thus, similar to the CDD-generating route, allylic conversion in the decatrienyl-NiII precursor is also not required along the DT-generating route. The competing cis-DT generating pathways with the h3,h1,D-cis isomers of 5 as precursors (cf. Scheme 2), are clearly seen to be entirely precluded, although these species exhibit a higher aptitude for undergoing H-transfer along 5Æ10 when compared to the operative trans-DT pathway [11]. The critical analysis of crucial elementary steps presented so far clearly rationalizes the negligible thermodynamic population of h3,h1,D-cis,-decatrienyl-NiII species (see above), as the decisive factor that prevents the generation of cis,cis-CDD and cis-DT, respectively. In contrast to the 5Æ8 CDD-generating route, the production of DT is not likely to be facilitated by the participation of additional monomers along the 5Æ10 route. None of the key species are found to be coordinatively stabilized by monomer complexation, which has to compete for coordination with the coordinated olefinic double bond of the C10 chain, either on the enthalpy or on the free energy surface [11]. A further conceivable DT-generating path consists of the hydrogen transfer from the alkyl terminus (b-H of the C9 carbon) to the unsubstituted C1 allylic terminus of the C10 chain. Commencing from the prevalent h3-anti,h1,D-trans precursor 5 this would give rise to deca-1,trans-4,cis-8,-triene (trans,cis-DT). Different from the preferable trans-DT generating path, the first b-H abstraction proceeds through a square-pyramidal transition-state structure with the shifting H-atom in axial position. This path is clearly seen to be almost entirely precluded kinetically, due to a prohibitively large free-energy barrier that is

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19.5 kcal mol–1 higher (DDG‡) than that predicted for the favorable trans-DT generating path.

5 Theoretically Verified and Refined Catalytic Cycle So far we have been able to predict the most feasible pathway for each of the critical elementary processes of the co-oligomerization reaction course and to characterize them by locating the involved key species. From the detailed insight achieved for all the individual steps, a condensed mechanistic scheme comprising of thermodynamic and kinetic aspects for the respective favorable pathways is presented and the mechanistic implications for the selectivity control is elucidated (cf. Scheme 3). The formal 16e– trigonal planar [Ni0(h2-butadiene)2(ethylene)] species 1b is the prevalent form of the active catalyst, with the bis(h2-trans) isomers being most stable. This species also represents the catalytically active form that undergoes oxidative coupling. Oxidative coupling preferably takes place via the establishment of a C-C s-bond between the terminal noncoordinated carbons of the two h2-butadiene moieties. This gives rise to the [NiII(h3,h1(C1),D,-octadienediyl)(ethylene)] species 2 as the initial coupling product along the ethylene-assisted 1bÆ2 path. The most feasible pathway occurs via t/c-butadiene (OF) coupling possessing a moderate kinetic barrier that affords the thermodynamically most stable h3-syn,h1(C1),D-cis isomer of 2 in a thermoneutral process. This indicates the oxidative coupling as a facile, reversible process. The alternative pathways for coupling of two cis-butadienes (kinetically impeded) and of two trans-butadienes (where the coupling product readily undergoes the more facile reverse 2Æ1b decoupling process) are pointed out to be less likely. From this, together with the kinetically difficult conversion between h3syn,h1(C1),D-cis and h3-anti,h1(C1),D-cis isomers, it can be concluded that the h3-syn,h1(C1),D-cis species is the isomer of 2 that occurs almost exclusively. The h3-syn,h1(C1),D-trans and h3-anti,h1(C1),D-cis species, however, are expected to be present in negligible concentrations. The dominant generation path of the decatrienyl-NiII complex proceeds through the insertion of ethylene into the h3-allyl-NiII bond of 2. A squareplanar transition-state structure is encountered along this path. This gives rise to h3,h1,D,-decatrienyl-NiII species 5 as the kinetic insertion product, which represents the thermodynamically favorable form of the decatrienyl-NiII complex.A moderate activation barrier, which is predicted to be very similar to that for oxidative coupling, is connected with the most feasible insertion pathway, thereby indicating the octadienediyl-NiII complex as a highly reactive intermediate, occurring in small stationary concentrations. Identical stereoisomers participate along the most feasible pathways for the oxidative coupling and ethylene insertion steps, thus making possible intervening allylic conversion processes in the octadienediyl-NiII complex unnecessary. Ethylene insertion

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Scheme 3 Condensed Gibbs free-energy profile (kcal mol–1) of the complete catalytic cycle of the co-oligomerization of 1,3-butadiene and ethylene catalyzed by zerovalent ‘bare’ nickel complexes affording linear and cyclic C10-olefins, focused on viable routes for individual elementary steps. The favorable [Ni0(h2-trans-butadiene)2(ethylene)] isomer of the active catalyst species 1b was chosen as reference.Activation barriers for individual steps are given relative to the favorable stereoisomer of the respective precursor (given in italics)

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into the syn-h3-allyl-NiII bond of the predominantly generated h3,h1(C1),D-cis isomer of 2 affords the h3-anti,h1,D-trans isomer of 5 in an exergonic, irreversible process. The formation of allyl,h1,D-cis,-decatrienyl-NiII species, however, is shown to be almost entirely disabled, because of: (first) the negligible thermodynamic population of the corresponding h3-anti,h1,D-cis precursor species 2 and (second) a prohibitively high insertion barrier for the corresponding stereochemical pathways. Consequently, the cis,cis-CDD and cis-DT generating paths are entirely precluded. This rationalizes why the two C10-olefin isomers are not observed in the catalytic co-oligomerization process. The h3-allyl,h1,D-trans,-decatrienyl-NiII form of 5 represents the precursor for the competing routes for generation of both linear and cyclic C10-olefins. CDD is formed via reductive elimination, where the C10-cycle has been shown to be preferably generated through the establishment of a C-C s-bond between the terminal carbons of the h3-allyl and alkyl groups along 5Æ8. On the other hand, the 5Æ10 DT generating route involves a stepwise transition-metal-assisted C9ÆC3 H-transfer, with an intervening metastable hydrido-NiII species 9 participating. The formation of both linear and cyclic C10-olefins occurs in a highly stereoselective fashion.Among the several isomers, cis,trans-CDD and trans-DT are generated almost exclusively along the competing 5Æ8 and 5Æ10 routes, respectively, that commence from the prevalent h3-anti,h1,D-trans isomer of 5. Incoming monomers are shown to not assist the DT-generating route. The transition state TS[5–8] and also 8, however, are substantially stabilized by ethylene complexation, giving rise to a significant acceleration of the CDD generating route. Commencing from the thermodynamically favorable precursor species 5, the cis,trans-CDD and trans-DT generating pathways are connected with the largest overall kinetic barrier among all the critical elementary steps, affording the [Ni0(h4-CDD)(ethylene)] and [Ni0(h6-DT)] products 8E and 10, respectively, in an exergonic, irreversible process.Accordingly, the decomposition of the decatrienyl-NiII complex along 5Æ8E and 5Æ10 to afford cyclic and linear C10-olefins is predicted to be rate-controlling. The two competing cis,trans-CDD and trans-DT generating pathways exhibit similar kinetics, with a free-energy barrier of 20.1 and 20.0 kcal mol–1, respectively. The predicted total barriers for the rate-determining step correspond very well with experimental estimates that can be derived from available turnover frequencies [5], thereby indicating the high accuracy of the theoretical modeling. In a rough approximation, one can derive effective rate constants k~1.52¥10–3/4.43¥10–2 s–1 and DG‡~22.4/22.9 kcal mol–1, respectively, from the reported turnover frequencies of 12.7 g of C10-olefin (g of Ni)–1 h–1 at 313 K (with cis,trans-CDD as the predominant product) and of 370 g of C10-olefin (g of Ni)–1 h–1 at 353 K (with trans-DT as the predominant product), by applying the Eyring equation with k=(2.08¥1010)T exp(–DG‡/RT). This shows that the production of C10-cooligomers requires moderate reaction conditions [5]. The C10-olefins are liberated in subsequent, consecutive smooth substitution steps with new ethylene and butadiene monomers. The overall substitu-

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tion process is exothermic by –9.2 and –9.3 kcal mol–1 (DH) for expulsion of cis,trans-CDD and trans-DT from 8E and 10, respectively, by the required monomers to recreate the active form of 1b. Overall, the co-oligomerization process is driven by a strong thermodynamic force with an exothermicity of –41.4 and –31.2 kcal mol–1 (DH for the non-catalyzed process) for the linkage of two trans-butadiene and one ethylene monomers to afford cis-trans-CDD and trans-DT, respectively.

6 Regulation of the Distribution Between Linear and Cyclic C10-Olefins As clarified in the previous section, the decomposition of 5, occurring along competing routes for production of linear and cyclic C10-olefins, is rate-controlling in the overall co-oligomerization reaction course. It furthermore involves identical stereoisomers. Accordingly, the product selectivity is entirely regulated kinetically by the difference of the highest overall free-energy barrier (DDG‡) for the competing cis,trans-CDD and trans-DT generating pathways. The two pathways are predicted to be very similar in both the kinetic as well as the thermodynamic aspects (cf. Scheme 3). Based on the almost identical predicted free-energy of activation (DDG‡=0.1 kcal mol–1 at 298 K), the two pathways should be crossed in comparable probabilities, giving rise to an approximate 1:1 ratio of linear and cyclic C10-olefins. This seems to be contradictory with the experimental observation of cis,trans-CDD as the predominant product at low temperatures [5b]. The production of CDD, however, is clearly shown to be assisted by incoming ethylene, while the DT-generating route is not. The prediction of accurate free-energies for transition-metalassisted processes in condensed phase, however, remains a challenge for computational chemistry, in particular when species of different stoichiometry are involved. There is still some uncertainty in the estimated entropic costs for monomer association and dissociation processes, caused by the theoretical methodology employed in the present study (see above) [13a].As a result, the computed DDG‡ value for the subtle energetic balance between the two competing pathways does not exactly reproduce the experimentally observed product ratio between linear and cyclic C10-co-oligomers. One should have in mind, however, that the experimentally observed 88:12 C10-olefin product ratio [5b] corresponds to a DDG‡ value of only 1.16 kcal mol–1 (293 K). The presented theoretical-mechanistic investigation, however, allows a detailed understanding and a consistent rationalization of the experimental results.As already outlined in the introduction, temperature and ethylene pressure are the dominant factors that regulate the selectivity of the co-oligomerization reaction. The computed DDG‡ value increases to 1.4 kcal mol–1 (353 K) at higher temperatures, with the 5Æ10 route having the lower barrier. Accordingly, production of trans-DT is indicated to become kinetically favorable at

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elevated temperatures, which is consistent with experimental findings [5]. The present analysis clearly revealed that both low temperatures (entropic effect) and high ethylene pressure (assistance of the 5Æ8E route) serve to favor the generation of cis,trans-CDD. This leads us to suggest the following directions for improving the selectivity. For the co-oligomerization occurring at room temperature the CDD selectivity can be enhanced by increasing the ethylene pressure. Furthermore, cis,trans-CDD should be the major C10-olefin at elevated temperatures as well, provided that the ethylene pressure is high enough to compensate for the entropic disfavor. On the other hand, trans-DT should be predominantly formed at low ethylene pressure even at ambient temperatures. This should be accompanied with increased portions of all-t-CDT as the preferably generated C12-cycloolefin product [2, 4c,d] as well, since the alternative reaction channel for 1,3-butadiene cyclotrimerization is more likely to be accessed at higher relative butadiene concentrations (see below).

7 Co-Oligomerization of 1,3-Butadiene and Ethylene vs Cyclooligomerization of 1,3-Butadiene Promoted by Zerovalent ‘Bare’ Nickel Complexes: A Mechanistic Comparison So far we have proposed a refined catalytic reaction cycle for the co-oligomerization process and have furthermore analyzed the catalytic structure-reactivity relationships for the regulation of the C10-olefin product selectivity. This, together with our recent theoretical-mechanistic exploration of the [Ni0]catalyzed 1,3-butadiene cyclooligomerization affording C12-cycloolefins [4c,d], enables us now to undertake a comparison of crucial mechanistic aspects of the two reactions. Furthermore, the interplay of the two alternative reaction channels for co-oligomerization and cyclooligomerization will be analyzed (Scheme 4). The first oxidative addition step follows the same preferred route for monomer-assisted (i.e., ethylene or h2-butadiene) coupling of two h2-butadienes that affords almost exclusively the [NiII(h3-syn,h1(C1),D-cis,-octadienediyl)(olefin)] species 2, 2¢¢ as the kinetic product. This isomer has also been established, from both by experimental [3e, 6a, 8] and theoretical [4a,b] evidence, as the initial coupling product of the [Ni0L]-catalyzed (L=PR3/P(OR)3) process. The oxidative coupling exhibits a very similar energy profile for the process to be assisted by either ethylene or h2-butadiene, indicating this step to occur in a smooth, reversible fashion. The octadienediyl-NiII complex represents the critical species that connects the alternative reaction channels for production of C10- and C12-olefins, which are entered by insertion of ethylene and h2-butadiene, respectively (cf. Scheme 4). The h3,h1(C1) form is the precursor for the olefin insertion step that affords the decatrienyl-NiII and dodecatrienediyl-NiII complexes, respectively, along the two reaction channels. Ethylene as well as h2-butadiene are seen to

Scheme 4 Interplay of the alternative reaction channels for production of C10-olefins via butadiene/ethylene co-oligomerization and of C12-olefins via butadiene cyclooligomerization with zerovalent ‘bare’ nickel complexes as the catalyst. Gibbs free energies (kcal mol–1) are reported relative to the favorable [NiII(h3-syn,h1(C1),D-cis,-octadienediyl)(ethylene)] isomer of 2, while activation barriers are given relative to the respective precursor

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insert preferably into the h3-allyl-NiII bond through a square-planar transition state. Notably, a similar preference of the h3-p vs h1-s coordination mode of the allyl-transition-metal bond has also been demonstrated in computational studies of the monomer insertion step in the allylnickel(II)-catalyzed [22, 23] and the allyltitanium(III)-catalyzed [24] 1,4-polymerization of butadiene and for the olefin insertion into the allyl-ZrIII bond [25]. Furthermore, the identical butadiene coupling stereoisomer (i.e., the predominantly generated h3syn,h1(C1),D-cis,-octadienediyl-NiII species) is seen to participate along the most feasible pathway for generation of the decatrienyl-NiII and dodecatrienediyl-NiII complexes. This leads to the conclusion that (first) the conversion of the terminal allylic groups of the octadienediyl-NiII complex is not required within the catalytic reaction course and (second) that the relative portion of the C10- and C12-olefin products is entirely determined kinetically by the difference in the free-energy barrier (DDG‡) connected with the two competitive 2Æ5 and 2¢¢ Æ11 insertion routes. Ethylene is predicted to display a higher aptitude for insertion relative to that of h2-butadiene (DDG‡= 0.7 kcal mol–1, cf. Scheme 4). This agrees with experimental observations [5c] and explains why, in the presence of sufficient amounts of ethylene, C10-olefins are predominantly generated, while C12-olefins are minor products. The variation of the ethylene-to-butadiene ratio might have a distinct influence on the C10-/C12-olefin product composition. C10-Olefins should always be the prevalent products at high ethylene pressure, while at low ethylene pressure increasing amounts of all-t-CDT, as the preferably generated C12-cycloolefin, can be expected. The two insertion routes lead to the generation of only specific stereoisomeric forms of the decatrienyl-NiII complex, where the formation of allyl,h1,Dcis isomers is entirely precluded, and of the dodecatrienediyl-NiII complex, where bis(allyl),D-cis isomers do not occur. Accordingly the corresponding pathways for generation of cis,cis-CDT and cis-DT and also for all-c-CDT production are not accessible, due to a negligible population of the precursor species. This elucidates why these product isomers are not observed in the catalytic process. The olefin insertion into the syn-h3-allyl-NiII bond of 2, 2¢¢ gives rise to the h3,h1,D-trans,-decatrienyl-NiII isomers of 5 and bis(h3)-allyl,D-trans,dodecatrienediyl-NiII isomers of 11, respectively, in an exergonic, irreversible process. These isomers, where the allylic groups preferably adopt the h3-p mode, are the thermodynamically favorable forms of the decatrienyl-NiII and dodecatrienediyl-NiII complexes, which furthermore represent the active precursor species for their decomposition into C10- and C12-olefins, respectively. Butadiene insertion, although kinetically disfavored (see above), is thermodynamically favorable when compared with ethylene insertion. This leads to strongly stabilized bis(h3),D-trans,-dodecatrienediyl-NiII species, which act as a thermodynamic sink in the catalytic reaction course, and hence is well suited for experimental isolation and characterization [3a, 6b, 26, 27].

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The decomposition of the decatrienyl-NiII complex via 5Æ8E reductive CC elimination and 5Æ10 transition-metal-mediated H-transfer to give cis,transCDD and trans-DT, respectively, and also the 11Æ12 reductive CC elimination commencing from bis(h3),D-trans,-dodecatrienediyl-NiII species, affording all-t-CDT as the prevalent C12-cycloolefin, are predicted to be rate-determining. The overall lowest, similar free-energy barrier of 20.0–20.1 and 23.0 kcal mol–1 for these steps in the [Ni0]-catalyzed co-oligomerization and cyclooligomerization processes imply that these processes, in agreement with experiment [3a, 5], require moderate reaction conditions. Notably, the cis,trans-CDD and all-t-CDT generating pathways are assisted by additional monomers, while the production of trans-DT is not.

8 Conclusions In this account we have presented a consistent and theoretically well founded mechanistic view of the catalytic reaction course for the co-oligomerization of 1,3-butadiene and ethylene to afford linear and cyclic C10-olefin products with a zerovalent ‘bare’ nickel catalyst. Crucial elementary processes have been critically scrutinized for a tentative catalytic cycle (cf. Scheme 1) by means of a gradient-corrected DFT method. The original mechanistic proposal by Wilke and co-workers [5] was confirmed in essential details, but enhanced and supplemented by novel insights into how the co-oligomerization reaction operates. The following have been achieved: (1) the most feasible among the various conceivable paths for each of the crucial elementary steps has been predicted, with special emphasis directed to the several stereochemical pathways, (2) the role played by the various configurations of the octadienediyl-NiII and decatrienyl-NiII complexes within the catalytic reaction course has been clarified, (3) the origin for the highly stereoselective formation of cis,trans-CDD and trans-DT, respectively, as the exclusively generated isomers of cyclic and linear C10-olefin products has been rationalized, (4) an enhanced insight into the regulation of the selectivity of the production of linear and cyclic C10-olefins has been provided. This leads us to propose a theoretically verified, refined catalytic cycle for production of linear and cyclic C10-olefin products (cf. Scheme 3). Furthermore, a detailed comparison of crucial mechanistic aspects of the catalytic reaction course for co-oligomerization of butadiene and ethylene and for cyclooligomerization of butadiene promoted by zerovalent ‘bare’ nickel complexes was undertaken. These contribute (first) to a more detailed understanding of mechanistic aspects of the [Ni0]-mediated co-oligomerization of 1,3-dienes and olefins and (second) to a deeper insight into the catalytic structure reactivity relationships in the transition-metal-assisted co-oligomerization and oligomerization reactions of 1,3-dienes.

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Acknowledgments The author wishes to thank Professor Tom Ziegler (University of Calgary, Canada) for his generous support. Excellent service by the computer centers URZ Halle and URZ Magdeburg is gratefully acknowledged. The author also wishes to acknowledge the valuable discussions with Professor Rudolf Taube.

References 1. (a) Jolly PW, Wilke G (1975) The oligomerization and co-oligomerization of butadiene and substituted 1,3-dienes. In: The organic chemistry of nickel, vol 2: Organic synthesis. Academic Press, New York, pp 133–212; (b) Jolly PW (1982) Nickel-catalyzed oligomerization of 1,3-dienes related reactions. In: Wilkinson G, Stone FGA, Abel EW (eds) Comprehensive organometallic chemistry. Pergamon, New York, Vol 8, pp 671–711; (c) Keim W, Behr A, Röper M (1982) Alkene and alkyne oligomerization, cooligomerization and telomerization reactions. In: Wilkinson G, Stone FGA, Abel EW (eds) Comprehensive organometallic chemistry, vol 8. Pergamon, New York, pp 371–462; (d) Heimbach P, Jolly PW, Wilke G (1970) Adv Organomet Chem 8:29; (e) Baker R (1973) Chem Rev 73:487 2. (a) Wilke G (1963) Angew Chem Int Ed Engl 2:105; (b) Wilke G (1988) Angew Chem Int Ed Engl 27:185; (c) Wilke G, Eckerle A (2002) Cyclooligomerizations and cyclo-co-oligomerizations of 1,3-dienes. In: Cornils B, Herrmann WA (eds) Applied homogeneous catalysis with organometallic complexes. VCH, Weinheim, Germany, pp 368–382 3. (a) Bogdanovic B, Heimbach P, Kröner M, Wilke G (1969) Justus Liebigs Ann Chem 727:143; (b) Brenner W, Heimbach P, Hey H, Müller EW, Wilke G (1969) Justus Liebigs Ann Chem 727:161; (c) Heimbach P, Kluth J, Schlenkluhn H, Weimann B (1980) Angew Chem Int Ed Engl 19:569; (d) Heimbach P, Kluth J, Schlenkluhn H, Weimann B (1980) Angew Chem Int Ed Engl 19:570; (e) Benn R, Büssemeier B, Holle S, Jolly PW, Mynott R, Tkatchenko I, Wilke G (1985) J Organomet Chem 279:63 4. (a) Tobisch S, Ziegler T (2002) J Am Chem Soc 124:4881; (b) Tobisch S, Ziegler T (2002) J Am Chem Soc 124:13290; (c) Tobisch S (2003) Chem Eur J 9:1217; (d) Tobisch S (2003) Adv Organomet Chem 49:167 5. (a) Heimbach P, Wilke G (1969) Justus Liebigs Ann Chem 727:183; (b) The following reaction conditions were found to be optimal for the catalytic co-oligomerization of 1,3-butadiene and ethylene: 1,3-butadiene and ethylene in a 1:1 molar ratio at 20 °C and 20–30 atm pressure,‘bare’ Ni0 complexes (for instance [Ni0(COD)2]) as catalyst, benzene as solvent. Under these conditions, the product mixture predominantly consists of cis,trans-CDD (~88%), with trans-DT being formed to a lesser extent (~12%); (c) For 1,3-butadiene and ethylene in a 1:1 molar ratio the co-oligomerization to yield C10-olefins has been observed to occur at an overall reaction rate that is approximately six times larger when compared to the competing cyclooligomerization affording C12-cycloolefins 6. (a) Jolly PW, Mynott R, Salz R (1980) J Organomet Chem 184:C49; (b) Jolly PW, Mynott R (1981) Adv Organomet Chem 19:257 7. Fischer K, Jonas K, Wilke G (1973) Angew Chem Int Ed Engl 12:565 8. (a) Jolly PW, Tkatchenko I, Wilke G (1971) Angew Chem Int Ed Engl 10:329; (b) Brown JM, Golding BT, Smith MJ (1971) J Chem Soc Chem Commun 1240; (c) Barnett B, Büssemeier B, Heimbach P, Jolly PW, Krüger C, Tkatchenko I,Wilke G (1972) Tetrahedron Lett 1457 9. Heimbach P (1973) Angew Chem Int Ed Engl 12:975 10. Büssemeier B, Jolly PW, Wilke G (1974) J Am Chem Soc 64:4726 11. Tobisch S (2004) J Am Chem Soc 126:259

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12. For an overview see, for instance, the special Issue: Computational transition metal chemistry (2002) Chem Rev 100:351–818 13. (a) Detailed descriptions of the employed computational methodology are provided elsewhere [11]; (b) A complete collection of all the stereochemical pathways for the crucial elementary processes of the co-oligomerization reaction cycle can be found elsewhere [11] 14. (a) Dirac PAM (1930) Proc Cambridge Philos Soc 26:376; (b) Slater JC (1951) Phys Rev 81:385; (c) Vosko SH, Wilk L, Nussiar M (1980) Can J Phys 58:1200; (d) Becke AD (1988) Phys Rev A38:3098; (e) Perdew JP (1986) Phys Rev B33:8822; (f) Perdew JP (1986) Phys Rev B34:7406 15. (a) Bernardi F, Bottoni A, Calcinari M, Rossi I, Robb MA (1997) J Phys Chem 101:6310; (b) Jensen VR, Børve K (1998) J Comput Chem 19:947 16. A facile rearrangement between different configurations has been observed by NMR for the PR3/P(OR)3-stabilized octadienediyl-NiII complex [3e] 17. Lukas J, van Leeuwen PWNM, Volger HC, Kouwenhoven AP (1973) J Organomet Chem 47:153 18. (a) Faller JW, Thomsen ME, Mattina MJ (1971) J Am Chem Soc 93:2642; (b) Vrieze K (1975) Fluxional allyl complexes. In: Jackman LM, Cotton FA (eds) Dynamic nuclear magnetic resonance spectroscopy. Academic Press, New York, pp 441–487 19. Tobisch S, Taube R (1999) Organometallics 18:3045 20. The h3-syn,h1(C3) (t/c-butadiene coupling) and h3-anti,h1(C3) (c/t-butadiene coupling) isomers are connected by a facile h3-syn,h1-antiah3-anti,h1-syn conversion. Linear transit calculations revealed no significant barrier for the process, thereby indicating that the intramolecular h3/h1ah1/h3 shift to proceeds readily 21. A very similar behavior was found while probing the alternative path with 6 as the precursor 22. (a) Tobisch S, Bögel H, Taube R (1996) Organometallics 15:3563; (b) Tobisch S, Bögel H, Taube R (1998) Organometallics 17:1177; (c) Tobisch S, Taube R (1999) Organometallics 18:5204; (d) Tobisch S, Taube R (2001) Chem Eur J 7:3681; (e) Tobisch S (2002) Chem Eur J 8:4756 23. Tobisch S (2002) Acc Chem Res 35:96 24. Tobisch S (2003) Organometallics 22:2729 25. (a) Margl PM, Woo TK, Ziegler T (1998) Organometallics 17:4997; (b) Lieber S, Prosenc MH, Brintzinger HH (2000) Organometallics 19:377 26. (a) Wilke G, Kröner M, Bogdanovic B (1961) Angew Chem 71:755; (b) Henc B, Jolly PW, Salz R,Wilke G, Benn R, Hoffmann EG, Mynott R, Schroth G, Seevogel K, Sekutowski JC, Krüger C (1980) J Organomet Chem 191:425 27. Bis(h3-anti),D-trans,-dodecatrienediyl-NiII stereoisomers with trans oriented h3-anti allylic groups have been confirmed by NMR as intermediates of the stoichiometric cyclotrimerization of butadiene [6b,26b], and are also computationally predicted to be the thermodynamically favorable dodecatrienediyl-NiII species. These stereoisomers are calculated to be 1.7 kcal mol–1 lower in free energy relative to the stereoisomer 11 depicted in Scheme 4 [4c,d]

Top Organomet Chem (2005) 12: 219 – 256 DOI 10.1007/b104404 © Springer-Verlag Berlin Heidelberg 2005

The Cluster Approach for the Adsorption of Small Molecules on Oxide Surfaces Volker Staemmler (

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Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, Universitätsstraße 150, 44780 Bochum, Germany [email protected]

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Abstract The correct description of the weak interaction between small molecules and oxide surfaces is still a challenge for theory. In the present review, the current status of the cluster approach to the calculation of adsorption geometries and energies by means of quantum-chemical ab initio methods is discussed. In the first part, the physical and chemical contributions to the bonding mechanism are briefly characterized and the different clusters models currently used for treating molecule/surface interactions are presented: free clusters, hydrogen saturated clusters and embedded clusters. We continue with a description of the

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possibilities and limitations of the most widely used electronic structure methods – density functional theory, Hartree-Fock approximation, and post-Hartree-Fock methods – applied in the field of molecule/surface interactions. Finally, the difficulties encountered in real calculations and the accuracy that can be obtained are discussed for three representative examples: The physisorption of CO on the inert MgO(100) surface, the weak chemisorption of NO on NiO(100), and the interaction between CO and the thermodynamically unstable polar surfaces of ZnO. Keywords Adsorption · Oxide surfaces · Cluster models · Ab initio calculations · Bonding mechanism

1 Introduction Adsorption and desorption phenomena occur frequently in all fields of our every days life as well as in many industrial and technical applications. This starts with simple glues and ends with the filters for pollutant gases in large power plants. Adsorption and desorption processes are also important elementary steps in the complicated chain of reactions that make up a typical mechanism in heterogeneous catalysis. Before the reaction can start at all, the reactant atoms or molecules must adsorb at the solid surface. Then they will diffuse along the surface, react with each other or with the surface to generate reaction intermediates, and eventually, in most cases after several reaction steps, the final products have to desorb from the surface. In most technical applications one is much more interested in optimizing the performance of a catalyst, e.g., in improving yield, turn-over-frequency, conversion rate, selectivity, long-term stability and so on, than in the underlying reaction mechanism itself. However, if one wants to get a detailed understanding of how a reaction proceeds it is compulsory to obtain accurate information on the energetics and kinetics of the different steps involved, in particular on the nature of the active sites, adsorption and desorption processes, energy barriers, short-lived intermediates and so forth. One source of information for such properties are quantum-chemical calculations. During the last few years, they have proven to be able to provide valuable and reliable data which are in many cases complementary to experimental data. In particular, they enable one to break up a complicated reaction chain into small pieces and to investigate the different steps separately, which is much more difficult to achieve in experiment. There is good reason to believe that without the help of good quantum-chemical calculations the reaction mechanisms of many processes, even of those which are used in large scale technical applications, will never be understood in detail. And the hope is, of course, that in the near future quantum-chemical calculations will help to design new and better catalysts.

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Due to its more complex nature, the theoretical treatment of heterogeneous catalysis is less advanced than that of homogeneous catalysis. Most of the catalysts consist of small metal particles on an oxidic support or are metal oxides, in the majority of cases not even simple one-component oxides. It is therefore necessary to describe simultaneously the properties of the surface at which the reaction occurs and of the adsorbed molecule. This means that the theory of heterogeneous catalysis is located somewhere between molecular quantum chemistry and surface science. In the present review we will discuss the current status of the quantumchemical treatment of the adsorption of small molecules on oxide surfaces. We will limit our attention to oxide surfaces, because the problems encountered here are quite different from those connected with the treatment of metal surfaces. There are essentially two approaches to deal with a system that consists of a small molecule and an extended solid surface, i.e., a local process on a semi-infinite substrate. One way is the “cluster approach” described in the following in which a small cluster of atoms is cut out of the surface and the system “molecule and cluster” is treated as a “supermolecule” with the methods of molecular quantum chemistry. The alternative way is the “supercell approach”, in which the adsorbed molecule is repeated periodically on the surface, and the system “surface with an ordered overlayer of adsorbed molecules” is treated by means of periodic calculations. We will only treat the cluster approach in the present review.We further refer the reader to a series of text books [1–4] and review articles [5–11] in which the geometrical and electronic properties of oxide surfaces and the theoretical treatment of the adsorption on such surfaces are covered in more detail.

2 Bonding at Oxide Surfaces The calculation of reliable adsorption geometries and energies or, more generally, the determination of accurate interaction potentials between adsorbed molecules and oxide surfaces is by no means a trivial task, not even for the adsorption of very small systems such as atoms or diatomic molecules. Only in a few cases could quantitatively reliable results for adsorption energies or geometries be obtained so far by theoretical methods; very often the agreement between theoretical and experimental data is not yet convincing. Quite recently, Hoeft and al. [12, 13] stated, when presenting their PhD (photoelectron diffraction) results for the geometrical structure of CO, NO, and NH3 adsorbed on the NiO(100) surface, that “the current theoretically derived adsorbate-substrate bond lengths on this surface are very seriously in error” and gave their paper the provocative title: “Molecular Adsorption Bond Lengths at Metal Oxide Surfaces: Failure of Current Theoretical Methods” [12]. There are several reasons why a reliable theoretical description of the adsorption on solid surfaces and in particular on oxide surfaces is rather difficult:

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1. In general, the adsorption energies to be calculated are rather small, ranging from a few meV for weak physisorption to hardly more than 0.5 to 1.0 eV for typical chemisorption. Errors of about 0.1 eV are tolerable for strong chemical bonds with binding energies of 4–5 eV as found for isolated gas phase molecules, but might even change qualitative predictions in the case of weak molecule/surface interactions. Parallel to the small adsorption energies, the adsorbate/substrate interaction potentials are generally quite shallow such that the determination of precise adsorption geometries is connected with large uncertainties. In particular, the binding energies for the adsorption at different adsorption sites, e.g., at the on-top, bridge or hollow position of a given surface plane, are often so similar that it is very difficult to determine the energetically favored adsorption position. 2. The interaction potential between a molecular adsorbate and an oxide surface is the sum of several contributions of different physical origin. In general, there is not just one single dominant interaction mechanism, but all contributions have similar orders of magnitude. They have even opposite signs and cancel each other to a large extent. This means that one can obtain reliable results only if one can calculate all contributions quite accurately, or if one can rely on favorable error cancellations. 3. The substrate itself is not a small molecule which can be treated with high accuracy, but a macroscopic semi-infinite system. Though the adsorption of a small molecule on a solid surface can be regarded as a local process in which only a small number of surface atoms is actually involved, it cannot be excluded that the geometrical and electronic properties of the whole solid might influence the adsorption energy and geometry. This is obvious for metals, since the electrons in a metal are delocalized over the whole crystal and the local perturbation caused by an adsorbate may modify the electronic structure of a quite extended part of the crystal. Due to the stronger localization of the electrons in semiconductors and insulators, the description of local properties in oxides is believed to be much simpler, but one has to check in every case whether this is really true. 4. Very often, adsorption processes are connected with strong changes in the geometrical structure of the surface (“adsorbate induced relaxations or reconstructions”) that have to be included in the theoretical treatment. Geometry optimizations are currently routinely performed with the existing quantum-chemical program packages for isolated molecules or for small weakly interacting systems. However, there is no easy answer to the question of how large a part of the surface has to be included into the geometry optimization in the treatment of a “local” interaction between a small adsorbate and an extended solid surface.

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2.1 Types of Molecule/Surface Interactions Table 1 contains a short overview over the dominant contributions to the interaction between a molecule and an oxide surface. It is useful to make the distinction between physical and chemical contributions. Contrary to most experimentalists who use the numerical value of the adsorption energy as criterion to discriminate between “physisorption” and “chemisorption” (e.g., “physisorption“ only for adsorption energies below about 0.30 eV [4]) we prefer to employ the distance dependence of the interaction potential for this purpose. We will speak of a “physical” contribution if the interaction potential decays with an inverse power dependence on the distance R between adsorbate and surface while a “chemical” interaction shows an exponential behavior. There are three contributions to the adsorbate/substrate interaction which are essentially physical in nature and two contributions of chemical origin. 2.2 Electrostatic Interaction This contribution to the total molecule/surface interaction is caused by the Coulomb interaction between the charge distributions of the ionic crystal and the adsorbed molecule or, stated differently, by the potential energy of the adsorbed molecule in the electrostatic field above the solid surface. In the theory of intermolecular forces, this interaction is generally expressed by means of a multipole expansion Q lA * Q lB Vel (R) = ∑ 08 R(lA + lB + 1)

(1)

Table 1 Contributions to the interaction between an oxide surface and an adsorbed molecule

Type

R-dependence

Electrostatic R–n interaction

Attractive/ repulsive

Orientation dependence

Classical/ quantum mechanical

Strength Method eV

Attractive Strong or repulsive

Classical

1.0

SCF, DFT

Induction

R–1

Attractive

Strong

Classical

0.1

SCF, DFT

Van der Waals interaction

R–3

Attractive

Weak

Classical

0.05

CI, CC, MP

Pauli repulsion

Aexp(-aR) Repulsive

Weak

Quantum 1.0 mechanical

SCF, DFT

Covalent chemical bond

Bexp(-bR) Attractive

Strong

Quantum 1.0 mechanical

SCF, DFT

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where QlA and QlB are the permanent electric multipole moment tensors of order lA and lB of the fragments A and B [14, 15]. Equation (1) is not very useful for describing the interaction between a molecule and an extended surface, since it is only asymptotically convergent. This means in practice that it can be used only for large separations R and converges extremely slowly – if it converges at all – in the region of the equilibrium geometry. Despite its little practical use, some qualitative conclusions can be drawn from Eq. (1). First, there can be large long-range contributions to the interaction, in particular if the adsorbed species possesses low order multipole moments, such as a charge (lA=0) or a dipole moment (lA=1). Asymptotically, the term with the lowest multipole moment will prevail, but at shorter separations other contributions might be more important. Second, the electrostatic interaction can be both repulsive or attractive, depending on the sign of the multipole moments and on the orientation of the molecule relative to the surface. 2.3 Induction (or Polarization Interaction) The (permanent) multiple moments of the adsorbed molecule can induce electric moments in the solid and interact with them, or vice versa. This interaction between permanent and induced multipole moments is called “induction” or “polarization interaction” and is always attractive. Similar to the interaction between the permanent multipole moments it possesses an R–n dependence. For small molecules the leading term is the charge-induced dipole moment contribution which is given by [14, 15] Vind (R) = –1/2 * qA2 * aB * R–4

(2)

where qA is the charge of one subsystem and aB the dipole polarizability of the other. If the interaction between a molecule and an oxide surface is to be considered the polarizability aB has to be replaced by the static dielectric constant e of the oxide and the R-dependence is changed from R–4 to R–1 because an integration over all atoms in the whole semi-infinite crystal is necessary. The induction potential will then read [4] e –1 Vind (R) = –1/4 * q2 * 7 * R–1 e +1

(3)

Because of the similarity between electrostatic and induction interaction it is sometimes difficult to discriminate between the two. It should be mentioned that the well-known Coulomb-type interaction of a charged species above a metal surface with its image charge Vimage (R) = –q2/4R is just a special case of the induction interaction.

(4)

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2.4 Van der Waals Interaction (Dispersion) If the two subsystems do not possess any permanent multipole moments neither the electrostatic nor the inductive interaction can exist. Nevertheless, there is always an attraction due to mutually induced multipole moments. This interaction is generally referred to as Van der Waals interaction or London-type dispersion or simply “dispersion”. The explanation of the origin of this interaction goes back to F. London [16, 17]. In the very simplest case of the interaction between two closed shell atoms, e.g., two He atoms in their electronic 1S ground states, the leading terms of the van der Waals interaction are given by VvdW (R) = –C6/R6 – C8/R8 – …

(5)

where the coefficients C6 and C8 are called “dispersion” coefficients. C6 can be expressed as 3h • C6 = 62 Ú dwaA (iw) * aB(iw) 2p 0

(6)

with aA(iw) and aB(iw) being the dynamic dipole polarizabilities of the two subsystems.Again, replacing one polarizability by the dielectric constant of the solid and integrating over all atoms in the semi-infinite crystal yields as the leading term VvdW (R) = –C3/R3 – …

(7)

with e (iw) –1 h • C3 = 62 Ú dwaA (iw) * 04 e (iw) +1 8p 0

(8)

for the van der Waals interaction between an adsorbed molecule and the solid surface [4]. The signs in Eqs. (5) and (7) indicate that the Van der Waals interaction is always attractive. It is generally very weak and can hardly be identified in case that stronger interactions (electrostatic, induction, covalent chemical bonds) are present. However, it does exist for all interacting systems and it must be included if accurate interaction energies are to be calculated. If the stronger interactions are not present, it is the only attractive contribution to the total interaction potential and therefore the real origin of physisorption. 2.5 Pauli Repulsion The “chemical” contribution to the total interaction consists of two parts. One of them is the repulsion between closed shells which is caused by the Pauli exclusion principle and is therefore mostly referred to as “Pauli repulsion” or

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“exchange repulsion” (XR). This contribution is always present and always repulsive. It depends on the overlap between the wave functions of the two subsystems, which means that it is of short-range nature and decays exponentially with increasing distance between adsorbed molecule and surface. Its functional form is given by VXR (R) = A* exp(–aR)

(9)

for the molecule/surface interaction. The parameters A and a characterize the strength and the range of the Pauli repulsion; sometimes a is replaced by Ç=1/a. Both parameters depend on the diffuseness and polarizability (or more vaguely, on the “softness”) of the electronic wave functions involved. Since the asymptotic behavior of the wave function of a quantum mechanical system is given by Y(R) µ exp(–eR)

(10)

where e is proportional to the lowest ionization potential of the system under consideration [18, 19], the range of the Pauli repulsion is larger for “soft” systems which are easier to polarize and possess smaller ionization energies than for “hard” systems. 2.6 Chemical Bonding The second “chemical” contribution to the total interaction energy is present if an ionic or a covalent chemical bond between the adsorbed molecule and the surface can be formed. Since covalent bonds also depend on the overlap between the wave functions of the subsystems, their distance dependence is exponential, see Table 1, as is that of the Pauli repulsion. In general, covalent bonds are only possible if at least one of the two partners possesses partially occupied valence orbitals. In contrast to the adsorption at metal or semiconductor surfaces, such a situation is rarely encountered at insulator and in particular at oxide surfaces. In most cases, the ions at the surface of an insulator try to adopt a closed shell electronic structure as they do in the bulk, as for instance the Na+ and Cl– ions in NaCl or the Mg2+ and O2– ions in MgO. Counterexamples are transition metal oxides in which the metal cations possess partially occupied d-shells which might form chemical bonds with the adsorbed molecule. One “famous” example is the interaction between NO and the NiO(100) surface where both the Ni2+ cations (d8 configuration with a 3A2g ground state) and the NO radical (2∏ ground state) have partially filled valence shells (see below). Pure ionic or charge transfer bonds between adsorbates and oxide surfaces are also very scarce. However, there might be some charge transfer from the adsorbed molecule to the surface or in the reverse direction, as for instance in the bonding between CO and metal surfaces.

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As we have indicated above, there will be always the Pauli repulsion and the Van der Waals attraction, even in systems which possess neither long-range electrostatic or inductive interactions nor short-range chemical bonds. Since the long-range Van der Waals attraction decays less quickly with increasing separation between molecule and surface, there is a separation R at which it starts to dominate the short-range Pauli repulsion. That means there will be always an attraction between adsorbate and substrate, but it might be very small and might occur only at rather large separations. On the other hand, the Van der Waals attraction is generally so weak that it can be hardly identified whenever long-range electrostatic or inductive interactions exist. Table 1 contains some further information useful to characterize the different contributions to the molecule/surface interaction: orientation dependence and the typical strength of the different contributions, and whether or not they can be understood on a purely classical basis. If one wants to calculate molecule/surface interactions by means of quantum-mechanical or quantumchemical methods, the most important question is whether standard density functional (DFT) or Hartree-Fock theory (self consistent field, SCF) is sufficient for a correct and reliable description. Table 1 shows that all contributions except the Van der Waals interaction can be obtained both by DFT and SCF methods. However, the results might be connected with rather large errors. One famous example is that the dipole moment of the CO molecule has the wrong sign in the SCF approximation, with the consequence that SCF might yield a wrong orientation of CO on an oxide surface (see also below). In such cases, the use of post Hartree-Fock methods or improved functionals is compulsory. The theoretical treatment of the Van der Waals interaction, on the other hand, definitely requires the application of more sophisticated, correlated methods such as perturbation theory (performed mostly in the form of MøllerPlesset perturbation theory, MP), configuration interaction (CI) or coupled cluster (CC) approaches (see below). 2.7 Bonding Analysis Though the different contributions to the total molecule/surface interaction have distinctly different physical origin, it is not straightforward to discriminate between them a posteriori, i.e., after a quantum-chemical calculation has been performed. The widely distributed commercial program packages contain a variety of methods for characterizing bonding mechanisms by analyzing electronic wave functions or densities, the most popular schemes are the Mulliken charge and bond order analysis [20], the “natural bond order” (NBO) analysis of Weinhold [21, 22], Bader’s topological analysis of the Laplacian of the electronic charge density [23, 24], and the Morokuma analysis [25–29]. The Mulliken analysis is certainly the simplest and most widely used of these methods; however, its results are extremely sensitive to the basis set employed and are of little use especially in calculations with large basis sets.

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One method that has proven to be particularly useful for the analysis of molecule/surface interactions is the “constrained space orbital variation “ (CSOV) scheme originally proposed by Bagus and Hermann [30, 31]. As does the Morokuma scheme, it allows for a decomposition of the total SCF or DFT interaction energy into its different contributions by calculating only energy quantities, and not as do most other decomposition schemes by analyzing electronic densities or wave functions. The CSOV analysis consists of several consecutive steps which can be roughly characterized as follows: 1. Calculation of the wave functions and energies of the isolated fragments. 2. Superposition of the frozen wave functions of the fragments at a given intermolecular geometry. This allows for independent calculations of the electrostatic energy and the Pauli repulsion between the frozen, unperturbed fragments. 3. Optimization of the wave function of one fragment in the presence of the frozen wave function of the other one. This accounts for the inductive effect (polarization energy) in one direction. 4. The same for the other direction. 5. Full optimization of the wave function of the whole system and calculation of the total energy. Since in this scheme only energy quantities are calculated it is largely free from the artifacts connected with the analysis of wave functions, and it is also quite insensitive to changes in the basis set. Only if one wants to decompose further the steps 3 and 4 into polarization and charge transfer contributions one has to rely on a method for analyzing partial charges at the fragments. The CSOV scheme has two more advantages: It can be easily formulated in a way free from basis set superposition errors [32] (see below) and it yields energy contributions which are essentially additive. This is different in the Morokuma scheme which is closely related to the CSOV analysis. It should be mentioned that most of the analysis methods quoted above are generally only applied at the SCF or DFT level. This is certainly a severe limitation, in particular whenever Van der Waals interactions or other correlation effects play an important role. However, it is generally quite easy to decompose correlation energies into different physical contributions, for instance by analyzing the effect of different types of excitations: Inter-molecular double excitations are mainly responsible for Van der Waals interactions, intra-molecular doubles for the improvement of the SCF wave functions or densities of the fragments.

3 Cluster Models There are essentially three types of cluster models that are currently used to calculate local properties of bulk metal oxides or to describe adsorption and

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desorption processes at oxide surfaces: Free clusters, saturated clusters, and embedded clusters. Which type of cluster model to choose for a specific application is partly a matter of taste or of the program package available, but more often dictated by the geometrical and electronic structure of the crystal under consideration or by the specific properties one is interested in. 3.1 Free Clusters The simplest model, of course, is a free cluster. This is merely a finite, mostly rather small part of the crystal, used without any modification. In most cases, such a cluster consists of an array of m¥n¥p atoms or unit cells, where m, n, and p denote the number of atoms or unit cells in the three Cartesian directions or along the crystallographic axes. Other cluster designs are also used occasionally. Figure 1 shows two examples: The first one in Fig. 1a is a small NiO cluster containing two layers of nine atoms each, i.e., a 3¥3¥2 cluster in the above notation. Clusters of this kind have been used frequently to represent the (100) surface plane of crystals with rock salt structure (see below). The second example in Fig. 1b is a Zn13O13 cluster which is part of the wurtzite structure of ZnO. It contains four layers with seven Zn, six O, six Zn, and seven O atoms, respectively, and exposes both the Zn-terminated ZnO(0001) and the O-terminated ZnO(000–1) surface. This cluster has been used for modeling the properties of the two polar surfaces of ZnO, ZnO(0001) and ZnO(000–1), respectively (see below). The use of free clusters has several apparent advantages. First of all, such clusters are nothing but small or medium sized molecules and can be therefore treated by any quantum-chemical program package designed to describe the properties of finite molecules. It is also straightforward to assess the reliability of the cluster model: One has simply to extend the size of the cluster and to

a

b

Fig. 1a,b Free clusters: a 3¥3¥2 cluster used to represent the (100) surface plane of metal oxides with rock-salt structure; b Zn13O13 cluster exposing the Zn-terminated ZnO(0001) and the O-terminated ZnO(000–1) faces of wurtzite-like ZnO. (Unless otherwise noted, in this and the following figures the metal atoms are represented by black spheres and the O atoms by gray spheres)

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monitor the convergence of the calculated properties with increasing cluster size. This can be done both for bulk properties such as lattice constants, cohesive energies, bulk modulus, local excitations or defects, as well as for similar properties at surfaces or interfaces [33, 34]. The main problem connected with the use of free clusters is of course that most of their atoms are surface atoms possessing a geometrical and chemical environment that is very different from that in the bulk solid. In a cubic 5¥5¥5 NiO cluster, which contains 125 ions, only 22% of them have a bulk-like sixfold coordination. In the much larger 11¥11¥11 cluster with 1331 ions still only 55% of the ions are bulk ions. Thus, bulk properties, more precisely properties that depend on the average coordination of all atoms in the cluster, as does the cohesive energy, converge in general quite slowly with increasing cluster size. This has been demonstrated in quite some detail by Jug and coworkers [33, 34] who used rather large free clusters to investigate the properties of alkali halides and metal oxides by means of semi-empirical quantum-chemical methods. The problem seems to be less severe if one is interested in local properties of the bulk or the surface, as for instance adsorption energies and geometries, the energies of defects, local excitations and F-centers, or X-ray photoelectron spectra (XPS), in which one electron is removed from a core level localized on a single atom. In particular, all local properties in which no additional charges are generated and no charge transfer processes are involved which will give rise to long-range polarization effects, can be treated quite reliably by means of rather small free clusters. However, even in such simple cases some care has to be taken. Multipole moments are additive! This means that an extension of the size of the cluster by the addition of layers or shells of unit cells will lead to an increase of all multipole moments of the cluster. This is most easily seen in the example of the Zn13O13 cluster in Fig. 1b which obviously has a non-zero dipole moment normal to the (0001) surface. If the size of this cluster is increased by the addition of more layers or by a larger lateral extent of the layers, its dipole moment will grow, since it is proportional to the number of the ZnO units. Consequently, the electrostatic interaction with charged species will also grow with the cluster size and one will never reach convergence of the calculated adsorption energy as a function of the cluster size (see below). 3.2 Hydrogen Saturated Clusters One very simple possibility to simulate bulk or surface properties of solids by means of small clusters, but to avoid cluster size and boundary effects, is to saturate the “dangling bonds” of the cluster towards the bulk in a reasonable way. This can be done by “pseudo atoms” [35], but in most applications the saturation by hydrogen atoms is used for this purpose. Figure 2 shows two examples. The first one in Fig. 2a, is the NiO5H8 cluster used in the early calculations of Pöhlchen and Staemmler [36, 37] for the adsorption of CO and NO on the NiO(100) surface. The NiO cluster itself consists

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Fig. 2a,b Hydrogen saturated clusters: a a NiO5H8 cluster used to describe the adsorption of CO on the (001) faces of MgO or NiO [37]; b a V10O31H12 cluster used to model the V2O5(010) surface [38, 39]

of one Ni atom and the five adjacent O atoms. This is the smallest possible cluster which is able to represent the Ni adsorption site and its nearest surrounding. This cluster carries a charge of –8, if one assumes that Ni is in its oxidation state of +2 and is surrounded by five O2– anions. In order to “saturate” the bonds between the oxygen atoms in the cluster and the Ni atoms in the bulk, protons were added to each of the five oxygen atoms, with O-H distances of 0.95 Å, which corresponds to the O-H equilibrium distance in OH– or H2O. The number of saturating protons and the geometry was chosen in such a way as to make the whole system charge neutral and as symmetric as possible. It is really surprising that such a small saturated cluster gave a rather satisfactory description of the adsorption of CO on NiO(100) [37]. Certainly, the saturation by protons cannot correctly reproduce the true electrostatic potential at the Ni adsorption site. However, it seems that the two properties which are essential for the interaction between CO and the NiO(100) surface are at least qualitatively reasonably represented: the local charge distribution as well as the Pauli repulsion between the CO molecule and the closed-shell O2– anions. The spatial extent and the hardness of the fully occupied 2p-shell in neutral H2O or in OH– seems to be similar to those of the O2– ions stabilized by the surrounding Ni2+ cations at the NiO(100) surface. However, of course, one can hardly expect very accurate adsorption geometries and energies from such a simple model. The second example in Fig. 2 is a V10O31H12 cluster of the type which has been used by Hermann, Witko and coworkers to model the V2O5(010) surface [38, 39].V2O5 has a layered crystal structure consisting of V2O5 layers which are bound to each other by Van der Waals forces. The cluster in Fig. 2b shows part of one V2O5 layer containing six central V atoms each of which is covered by one

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vanadyl-type oxygen atom pointing upwards, i.e., out of the bulk, and four terminal V atoms with their vanadyl-type oxygen atom pointing downwards into the bulk. The V atoms are bridged by twofold and threefold coordinated oxygen atoms in the (010) layer. All the terminal oxygen atoms which are not bound to V atoms in the cluster are saturated by hydrogen atoms. If one assumes that in V2O5 all V atoms have the oxidation state of +5 and all O atoms the oxidation state of –2 the charge neutrality requires the saturation by twelve protons. As for the free clusters, it is necessary to assess the quality of the hydrogen saturated cluster model prior to the final calculations.As one example we refer to the work of Rittner et al. who have employed both hydrogen saturated and embedded clusters for studying the adsorption of N2 on the (110) surface of TiO2 (rutile) [40]. These authors extended the size of both cluster models till the local charges and the N2 adsorption energies became virtually identical. Because of the partial covalency of TiO2 it was necessary to use clusters containing at least 9 Ti and 18 O atoms before the properties calculated with the two different cluster models agreed with each other. 3.3 Embedded Clusters Currently, the vast majority of cluster calculations for local properties of bulk oxides or oxide surfaces is performed by means of embedded clusters. Several embedding schemes have been proposed in the literature [6, 7]. A typical scenario used for modeling a local adsorption site at an oxide surface is depicted in Fig. 3. The whole cluster consists of three regions: 1. The vicinity of the adsorption site is described by a small quantum cluster which is treated explicitly by quantum-chemical methods (DFT, SCF, MP2, CI). Size, shape and composition of this cluster have to be chosen in such a way that both the local properties of the surface at the adsorption site as well as the interaction with the adsorbate are correctly taken care of. That means that the chemical bonding within the surface, the local charge distributions and the electrostatic field above the surface, but also possible modification of the local properties due to the adsorption of the molecule, must be correctly described within the quantum cluster. In most cases it is chosen to be neutral and stoichiometric, but this is not compulsory. 2. The quantum cluster is embedded in an extended point charge field (PCF) which has to reproduce the correct Madelung potential at the surface and above the surface. In most cases, the positions of the point charges are taken to coincide with the lattice points of the crystal and the charges are chosen as the formal charges of the respective ions, e.g., +2 for Ni and –2 for O in NiO. This is generally a good choice for crystals which are strongly ionic, but causes uncertainties for systems with a higher degree of covalency, such as, e.g., TiO2. It has turned out to be quite difficult, if not impossible, to deter-

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Fig. 3 Schematic picture of an embedded oxide cluster

mine the effective charges of the ions in ionic crystals by theoretical methods. The calculated values depend quite sensitively on the electronic structure method used – there are for instances large differences between DFT and SCF results [41] – and on the method of analyzing the wave function or the electron density. Unfortunately, the Mulliken analysis which is the most frequently used method is the least reliable one. An illustrative example of how strongly different schemes for analyzing charge distributions can deviate from one another has been given by Meister and Schwarz [42]. On the other hand, experimental techniques for determining effective charges are by no means less ambiguous. A compilation of different experimental estimates for the ionic charges in ZnO can be found in [43]; the resulting values range between 0.4 e and 2.12 e. Another crucial point is the convergence of the electrostatic potential as a function of the size and shape of the embedding point charge field. Special summation techniques have to be used in order to achieve a fast and correct convergence [44]. Many authors use the method of fractional charges for this purpose, which has been originally proposed by Evjen [45] and was later extended by Piela and coworkers [46, 47]. 3. The electrons located at the atoms in the quantum cluster are too strongly attracted by the positive point charges in the surrounding point charge field. For instance, the electrons in the O2p shells of the O2– anions in MgO or NiO are strongly polarized by the adjacent twofold positive ions and will eventually try to occupy their empty 1s orbitals.Whether that is possible depends very sensitively on the basis set used for describing the quantum cluster. The better the basis set is, the larger is this effect, since more extended basis sets facilitate the flow of electrons from the cluster to the positive point charges. This effect leads to large errors in the calculated properties of the quantum cluster. Fortunately, it can be easily avoided by equipping the point charges in a “boundary region” around the quantum cluster by repulsive effective core potentials (ECPs), pseudo potentials (PPs) or model potentials (MPs) which prevent the electrons from flowing into the point charge field. The width of the boundary zone will depend on the form of the quantum

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cluster, the ionic charges and very strongly on the basis set used for the quantum cluster. A wide variety of different types of pseudo potentials has been used for this purpose. One example are the ab initio model potentials (AIMP) proposed by Barandiaran and Seijo [48, 49]. In this approach, the wave functions of the environment of the quantum cluster, as calculated in a prior calculation, are used to construct an effective one-electron “model” Hamiltonian for the electrons of the quantum cluster. It contains the Coulomb and exchange potentials generated by the environment as well as the necessary orthogonality constraints. It goes without saying that one has again to check in every case by a series of tests prior to the final calculation whether the quantum cluster, the embedding point charge field and the boundary region provide a reasonable description of the adsorbate/substrate system. Similar to the case of free clusters this can be achieved by monitoring certain properties (effective charges, Madelung energies, adsorption or excitation energies and others) as a function of the whole embedding scheme. However, one can find many applications in which this “additional” effort has not been undertaken. In the embedding model described so far, the ions in the point charge field are fixed in space, they have well defined charges and are not polarizable. That means in particular that the embedding point charge field cannot respond to changes in the quantum cluster, caused for instance by local excitations or by the adsorption of molecules at the surface. To account for such effects some authors use polarizable embedding schemes. The simplest one is the “shell model” first proposed by Dick and Overhauser [50] and used frequently in the simulation of bulk and surface properties of metal oxides [51]. In this model, each ion is described by a core, consisting of the nucleus and the innermost electrons, and a shell of opposite charge representing the valence electrons. The core and the valence shell are coupled by a harmonic force with a force constant k. Neighboring ions can exert a force on both the core and the shell, thus polarizing the ion. The polarizability is proportional to 1/k, where k can be treated as an adjustable parameter. The shell model has been recently extended in the EPE (elastic polarizable environment) embedding scheme derived and applied successfully by Rösch and coworkers [52, 53]. In this model, the quantum cluster is surrounded like an onion by several shells, in which the displacement of the ions and their polarizability can be accounted for self-consistently, with decreasing flexibility from the ions adjacent to the quantum cluster down to a static Madelung point charge field in the most distant shell. It should be noted that these embedding schemes are closely related to the QM/MM approaches (quantum mechanical description of the active site and molecular mechanics description of the environment) [54] which are currently widely used in the treatment of homogeneous catalysis and in particular biocatalysis [55]. It should also be mentioned that many different schemes have been proposed for embedding quantum clusters into metallic substrates

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[56–58]. Due to the strong delocalization of the valence and conduction electrons in metals, the embedding in metals is much more difficult than that for insulating materials.

4 Electronic Structure Methods 4.1 SCF and DFT Most of the cluster calculations for molecule/surface interactions are currently performed at the ab initio SCF or DFT levels of theory. (In the following we will use the abbreviations SCF=“self consistent field” and HF=“Hartree-Fock” synonymously. DFT stands for “density functional theory”.) We will not describe these methods here, but refer the reader to the text books on electronic structure theory in which these methods are treated in detail [59–61]. Some of the characteristic features of these approaches, as far as molecule/surface interactions are concerned, are summarized in Table 2. We have included three types of DFT functionals which are used in calculations for adsorption properties: local density functionals (local density approximation, the LDA Table 2 Some characteristic properties of DFT and SCF approaches for molecule/surface interactions

Type

Local density functionals, e.g., LDA

Gradient corrected functionals, GGA

Hybrid functionals, e.g., B3LYP

SCF

Electrons treated

All electrons, Valence el.

All electrons, Valence el.

All electrons, Valence el.

All electrons, Valence el.

Basis sets

Plane waves, atom centered

Plane waves, atom centered

Atom centered

Atom centered

Number of atoms in the cluster

500

500

100

100

Scaling of the numerical efforta

N2–N3

N2–N3

N3–N4

N3–N4

Typical accuracy of the calculated adsorption energy

+1.0 eV overbinding

+0.3 eV overbinding

±0.2 eV

–0.3 eV underbinding

a

N=number of atoms in the cluster.

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functional serves as an example), gradient corrected (or semi local) functionals (general gradient approximation, GGA), and hybrid functionals (mixture of local and Hartree-Fock exchange, e.g., B3LYP). More details can be found in particular in [61]. Apart from the electronic structure method, cluster calculations for molecule/surface interactions also differ in the type of basis functions employed. Some of them, mostly those with local density and gradient corrected functionals, use plane wave basis sets for the valence electrons and simulate the effect of the core electrons by means of pseudo potentials of different kind. The majority of the cluster calculations, SCF as well as DFT with gradient corrected and hybrid functionals like B3LYP, are carried out in conjunction with atom centered basis functions. This allows for both possibilities to perform all-electron calculations or to use pseudo potentials for the core electrons. As shown already in Table 1, both SCF and DFT are in principle able to account for all types of intermolecular interactions except for the Van der Waals forces. However, the accuracy of the results as well as the numerical effort are largely different in the two approaches and also quite different in DFT calculations performed with different functionals. Table 2 tries to give a very rough account of these differences. One first realizes that the scaling of the necessary computer time with the size of the system greatly favors DFT: while the numerical effort scales approximately with N3–N4 in SCF calculations, the scaling is only proportional to N2–N3 in the various DFT approaches (N being the number of basis functions which in turn is roughly proportional to the size of the system). Furthermore, DFT results for adsorption energies and in particular for geometries are generally superior to SCF results since large part of electronic correlation is included implicitly in the functional. Therefore, it is not surprising that most cluster calculations for molecule/surface interactions are presently performed with DFT. In the majority of recent applications the B3LYP hybrid functional is employed because is shows the best performance as far as adsorption geometries and energies are concerned. Table 2 indicates that for adsorption energies an accuracy of about 0.2 eV can be expected from such calculations, while the LDA functional, which is more popular in solid state physics, generally shows a strong overbinding, the gradient corrected functionals a moderate overbinding, and SCF generally underestimates binding energies. 4.2 Correlation Effects As indicated above, neither the SCF nor the DFT method is able to treat the Van der Waals interaction. This is well established for the SCF approximation [14, 15]. The Van der Waals interaction is a typical “correlation effect”; therefore, its description requires the use of a “correlated method”. In wave function based ab initio methods correlation effects are described by adding singly, doubly and higher excited configurations to the SCF or to a multi-configuration SCF (MC-SCF or complete active space SCF, CASSCF) wave function. This can be done by means of perturbation theory (PT), by configuration interaction (CI)

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or by coupled cluster (CC) methods. The description of the Van der Waals interaction, which is caused by the attraction of mutually induced, fluctuating multipole moments, needs the inclusion of a specific type of doubly excited configurations, namely configurations in which each of the two interacting fragments is singly excited with respect to the SCF wave function. Unfortunately, the Van der Waals energy is only a very small part of the whole correlation energy of the system, and one encounters rather large errors if one tries to calculate only the van der Waals attraction and to ignore the rest of the total correlation energy. The situation is less clear in DFT. One of its intentions is to incorporate correlation effects into the independent particle model by introducing a correlation functional or correlation potential Vcorr into the one-particle Hamiltonian. The overwhelming success of DFT is a consequence of the fact that it was possible to derive approximate correlation functionals which are able to cover large part of the correlation energy. Therefore, one might hope that DFT would be able to account also for the Van der Waals contribution to the total correlation energy. According to the Hohenberg-Kohn theorem [62], DFT does indeed cover the full correlation energy including the Van der Waals part, provided that the exact functional is used, since in this case DFT yields the exact solution of the Schrödinger equation for the system under consideration. However, in real calculations approximate functionals have to be employed since the exact correlation functional is unknown. It has been shown by many authors, e.g., by Wesolowski et al. [63], that local functionals are in principle not able to account for the Van der Waals interaction. Nevertheless, DFT calculations with semilocal and hybrid functionals are frequently performed for weakly interacting systems and seem to be able to account for part of the dispersion. This seems to be due to the fact that some correlation in the region of the minima of the potential energy surface, where the overlap of the fragments’ wave function is considerably different from zero, is indeed covered by the functional (Kristyan and Pulay [64] and Wu et al. [65]). On the other hand, most of the functionals used in current DFT calculations give rise to a certain “overbinding”, as indicated in Table 2. This would mean that the “Van der Waals bonding” which is found in DFT applications is nothing but an artifact of the approximate nature of the functional. This statement is corroborated by the observation that the calculated interaction energies in weakly bound systems depend very sensitively on the functional used [64, 65]. There is one essential requirement to an electronic wave function if it is to be used for a reliable calculation of intermolecular interactions: It has to be “size consistent”. That means that in the limit of infinite separation between the two fragments the wave function of the full system has to approach the product of the wave functions of the fragments and the total energy has to approach the sum of the fragment energies YAB Æ YA * YB

(11)

EAB Æ EA + EB

(12)

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This requirement is satisfied by two of the methods most frequently used to calculate correlation effects: Many body perturbation theory (MBPT) and coupled cluster theory (CC). In principle, configuration interaction (CI) is also size consistent, but only if it is not truncated at a certain excitation level. Since untruncated CI expansions become untractably large even for medium-size systems, CI is not a method that can be used for the calculation of molecule/ surface interactions. This is not the place for a full overview of the wave function based post Hartree-Fock methods currently applied for the calculation of intermolecular interactions and in particular molecule/surface interactions. Table 3 contains a brief characterization of the most widely applied schemes. The two most popular methods are MP2 (second order Møller-Plesset perturbation theory), because it covers large part of electronic correlation at comparably low exTable 3 Some characteristic properties of post Hartree-Fock methods used for calculating the Van der Waals contribution to molecule/surface interactions

Acronym

Name

Computational effort

Comment

MP2

Møller-Plesset perturbation theory, second order

N5

Cheap, 20% overbinding

MP4

Møller-Plesset perturbation theory, fourth order

N6

Comparable to CCSD

CI

(Truncated) configuration interaction

N4 up to very large (depending on the truncation)

Useless

CCSD

Coupled cluster with single and double excitations

N6

Slight underestimate of bonding

CEPA

Coupled electron pair approach

N6

Slight underestimate of bonding

CCSD(T)

CCSD plus perturbationally treated triple excitations

N7

Best for single reference cases

MR-CI

Multi-reference CI

Strongly depending on reference and truncation

As CI

CASPT2

Second order perturbation theory on top of a CASSCF wave function

M2* N5

Cheapest for multireference states

MR-CC MC-CEPA

Multi reference CC Multi configuration CEPA

M2* N6

Best for multireference states

N=number of atoms in the cluster. M=number of configurations in the reference wave function (M=1 in normal single reference cases).

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pense, and CCSD(T) (coupled cluster approach with singly and doubly excited configurations plus a perturbation estimate of triply excited configurations) which is currently the most accurate, but also the most time consuming quantum-chemical ab initio method. More details can be found in the text books on electronic structure theory [59, 60]. 4.3 Basis Set Superposition Error Most of the cluster calculations for molecule/surface interactions are performed by means of finite atom-centered basis sets, in particular Gaussian basis sets. Since such basis sets are incomplete, the results have to be corrected for the so called “basis set superposition error” (BSSE). This error arises since the basis set centered at one fragment A helps to improve the description of the other fragment B and vice versa, as soon as the two fragments are brought to a finite separation R. This error is unavoidable in the “supermolecule” approach of intermolecular interactions and leads to an overestimation of the calculated binding energies. In the supermolecule approach the binding energy of the system A-B consisting of the two fragments A and B is calculated as the difference between the total energies of the full system A-B and the isolated fragments A and B DE = EAB(AB) – EA(A) – EB(B)

(13)

It seems quite natural to calculate the energy of the full system with the full basis set AB and the energies of the fragments with their individual basis sets A and B, respectively, as indicated in Eq. (13) by the parentheses. This would indeed lead to the correct interaction energy provided that complete basis sets are used, but is affected by the BSSE as soon as the basis sets are incomplete. Boys and Bernardi [66] proposed a simple scheme for correcting the BSSE, the so called “counterpoise correction”. It consists in calculating all energies, i.e., also the energies of the fragments A and B, in the full basis set AB. The counterpoise-corrected binding energy is then given by DEcc = EAB(AB) – EA(AB) – EB(AB)

(14)

Of course, the BSSE varies with the intermolecular geometry, since it depends on the overlap of the two fragments which in turn depends on the their separation and to a smaller extent on their orientation. The consequence is that the calculations for the fragments A and B have to be repeated for each intermolecular geometry. Of course, this leads to an increase of the necessary computational effort. The size of the BSSE depends on a) the nature of the fragments, b) the size and quality of the basis sets used, c) the intermolecular geometry, and d) the method of the electronic structure calculation. Since it is much simpler to saturate basis sets at the SCF or DFT than at the MP and CI level, BSSE correc-

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tions are generally larger for correlated (MP, CI, CC) than for SCF or DFT calculations. In the case of molecule/surface interactions treated with reasonable basis sets (triple zeta quality plus one set of polarization functions, TZ+P, or 6–311G** in the terminology of the Gaussian program package) the counterpoise correction in the region of the equilibrium adsorption geometries amounts to about 0.1–0.3 eV. Very often, this is comparable to the adsorption energy itself, therefore all calculations not corrected for the BSSE have to be considered with some care. Since the BSSE always leads to an overestimate of binding energies, the use of small basis sets, on the other hand, to an underestimate (sometime called “basis set incompleteness error”, BSIE), there might be occasionally a favorable error cancellation in the uncorrected adsorption energy. However, can one always rely on error cancellations? Finally, two comments should be added. First, there has been some discussion in the past whether the “full” Boys-Bernardi counterpoise correction as given in Eq. (14) might overestimate the BSSE correction, since only the virtual orbitals at one fragment are available for improving the description of the other fragment. However, there is convincing theoretical and numerical evidence that the full counterpoise correction of Eq. (14), though still an approximation, does indeed yield the most reliable correction of the BSSE [67]. (This reference contains an excellent discussion of all aspects of the counterpoise correction.) Second, the formula for the counterpoise corrected binding energy gets more complicated than the one given in Eq. (14) if the geometries of the fragments change during the interaction. More details are given in [68, 69].

5 Case Studies 5.1 CO/MgO(100) The simplest adsorption systems are those in which an inert molecule with a closed-shell electronic configuration is adsorbed on a regular neutral surface of an insulator or a large band gap semiconductor. The prototype for such a situation is the adsorption of CO on the (100) surface plane of alkali halides or simple cubic metal oxides with rock-salt structure, such as MgO. Indeed, the adsorption of CO on the regular MgO(100) surface can be considered as the prototype for physisorption systems. It has been studied extensively both experimentally and theoretically; the theoretical treatments comprise cluster approaches as well as periodic calculations, performed both by means of DFT and wave function based methods [70–84]. There are several reasons why the CO/MgO(100) adsorption is particularly simple. First, the MgO(100) surface is unreconstructed and constitutes the unmodified (100) termination of the bulk MgO crystal. Relaxations of the

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interatomic distances at the surface – both within the surface and normal to it – are only of the order of 1–2% [70, 71] and can be safely neglected in the calculations. Second, the MgO structure is so rigid and the adsorption of CO is so weak that adsorption induced relaxations or reconstructions will be very small and can be ignored as well. Third, both the induction and the chemical contribution to the interaction are negligible [72], thus one has only to treat the electrostatic interaction and the ubiquitous Pauli repulsion and dispersion forces. And finally, there are accurate and reliable experimental data for the adsorption energy available. It is therefore possible to check the reliability of the theoretical results. Table 4 gives an overview over the experimental and theoretical results for the adsorption energy of CO on the (100) plane of MgO. The most accurate experimental value has been determined by Wichtendahl et al. [73] by means of temperature programmed desorption (TPD) of CO from carefully prepared MgO(100) single crystal surfaces. The value of 0.14 eV indicates that this adsorption is a rather weak physisorption. It is in reasonable agreement with data from infrared (IR) spectroscopy experiments on MgO microcrystals and powder samples [74–77]. The data of He et al., obtained for the adsorption of CO on ultrathin MgO films on metallic support [74], seem to indicate a much stronger CO/MgO(100) bond with an adsorption energy of 0.43 eV, but this is Table 4 Adsorption energy for the system CO/MgO(100)

Method

MgO model

Eads (eV)a

Reference

Temperature programmed desorption (TPD)

Single crystal MgO(100) surface

0.14

73

Infrared (IR) spectroscopy

Thin MgO film

0.43

74

IR spectroscopy

MgO microcrystals

0.13

75

IR spectroscopy

MgO powder samples

0.15–0.17

76,77

MgO 58–

SCF (without BSSE correction)

Embedded

cluster

0.20

78

DFT, LDA functional

Embedded Mg9O9 cluster

0.97

79

DFT, BLYP functional (BSSE corrected)

Mg25O25 cluster

0.09

80, 81

SCF (BSSE corrected) Correlated (BSSE corrected)

Embedded MgO 58– cluster

0.014 0.066

83

DFT, PW91 functional

Embedded Mg9O9 cluster

0.288

82

DFT, B3LYP functional

Periodic approach (1¥4) coverage

0.034

72

DFT, B3LYP functional, and ONIOM-MP2 estimate

Mg9O9 cluster

0.137

84

a

All adsorption energies, which are given in different units in the quoted papers, have been converted to eV.

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probably attributable to adsorption on defects rather than on regular terrace positions on the MgO(100) surface plane. The number of theoretical treatments of the CO/MgO(100) adsorption is so large that we could not include all of them in the table, but quote only the most important ones. (More details can be found in [9].) We also do not include experimental and calculated results for the adsorption geometry and for the shift of the C-O vibration frequency upon adsorption. The reader is referred to the references given in Table 4. All calculations, irrespective of their character, agree that the CO molecule is adsorbed at a Mg2+ cation on the MgO(100) terrace, it is oriented perpendicular to the surface with the C atom towards the surface (normal adsorption, C-down). However, there are large differences as far as the calculated adsorption energies are concerned. The early SCF cluster result of Pacchioni et al. from 1992 [78], 0.20 eV, seems to be very close to the best experimental value of 0.14 eV (which was not known in 1992), but the binding energy was certainly overestimated in this calculation, since the basis set superposition error (BSSE) was not corrected. At the same time, Neyman and Rösch obtained a very large adsorption energy of 0.97 eV by means of DFT cluster calculations using the LDA functional [79]; in this study, the overbinding typical for the LDA functional was responsible for the strong adsorption.As soon as the LDA functional is replaced with a gradient corrected functional, the binding energy is greatly reduced, e.g., to about 0.10 eV in the calculations of Rösch and coworkers using the BLYP functional [80, 81]. This effect has been confirmed by Vulliermet et al. [82] who employed a DFT scheme particularly developed for treating weakly interacting systems (denoted by “Kohn-Sham equations with constrained electron density”, KSCE) together with the gradient corrected PW91 functional and found a moderate overbinding of 0.288 eV for CO adsorbed on an embedded Mg9O9 cluster. Similarly, if the counterpoise correction is applied in the SCF calculations, the artificial overbinding due to the BSSE is avoided and rather small adsorption energies are obtained as well, e.g., a value of only 0.02 eV in the study of Nygren et al. [83] using a small MgO58– cluster embedded in a large point charge array with ab initio model potentials (AIMP). Of course, the size of the quantum cluster and the embedding scheme will also have some influence on the calculated adsorption energy. This was investigated by Neyman et al. [81] who systematically varied the cluster size for the CO/MgO(100) adsorption. The result of this and related studies can be briefly summarized as follows: as long as the cluster is too small, the calculated binding energy is too large, but it converges rapidly with increasing cluster size. In the favorable case of MgO with its cubic structure, a Mg25O25 cluster can be safely regarded as large enough. Too large binding energies are also obtained if small hydrogen saturated or small free clusters are used. Or, even worse, if a small quantum cluster is embedded in unscreened point charges (PCs) and is not surrounded by a coordination shell of point charges carrying pseudo potentials. The reason is easily understood: In all these cases, the 2p orbitals of the O2– anions adjacent to the Mg2+ adsorption site extend too much into the

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bulk crystal or towards the hydrogen atoms or the positive point charges of the embedding PC field. This reduces the Pauli repulsion with the approaching CO molecule and leads to a too strong bond. Stated differently, the presence of a larger number of coordination shells “squeezes” the electrons of the spatially extended O2– anions immediately adjacent to the adsorption site out of the surface and leads to a larger Pauli repulsion and a smaller adsorption energy. The next question is, how important are correlation effects for the CO/MgO(100) adsorption? Nygren et al. [83] applied the modified coupled pair functional method (MCPF, an approximation to CCSD, see Table 3) in their calculations with the embedded MgO58– cluster. When all the 50 valence electrons of CO and the quantum cluster were correlated, an increase in the calculated adsorption energy from 0.014 eV at the SCF level to 0.066 eV was found (BSSE corrected). This indicates a correlation contribution of about 0.05 eV. Certainly, this is a lower bound, since only part of the semi-infinite MgO(100) surface could be included in the correlation treatment. A similar estimate has been obtained by Ugliengo and Damin [72, 84]. These authors used a periodic “supercell” model with a (1¥4) coverage of CO on MgO(100). The BSSE corrected DFT calculations with the B3LYP functional and a basis set of polarized triple zeta quality yielded an adsorption energy of only 0.034 eV [72]. An ONIOM-MP2 type estimate of the correlation contribution performed with the help of a free Mg9O9 cluster increased the adsorption energy to 0.137 eV, very close to the best experimental value. A further analysis of the intra- and intersystem correlation contributions gave a value of 0.068 eV as due to the Van der Waals interaction between CO and MgO(100) [84]. Several authors have also performed a detailed analysis of the different components to the total binding energy [72, 78]. The results obtained at the SCF [78] and DFT [72] levels are very similar. There is a delicate balance between Pauli repulsion and electrostatic attraction, the contributions of induction and chemical bonding (covalent bond and charge transfer) are nearly negligible. However, the electrostatic interaction is not only caused by the attraction of the dipole moment of CO by the Mg2+ ions at the surface, the contribution of the quadrupole moment is even more important. The multipole expansion of the electrostatic interaction, as given in Eq. (1), is only useful for large molecule/ surface separations, in the vicinity of the equilibrium geometry it is too slowly convergent. As indicated by the data in Table 4, the delicate balance between Pauli repulsion and electrostatic interaction can be greatly perturbed if too small clusters, bad embeddings, inflexible basis sets or inappropriate functionals are used in the calculations. A summary of these and several more theoretical treatments yields the following picture: At the SCF level one obtains only a small part of the experimental adsorption energy, between about 0.01 and 0.02 eV. The same is true for DFT calculations with hybrid functionals (e.g., 0.04 eV with the B3LYP functional) while local and semi-local gradient corrected functionals overestimate the binding energy. Inclusion of correlation effects on top of SCF largely enhances the binding energy and improves the agreement with experiment.

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Electron correlation is needed for three reasons: The inter-system correlation, contained neither in the SCF nor in the DFT approach, describes the Van der Waals interaction; it amounts to about 0.05–0.08 eV in the case of CO/MgO. The intra-system correlation, also not included in the SCF approximation, but partly so in the DFT functionals, is mainly necessary to improve the electronic densities and to correct wrong SCF or DFT values of the permanent multipole moments of the fragments. For the CO/MgO adsorption this effect contributes also about 0.05 eV to the total adsorption energy. And finally, there is another contribution to the intra-system correlation which is generally slightly reduced in the supermolecule as compared to the isolated fragments [14, 85], but this effect is probably very small for CO/MgO(100). To conclude, it can be safely stated that the mechanism of the interaction between CO and the MgO(100) surface is well understood. The difficulties connected with a reliable calculation of adsorption energies as well as adsorption geometries, vibration frequency shifts and so forth are also well understood. Therefore it seems straightforward, though it might be quite tedious, to proceed from this simple prototype system to more complex cases. 5.2 Small Molecules on NiO(100) Since NiO has the same crystal structure as MgO, with nearly the same lattice constant (4.21 Å in MgO and 4.17 Å in NiO [86]) and is a good insulator as well (the band gap of NiO is about 3.5 eV [87]) it can be expected that the adsorption of small molecules on its (100) surface plane is very similar to that on MgO(100). However, there are two differences between the electronic structures of MgO and NiO. While the Mg2+ cations in MgO have a closed shell structure with a fully occupied 2p shell, the Ni2+ cations have a d8 configuration with two unpaired electrons and a 3A2g ground state in the octahedral environment in NiO. Further, the spins at the Ni2+ cations are antiferromagnetically coupled. This raises two immediate questions: first, is there the possibility of a covalent chemical bond between the partially occupied orbitals at the Ni adsorption site and the adsorbed molecule, and second, are the d-orbitals at the Ni2+ cations completely localized or do they form delocalized, metal-like bands and how does this affect the adsorption properties? Most of the cluster treatments for the adsorption of CO, NH3, NO and other small molecules on NiO(100) simply ignored the second problem. They used very small clusters containing just one Ni atom, either the hydrogen-saturated NiO5H8 cluster of Pöhlchen and Staemmler [36, 37, 88] or MgO clusters doped with one Ni atom [89–94]. Only in a few more recent papers was the attempt made to use larger NiO clusters: an embedded Ni5O5 cluster by Klüner and Staemmler [95], Ni9O9 clusters and NiO slabs by Bredow [96] and by Pacchioni and coworkers [92–94] and the recent periodic DFT slab calculation with a LSDA+U functional by Rohrbach et al. [97]. The use of larger NiO clusters is severely hampered by the fact that NiO is antiferromagnetic, therefore all

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cluster treatments are forced to use the spin-contaminated unrestricted Hartree-Fock approximation or to work with the high-spin state of the cluster which is not its electronic ground state. The adsorption of the closed shell molecules CO and NH3 on NiO(100) shows similar characteristics as on MgO(100), though the adsorption energies are a little larger, 0.30±0.04 eV for CO [98] and 0.80 eV for NH3 [12, 13]. At the SCF level only very small binding energies of 0.15 eV or even less can be obtained [92–96]; DFT treatments show the same qualitative behavior as for MgO: local density functionals exhibit strong overbinding, gradient corrected functionals a little overbinding, while the hybrid functional B3LYP is again quite close to the SCF results [92–94, 96, 97]. Correlation effects on a wave function based level have not been treated so far for these systems. Of course, the same care with basis sets and counterpoise corrections has to be applied as in the simpler CO/MgO case. The adsorption of NO on NiO(100) is quite different. Since NO has an open shell structure with a singly occupied 2p* orbital, there is the possibility of a covalent bond between this orbital and the partially occupied 3d orbitals on Ni. A detailed analysis has shown [36] that the two singly occupied 3d orbitals at Ni, 3dz2 and 3dx2–y 2 , and the two components of the 2p* orbital at NO have different symmetries and cannot form a covalent chemical bond as long as NO is adsorbed normal to the NiO(100) surface. In a tilted adsorption geometry, however, the symmetries match and a covalent bond can be formed. This is in complete agreement with experiment: NO adsorbs tilted on NiO(100), with a tilt angle of about 50° [12, 36, 98]. However, this bond is still rather weak, since the Pauli repulsion between the fully occupied 2p orbitals of the O2– ions adjacent to the Ni2+ adsorption site and the doubly occupied orbitals of NO prevents NO from approaching the surface so closely that the short-range chemical bonding becomes effective. Therefore, the system NO/NiO(100) exhibits a “weak chemisorption”. The experimental adsorption energy of 0.57±0.04 eV [99] is substantially larger than that for the adsorption of CO on MgO(100) or NiO(100). As stated by Hoeft et al. [12, 13], the calculation of accurate adsorption geometries and energies for NO/NiO(100) is still far from being satisfactory. It follows from the above discussion that NO/NiO(100) is not a “single reference” case, i.e., the chemical bond cannot be properly described by a wave function in the form of a single determinant. The consequence for wave function based approaches is that one has to start from a multi-configuration SCF method (MC-SCF or complete active space SCF, CASSCF) and has to include correlation effects on top of this reference wave function. This can again be done by perturbation theory (CASPT2) or by multi-reference coupled cluster theory (e.g., the MC-CEPA approach mentioned in Table 3). On the other hand, its is not clear whether DFT can properly describe such a situation at all. Indeed, all previous attempts to calculate reasonable adsorption energies for NO/NiO(100) by DFT failed [93]. The conclusions obtained in a recent study, reported by Pacchioni et al. [94], can be summarized as follows: DFT is inappropriate for

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such cases; the results are either seriously in error or depend so sensitively on the functional and the model (cluster or slab) that they are completely useless. At the CASSCF level, there is only very weak bonding, <0.1 eV, which is in line with the weak bonding obtained with SCF for the closed shell cases such as CO/MgO(100). If correlation effects are added at the CASPT2 level, fair agreement with experiment can be achieved both for the adsorption geometry and energy, but part of this agreement has to be attributed to the overestimation of correlation energies by second order perturbation theory. Finally, the approximate multi-reference coupled cluster calculations (MC-CEPA) yield still a too small adsorption energy [94, 95]; but these calculations are not yet completely finished. 5.3 CO on the Polar Surfaces of ZnO The situation is even more complicated for another, seemingly also quite simple system, namely the adsorption of CO on ZnO. ZnO is one component in the Cu/ZnO/Al2O3 catalyst which is used commercially for the synthesis of methanol from CO or CO2 and H2. A large number of experimental and theoretical studies have been performed to elucidate the mechanism of this process and to characterize active sites, reaction paths and short-lived intermediates [100–104]. Since the catalytic activity takes place not only on the three-component system Cu/ZnO/Al2O3, but already on pure ZnO, the first step in a thorough analysis of the reaction mechanism is to investigate how the reactants, intermediates and products adsorb on ZnO. However, since ZnO catalysts are mostly prepared in wet chemical processes, it is difficult to find out whether the active sites are Zn or O atoms on regular low-index surface planes, edges or corners of ZnO microcrystals, defects such as O vacancies, or even more complicated species. Of course, the simplest possibility is to study processes at regular ZnO surface planes, as is always done in the “surface science” approach to heterogeneous catalysis. ZnO surfaces are more complex than those of the rock-salt type oxides like MgO and NiO. ZnO crystallizes in the wurtzite structure in which each Zn2+ cation is tetrahedrally coordinated to four O2– anions and vice versa [105]. This crystal structure has no inversion center. The most important low-index surface planes are two polar planes, the Zn-terminated ZnO(0001) and O-terminated ZnO(000–1) plane, and two neutral planes, ZnO(10–10) and ZnO(11–20). According to Nosker et al. [106] and Tasker [107], the two polar surfaces are thermodynamically unstable, however, they can be easily prepared and characterized experimentally, and do even show rather regular (1¥1) LEED patterns [108]. This indicates that they are not stabilized by major reconstructions or other modifications. Therefore, it was believed for a long time that both polar surfaces exist in an unreconstructed bulk-like truncation. Several contradicting proposals have been made to explain how the stability of the polar “un-

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stable” ZnO surfaces could be achieved: Metallization at the two surfaces [109, 110], large reconstructions which might be even different on the Zn- and the O-terminated surfaces (triangular islands on the (0001) plane [111, 112], (1¥3) reconstructions on the (000–1) plane [113–115]), adsorption of charged species such as H+ on the O-ZnO(000–1) plane or OH– ions on the Zn-ZnO(0001) plane [115]. The two neutral planes, ZnO(10–10) and ZnO(11–20), on the other hand, are thermodynamically stable and need not be reconstructed.We will not present all the details here; this discussion is by no means finished at present. Similar to the contradicting findings concerning the stability of the different polar surface planes of ZnO, the adsorption of the probe molecule CO has given rise to much controversy. Gay et al. [116] studied the adsorption of CO on the four low-index surfaces mentioned above by means of ultraviolet photoelectron spectroscopy (UPS) and found virtually no difference in the initial heat of adsorption, 0.52±0.02 eV for all four faces; see Table 5. Room temperature TPD experiments, on the other side, found desorption from the (0001) and (10–10) faces with activation energies for desorption of about 1.0 eV, but no indication of a desorption peak from the (000–1) plane [117]. This was later confirmed in TPD and IR experiments at lower temperatures (130 K) [118, 119]. Au et al. [120] and Lindsay et al. [121] using spectroscopic methods (XPS, UPS, NEXAFS) found evidence for CO adsorption also on the (000–1) surface, but they did not report an adsorption energy and could not discriminate between adsorption on regular lattice positions and adsorption on edges, corners or defects.Very surprisingly, Becker et al. [122–124] found by means of advanced molecular beam techniques that there is essentially no difference in the heat of adsorption of CO on the two polar faces, but their value of 0.30 eV at low coverage was considerably lower than the one reported much earlier by Gay et al. [116]. Only a few theoretical studies for the interaction of CO with ZnO surfaces have been published so far in the literature. The earliest one is the cluster study of Rodriguez and Campbell [125] using semiempirical quantum-chemical approximations (INDO/S and INDO/2 parametrizations) to analyze the bonding between CO and free Zn9O9 and Zn13O13 clusters. In these calculations only the on-top position of CO on a Zn atom at the ZnO(0001) surface was considered and the Zn-C distance was fixed at 2.05 Å. The INDO approximation did not allow to calculate the adsorption energy; the analysis of the CO/ZnO bonding mechanism showed that there is a little charge transfer (<0.1 e) from the clusters to CO as well as a slight polarization of CO by the clusters [125]. Casarin et al. [126, 127] used an embedded Zn22O22 cluster (embedding in pseudoatoms) in DFT calculations with the LDA functional and obtained an adsorption energy of 1.13 eV for CO in the on-top position on the ZnO(0001) surface; the calculated adsorption energy at the neutral (10–10) surface was substantially smaller, only 0.56 eV. A very similar result was obtained by Vulliermet et al. [82] in DFT cluster calculations using an embedded Zn9O9 cluster together with the PW91 functional: 0.45 eV for CO adsorbed at the neutral (10–10) surface.

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Table 5 Adsorption of CO on the different surface planes of ZnO

Method

Surface plane

Eads (eV) a

Reference

UPS

(0001), (000–1), (10–10), (11–20)

0.52±0.02

116

Temperature programmed desorption (TPD) (room temperature)

((0001), (10–10) (000–1)

1.05–1.10 no adsorption

117

TPD and IR spectroscopy (130 K)

(000–1)

No adsorption

118, 119

XPS and UPS

(000–1)

Adsorption, no binding energy given

120

NEXAFS

(000–1)

Adsorption, no binding energy given

121

He atom scattering (HAS)

(0001) and (000–1)

0.30

122–124

Free Zn9O9 and Zn13O13 clusters Semiempirical INDO method

(0001)

No binding energy given

125

Embedded Zn22O22 cluster DFT (LDA functional)

(0001) (10–10)

1.13 0.56

126, 127

Embedded Zn9O9 cluster DFT (PW91 functional)

(10–10)

0.45

82

Free Zn4O4 cluster SCF and MC-CEPA

(0001)

0.21 (SCF) 0.33 (MC-CEPA)

128

Periodic SCF With correlation correction

(10–10)

0.24 (SCF) 0.41 (SCF+corr.)

130

a

All adsorption energies, which are given in different units in the quoted papers, have been converted to eV.

Our own cluster calculations were performed at different levels of approximation.We started with a free Zn4O4 cluster with the wurtzite-like structure of bulk ZnO [128]. This cluster is shown in Fig. 4a. It has the advantage that its dipole moment is still so small (in contrast to the Zn13O13 cluster shown in Fig. 1b) that it will not affect the results too much. Furthermore, it contains threefold (3C) and twofold (2C) coordinated Zn and O atoms and can therefore serve as a model for threefold coordinated Zn atoms on the terraces of the (0001) plane or at edges on the (10–10) plane as well as for twofold coordinated Zn atoms at various types of corners. The results for all those configurations of CO on Zn4O4 which exhibit an attractive interaction are collected in Table 6. They show without any doubt that CO will only bind to Zn atoms, with

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a

249

b

Fig. 4a,b Clusters used to investigate the adsorption of CO on the polar surfaces of ZnO: a free Zn4O4 cluster with twofold and threefold coordinated Zn and O atoms; b embedded hydroxylated Zn13O13 cluster with part of the embedding point charge field

the bond towards Zn2C slightly favored over the one to Zn3C. The approach towards the O2– ions is nearly always purely repulsive or shows at most very weak minima (<0.05–0.10 eV). The CSOV analysis of the bonding mechanism (see above) has shown that the main difference between the approaches towards the Zn and O atoms is caused by the Pauli repulsion: the O2– anions at the surface are spatially so extended that the Pauli repulsion between them and the approaching CO molecule dominates all other attractive contributions to the interaction. This is not the case for the approach of CO towards the much smaller Zn2+ cations. Furthermore, the bond to the Zn atoms is facilitated by a small charge transfer from CO to the Zn2+ cations [128]. The comparison between the SCF and the correlated results (in the MC-CEPA approximation, see Table 3) in Table 6 shows that correlation effects increase the binding energies for all configurations except for the end-on O-down conTable 6 Adsorption of CO on a free Zn4O4 clustera

Adsorption site

CO orientation

R/Åb

Eads (eV), SCF

Eads (eV), MC-CEPAc

Zn2C Zn2C Zn3C Zn3C O2C O3C

End-on, End-on, End-on, End-on, Side-on Side-on

2.33 2.17 2.46 2.27 3.16 3.60

0.21 0.33 0.07 0.21 0.07 0.01

0.18 0.52 0.08 0.33 0.08 0.02

a

O-down C-down O-down C-down

Only those configurations are included in the Table which are attractive in the SCF approximation [128]. b Optimized at the correlated MC-CEPA level. c That part of the Van der Waals interaction which is not included explicitly in the MC-CEPA calculation is estimated to enhance the binding energies for all configurations by about 0.05 eV and to shorten the molecule/surface distance by 0.05–0.10 Å[128].

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figuration for CO adsorbed on the Zn2C atom. This exception is the consequence of the well-known fact that the SCF approximation yields a wrong sign for the permanent dipole moment m of CO. m is rather small, its experimental value being only 0.12 D with the polarity C–O+ [129], and gives rise to only a minor contribution to the total interaction energy. However, the wrong sign of this contribution favors the O-down adsorption over the C-down adsorption at the SCF level.As discussed above for the CO/MgO system, correlation effects are needed also in this case both for describing the genuine Van der Waals attraction and for correcting the errors in the SCF results for the permanent multipole moments of the fragments. These cluster results are in remarkably good agreement with the periodic calculations of Jaffe and Hess [130] for the adsorption of CO on the non-polar ZnO(10–10) surface, both at the SCF and the correlated levels (Table 5). The Zn atoms at this surface are threefold coordinated as are those on the terraces of the ZnO(0001) surface plane. Therefore, the adsorption of CO at the Zn3C atom of the free Zn4O4 cluster can be taken as a model for the adsorption on the Zn atoms in both surfaces. The good agreement is quite surprising since completely different methods have been used: periodic approach vs free cluster at the SCF level, perturbation theory (MP2) vs approximate coupled cluster approach (MC-CEPA) at the correlated level. This is also an indication that both treatments will converge to similar results, provided that the calculations are performed correctly. So far, the big discrepancy between theory and experiment still remains. On the basis of general theoretical considerations the bulk-like terminated polar ZnO surfaces should be unstable [106, 107], furthermore, the cluster results state very clearly that CO cannot adsorb at the O-terminated ZnO(000–1) surface [128]. On the other hand, both polar surfaces were found experimentally to be stable and CO was found to be adsorbed on ZnO(000–1), at least under certain conditions [116, 122–124]. In order to resolve this discrepancy, our cluster calculations were extended in two ways [131]. First, the free Zn4O4 cluster was replaced by a larger Zn13O13 cluster embedded in an extended point charge field, in which fractional charges were added at the outermost border in order to compensate the dipole and quadrupole moments. (The free Zn13O13 cluster could not be used because of its large dipole moment along the (0001) direction.) Then, the ZnO clusters were saturated by hydrogen atoms to simulate the possibility that the polar ZnO surfaces are not bulk-terminated, but covered with hydrogen. The hydroxylated embedded Zn13O13 cluster is shown in Fig. 4b.And finally, these cluster calculations were compared with slab calculations for the unmodified (1¥1) terminated and for the fully hydroxylated polar surfaces. The results of these calculations are summarized in Table 7 [131]. From the technical point of view, they confirm the observations made already in the previous sections. (i) Inclusion of correlation yields larger binding energies than does SCF. (ii) DTF with a gradient corrected functional gives rise to a moderate overbinding. The results of both methods are in fair agreement with each other

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Table 7 Calculated adsorption energies for CO on different surface models for ZnO(0001) and ZnO(000–1) (adsorption energies in eV)a

ZnO(0001) (1¥1) H-saturated ZnO(000–1) (1¥1) (1¥3) reconstructed H-saturated a b

Free Zn4O4 cluster SCF

Free Zn4O4 cluster MC-CEPA

Free Zn4O4 cluster DFT

Embedded Periodic Exptl. Zn13O13 DFT cluster SCF

0.21 Repb

0.33

0.54 Rep

0.19

0.38 Rep

0.01

0.02

Rep

<0.02

0.11

0.12

0.15

0.04 0.14 0.19

0.19

0.28 Rep

0.18 0.20

[131]. Rep=purely repulsive potential.

and with experiment. The consequence for the properties of the polar ZnO surfaces are more important: CO definitely does not bind to the bulk-terminated O-ZnO(000–1) surface, but it does bind to a hydroxylated ZnO(000–1) surface with a binding energy that is comparable to the one for the Zn-terminated ZnO(0001) surface. The main conclusion of these calculations is that many experimental studies for the O-terminated ZnO(000–1) surface were probably not performed for the pure bulk-terminated surface, but for a surface covered fully or partly by hydrogen. This conclusion was also confirmed by a series of experiments in which the hydroxylation of the ZnO(000–1) surface could be proven by O(1s) X-ray photoelectron spectroscopy (XPS) [113–115].

6 Conclusion In this review we have tried to give a brief account of the present status of the cluster approach to calculate adsorption properties of insulating surfaces. The main results can be summarized as follows. The interaction between small molecules and oxide surfaces is characterized by a delicate balance of attractive and repulsive contributions which have different physical and chemical origin. In most cases, several of these contributions have the same order of magnitude, but different distance and orientation dependence. Reliable results for adsorption geometries and energies can be only obtained if all of these contributions are properly taken into account and are quantitatively correctly described. Otherwise, one will get results of doubtful quality, maybe accidentally even the correct answer.

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Since the adsorption is a local process, the cluster approach seems to be the most natural way to treat adsorption phenomena. Indeed, it can yield reliable results provided that the quantum cluster and its embedding are designed properly and are carefully tested. The size and form of the quantum cluster as well as of the embedding point charge field depend strongly on the crystal structure of the oxide substrate and on the property one wants to calculate. Cluster and periodic calculations do yield similar results if both of them are performed properly. The main problem for the calculation of small interaction energies, as they are usually found for the physisorption of small molecules on insulating surfaces, is the treatment of the Van der Waals interaction (London dispersion forces). They are not accounted for in the SCF or MC-SCF approximation and are also not covered by the local or semi-local functionals used in current DFT applications. The consequence for the wave functions based methods is that correlation effects have to be included, which can be done by means of perturbation theory (e.g., MP2 or CASPT2) or coupled cluster methods (e.g., CCSD(T)), however, this will increase the numerical effort by at least an order of magnitude. DFT treatments, on the other hand, very often yield results in reasonable agreement with experiment, but this is an artifact connected with the overbinding generated by most of the approximate functionals. The problem with the Van der Waals interaction is even more severe for the adsorption of larger molecules, e.g., hydrocarbons, on oxide surfaces since the dispersion forces increase linearly with the size of the adsorbate. In more complicated cases, in particular if covalent chemical bonding, adsorption induced relaxations of the surface or partially occupied electronic surface bands play a role for the adsorption, an accurate description of weak molecule/surface interactions is still a challenge for the current theoretical methods. The development of DFT functionals capable to account for the Van der Waals interaction as well as of fast wave function based correlation methods (e.g.,“local” correlation approaches) is therefore highly welcome. Acknowledgements I thank my coworkers K. Fink, B. Meyer and I. Hegemann for their help with the manuscript and the figures.

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