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High Pressure Chemistry Synthetic, Mechanistic, and Supercritical Applications Edited by Rudi uun Eldik and Frank-Gerrit Klamer

Further Titles of Interest B. Comils, W. A. Herrmann, R. Schlogl, C.-H. Wong (Eds.)

Catalysis from A to Z A Concise Encyclopadie 2000

ISBN 3-527-29588-X

F. Diederich, P. J. Stang (Eds.)

Metal-catalyzed Cross-coupling Reactions 1999

ISBN 3-527-29421-X

P. Braunstein, L. A. Oro, P. R. Raithby (Eds.)

Metal Clusters in Chemistry Three Volumes 1999 ISBN 3-527-29549-6

D. E. De Vos, I. F. J.Vankelecom, P. A. Jacobs (Eds.)

Chiral Catalysts Immobilization and Recycling 2000

ISBN 3-527-29952-1

II

FIZ CHEMIE Berlin (Ed.)

Dictionary o f Common Names Second, Extensively Enlarged Edition (5 Vol.) 2001 ISBN 3-527-30288-3

High Pressure Chemistry Synthetic, Mechanistic, and Su percritical Applications

Edited by Rudi van Eldik and Frank-Cerrit Klarner

@WILEY-VCH

Prof: Dr. Rudi yon Eldik University of Erlangen-Numberg Institute of Inorganic Chemistry EgerlandstraBe 1 91058 Erlangen Germany

Pro$ Dr. Frank-Cerrit Klarner University of Essen Institute of Organic Chemistry UniversitatsstraXe 5 45141 Essen Germany Cover Dr. Frank Wurche

University of Essen

This book was carefully produced. Nevertheless, editors, authors and publisher do not warrant the information contained therein to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate. Library of Congress Card No.: applied for A catalogue record for this book is available from the British Library. Die Deutsche Bibliothek - CIP Cataloguing-in-Publication-Data A catalogue record for this publication is available from Die Deutsche Bibliothek

0WILEY-VCH Verlag GmbH, 69469 Weinheim (Federal Republic of Germany). 2002 All rights reserved (including those of translation in other languages). No part of this book may be reproduced in any form by photoprinting, microfilm, or any other means - nor transmitted or translated into machine language wrthout written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law Printed in the Federal Republic of Germany. Printed on acid-free paper. Typesetting Asco Typesetters, Hong Kong Printing betz-dmck gmbH, Darmstadt Bookbinding J. Schaffer GmbH & Co. KG,

Griinstadt ISBN 3-527-30404-5

lv

Contents

I

Basic Principles

1

Effect of Pressure on Inorganic Reactions: Introduction and Mechanistic Applications 3 Rudi van Eldik and Colin D. Hubbard

1

Introduction 3 1.1 Determination of Volumes of Activation 6 1.2 1.3 Thermal-Induced Reactions 12 Ligand Substitution Reactions 12 1.3.1 1.3.1.1 Octahedral Complexes 13 1.3.1.2 Square-Planar Complexes 19 1.3.2 Electron Transfer Reactions 21 1.3.2.1 Self-ExchangeReactions 22 1.3.2.2 Non-SymmetricalReactions 22 1.3.3 Actvation of Small Molecules 25 Addition and Elimination Reactions 30 1.3.4 1.4 Photo- and Radiation-Induced Reactions 32 1.5 Concluding Remarks 35 Acknowledgments 36 References 37 2

The Effect of Pressure on Organic Reactions: Basic Principles and Mechanistic Applications 41 Frank Wurche and Frank-Cerrit Kliirner

2.1 2.2 2.2.1 2.2.2 2.2.3 2.2.4 2.2.5 2.2.6 2.3 2.3.1

Introduction 41 Cycloadditions 45 Diels-Alder Reactions, Mechanistic Aspects 45 Complex Reactions and Synthetic Applications 56 1,3-Dipolar [3 21 Cycloadditions 64 [2 21 Cycloadditions 66 [6 41 and [ 8 21 Cycloadditions 68 Cheletropic Reactions 70 Pericydic Rearrangements 71 Sigmatropic [ 3.31 Shifts: Cope and Claisen Rearrangement

+ +

+ +

71

vi

I

Contents

2.3.2 2.3.3 2.3.4 2.3.5 2.4 2.4.1 2.4.2 2.4.3 2.5 2.6

Electrocyclic Rearrangements 74 Intramolecular Diels-Alder Reactions 76 Ene Reactions 77 The Relationship Between Activation or Reaction Volume and Ring Size 81 Free-Radical Reactions 84 Homolytic Bond Dissociations 84 Quinone Oxidations (Hydrogen Transfer Reactions) 85 Free Radical Cyclizations 87 Ionic Reactions 88 Concluding Remarks 90 Acknowledgments 91 References 91

3

High-pressure Kinetics and Highly Viscous Media Tsutomu Asano

3.1 3.2 3.3 3.4 3.5 3.6 3.7

High Pressure and Dynamic Solvent Effects 97 Selection of Reaction Systems 101 Z / E Isomerization of N-Benzylideneanilines 103 Z / E Isomerization of Push-Pull Substituted Azobenzenes 109 Z / E Isomerization of Carbocyanine Cations 124 Z / E Isomerization of DNAB in a Polymeric Medium 122 Concluding Remarks 125 Acknowledgments 126 References 126

II

Mechanistic and Synthetic Applications o f High Pressure

4

Water Exchange on Metal ions: The Effect o f Pressure Lothar Helm and Andrh E. Merbach Introduction 131

4.1 4.2 4.3 4.3.1 4.3.2 4.3.3 4.3.4 4.4 4.5

97

129 231

Concepts of Solvent Exchange Reactions 133 Water Exchange from the First Coordination Shell 136 First Row Transition Metal Ions 136 Second- and Third-Row Transition Metal Ions 142 Lanthanides 144 Main Group Elements 151 Water Exchange from the Second Coordination Shell 255 Conclusions 157 Acknowledgments 157 References 158

5

insights into Solution Chemistry from High Pressure Electrochemistry Thomas W.Swaddle

5.1 5.2

Introduction 161 Pressure Effects on the Kinetics of Self-Exchange Reactions

162

261

5.2.1 5.2.2 5.2.3 5.2.4 5.3 5.4 5.4.1 5.4.2 5.5

Principles 162 Experimental Observations with Aqueous Media 164 Experimental Observations with Non-aqueous Media 167 Approaches Involving Electrochemistry 168 Electrochemical Measurements at High Pressure 170 Homogeneous Versus Heterogeneous Electron Transfer 172 Aqueous Solutions 171 Non-aqueous Media 174 Conclusions 180 Acknowledgments 181 References 181

6

Pressure Effects on the Photoreactions o f Transition Metal Complexes

6.1 6.1.1 6.1.2 6.2 6.2.1 6.2.2 6.3 6.3.1 6.3.2 6.3.3 6.4 6.5

7

Pressure Effects on Excited State Energies 186 Pressure Effects on Excited State Kinetics 188 Unimolecular Excited State Reactions 196 Ligand Photosubstitution Reactions 196 Unimolecular Photoredox Decompositions 205 Bimolecular Pathways For Excited State Deactivation 206 Excited State Electron and Energy Transfer Reactions 207 Brarnsted Base Quenching 211 Reactions with Lewis Bases to Give an Excited State Complex Photochemically Generated Reactive Intermediates 213 Summary 218 Acknowledgments 22 9 References 22 9

212

Application of High Pressure in Transition Metal-Catalyzed Reactions

Oliver Reiser

7.1 7.1.1 7.2 7.2.1 7.2.2 7.2.3 7.3 7.4 7.5

Introduction 223 General Principles 224 Lewis Acid Catalyzed Reactions 224 Cycloadditions 224 Nucleophilic Substitution 229 Addition of Nucleophiles to Carbonyl Compounds Palladium Catalyzed Reactions 230 Rhodium-Catalyzed Hydroboration 236 Conclusion 237 References 237

8

High Pressure in Organic Synthesis: Influence on Selectivity Lutz F. Tietze and Peter L. Steck Introduction 239

8.1 8.2

184

Peter C. Ford and Leroy E. Laverman Introduction 284

Influence of High Pressure on Selectivity

243

229

239

223

viii

I

Contents

8.2.1 8.2.2 8.2.3 8.2.3.1 8.2.3.2 8.2.4 8.3

General Remarks 243 Chemo- and Regioselective Transformations 245 DiastereoselectiveTransformations 253 Reactions with Simple Diastereoslectivity 253 Reactions with Induced Diastereoselectivity 267 Enantioselective Transformations 275 Conclusion 280 Acknowledgements 281 References 281

9

High-pressure Promoted Cycloadditions for Application in Combinatorial Chemistry 284 George J. T. Kuster and Hans W. Scheeren

9.1 9.2 9.3 9.3.1

Introduction 284 High-pressure Diels-Alder Reactions on the Solid Phase 285 High-pressure Multicomponent Domino Cycloaddition Reactions 286 High Pressure-Promoted One-Pot Three-Component [4 2]/[3 21 Cycloadditions: Scope and Limitations 287 Mono Substituted Dipolarophiles 291 Di-Substituted and Cyclic Dipolarophiles 292 Novel 5,5-Membered Bi- and Tricyclic Nitroso Acetals 295 Pressure and Solvent Dependency 296 High Pressure-Promoted Domino [4 2]/[4 2]/[3 21 Cycloaddition of 2-Methoxy- 1,3-Butadieneand p-Nitrostyrene 298 High-pressure Domino [4 + 2]/[3 21 Cycloaddition Reactions on the Solid Phase 299 Conclusions and Outlook 302 References 303

9.3.1.1 9.3.1.2 9.3.2 9.3.2.1 9.3.3 9.4 9.5

+

+

+

+

+

+

10

Catalytic and Solvophobic Promotion o f High Pressure Addition Reactions 305 GerardJenner

10.1 10.2 10.2.1 10.2.2 10.2.3 10.2.4 10.3 10.3.1 10.3.2 10.3.2.1 10.3.2.2 10.3.2.3 10.3.3

Introduction 305 Chemical Activation 306 Catalysis by Lithium Salts 309 Catalysis by Lanthanides and Related Periodic Elements 312 Catalysis with Other Lewis Acids 319 Catalysis by Phosphines 320 Solvophobic Activation 321 Water and Water-like Solvents 322 Kinetic Studies in Water and Water-like Solvents 324 Michael Reactions 325 Diels-Alder Reactions 327 Effect of Addition of Micelles and Cyclodextrines in Aqueous Media Synthetic Applications 337

336

Contents

10.3.3.1 10.3.3.2 10.3.2.3 10.3.3.4 10.4

Diels-Alder Reactions 338 Michael Reactions 342 Baylis-Hillman Reactions 343 Triactivation 343 Conclusions 344 References 345

11

Future Perspectives: Applications o f High Pressure in Supramolecular Chemistry 348 Robert Rulofl Christophe Saudan, Andri E. Merbach and Frank-Cerrit Klarner Introduction 348 Biomolecules under Extreme Conditions 349

11.1 11.2 11.3 11.3.1

The Effect of Pressure on the Formation of Host-Guest Complexes 352 Inclusion of Helium Atoms or Acetonitsile Molecules in C ~ or Oa Hemicarcerand as Molecular Containers 351 11.3.2 Complexation of Cations and Cboas Guests with Crown Ethers, Cryptands, and Calixarenes as Hosts 353 11.3.3 Molecular Tweezers as Synthetic Receptors: Focussing on Volume and Entropy of Association 354 11.3.4 Formation of Host-Guest Complexes of a-Cyclodextrins with Azo Dyes: Determination of Activation and Reaction Volumes 357 11.3.4.1 Inclusion of Short Guests into the a-Cyclodextrin Cavity 357 11.3.4.2 Sequential Threading of a-Cydodextrin onto a Long Guest 362 11.3.5 Self-Assembled Multinudear Coordination Species with Chiral Bipyridine Ligand 363 Conclusion and Outlook 367 11.4 Acknowledgments 368 References 368 Ill

Chemical Reactions in Supercritical Fluids

12

Catalytic Reactions in Supercritical Fluids 372 Jason Hyde, Walter Leitner and Martyn Poliakoff

12.1 12.1.1 12.1.2 12.1.3 12.2 12.2.1 12.2.2 12.3

Introduction to Catalytic Reactions in Supercritical Fluids 372 Solvent Properties of Supercritical Fluids 372 Temperature and Pressure Relations 372 Decaffeination of Coffee via scCOz Extraction of Caffeine 374 Practical Aspects of Catalpc Reactions in scC02 375 Heterogeneously Catalyzed Reactions 375 Homogeneously Catalyzed Reactions 377 Acid-Catalyzed Continuous Flow Processes in Supercritical Fluids 379 Heterogeneously Catalyzed Alkylation Reactions 379 Heterogeneously Catalyzed Etherification and De-symmeterization Reactions 380

12.3.1 12.3.2

~

369

I

ix

x

I

Contents

12.4 12.5 12.5.1 12.5.2 12.6 12.6.1 12.6.2 12.7

Homogeneously Catalyzed C-C Coupling Reactions 381 Hydrogenation Reactions 383 Heterogeneously Catalyzed Hydrogenation Reactions 383 Homogeneously Catalyzed Hydrogenation Reactions 386 Hydroformylation Reactions 389 Homogeneously Catalysed Hydroformylation Reactions 389 Heterogeneously Catalyzed Hydroformylation Reactions 393 Closing Remarks 394 References 395

13

Application of Supercritical Fluids in the Fine Chemical Industry

398

Werner Eonrath and Reinhard Karge

13.1 13.2 13.2.1 13.2.2 13.3 13.3.1 13.3.2 13.3.3 13.3.4 13.3.5 13.4

Introduction 398 Supercritical Fluids in Separation/Purification 400 Supercritical Fluid Extraction (SFE) 400 Supercritical Fluid Chromatography (SFC) 403 Catalytic Reactions in Supercritical Fluids 405 Hydrogenation 406 Methylation 42 1 Friedel-Crafts Alkylation Reactions 412 Oxidation 415 Other Reaction Types 41 7 Concluding Remarks 419 Acknowledgments 41 9 References 41 9

14

Applications of Supercritical Water Eckhard Dinjus and Andrea Kruse Introduction 422

14.1 14.2 14.3 14.3.1 14.3.1.1 14.3.1.2 14.3.1.3 14.3.1.4 14.3.1.5 14.3.1.6 14.3.1.7 14.3.2 14.3.2.1 14.3.2.2 14.3.2.3 14.3.3

422

Physico-Chemical Properties of Water at High Temperature and Pressure and their Relation to Applications 423 Supercritical Water in Chemical Synthesis 425 Organic Reactions 425 Hydrolysis Reactions 425 Condensations 427 Diels-Alder Reactions 427 Rearrangements 428 Friedel-Crafts Reactions 429 Partial Oxidations 430 Reduction Reactions 43 I Organornetallic Reactions 43 I Heck Coupling 431 Cyclotrimerization of Alkynes 432 Hydroformylation 433 Inorganic Reactions 434

Contents

14.4 14.4.1 14.4.2 14.5 14.6

Supercritical Water in Decomposition Reactions Oxidation in Supercritical Water 434 Gasification in Supercritical Water 437 Conclusions 440 Outlook 441 References 442 Index

447

434

I

xi

I

Preface High pressure chemistry is an area that has developed a vigorous activity over the past decades. Although most of the earlier work was mainly performed in the area of organic chemistry, a major contribution from inorganic chemists over the past two to three decades resulted in the development of sophisticated instrumentation that enables the study of fast chemical reactions under high pressure. More recently, the application of supercritical fluids has received much attention especially in chemical industry. Numerous reviews have reported on the progress made in these areas over the past years. The monograph consists of fourteen contributions bascd on oral presentations at the European High Pressure Research Group Meeting held at Kloster Banz, Germany, in September 2000. The theme of the meeting was High Pressure Chemistry. It covers contributions from high pressure inorganic and organic chemistry, as well as the application of supercritical fluids in chemical synthesis and processes. The monograph is subdivided into three sections. The first three chapters are devoted to basic principles involved in the application of high pressure techniques in inorganic and organic chemistry. The subsequent eight chapters are devoted to mechanistic and synthetic applications of high pressure in inorganic, organometallic, organic, and supramolecular chemistry. The final three chapters are devoted to chemical reactions in supercritical fluids and cover catalytx reactions, applications in the fine chemical industry and the application of super critical water. All in all, the individual chapters reveal the present status of high pressure chemistry and its application in a variety of areas. The editors appreciate the co-operative support they received from the individual authors of the chapters, as well as the effective interaction with Wiley-VCH. The efforts of numerous scientific coworkers and the financial support from many funding agencies have all contributed to bringing high pressure chemistry to where it stands at present. May we all in future benefit from these developments and stimulate further activities of the next generation in this area of chemistry. Rudi van Eldik University of Erlangen-Niirnberg

Frank-Gerrit Klarner University of Essen

xiii

I

xv

List of Authors Tsutomu Asano Department of Applied Chemistry Faculty of Engineering Oita University 700 Dannoharu Oita 870-1192 Japan Werner Bonrath Vitamins and Fine Chemicals Division Chemical Process Technology F. Hoffmann-LaRoche Ltd. Grenzacherstrage 124 CH-4070 Basel Switzerland

CH-1015 Lausanne Switzerland Colin D. Hubbard Institute for Inorganic Chemistry University of Erlangen-Niirnberg Egerlandstrage 1 91058 Erlangen Germany lason Hyde School of Chemistry University of Nottingham University Park Nottingham NG7 2RD U.K.

Eckhard Dinjus Institut fur Technische Chemie Chemisch Physikalische Verfahren Forschungszentrum Karlsruhe Hermann-von-Helmholt-Platz 1 76344 Eggenstein-Leopolshafen Germany

Gerard Jenner Laboratoire de Pikzochimie Organique Universite Louis Pasteur 1: Rue Blake Pascal 67008 Strasbourg Cedex France

Rudi van Eldik Institute for Inorganic Chemistry University of Erlangen-Nurnberg Egerlandstrage 1 91058 Erlangen Germany

Reinhard Karge Vitamins and Fine Chemicals Division Chemical Process Technology F. Hoffmann-LaRoche Ltd. Grenzacherstrage 124 4070 Basel Switzerland

Peter C. Ford Department of Chemistry and Biochemistry University of California Santa Barbara CA 93106 U.S.A. Lothar Helm Institut de Chimie Minerale et Analytique Universite de Lausanne BCH

Frank-Gemt Klarner Institut fur Organische Chemie Universitat Essen Universitatsstrage 5 45141 Essen Germany Andrea h s e Institut fur Technische Chemie, Chemisch Physikalische Verfahren

xvi

I

List ofAuthors

Forschungszentrum Karlsruhe Hermann-von-Helmholtz-Platz 1 76344 Eggenstein-Leopolshafen Germany

George J. T. Kuster Department of Organic Chemistry NSR Center for Molecular Structure, Design and Synthesis University of Nijmegen Toernooiveld 1 6525 ED Nijmegen The Netherlands Leroy E. Laverman Department of Chemistry and Biochemistry University of California Santa Barbara CA 93106 U.S.A. Walter Leitner Max-Planck-Institut fur Kohlenforschung Kaiser-Wilhelm-Platz 1 45470 Miilheim an der Ruhr Lehrstuhl fur Technische Chemie und Petrolchemie RWTH Aachen Woringer Weg 1 52056 Aachen Germany Andre E. Merbach Institut de Chimie Minkale et Analytique Universiti. de h u s a n n e BCH 1015 Lausanne Switzerland Martyn Poliakoff School of Chemistry University of Nottingham University Park Nottingham NG7 2RD U.K. Oliver Reiser Institut fur Organische Chemie Universitat Regensburg UniversitatsstraBe 31 93053 Regensburg Germany

Robert Ruloff lnstitut de Chimie Mmerale et Analytique Universite dc Lausanne BCH 1015 Lausanne Switzerland Christophe Saudan Institut de Chimie Minerale et Analytique Universitk de Lausanne BCH 1015 Lausanne Switzerland Hans W. Scheeren Department of Organic Chemistry NSR Center for Molecular Structure. Design and Synthesis university of Nijmegen Toernooiveld 1 6525 ED Nijmegen The Netherlands Peter L. Steck Institut fur Organische Chemie Georg-August-Universitat Tammannstrasse 2 37077 Gottingen Germany Thomas W. Swaddle Department of Chemistry University of Calgary Calgary Alberta T2N 1N4 Canada Lutz F. Tietze Institut fur Organische Chemie Georg-August-Universitat Tammannstrasse 2 37077 Gottingen Germany Frank Wurche Institut fur Organische Chemie Universitat Essen UniversitatsstraRe 5 45141 Essen Germany

I’

I

Basic Principles

High Pressure Chemistry Synthetic, Mechanistic, and Supercritical Applications

Edited by Rudi van Eldik and Frank-Gerrit Kliirner

0WILEY-VCH Verlag GmbH, 2002

13

1

Effect o f Pressure on Inorganic Reactions: Introduction and Mechanistic Applications Rudi van €Idib: and Colin D. Hubbard I. I

Introduction

Chemistry literature is to a large extent concerned with preparative work and the structural and spectroscopic characterization of reaction products. The velocity of the reactions and efficiency of product formation as manifested in the reaction yield, are also of importance in synthetic studies, particularly when the products are of direct use or are intermediates in commercially relevant activities. The kinetics of reactions can be very informative in combination with other information for revealing the details of the reaction mechanism. Once a chemical reaction mechanism is fully understood, the insight gained can be used to tune the chemical process in any desired direction. The evidence for a particular mechanism is often circumstantial, and therefore kineticists try to employ the widest set of experimental variables available in an effort to interpret the resulting kinetic data in the least equivocal manner possible. The value of the mechanistic information that emerges from kinetics measurements over a series of elevated pressures for solution reactions in inorganic and organic chemistry has been realized for some time [ l - 3 ) . However, many inorganic reactions are too fast to follow using conventional instrumentation. Hence the momentum regarding investigations at high pressures vis-a-vis organic reactions was delayed somewhat until adaptation of rapid reaction techniques for operation at high pressures had been achieved, mostly in the period from 1975 to 1985. This fertile period has been recorded in reviews, in conference proceedings, and in monographs, and readers may obtain a thorough background and sense of historical development by consulting this literature [4-111. Even until quite recently, suitable instrumentation was not widely available. The purpose of this chapter is to familiarize the reader with the current status of activities in the application of hydrostatic pressure to mechanistic studies in the areas of inorganic and organometallic chemistry, as well as in the blossoming field of bioinorganic chemistry. Although the basic principles involved in high pressure kinetics for reactions in general have been the subject of many reports [12-141, some essential aspects and the most frequently used methods will be presented

4

I

7 Effect of Pressure on Inorganic Reactions: Introduction and Mechanistic Applications

here to form a basis for the subsequent chapters dealing with the effect of pressure on particular types of reactions in inorganic and organic chemistry. The parameter that is derived from high pressure kinetic experiments in solution is the difference in partial molar volume between the activated complex of transition state theory and the reactant state, and is known as the volume of activation. AVf . If the particular reaction is reversible and the system experimentally accessible, AVf for the reverse reaction can also be obtained and the difference between these two quantities results in the reaction volume, AVO. The latter quantity may also be determined by measuring the equilibrium constant ( K ) for the reaction as a function of pressure, or from the partial molar volumes of the reactants and products, derived from solution density measurements. The volume of activation itself is determined from measurements of the reaction rate constant k at different hydrostatic pressures p at a given absolute temperature T, since (? In k/?p), = -AV#/RT (R is the ideal gas constant), an equation was developed within transition state theory based upon the analogous equilibrium constant relationship, ( 3 In K/Sp), = -AVo/RT. The former equation, upon integration. can be employed to determine AVz from a plot of In k versus p . Providing the pressure is no higher than 200 MPa, in the vast majority of cases AV# is pressure independent and the plot is linear. A nonlinear behaviour is usually encountered when dealing with a compressible solvent where both the reaction and activation volume become pressure sensitive. For such cases often encountered in organic systems (see Chapter 2), where it is necessary to consider the pressure dependence of AV#, i.e. to extrapolate the data to ambient pressure, there are various treatments available for processing the primary data [5, 151. In this introductory chapter the focus will be on reactions in which there is a negligible or absence of pressure dependence of the volume of activation. In general, volume of activation data quoted in this report will refer to ambient conditions, i.e. close to room temperature, and readers are advised to consult the cited literature for more detailed information on the exact experimental conditions employed. Equilibrium and kinetic parameters obtained as a function of temperature permit the drawing of diagrams illustrating the Gibbs free energy (C), enthalpy (H) and entropy (S) changes in proceeding in the sequence reactant state/transition state/product state, and including intermediates when they are formed. Correspondingly, a volume diagram or volume profile can chart the respective volume changes along the reaction coordinate, and when appropriate actual partial molar volumes are known, on an absolute rather than a relative basis, something that cannot realized for G, H or S. Hence if reactants A and B form a product AB and no intermediates are formed, i.e. there is a single step reaction, a volume profile in which the reaction volume is, for example, negative and the volume of activation is such that the transition state is almost halfway between reactant and product states, is depicted in Fig. 1.1. As shown in Fig. 1.1,other forms of the volume profile are possible depending on the particular character of the system. Thus, in principle, a volume profile represents a simple and lucid way of describing a reaction and diagnosing the mechanism, but with the caveat that mechanistic diagnosis is uncomplicated when only intrinsic changes (changes in bond lengths, bond angles for example) occur. In

7 . 1 Introduction

15

r

I

I

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

A+B

Reactants

Transition State

Products

Reaction Coordinate Fig. 1.1.

Volume profile for the overall reaction A

+B

-+

AB. The activated complex is [A----B]#.

many actual reactions, when charged species are produced or neutralized during the reaction, or increases or decreases in polarity occur, then there is also a change in the volume occupied by the solvent molecules surrounding the system by virtue of an increase or decrease in (at least) the first solvation layer. Volume reduction of solvent from this source is known as electrostriction. Thus the facile interpretation of measured values of AVO or AV# can be compromised by the existence of the two contributions which are difficult to quantify. The intrinsic and solvational contributions to AVf can schematically be visualized as shown in Fig. 1.2.

A

B

(A---B)*

A- B

o+o-m-m --

Forward reaction: Reverse reaction:

A + B AB

A

AViZtr = AVittr = +

AB B

+

o +0-00- -m

Forward reaction: Reverse reaction:

-*

A' + BAB A+

Overall volume effect: AV Fig. 1.2.

+

AV:, = AV&,, =

A8 B-

*

*

= AVintr + AVsolv

Intrinsic and solvational contributions t o the volume of activation.

+

-

6

I

7 Effect of Pressure on Inorganic Reactions: Introduction and Mechanistic Applications

Clearly a reaction accelerated by pressure has a negative volume of activation and one retarded by pressure. a positive volume of activation. Most inorganic reactions that have been studied yield AVc values within the range of 30 to -30 cm' mol-'. which corresponds to retardation and acceleration respectively of a factor of about 4 at 100 MPa (1 kbar) compared to 0.1 MPa (atmospheric pressure;. In the absence of solvational contributions. positive AVf values are indicative of' the commencement of bond breakage. whereas negative AVc values are indicative of reactions in which a bond is beginning to be established upon reaching the transition state. Further classification of reaction types will be presented later. A brief account of experimental methods follows with illustrations in some cases. Thereafter thermal reactions grouped by reaction type from inorganic, organometallic and bioinorganic chemistry will be described from the perspective of the mechanistic insight gained from the application of high pressure techniques. A section on photo- and radiation-induced chemical reactions is also included. At this stage readers are referred to more detailed reports on water cxchange processes in Chapter 4,application of electrochemical techniques in Chapter 5. and photochemical processes in Chapter 6. '

1.2

Determination of Volumes of Activation

The scope of activity in the overall field in question may be gauged by the number of pertinent papers published or the number of volume parameters reported. Up to 1978 about 170 of the latter values had been published. while in the subsequent two decades approximately 1000 and 1600 values of the activation volume. respectively. have been reported [8, 16, 171. The most frequently used method of rnonitoring a rcaction in coordination chemistry is by following changes in the UV:Vis spectrum either with a conventional spcctrophotometer or with a stopped-flow instrument. For conventional time range reactions (reaction times longer than a few minutes) using Uy/Vis spectroscopy, a two-window cell (Fig. 1.3) and a pressurizable cuvette (pill-box)(Fig. 1.4)may be used for high pressure measurements 1181. The advantage of the pill-box cuvette is that pressure can be transmitted through the compression of the movable, closcly fitting cylindrical parts: it can be easily filled using a syringe needle techniquc. after which the two cylindrical parts are turned 180" to seal the cuvette. When the cell is pressurized. the two cylindrical parts move closer together as a result of the compression of the solvent used in the sample solution within the cell. and therefore the pressure from the pressurizing medium is transmitted to the sample solution. The cell is pressurized with a pressure generating system which typically consists of the components shown in Fig. 1.5. An hydraulic p u m p is used to gcnerate an oil pressure. which is then transmitted by the separator to the pressurizing medium (for instance water) used within the optical cell. Compression and expansion can be controlled with the series of mechanical valves and monitored with a pressure gauge. The type of high pressure cell in Fig. 1.3 can also be used to construct a three-

1.2 Determination of Volumes of Activation 17

I Fig. 1.3. Schematic view o f a two-window high-pressure cell: 1 - pressure plug; 2 - O-ring; 3 - reaction compartment; 4 A- and O-ring; 5 - sapphire window; 6 - pressure connection

or four-window cell which may be used for flash photolysis and pulse radiolysis applications. Technical details of these cells and methods of use may be found in recent literature [ 18-20]. The development of high pressure stopped-flow instruments opened up the possibility to study reactions in the millisecond and second time range as a function of pressure [21-271. A stopped-flow instrument is designed to enable the rapid

Fig. 1.4. Schematic presentation of a "pill-box'' optical cell for measurements i n a high pressure optical cell. The slot and hole allow the pill-box cell t o be filled and extra liquid t o be released on closing the cell.

8

I

7 €fled of Pressure on Inorganic Reactions: Introduction and Mechanistic Applications

1

7 reservoir filled with n-heptane

valve oil reservoir

high-pressure cell compartment with optical windows and pill-box cell

teflon membrane in a steel cylinder, used for pressure transmission and for separatlon of oil and n-heptane

to vacuum pump

~-

Fig. 1.5.

Typical system to generate high pressure.

mixing of two solutions containing the reactants, followed by the monitoring of the reaction progress when mixing is completed. Two high pressure versions of stopped-flow instruments are shown in Figs 1.6 and 1.7, with the difference that in the first case (Fig. 1.6) the activation of the syringes occurs by means of a motor inside the high pressure cell, whereas in the second case (Fig. 1.7) the syringes are activated from outside the cell. Activation of the sample syringes causes a flow of the two reagent solutions through a mixing jet and optical path into a receiver syringe, which is followed by the activation of the optical detection system that then monitors the reaction progress of the rapidly mixed reagents occurring in the optical path. The deadtime of the mixing process is between 2 and 10 ms. A second important method for determining AV# is by application of N M R spectroscopy. Progress in NMR instrumentation from electromagnets to superconducting magnets and higher field strengths has largely been matched by developments in construction of suitable high pressure probes for newer instruments in individual laboratories [29-38). Investigations of solvent exchange (see Chapter 4) and electron self-exchange reactions have been the principal beneficiaries of progress in high pressure NMR techniques. A typical example of an NMR high pressure probe developed in our laboratories, is shown schematically in Fig. 1.8. The operation principle of both these high pressure probes is that the NMR sample tube is placed within a high pressure cell and is pressurized with a suitable fluid by a movable stopper that transmits the pressure from the pressurizing fluid to the sample solution by moving down the NMR tube, which is controlled by the compressibility of the solvent used in the sample solution. With the aid of these high pressure probes practically all possible NMR measurements can be performed as a function of pressure up to 200-300 MPa (i.e. 2 to 3 kbar) at a fixed

7.2 Determination of Volumes of Activation

_

_

_

~

Fig. 1.6. Schematic representation of a high pressure stopped-flow unit: 1 - lid t o overall unit; 2 - outer vessel; 3 - window holder; 4 quartz windows; 5 - electric motor; 6 - motor actuator; 7 - stopped-flow unit positioning

__

rod; 8 - syringe-driving plate; 9 - drive syringe (inner); 10 - drive syringe (outer); 11 - block holding windows, mixer and syringe attachment points; 12 - mixing jet; 13 - stop syringe (outer); 14 - stop syringe (inner).

temperature. The only restriction is that the sample tube within the high pressure probe cannot be spun. The temperature-jump technique [39, 401 is frequently used to study the kinetics of rapidly equilibrating processes in solution on a microsecond time scale. This technique can only be applied to equilibria that are sensitive to temperature, such that a rapid temperature jump of a few degrees will result in a relaxation of the system to the new temperature, a process that can be followed on a micro- or millisecond time scale.

19

10

I

7 Efect of Pressure on Inorganic Reactions: lntroduction and Mechanistic Applications

_

_

b-.Thrust

_

_

_

~ rod

7

Mndow mount for the entwing light

Observatim cell

Hydraulic pressure connection Port of the temperature Sensor

L Lower tiate I

Coolant

ObservationCell Absorbance sapphirewindow Fluorescence sapphirewindow Fluorescence window mount

Fig. 1.7. Schematic representation of the commercially available Hi-Tech HPSF-56 high pressure stopped-flow unit [28].

Electrochemical methods have also been adopted for application of high pressure [41-431 (see Chapter 5). Correlations emerging from these investigations have val-

uable application in the interpretation of partial molar volume changes associated with electron transfer reactions (see Sect. 1.3.4).A potential future interest is in reactions carried out at elevated pressures in a supercritical fluid medium; in view of this a special optical cell has been developed for studying organometallic reactions initiated by flash photolysis in supercritical fluids [lo] (see Chapters 12 to 14).

The principles and instrumentation outlined above have been applied to numerous types of reactions in inorganic chemistry. A systematic treatment of the different reaction types and specific examples to illustrate the role of high pressure measurements in such studies, now follows.

7.2 Determination of Volumes of Activation

1

15

2

3 aluminum

a

4

16

17

probe jacket lower plug titanium ring

lower pressure screw

18

eroded titanium tube rnacor

19

..

PTFE

5 6 20

7

8

9

10

21

11

12

22

13

23

14

24

Fig. 1.8. Design features of a probe head for high-pressure N M R (400 MHz) measurements: 1 - O-ring; 2 - probe jacket; 3 - thermal insulation; 4 - polyvinyl chloride; 5 - O-ring; 6 - O-ring; 7 - semi-rigid coaxial cable; 8 - connection to thermostat; 9 - titanium tube; 10 - lid; 11 - screw; 12 - capacitor;

13 - capacitor holder; 14 - aluminum tube; 15 - upper plug; 16 - sample tube; 17 saddle coil; 18 - Macor; 19 - TiA16V4 vessel; 20 - lower plug; 21 - lower pressure screw; 22 - capacitor; 23 - coaxial cable; 24 capacitor holder.

I

”

12

I

7 Effect of Pressure on lnorganic Reactions: lntroduction and Mechanistic Applications

1.3

Thermal-Induced Reactions

In this section of our presentation we will focus on different types of reactions in inorganic chemistry that occur thermally. In Sect. 1.4 we will present an account of radiation-induced inorganic reactions. Photo-induced inorganic reactions are dealt with in Chapter 6. 1.3.1

Ligand Substitution Reactions

Ligand substitution reactions of metal complexes have been the topic of many mechanistic studies in coordination chemistry because of the fundamental role of such reactions in many chemical, biological and catalytic processes. For a general ligand substitution reaction as shown in Eq. (1.1),

where X is the leaving group, Y the entering ligand, and L,, the spectator ligand(s) (charges are omitted for clarity), there are basically three simple pathways: (i) the dissociative (D) process with an intermediate of lower coordination number; (ii) the associative (A) process with an intermediate of higher coordination number; (iii) the interchange (1) process, in which no intermediate of lower or higher coordination number is involved. The interchange of the ligands X and Y can be more dissociative ( I d ) or more associative (Ia) in nature, depending on whether bond breakage or bond formation is more important, respectively. These mechanisms are outlined schematically in Fig. 1.9, Such ligand substitution reactions should exhibit very characteristic AV# values depending on the degree of bond breakage or bond formation in the transition state. The most simple type of ligand substitution reaction involves the symmetrical exchange of coordinated solvent or ligand with bulk solvent or ligand molecules, respectively. [M(S),]"+

+ S'

--f

+S

[M(S),-,(S')]"'

Exchange of a unidentate solvent molecule (S) between the first coordination sphere of a solvated metal ion (M"+)and the bulk solvent (Eq. (1.2)) has been studied for cations of many elements of the Periodic Table. The incoming solvent molecule S" is denoted with an to distinguish it from the initially coordinated molecule with which it exchanges. Such reactions are very important and a knowledge of the kinetic and associated activation parameters represents important background to the understanding and tuning of substitution of a solvent by other ligands 144).The focus has frequently been; but by no means exclusively, on water as solvent. There is no reaction volume and the solvent exchange process is assumed to have zero solvational change. Thus A V f should be a direct measure of the intrinsic volume changes that occur, such that a continuous spectrum of tranQ

1.3 Thermal-lnduced Reactions

Reaction: MLnX + Y

-

MLnY

+

X

Mechanism:

D

Id

Schematic presentation of the possible ligand substitution mechanisms. In the case of the limiting D and A mechanisms, the transition states indicate the degree of bond breakage or bond formation, respectively. Fig. 1.9.

Ia

A

!

For the interchange mechanisms I d and la, the reactants are suggested t o form a precursor complex in a rapid pre-equilibration prior to the rate-determining interchange o f X and Y.

sition configurations can be envisaged, ranging from a very expanded, highly dissociative one (large and positive A V z ; rate constant significantly slowed down by pressure) to a very compact, highly associative one (large and negative A V # ; rate constant significantly accelerated by pressure). A detailed treatment of the effect of pressure on water exchange processes is given in Chapter 4;readers are referred to that chapter for more details. A typical non-symmetrical ligand substitution reaction was presented in Eq. (3.1). When X is a solvent molecule, this process is referred to as complex-formation or anation reaction, depending on whether the entering ligand Y is neutral or anionic, respectively. When X is not the solvent and Y is, then the reaction is an aquation reaction in aqueous medium or a solvolysis reaction in other solvents. Another category of substitution reactions is base hydrolysis, in which typically for a six coordinate complex, with n = 5, and X a variety of unidentate ligands, Y is either the hydroxide ion or supplies the OH- ion. Thus ligand substitution reactions encompass a wide variety of chemical reactions, and each type has received mechanistic benefit from high pressure kinetics studies. 1.3.1.1

Octahedral Complexes

Complex-formation reactions are intimately connected mechanistically with solvent exchange reactions since solvent departure may be rate determining following

14

I

I Effect of Pressure on Inorganic Reactions: Introduction and Mechanistic A p p h t i o n s

the rapid formation of an outer sphere complex or, in the case of Y being charged, an ion-pair. It is therefore not surprising that such ligand substitution reactions exhibit pressure dependencies that correlate closely with those found for solvent exchange processes [lo, 171. In the case of substitution by a ligand for one or more solvent molecules, the volume profile reveals the location of the transition state with respect to the reactant and product states, such that A V f can be related to the reaction volume AV. The formation of the mono 2,2'-bipyridine (bpy) complexes of Zn(I1) and Cd(I1) aqua ions [45, 461 provides excellent straightforward examples of both size influence on mechanistic determination and complementarity of activation volume and reaction volume measurements. An improved access to the coordinated solvent by the ligand in the outer sphere permits reaction via an I, mechanism for formation of [Cd(bpy)(H20)4]2 + , a process not possible in the formation of the analogous Zn(I1) complex, which is formed from a smaller hexaaqua ion, resulting in an Id mechanism. Figure 1.10 displays the volume profiles for these two complex-formation reactions. The mechanism proposed for the zinc complexformation is entirely consistent with recent calculations for water exchange on [Zn(Hz0)6I2' [471. Thus the corresponding volume profiles illustrate the looseness or compactness of the transition state during the ligand substitution process. Such analyses have also been applied to mechanistic questions in organometallic chemistry. In one case the volume profile for the reversible substitution of coordinated CO by P(OMe)3 on [Cr(phen)(C0)4],phen = 1,lO-phenanthroline, could be constructed on an absolute partial molar volume scale, since the partial molar volumes of all reactant and product species were determined through density measurements [48]. The volume profile in Fig. 1.11 demonstrates the significantly higher partial molar volume of the transition state and the operation of a dissociative (D) mechanism in both directions. The overall reaction volume is negative and indicates a volume decrease during the reaction. In reality the complex-formation rate constant is a composite of the precursor complex or ion-pair formation constant (KO)and the subsequent interchange rate constant (ki), i.e. k = Koki, as shown in Eqs (1.3) and (1.4). ML,X

+ Y + {ML,X

{ML,X. Y}

+

ML,Y

.Y}, &

+ X,

k,

(1.4)

The contributions from these terms frequently cannot be separated with the result that only the composite term k is known. One example for which the separation of these terms was possible, concerns the complex-formation reaction of aquacobalamin (vitamin B12). Here the usually inert Co(II1) center is labilized by the corrin ring, which induces a dissociative substitution mode. From the non-linear dependence of the observed pseudo-first-order rate constant on the entering ligand concentration for the reaction shown in Eq. (1.5), the precursor formation constant and rate-determining interchange constant can be determined, as can their pressure dependences.

7.3 Thermal-Induced Reactions 115

M=Zn

-----f--

AVO= +3.5 f 0.5

M=Cd V

Fig. 1.10. Volume profiles for the reversible formation of [M(H2O)d(bpy)l2+ complexes M = Zn(ll) and Cd(l1).

A typical volume profile for Eq. (l.S), where L = pyridine (py), is shown in Fig. 1.12, which clearly demonstrates the dissociative nature of the transition state and supports the operation of an Id mechanism [49,501. The small volume increase associated with precursor formation is ascribed to partial desolvation on forming the encounter complex. As in the case of solvent exchange reactions, the rate and mechanism of ligand substitution reactions can be systematically tuned through manipulation of steric and electronic effects. The introduction of a metal-carbon bond on an inert metal

16

I

I EfPect of Pressure on Inorganic Reactions: lntroduction and Mechanistic Appkations

E

[Cr(phen)(CO)g+ CO

+

P(OMe)31z

+13.82 0.5 +19.2 f 0.5 Cr(phen)(C0)4+ P(OMel3 ........

.c L

n

3501

-

I

Cr( phen)( C05P( OMe), calc: -5.4t1.0 exp: -4 :1 _._. ......... ' co

Reactants

'Transition State'

Fig. 1.11. Volume profile for the reversible reaction [Cr(phen)(CO)sJT P(0Me)S + [Cr(phen)(CO),P(OMe),]

Products t CO.

center such as Rh(II1) should also lead to a drastic increase in reactivity, accompanied by a possible changeover in mechanism. A system studied in detail in our group concerned the substitution behavior of rhodoxime complexes of the type trans-[Rh(dmg)2(R)H20],where dmg = dimethylglyoximate and R = CH3, CH2C1, or CH2CF3 [Sl]. Depending on the donor properties of R, the rate of complexformation with nucleophiles such as pyridine (Py), thiourea (TU), and tetramethylthiourea (TMTU) can be varied over several orders of magnitude. This is demonstrated in Fig. 1.13 for a particular entering ligand concentration for different Rs as a function of pressure. The reaction rate is largest when R = methyl, and the

+7.1

- _.

+ 16.9

Q

a, z ._ c

a

-?

-1 0

-15

LII Fig. 1.12.

Reactants

I

Precursor

I Transition stale I

Products

Reaction coordinate Volume profile for the overall reaction [B12-H20]-

t

L + [Blz-LI-

+ H2O

-

7.3 Thermal-Induced Reactions

3p

2

rMTU

PY

ru

-

-2 0

ru

50 100 15

Fig. 1.13. Plots of In kobz versus pressure for the reaction

+

trans-[Rh(drng)z(R)HzO] L ---* trans-[Rh(dmg)z(R)L] i H20.

reaction is characterized by a small positive volume of activation, typical for an Id mechanism. On decreasing the donor strength of R by the introduction of electronwithdrawing groups, the observed rate constant decreases by up to 5 orders of magnitude. In addition, there is no pressure dependence in the case of R = CH2C1, consistent with a pure interchange (I) mechanism, whereas the rate constant increases with pressure for R = CH2CF3and results in a small negative volume of activation typical for an I, mechanism. This means that the nature of the transition state can be tuned very accurately through the donor properties of R, which then determines the rate as well as the mechanism of the substitution process. This is demonstrated schematically in Fig. 1.14. Thus a decrease in donor strength slows down the substitution reaction and causes a changeover in substitution mechanism from more dissociative ( I d ) to more associative ( Ia) [ 511. Interestingly enough, whether the organic group was varied or not for a given nudeophile, all reactions studied were characterized by moderately negative entropies of activation, which by contrast demonstrates the mechanistic discrimination power of pressure versus temperature as a physical variable. The introduction of a tripodal tetradentate ligand such as tren or tmpa on the aqua Cu(I1) ion induces a changeover in the water exchange mechanism [52-541. Complex-formationreactions of these complexes exhibited a similar trend. Volume profiles for the complex-formation reactions (with pyridine) of [Cu(tren)HzO]2+ and [Cu(Me3tren)HzO]2+ (Me3tren is momomethylated on each primary amine

117

18

I

7 Efict of Pressure on inorganic Reactions: introduction and Mechanistic Applications

*

r

R = -CH3, -CH2CI, -CH2CF3 Fig. 1.14. Suggested transition state for the reaction trans[Rh(dmg)z(R)H20] t L + trans-[Rh(drng)2(R)L] H20.

+

group), for which a typical example is given in Fig. 1.15, clearly underline the compact nature of the transition state and the operation of an I, mechanism [53, 551. Increasing the steric hindrance on the tren ligand by introducing six methyl substituents on the terminal amino groups, slows down the substitution reaction of [Cu(Me6tren)H2OI2+ by about five orders of magnitude as compared to the unsubstituted tren complex, which is accompanied by a changeover in mechanism from I, to Id [55, 561. This example is an excellent illustration of how an increase in steric hindrance on the spectator ligand can cause a changeover to a more dissociative mechanism. This does not always have to be the case as an example in the following section will show.

3

8 Mg

Cu(Me3tren)(H20>2’+ py

‘F

Cu(Me3tren)(py>2’+H,C

3

0 >

a

py-Cu(Me3tren)(H20$+

3

-8

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

................... ....._

a

.A

5a

-2

I

I

7.3 Thermal-Induced Reactions 119

t v5

AVY

Cm3mo'-1

RCOOH

:I1

.... .. .......... . .. ...... .......................... .....,,,.,...... . ..,.,,....,. .......,....,... . ............,

/2.3

\

8.9

\

\ G -

1.7

Reaction Coordinate

$: Pd(H20)T+ RCOOH

, -

CH3CooH - 1.7 7 cn,cn2coon

+

Pd(H20)300CRt

t

Fig. 1.16. Volume profiles for the reversible reaction [Pd(HzO),]" RCOOH [Pd(HzO),(OOCR)]' H3O'

+

+

1.3.1.2 Square-Planar Complexes

Square-planar d8 complexes of Pt(I1) and Pd(I1) are, in general, accepted to undergo substitution reactions according to an associative mechanism. Recently, activation and reaction volume data were reported for complex-formation reactions of [ P ~ ( H Z O ) ~ with ] ~ +a series of organic acids 1571. A few typical volume profiles for reactions of acids are presented in Fig. 1.16, from which the compact associative nature of the transition state can be seen. A good linear correlation between AV# for the complex-formation reaction and the overall reaction volume AVO was found (see Fig. 1.17), demonstrating that the location of the transition state is controlled by the overall reaction volume. In these cases AV# and AVO are composite quantities resulting from a volume collapse due to bond formation and a volume increase due to a decrease in electrostriction as a result of charge neutralization. Since substitution reactions of square-planar complexes in most cases tend to follow an associative mechanism, a large number of complexes were synthesized in efforts to determine whether a changeover in mechanism is induced. The increase in steric hindrance caused by introducing alkyl substituents on the three N donor atoms of diethylenetriamine (dien) in going from dien to Mesdien to Etsdien, caused a decrease in the aquation rate constant for (Pd(Rsdien)Cl]+ of six orders of magnitude, but not a changeover in mechanism. The reported activation

H30+

20

I

I Ec’t

of Pressure on Inorganic Reactions: Introduction and Mechanistic Applications

Fig. 1.17. Linear correlation reported between AV’ and AVO for the reversible reaction [Pd(H20),]” LH/L +

+

+

[Pd(H20)3(L)]+/*+ H30+/H20.1 - MezSO; 2 - propionic acid; 3 - acetic acid; 4 - malonic acid; 5 - MeCN; 6 - citric acid; 7 - glycolic acid; 8 -water.

volumes remained strongly negative (between -10 and -15 cm3 mol-’) throughout the series studied and support the operation of an associative mechanism, independent of the degree of steric hindrance on the chelate ligand [S]. Two typical volume profiles for such reactions are shown in Fig. 1.18, from which the associative nature of the transition state can clearly be seen [ 51. The introduction of a metal-carbon cr bond could be an alternative way to induce an increase in lability and a possible changeover in mechanism. In the case of NCN donor complexes of Pt(II), where NCN represents ~ , G - C G H ~ ( C H ~ N van M~~)~, Koten and collaborators were able to compare the ligand substitution kinetics in water directly with the data for water exchange on [Pt(NCN)H20]+[58. 591. The AVf values for ligand substitution and water exchange are between -9 and -12 cm3 mol-’, and clearly support the associative character of the reactions. A typical volume profile for a closely related system also involving NCN donor ligands is presented in Fig. 1.19, from which the compact and associative nature of the transition state can be seen [GO]. Irrespective of the entering ligand, the AVf values are all strongly negative and support a five-coordinate transition state for the substitution process. In other complexes the introduction of a C atom as a strong cr-donor ligand, increases the reactivity of Pt(11) by six orders of magnitude compared to [ Pt( H20)4] but does not induce a changeover in mechanism. Surprisingly, there is only one example in the literature where the authors report activation volumes in support of a changeover in the substitution mechanism, i.e. from the usual associative to the unusual dissociative mechanism. The authors point out that at least two strong

’+,

7.3 Thermal-Induced Reactions

i

Reactants

i

Transition State

Products

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

______ ___ -..,-..-......-.-... J.

AV*= -13.4

V

cm'rnol-

1

1

L = 1,1,7,7-Et4dien

I

1 AV = - 1 1.9

AV*= -14.9

I

j Transition State

Reactants

i

Products

Reaction Coordinate Fig. 1.18. Volume profiles for the reversible reactions [Pd(L)Cl]+

+ H20 * [Pd(L)H20l2+ + CI-.

a-donors are needed to change the reaction mechanism [ 611. Various attempts followed to increase the donor capacity of the non-labile ligand in order to weaken the trans position. 1.3.2 Electron Transfer Reactions

A fundamental understanding of oxidation-reduction reactions is vital to the inorganic chemist in contexts ranging from energy transduction - chemical to electrical and the converse, in technical matters in corrosion processes and metallurgy, redox processes in environmental chemistry and metalloenzymes and metalloproteins involved in electron transfer. Electron-transfer reactions of transition metal complexes are accompanied by a change in the oxidation state of the metal

I

22

I

7 Effect of Pressure on Inorganic Reactions: Introduction and Mechanistic Applications

PtiN,C%)N3+ HzO

" I

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

N3-Pt(N,WH*O)

I

Reactants

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

I

Transition State

Products

Fig. 1.19. Volume profile for the reversible reaction [Pt(N,N-C)(H20)]' N, + [Pt(N,N-C)N3] H2O.

+

+

atom and the overall charge on the complex ion. This can cause both intrinsic and solvational volume changes, such that it is reasonable to expect that electrontransfer reactions should exhibit characteristic AVf values. Here we will confine ourselves (see Sect. 1.3.2.2) to electron self-exchange reactions for which considerable success in correlating experimental AV# values with theoretical calculations of the same parameters has been achieved [G2], and to some recent examples of bioinorganic electron transfer reactions. 1.3.2.1

Self-Exchange Reactions

Self-exchange reactions are of fundamental importance in the understanding of electron transfer processes, in a similar way mechanistic studies of solvent exchange reactions form the basis for understanding ligand substitution reactions. These are symmetrical processes for which the reaction volume AV is zero. The progress made recently has been concisely and thoroughly summarized [ G 2 ] . A detailed account on the effect of pressure on self-exchange reactions is given in Chapter 5. 1.3.2.2

Non-Symmetrical Reactions

For the mechanistic interpretation of activation volume data for non-symmetrical electron-transfer reactions, it is essential to have information on the overall volume change that can occur during such a process. This can be calculated from the partial molar volumes of reactant and product species when these are available. or can be determined from density measurements. Efforts have in recent years have focused on the electrochemical determination of reaction volumes from the pressure dependence of the redox potential. Tregloan and coworkers [42, 431 have demonstrated how such techniques can be employed to provide estimates of the intrinsic and solvational volume changes associated with electron-transfer reactions of transition metal complexes.

1.3 Thermal-Induced Reactions

I

23

We will restrict the discussion of non-symmetrical electron-transfer reactions to a number of systems that are ofbiological interest. In collaboration with other groups, we have investigated intermolecular and intramolecular electron-transfer reactions between various Ru complexes and cytochrome c. A variety of high pressure experimental techniques, including stopped-flow, flash-photolysis, pulse-radiolysis and voltammetry, was employed in these investigations. As the following presentation will show, remarkably good agreement was found between the volume data obtained with the aid of these different techniques, which clearly demonstrates the complementarity of these methods for the study of electron-transfer processes. Application of pulse-radiolysis techniques (see Sect. 1.4 for more details on the experimental set-up) revealed that the following intramolecular (Eqs 1.6 and 1.7) and intermolecular (Eq. 1.8) electron-transfer reactions, where cyt c represents cytochrome c, all exhibit a significant acceleration with increasing pressure. The reported volumes of activation are -17.7 f 0.9: -18.3 f 0.7, and -15.6 f 0.6 cm3 mol-', respectively, and clearly demonstrate a significant volume collapse upon reaching the transition state [ 631.

(NH3)~Ru~~-(His33)cyt c"' i (NH3)5Ru"1-(His33)cytc'l (NH3)5 RIA"-( His39)cyt clll

i

(NH3)5 Ru"'-( His39)cyt cI1

(1.6) (1.7)

At this stage there was uncertainty regarding the origin of the negative volumes of activation and their interpretation; the overall reaction volumes which would be of assistance in the analysis were not available. There was, however, data [42, 431 that suggested that the oxidation of [ Ru(N H ~ ) (2+ I ] to [ Ru(NH3)6]3+ is accompanied by a volume decrease of ca. 30 cm3 mol-l, which would mean that the activation volumes quoted above could arise mainly from volume changes associated with the oxidation of the ruthenium redox partner. In order to obtain further information on the magnitude of the overall reaction volume and the location of the transition state along the reaction coordinate, a series of intermolecular electron-transfer reactions of cyt c with pentaamminemthenium complexes was studied, where the sixth ligand on the ruthenium complex was selected in such a way that the overall driving force was low enough so that the reaction kinetics could be studied in both directions [64, 651. The substituents selected were isonicotinamide (isn), 4-ethylpyridine (etpy), pyridine (py), and 3,s-lutidine (lut).The overall reaction can be formulated as shown in Eq. (1.9). [RU"'(NH~)SL]~' + cyt c"

+ [RuT1(NH~)5L]'+ + cyt c"'

In all cases, the forward reaction was significantly decelerated by pressure, whereas the reverse reaction was significantly accelerated by presssure. The absolute values of the volumes of activation for the forward and reverse processes were indeed very similar, demonstrating that a similar rearrangement, in volume terms, occurs in order to reach the transition state. In addition, the overall reaction volume for these

24

I

1 Effect of Pressure on fnorganic Reactions: fntroduction and Mechanistic Applications

Reactants

Transition State

Products

Reaction coordinate Volume profile for the reversible electron-transfer reaction [ R u " ' ( N H ~ ) ~ L-t ] ~cyt + c ' l + [ R U " ( N H ~ ) ~ L ] ~cyt + clll.

Fig. 1.20.

+

systems could be determined spectrophotometrically by recording the spectrum of an equilibrium mixture as a function of pressure, and electrochemically by recording cyclic and differential pulse voltammograms as a function of pressure [GG] . A comparison of the AV data demonstrated the generally good agreement between the values obtained from the difference in the volumes of activation for the forward and reverse reactions, and those obtained thermodynamically. Furthermore, the values also clearly demonstrated that JAVz 1 N O.S)AVJ,i.e. the transition state lies approximately halfway between the reactant and product states on a volume basis independent of the direction of electron transfer. The typical volume profile in Fig. 1.20 presents an example of the overall picture, from which the location of the transition state can clearly be seen. At this point it is important to ask the question, what is the source of these volume changes? We argued that the major volume change arises from changes on the redox partner and not on cytochrome c itself. This was suggested by the fact that the change in partial molar volume associated with the oxidation of the Ru(11) complexes, as obtained from electrochemical and density measurements, almost fully accounted for the observed overall reaction volume. Thus the reduction of cytochrome c can only make a minor contribution towards the overall volume change. An investigation of the electrochemistry of cytochrome c as a function of pressure, using cyclic and differential pulse voltammetric techniques [GG], revealed a reaction volume of -14.0 0.5 cm3 mol-' for the reaction shown in Eq. (1.10). cyt ClIl

+ Ag(s) + C1

+

Cyt cii

+ AgCl(s)

(1.10)

A correction for the contribution from the reference electrode can be made on the basis of the data published by Tregloan et al. [43], and a series of measurements of

7.3 Thermal-lnduced Reactions

the potential of the Ag/AgCl(KC1 sat'd) electrode relative to the Ag/Ag+ electrode as a function of pressure. The contribution of the reference electrode turned out to be --9.0 0.6 cm3 mol I , from which it then followed that the reduction of cytochrome c"' is accompanied by a volume decrease of 5.0 0.8 cm3 mol-*. Thus we conclude that the observed activation and reaction volumes mainly arise from volume changes on the Ru complexes, which in turn will largely be associated with changes in electrostriction in the case ofthe ammine complexes. The oxidation of the Ru( 11) ammine cornplcxes will be accompanied by a large increase in electrostriction and almost no change in the metal-ligand bond length, whereas in the case of Co complexes a significant contribution from intrinsic volume changes associated with the oxidation of Co( 11) will partially account for the observed effects [43]. Thc available results demonstrate readily the complementarity of the kinetic and thermodynamic data obtained from stopped-flow, UV-Vis, electrochemical and density measurements, and yield a mutually consistent set of trends allowing further interpretation of the data. The overall reaction volumes determined in four different ways are surprisingly similar and underline the validity of the different methods employed. Thc volume profile in Fig. 1.20 illustrates the symmetric nature of the intrinsic and solvational reorganization in order to reach the transition state of the electron-transfer process. In these systems the volume profile is controlled by effects on the redox partner of cytochrome c, but this does not necessarily always have to be the case. The location of the transition state on a volume basis is informative regarding the "early" or "late" nature of the transition state, and therefore details of the actual electron-transfer route followed. Recent investigations on a series of intramolecular electron transfer reactions, closely related to the series of intermolecular reactions described above, revealed non-symmetrical volume profiles [ 671. (1.11)

Reactions of the type shown in Eq. ( L l l ) , where L = isonicotinamide, %ethylpyridine, 3,5-lutidine, or pyridine, all exhibited volumes of activation for the forward reaction of between $3 and +7 cm3 mol-', compared to overall reaction volumes of between +19 and +26 cm3 mol-'. This indicates that electron transfer from Fe to Ru is characterized by an "early" transition state in terms of volume changes along the reaction coordinate (see Fig. 1.21). The overall volume changes could be accounted for in terms of electrostriction effects centered around the ammine ligands on the ruthenium center. A number of possible explanations in terms of the effect of pressure on electronic and nuclear factors were offered to account for the asymmetrical nature of the volume profile [ 671. 1.3.3 Actvation of Small Molecules

Mechanistic understanding of the binding of diatomic molecules such as 02,CO and NO to ferrous hemes and hemoproteins is essential as part of a description of

I

25

26

I

7 Efect of Pressure on inorganic Reactions: introduction and Mechanistic Applications

-0

7-

-15.9

ki

5 E

b23.3

10-

[(L)RuIII/II -c). c 111/11

1f

Reaction coordinate Fig. 1.21.

Volume profile for the reversible electron-transfer reaction ( N H3)4(L) Ru "'-(His33)-Cyt cil F! (NH3)4(L) Ru "-(His33)-Cyt clll

the overall transport of such molecules in biological systems and in terms of their activation. In order to obtain further mechanistic insight, volume changes for the binding of 0 2 and CO to myoglobin, and for the binding of 0 2 to hemerythrin [ 68, 691 were determined and volume profiles were constructed. These are shown in Figs 1.22 and 1.23, respectively. For the oxygenation of the iron proteins, positive activation volumes of +13.3 1.1 and +5.2 f 0.5 cm3 mol-' for hemerythrin and myoglobin, respectively, were found. Since bond formation processes are usually characterized by a decrease in volume [8, 13, 171, the positive values were assigned to desolvation of oxygen during its entrance into the protein and to conformational changes on the protein itself. The release of oxygen is characterized by very positive activation volumes, f52 f 1 and f23.2 i 1.8 cm3 mol-', for hemerythrin and myoglobin, respectively, such that the overall reaction volume for the oxygenation process is strongly negative in both cases. The activation and reaction volumes for mononuclear myoglobin are about half of those found for binuclear hemerythrin. In the hemerythrin system, two Fe(I1) centers are oxidized to Fe(II1) during which dioxygen is reduced and bound as hydroperoxide to one Fe(II1) center. The significant volume decrease that occurs following the formation of the transition state can be ascribed to the oxidation of the Fe(I1) centers and the reduction of 0 2 to O:-. The fact that the overall volume collapse is almost double that observed for the oxygenation of myoglobin may indicate similar structural features in oxyhemerythrin and oxymyoglobin. This suggests that a description of the bonding mode as

1.3 Thermal-Induced Reactions 127

1

-lo ~

[Mb-CO]

-5.9

1

MbCO

+4.1

MbO2

Reactants

Products

Transition State

Reaction coordinate Fig. 1.22.

Volume profiles for the binding o f 0 2 and CO to myoglobin.

Fe"'-O; or Fe1"-02H ( H from histidine E7) instead of Fe"-02, is more appropriate for oxymyoglobin. A fundamental question regarding the activation of dioxygen by transition metal complexes is whether the process is controlled kinetically by ligand substitution or by electron transfer. A model system that involved the binding of dioxygen to a macrocyclic hexamethylcydam Co(11) complex to form the corresponding Co(111) superoxo species is shown in Eq. (1.12), thus modeling the first redox activation step of dioxygen; the reaction was studied in detail [70].

+0 2

[CO"(L)(HZO)~]"

[CO"'(L)(H,O)(O;)]~'

+ H2O

(L = Mebcyclam) r

[ Hr-Op]'

-

9

-z -39 Q m

a!

d Reactants Fig. 1.23.

Transition State

Volume profile for the binding o f 0

2

Product

to hemerythrin.

(1.12)

28

I

7 €@ct

-7 [(L)co. l;29

of Pressure on Inorganic Reactions: Introduction and Mechanistic A p p h t i o n s I

0

I

(L)C02+ + 0

. ....,.. . ,. ....

-

-10-

-

-15-

-

-20 ,. ....,.......................... .......................,...........,,. ............................

4 5-

Fig. 1.24.

I

I

(L)cooo2+

-

Volume profile for the reversible binding of dioxygen t o [Co"(Me~cyclarn)(H~O)~]*'

The overall reaction involves ligand substitution and electron transfer, the question being which occurs first. From the pressure dependence of the overall equilibrium constant a reaction volume of -22 cm3 mol-' was determined, which demonstrated that the displacement of a water molecule on the Co(I1) complex by dioxygen is accompanied by a significant volume collapse, probably mainly due to the oxidation of Co(I1) to Co(II1) during the overall reaction. The kinetics of the reaction could be studied by flash-photolysis,since the dioxygen complex can be photodissociated by irradiation into the charge-transfer (CT) band, and the subsequent reequilibration could be followed on the microsecond time scale. From the effect of pressure on the binding and release of dioxygen, the activation volumes for both processes could be determined. A combination of these activation volumes resulted in a value for the reaction volume that is in excellent agreement with that determined directly from the equilibrium measurements as a function of pressure. The volume profile for this reaction is given in Fig. 1.24.The small volume of activation associated with the binding of dioxygen is clear evidence for a rate-limiting interchange of ligands, dioxygen for water, which is followed by an intramolecular electron-transfer reaction between Co(I1) and O2 to form Co"'-O;, the superoxo species. It is the latter process that accounts for the large volume reduction en route to the reaction products. Thus during flash-photolysis, electron transfer in the reverse direction occurs due to irradiation into the CT band, which is followed by the rapid release of dioxygen. CO has been used in many studies as a model for the binding step component of the activation of dioxygen since CO does not undergo activation in the systems studied. The absence of subsequent electron transfer reactions simplifies the kinetic analysis and provides more mechanistic insight into the actual binding process. A typical example concerns the comparative binding of 0 2 and CO to deoxymyoglobin [68].The volume profile for the binding of 0 2 , as described above, is

1.3 Thermal-Induced Reactions

I

29

characterized by a substantial increase in volume in going from the reactant to the transition state, followed by a significant volume reduction on going to the product state. The volume profile for the binding of CO (see Fig. 1.22), however, shows a considerable volume decrease on going from the reactant to the transition state, which was ascribed to rate-determining bond formation. The reverse bond cleavage reaction is accompanied by a volume decrease, which may be related to the different bonding mode of CO compared with 0 2 . This difference in bonding mode must also account for the much smaller absolute reaction volume observed in this case. In another investigation of a metal center-diatomic molecule interaction, the binding of CO to lacunar Fe(I1) complexes was studied in detail as a function of temperature and pressure [71, 721. In such a system the high spin Fe(II) center is five-coordinate and has a vacant pocket available for the binding of CO. These systems can, therefore, be considered as ideal for the modeling of biological processes. A detailed kinetic analysis of the “on” and “off” reactions, as well as a thermodynamic analysis of the overall equilibrium reaction, enabled the construction of the energy and volume profiles for the binding of CO to [ Fe“(PhBzXy)](PF6)2;the volume profile is shown in Fig. 1.25 [ 7 3 ] .The free energy profile demonstrates the favorable thermodynamic driving force for the overall reaction, as well as the relatively low activation energy for the binding process. The entropy profile demonstrates the high degree of order in the transition state on the binding of CO.

r

F&L)

+ co

REACTION COORDINATE

Fig. 1.25.

Volume profile for the reversible binding o f CO t o a lacunar Fe(ll) complex.

30

I

7 Efict of Pressure on lnorganic Reactions: introduction and Mechanistic Applications

The large volume collapse associated with the forward reaction is very close to the partial molar volume of CO, which suggests that CO is engulfed and completely “disappears” within the ligand pocket of the complex in the transition state during partial Fe-CO bond formation. It is also known [71] that Fe”-CO bond formation is accompanied by a high-spin to low-spin conversion of the Fe(11) center. In forming the six-coordinate, low-spin Fe(11) complex, the metal moves into the plane of the equatorial nitrogen donors. Thus following the formation of the transition state for the binding of CO, there is a high-spin to low-spin change during which bond formation is completed and the metal center moves into the ligand plane. These processes account for the subsequent volume decrease accompanying the formation of the product from the transition state. The overall reaction volume of -48 cm3 mol therefore consists of a volume decrease of ca. -37 cm3 rno1-l associated with the apparent disappearance of CO into the ligand cavity, and ca. -12 cm3 mol-’ for the high-spin to low-spin transition. In a recent study the volume profile for the reversible binding of NO to metmyoglobin was determined using a combination of stopped-flow and flash-photolysis techniques [73]. The reported volume profile (see Chapter 6, Fig. 6.18) demonstrates the dissociative nature of the binding process. By way of comparison, the volume of activation found for the “on” reaction is significantly smaller than that reported for the corresponding reaction with the Fe(111) porphyrin complex [74], suggesting that the formation of the five-coordinate Fe(111) intermediate (within the concept of a dissociative mechanism) is accompanied by structural changes on the protein that result in an additional volume increase. In the case of the porphyrin systems it has recently been shown that the binding of NO is controlled by the rate and mechanism of water exchange on such complexes [75]. 1.3.4

Addition and Elimination Reactions

In principle, addition or elimination reactions involve significant bond formation or bond breakage in the transition state, such that an acceleration or deceleration is expected at elevated pressure, respectively. For instance, [2 21 cyclo-addition reactions of the type shown in Scheme 1.1were significantly accelerated by pressure, and there was almost no dependence on the polarity of the solvent [76].

+

X = Cr(CO)5, R1= Me, R2 = M e X = W(CO)5, R1 =Me, Rz = M e X = W(CO)5, R1= Ph, R2 = Et Scheme 1.1

7.3 Thermal-lnduced Reactions

1 cm3 mol-' and the solvent independence of the The average AV# of - l G process suggested that the reaction follows a nonpolar concerted, synchronous onestep mechanism. The observed pressure acceleration is very similar to that found for the insertion of dipropylcyanamide and 1-(diethy1amino)propene into the metalcarbene bond of pentacarbonyl(methoxypheny1-carbene)chromium and -tungsten (shown in Scheme 1.2) for which AVf varies between -17 and -25 cm3 mol-I [ 771. Addition reactions of a,p-unsaturated Fischer carbene complexes, as shown in Scheme 1.3, all exhibit AVf values of between -15 and -17 cm3 mol-' in acetonitrile. On decreasing the solvent polarity, AV# becomes significantly more negative and exhibits a good correlation with the solvent parameter qp (i.e. the pressure derivative of q, the polarizability of the solvent) [78].

,OMe (CO)sM=C\ Ph

,OMe (CO)sM=C\ Ph

+

PrzN-CEN

+ E$N-C=C-Me

-

N=C\ (CO)5M=C: NPrz

Me\

,c=c,

(CO)sM=C,

,OMe Ph

,OMe Ph

NEt2

M=Cr,W Scheme 1.2

Cr Ph MoPh W Ph W Me

Et Et Et Me

Scheme 1.3

It was concluded that the addition of pyrrolidine follows a two-step process with a polar transition state leading to a zwitterionic intermediate. The addition of a series of p-substituted anilines to a Fischer carbene complex as shown in Scheme

I

31

32

I

7 Effect of Pressure on Inorganic Reactions: Introduction and Mechanistic Applications

’

1.4 is characterized by AV# values between -21 and -27 cm3 mol [79], i.e. significantly more negative than for the reaction with pyrrolidine mentioned above. The second order rate constant for the addition reactions exhibitcd an excellent correlation with the basicity of the selected aniline. The observed trcnd in the activation volumes could be correlated with an “early” or “late” transition state for the fast and slow addition reactions, respectively.

6MeCN

X

X = CN, CH,CO, CI, F, H, CH,, CH,O

Q x

Scheme 1.4

We now turn to oxidative addition and reductive elimination reactions. Such reactions not only undergo significant bond formation and bond breakage, respectively, in reaching the transition state, but also undergo a change in the oxidation state and coordination number of the metal complex. These effects are expected to cause large volume changes, such that these reactions should exhibit a high pressure sensitivity. One interesting example involves the addition of Me1 to the Pd(11) complex, [ PdMez(bpy)], to form [Pd(I)Me3(bpy)],which is accompanied by a AV# value of -11.9 cm3 mol-’ 1801. A similar value was reported for the corresponding reaction with the Pt(I1) complex [81]. This value confirms the operation of an S N ~ mechanism. The reductive elimination of C ~ H from G the Pd(IV) complex forming [Pd(I)Me(bpy)] as product, yielded a AV# value of f17.5 cm3 mol-*, which is in line with the formal change in oxidation state and bond breakage. With the assumption that the transition states for the oxidative addition and reductive elimination processes have a similar partial molar volume, then an overall reaction volume of 29 cm3 mol-’ can be calculated for such reactions (see volume profile in Fig. 1.26).

1.4

Photo- and Radiation-Induced Reactions

The effect of pressure on photochemical and photo-induced reactions has been investigated in detail for many systems, and a number of reviews have appeared on this subject recently [82-84). This topic is treated in more detail in Chapter 6, and readers are referred to that chapter for more information. Pulse-radiolysis is a well-established technique for investigating the interaction of free radicals with metal complexes. For instance, with this technique metal

1.4 Photo- and Radiation-Induced Reactions

I

33

I

Reactants

state

Intermediate

Products

State

Fig. 1.26. Volume profile for the combined oxidative addition and reductive elimination reaction [PdMez(bpy)] Me1 --t [Pd(l)Me3(bpy)l [Pd(l)Me(bpy)l C2H6.

+

+

+

complexes can be prepared in unique oxidation states either as intermediates or as stable species. In addition, the formation and stability of metal-carbon c bonds through reaction with organic radicals can be studied. In many systems little is known about the details of the reaction mechanism, such that the combination of high pressure and pulse-radiolysis techniques seemed one avenue of approach to increase our understanding of such processes. Before these investigations were possible, it was essential to modify the high pressure cell shown in Fig. 1.3 in such a way that the electron beam (originating from a 5-MeV linear accelerator or a 2MeV van de Graaff accelerator) could reach the sample within the pill-box sample cell. This was not possible with the thick sapphire windows used in the standard cell. One of the windows of a four-window cell was therefore replaced by a honeycomb-type metal grid, the details of which are shown in Fig. 1.27. The ultimate wall thickness of less than 1 m m enabled the efficient entry of the electron beam into the cell. Very reproducible results could be obtained independent of the applied pressure. A review on the work performed using this technique has appeared [SS]. Two examples will be given to demonstrate the application of this combination of techniques. A typical example of a volume profile for the formation and cleavage of a Co-CHj bond is reported in Fig. 1.28 for the reaction shown in Eq. (1.13) [86].

+

+

[ C ~ " ( n t a ) ( H ~ O ) ~ 'CH3 l+ [Co1"(nta)(CH3)(H2O)]- H2O

(1.13)

34

I

I Effect of Pressure on Inorganic Reactions: Introduction and Mechanistic Applications

-r 4mm 1

t

*r

16 m m

1

L Fig. 1.27.

+17

m

4

Details o f the special window used for high pressure pulse-radiolysis studies.

The volume profile indicates an increase in partial molar volume in proceeding to the transition state, which is interpreted in terms of an Id substitution controlled binding o f the methyl radical to the Co(I1) complex. The large volume collapse that occurs subsequent to the formation of the transition state is ascribed to metalcarbon bond formation which is accompanied by oxidation of Co(I1) to Co( 111) and accompanied by a large volume contraction [86]. The reaction o f aquated Cr(I1) with 10 different aliphatic radicals R, showed a decrease in rate with increasing pressure, and resulting volumes of activation were between $3.4 and +6.3 cm3 mo1-l [87]. These data could be interpreted in terms of a water-exchange-controlled formation o f the Cr-R bond, from which it followed that water exchange on Cr(I1) must proceed according to an I d mechanism. The

-z

7

+lo-

[L(H,O)cQ:.,,OH,]*

L = nta

15-

d

?l0

3

>

0 0

LCo(H,O); + ‘R --

1.-*.-T-.-

2

-E

0

-10-

calc : -12.6 54.5 exp : -16.4 f 1.6

0

.->

-2

+18.6 f 2.0

-5-

m

3a

I

/ I

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

LCo(H,O)R- + H 2 0

4-

m

-15-15

Reactants

I

Transition State

I

Reaction coordinate Fig. 1.28. Volume profile for the reaction o f methyl radicals with the nitrilotriacetate complex o f Co(ll), R = CH3.

Products

1.5 Concluding Remarks

+lo-

[ (q+ c'':...R .43"2]*

+5Cr(H.$l):+ 0

'R

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

+15.1 -5-

Cr(%O)5 R2'+ -10-

30

............................. II

Reaction coordinate Fig. 1.29. Volume profile for the reaction of an aliphatic radical with [Cr(H20),]'*, R = C(CH3)20H.

volume profile in Fig. 1.29 demonstrates this point; the large volume collapse following the transition state was assigned to Cr-R bond formation accompanied by the conversion of Cr"-R to Cr"'-R-. In general it has been found in reactions of metal complexes with free radicals, based on the observed pressure effects: that the radicals can be treated as normal nucleophiles in ligand substitution processes; the latter are often controlled by solvent exchange on the metal complex [88].

1.5 Concluding Remarks

It was the objective of this contribution to demonstrate how the application of high pressure thermodynamic and kinetic techniques can contribute to the elucidation of inorganic reaction mechanisms. The analysis of a chemical process in terms of volume changes along the reaction coordinate can help us to visualize the nature and structure of the transition state in terms of intrinsic and solvational changes in partial molar volume. In many cases the insight gained with these techniques is unique and has added a further dimension to the study of reaction mechanisms in solution. The construction of volume profiles provides a helpful visualization of details of the molecular organization and solvation of the transition state. There are many cases where it is experimentally impossible to acquire sufficient data to construct a volume profile; examples of such limitations are where subsequent reactions occur or when the reaction is irreversible as found for many electron transfer and photo- or irradiation-induced reactions. Nevertheless, the volume of activation for such processes can still be employed very successfully to obtain information on the nature of the transition state.

I

35

36

I

7 Efect of Pressure on fnorganic Reactions: fntroduction and Mechanistic Applications

The fact that the rate-determining step of a particular process exhibits a characteristic pressure dependence, creates the possibility of tuning the reactivity of particular systems via the application of moderate pressures. This can lead to the selective synthesis of particular reaction products in cases where product distribution proves to be presssure dependent, or to the optimization of design of industrial chemical processes. In some of the simplest cases (namely, solvent exchange and self-exchange reactions), the experimental data could be supported by theoretical calculations. Significant developments are expected to occur in this area, such that the theoretical optimization of transition state structures will become standard practice in mechanistic studies. Here again volume of activation data will play a crucial role, since they present an experimental measure of the intrinsic and solvational volume changes in the transition state and form a basis for comparison with theoretical predictions. It will be an ideal situation when volume profiles can be constructed for more complex reaction sequences, for instance for catalytic cycles in enzymatic processes. This will, as in the case of more simple reactions, enhance our understanding of complex chemical processes and improve our ability to tune them. The correlation of kinetic data with activation volume data for a series of closely related reactions in terms of an “early” or “late” transition state. has been reported in a number of cases. The ultimate goal will be to correlate energy and volume profiles for series of related reactions, where a low activation barrier (fast reaction) will correspond to an “early” transition state, and a high activation barrier (slow reaction) will correspond to a “late” transition state. A schematic presentation of such a correlation between the location of “early” and “late” transition states on energy and volume profiles is shown in Fig. 1.30. A three-dimensional presentation of free energy and partial molar volume changes along the reaction coordinate should represent the ultimate way to combine energy and volume profile information. In our opinion as indicated in the Introduction, when pursuing mechanistic studies, one should investigate as many chemical and physical variables as possible in order to obtain as much information as possible on the nature of the underlying reaction mechanism. Only then can the suggested mechanism come close to the “real” mechanism, which is a goal set in many mechanistic studies, but only accomplished in few. If we can in this way contribute to a better understanding of the mechanism of chemical reactions in solution, then we have fulfilled our educational and research objectives, and have made a modest contribution to existing knowledge.

Acknowledgments

The authors gratefully acknowledge financial support from the Deutsche Forschungsgemeinschaft, Fonds der Chemischen Industrie, Volkswagen Stiftung, MaxBuchner Forschungsstiftung, NATO Scientific Affairs Division and the German-

References I 3 7

7

Schematic comparison of energy and volume profiles: 1 - “early” transition state; 2 - “late” transition state. Fig. 1.30.

Israeli Foundation. The very stimulating collaboration with numerous graduate and post-graduate students, post-doctoral associates, visiting scientists and various research groups all over the world, is greatly appreciated and respected.

References 1 2 3 4

5

6

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M. K o r o w s ~ rR. , VAN ELDIK, Coord. Chem. Rev. 1989, 93, 19. 8 R. VAN ELDIK,T. ASANO,W. J. LE NOBLE, Chem. Reu. 1989, 89, 541. 9 A. E. MERBACH, J. W. Akitt, in N M R Basic Principles and Progress, vol 24, Springer Verlag, Berlin, 1990, 189. 10 (a) R. VAN ELDIK,A. E. MERBACH, Comments Inorg. Chem. 1992, 22, 341; (b) S. F. LINCOLN, A. E. MERBACH, Adu. Inorg. Chem. 1995, 42, 1; ( c ) L. HELM,A. E. MERBACH, Coord. Chem. Rev. 1999, 287, 151; (d) G. STOCHEL, R. V A N ELDIK,Coord. Chem. ReG. 1999, 187, 329; (e) T. W. SWADDLE, P. A. 7

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7 Effect of Pressure on inorganic Reactions: Introduction and Mechanistic Appkations

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44 45 46 47

48 49

33, 6180; (b) J . I. SACHINIDIS, R. D. P. A. TREGLOAN, Inorg. SHALDERS, Chem. 1996, 35, 2497. J , BURGESS, Metal Ions in Solution, Ellis Horwood, Chichester, 1978. T. ITOH, Y. KITAMURA, K. YOSHITANI, Inorg. Chem. 1988, 27, 996. Y. DUCOMMUN, G . LAURENCZY.A. E. Inorg. Chem. 1988, 27, 1148. MERBACH, M. HARTMANN, T. CLARK.R. V A N ELDIK,J. Am. Chem. Soc. 1997, 119, 5867. K. SCHNEIDER, R. VAN ELDIK. Organometallics 1990, 9, 1235. G . STOCHEL, R. VAN ELDIK,Inorg. Chem. 1990, 29, 2075.

M. MEIER,R. VAN ELDIK,Inorg. Chem. 1993, 32, 2653. 51 C. DUCKER-BENFER, R. DREOS,R. VAN ELDIK,Angm. Chem. 1995, 107, 2414. 52 D. H. POWELL, P. FURRER,l'.-T. PITTET, A. E. MERBACH,]. Phys. Chem. 1995, 99, 16622. 53 D. H. POWELL, A. E. MERBACH,I. FABIAN,S. SCHINDLER, R. VAN ELDIK, Inorg. Chem. 1994, 33,4468. 54 A. NEUBRAND, F. THALER,C. D. HUBBARD, A. ZAHL,R. VAN ELDIK, J . Chem. Soc., Dalton Trans., in press. 55 F. THALER,C. D. HUBBARD, F. W. HEINEMANN, R. VAN ELDIK,S. SCHINDLER, 1. FABIAN,A. M. DITTLERKLINGEMANN, F. E. HAHN,C. ORVIG, Inorg. Chem. 1998, 37, 4022. 56 S. F. LINCOLN,A. M. HOUNSLOW, D. L. PISANIELLO, B. G. DODDRIDGE, J. H. COATES,A. E. MERBACH, D. ZBINDEN,Inorg. Chem. 1984, 23, 1090. 57 T. S H I , L. I. ELDING,Inorg. Chem. 1997, 36, 528. 58 U. FREY,D. M. GROVE,G. VAN KOTEN, Inorg. Chim. Ada 1997, 269, 322. 59 M. SCHMULLING, D. M. GROVE,G. VAN KOTEN,R. VAN ELDIK,N. A. L. SPEK,Organometallics VELDMAN, 1996, 15, 1384. 60 M. SCHMULLING, A. D. RYABOV,R. VAN ELDIK,]. Chem. Soc., Dalton Trans. 1994, 1257. 61 U. FREY,L. H E L M A. , E. MERBACH, R. ROMEO,J. Am. Chem. SOC.1989, 111,

62

T. W. SWADDLE, Can. J. Chem. 1996,

63

74, 631. J . F. WISHART,R. 31, 3986.

64

65

B. BANSCH,M. MEIER,M. M A R T I N I X , R. VAN ELDIK,C. S u , I. SUN, S. S. ISIED,J. F. WISHART,Inorg. Chem. 1994, 3 3, 4744. M. MEIER,J. SUN, J. E'. WISHART,R. VAN EI DIK,Inorg. Chem. 1996, 35, 1564.

66

67

50

8161.

V A N ELDIK,J. SUN, C. S u , S. S. ISIED,Inorg. Chem. 1992,

68 69

J . S U N ,J . F. WISHART,R. VAN ELDIK, R. D. SIIALDERS, T. W. SWADDLE, J. Am. Chem. SOC.1995, 117, 2600. J. S U N ,C. Su, M. MEIER,s. S. ISIED, J , F. WISHART,R. VAN ELDIK,Inorg. Chem. 1998, 37, 6129. H.-D. PROJAHN,R. VAN ELDIK,lnorg. Chem. 1992, 30, 3288. H.-D. PROTAHN, s. SCHINDLER, R. VAN ELDIK,D. G. FORTIER,C. R. ANDREW, A. G. SYKES,Inorg. Chem. 1995, 34, 5935.

70

71

72

M. ZHANG,R. VAN ELDIK,J. H. ESPENSON,A. BAKAC,Inorg. Chem. 1994, 33, 130. M. BUCHALOVA, P. M. WARBURTON, R. VAN ELDIK,D. H . BUSCH,]. Am. Chem. SOC.1997, 119, 5867. M. BUCHALOVA, D. H. BUSCH,R. VAN ELDIK,Inorg. Chem. 1998, 37, 1116.

73

L. E. LAVERMAN, A. WANAT,J. OSZAJCA,C. STOCHEL,P. C. FORD,R. VAN ELDIK,J. Am. Chem. SOC. 2001,

74

L. E. LAVERMAN, M. HOSHINO,P. C. FORD,J. Am. Chem. Soc. 1997, 119,

75

T. SCHNEPPENSIEPER, A. ZAHL,R. VAN ELDIK,Angew. Chem. Int. Ed. 2001, 40,

123, 285.

12663.

1678. 76

77

78 79

R. PIPOH, R. VAN ELDIK,s. L. B. WANG,W. D. WULFF,Organometallics 1992, I I, 490. K. 1. SCHNEIDER, A. NEUBRAND, R. VAN ELDIK,H. FISCHER, Organometallics 1992, 11, 267. R. P I P O H , R. VAN ELDIK,G. HENKEL, Organornetah 1993, 22, 2236. R. PIPOH,R. VAN ELDIK, Organometallics 1993, 12, 2668.

40

I

7 Effect of Pressure on Inorganic Reactions: Introduction and Mechanistic Applications 80 C. DUCKER-RENFER. R. VAK E L D I K A. .

1.

CANTY,Organometallics 1994, 13, 2412. 81 A. R. L. SKAUGE, R. D. SHALDERS, T. W. SWADDLE, Can. 1. Chem. 1996, 74, 1998. 82 P. C. FORD, D. R. CRANE,Coord. Chem. Reu. 1991, 111, 153. 83 G. STOCHEL and R. VAN ELDIK, Coord. Chem. Reu. 1997, 159, 153. 84 R. V A N ELDIIC, P. C. FORD, Adv. Photochem. 1998,24, 61.

R. V A N ELDIK, D. MEYERSTEIK, Acc. Chem. Res. 2000, 33, 207. 86 R. VAN ELDIK, 11. COHEN,D. MEYFRSTEIN, A n g m . Chem.. Int. Ed. Engl. 1991,30, 1158. 87 R. VAN ELDIK,W. GAEDE,H. COHEN. D. MEYERSTEIN, Inorg. Chem. 1992.31. 3695. 88 R. VAN ELDIK,H. COHEN.D. MEYERSTEIN, Inorg. Chem. 1994. 33, 1566. 85

High Pressure Chemistry Synthetic, Mechanistic, and Supercritical Applications

Edited by Rudi van Eldik and Frank-Gerrit Kliirner

0WILEY-VCH Verlag GmbH, 2002

I 2

The Effect o f Pressure on Organic Reactions: Basic Principles and Mechanistic Applications Frank Wurche a n d Frank-Gerrit K/arner$r 2.1 Introduction

Pressure in the range of 1-20 kbar strongly influences the rate and equilibrium position of many chemical reactions. (Units of pressure: 1 kbar = 100 MPa = 0.1 GPa = 14503.8 p.s.i. = 986.92 atm). Processes accompanied by a decrease in volume such as a C- C bond formation, in which the distance between two carbon atoms decreases from the van der Waals distance of ca. 3.6A to the bonding distance of ca. 1.5 A, are accelerated by pressure (volume of activation: AVz < 0) and the equilibria are shifted toward the side of products (volume of reaction: AV < 0). The reverse reaction, a homolytic bond cleavage, leads to an increase in volume ( A V t > 0, AV > 0). Pressure induces a deceleration of such a process and a shift of the equilibrium toward the side of reactants (Fig. 1.2, Chapter 1).Therefore, the effect of pressure seems to be particularly useful in controlling the course of competitive and consccutive reactions. Provided, that the activation volumes of the single reaction steps are different from each other, the application of high pressure can lead to an improvement of chemo-, regio- and stereoselectivity. Pressure also influences the physical properties of matter such as boiling and melting point, density, viscosity, solubility, dielectric constant, or conductivity. Before carrying out high pressure experiments it is important to have some knowledge of these effects. The melting points of most liquids used as common organic solvents are raised by increasing the pressure (Table 2.1). To perform a reaction in compressed solution it is necessary to use a solvent which does not solidify under the chosen conditions. The pressure-induced increase of the melting points (ca. 15-20 "C per 1 kbar), however, offers the possibility of running reactions in relatively thermally stable matrices. The solubility of gases in liquids is increased and that of solids is usually decreased by raising the pressure. Therefore, the solid solute of a saturated solution may precipitate during the generation of pressure and is no longer accessible for the reaction. The viscosity of liquid increases approximately twice every kilobar. This effect is particularly important for reactions containing diffusion-controlled steps. Finally, the compressibility of liquids is usually small compared to that of

41

42

I

2 The Effect of Pressure on Organic Reactions: Basic Principles and Mechanistic Applications

Tab. 2.1. Pressure-induced increase in the melting points (m.p.) of common organic solvents [I]. m.p. ("C/1 bar)

m.p. ("C)

p (kbar)

~

~~

Acetone Benzene Cyclohexane Ethanol Diethylether Dichloromethane Pentane Toluene Water

-94.8

+20

i 5.5

+114 f97

f6.5 -117.3 -116.3 -96.7 -130.0 -95.1 0.0

+25 735 +25 0 +30 -9

(8.0) (5.5) (4.0) (20.0)

(12.0) (13.0) (12.0)

(94 (1.0)

gases. It amounts to 1 kbar between 4 % (water) and 18 % (pentane) of the original volume at 1 bar approaching rapidly an upper limit at higher pressure. For that reason experiments with compressed liquids and solids are less dangerous than those with compressed gases. A detailed discussion of the effects of pressure on physical properties of matter can be found in reference [ 11. The effect of pressure on chemical equilibria and rates of reaction can be described by the well-known relationship between pressure and Gibbs' enthalpy of reaction and activation, respectively (Scheme 2.1). The volume of reaction and

+

A + B [A-----B]** A - B AV= V(A-B)-[V(A)+ V(B)] AV* = V ( [A-----B]? - [V(A) + V(B)] AV, AV' : volumes of reaction and activation

v : partial molar volume KP : Equilibrium constant at pressure p

KP : Rate constant at p AG, AG' : Gibbs enthalpy and Gibbs enthalpy of activation

Scheme 2.1.

Volumes of reaction (AV) and activation ( A V f )

2.1 Introduction

activation can be determined from the pressure dependence of the equilibrium constant and rate constant, respectively. The volume of reaction also corresponds to the difference between the partial molar volumes of reactants and products and is usually determined from these quantities experimentally. Within the scope of transition state theory the volume of activation can be, accordingly, considered to be a measure of the partial molar volume of the transition state with respect to the partial molar volumes of reactants (Scheme 2.1). Volumes of activation are experimentally determined from the pressure dependence of the rate constants. The volumes of activation and reaction are themselves also pressure dependent as shown for the volumes of activation in Scheme 2.1. There is no theory explaining this pressure dependence which would allow the volumes of activation or reaction to be determined over a large range of pressure. Therefore, several empirical equations are employed to fit the pressure dependencies of rate and equilibrium constants [ 21. The volumes of activation and reaction derived from the pressure dependence of the rate or equilibrium constants by the use of these empirical equations are generally given at p = 0. These values at p = 0 differ only by immeasurably small amounts from those at atmospheric pressure ( p z 1 bar), so that the comparison

VW, VW’ : van der Waals volume [cm3-mol-’] (intrinsic molar volume of ground or transition structures related to one mole)

V:

M

molar volume of a pure liquid [cm3.mol-’] or

V =d

partial molar volume of a solute [cm3,mo~-‘]

v = IimQ

q, q’ : packing coefficient

C+O

q=vw; V

M (g.mol-’] : molar mass of the solute d

[g.cm”] : density of the solution

do [ g . ~ m - ~ : density ] of the pure solvent

c

[mol.l-’] : concentration of the solute

Van der Waals volumes ( V w ) , partial molar volumes ( V ) , and packing coefficients (77). Scheme 2.2.

D

M --.__ 1 d-do =do

V’ $=-W

V’

c

do

I

43

44

I

2 The Efect of Pressure on Organic Reactions: Basic Principles and Mechanistic Applications

with volumes of reaction, calculated from the partial molar volumes of the reactants and products determined at atmospheric pressure, is feasible. The change in the intrinsic volumes of reacting molecules, as discussed for homolytic bond formation and dissociation is only, to a minor extent, responsible for the overall change in molar volumes measured experimentally from the densities of reactants and products and from the activation volumes. The intrinsic volume of a ground or transition structure is defined by the space occupied by the van der Waals spheres and can be calculated from the Cartesian coordinates of the molecular structure resulting from experimental data, molecular mechanics, or quantum-mechanical calculations and from the van der Waals radii of the different types of atom (e.g. R,(C) = 1.80A, R,(H) = 1.17A) derived from crystallographic data [ 31. The intrinsic volumes of ground structures can also be calculated from the table of group contributions [4].The van der Waals volumes, V,, is the intrinsic volume of a ground or transition structure multiplied by Avogadro’s number. The ratio, Vw/V or V$/V#, is defined as the packing coefficient, q or q # , of a ground or transition structure. The packing coefficients calculated for simple hydrocarbons are in the range = 0.5 to 0.G [ S ] . The empty space between the single molecules can be attributed to the so-called void volume and expansion volume required for thermally-induced motion and collision of the molecules in the liquid state [ S ] . The importance of the change in packing coefficients and, hence, in the void and expansion volume for the effect of pressure on chemical reactions, in particular on cyclizations, will be discussed in the following sections. The importance of considering the whole ensemble of molecules rather than single molecules in the explanation of pressure effects can be demonstrated with reference to electrostriction. In a heterolpc bond dissociation the attractive interaction between the newly generated ions and the solvent molecules leads to a contraction of volume that is, generally, much larger than the expansion of volume resulting from the dissociation. Thus, the overall effect, called electrostriction, leads to negative volumes of activation and reaction (AV# < 0, AV < 0). Neutralization of charges releases the molecules of the solvent cage, leading to positive volumes of activation and reaction (AV# > 0, AV > 0). A similar but less pronounced trend due to the effect of electrostriction is observed for charge concentration and charge dispersal. An increase in steric crowding in the transition or product states also results in a volume contraction (AV# < 0, AV < 0). Table 2.2 provides a survey on the expected contribution of various elementary reactions to their volumes of activation. There are many excellent monographs [l,71 and reviews [8, 91 on organic reactions at high pressure. Particularly, we would like to mention the three reviews written by le Noble and Asano in 1978 [GI, and by le Noble, Asano, van Eldik et al. in 1989 and 1998, which give the most complete survey on activation and reaction volumes up to 1998 [lo]. In this chapter we will discuss the effect of pressure on pericyclic reactions, such as cycloadditions, electrocyclic and sigmatropic rearrangements focussing on mechanistic information gained by the investigation of the pressure effect on organic reactions. Furthermore, the effect of pressure on freeradical reactions, ionic reactions and a few of the most recent applications of high pressure in organic synthesis will be discussed.

2.2 Cycloadditions Possible mechanisms to account for activation volumes o f various elementary processes 161. Tab. 2.2.

Mechanistic feature

Homolyhc bond cleavagc Homolytic association Bond deformation Ionization Neutralization Charge concentration Charge dispersal Displacement Stcric hindrance Diffusion control

Contribution in cm3 mol-'

-- +5" - -5 f10 -10 -0

-20"

t20a -5a

(-) >+20

aDependent on the solvent polarity

2.2

Cycloadditions 2.2.1

Diels-Alder Reactions, Mechanistic Aspects

Many Diels-Alder reactions show a powerful pressure-induced accelcration which is often effectively utilized for synthetic purposes [ 111.The activation volumes AV+ resulting from the pressure dependence of the rate constants are usually highly negative (AV' z -25 to -50 cm3 mol-I), sometimes even more negative than the corresponding reaction volumes AV, so that the ratio 0 = AV#/AV is close to or even larger than unity. For a comparison between activation and reactions volumes it is necessary to determine both data at the samc temperature which is, however, not feasible in many cases. The measurement of the pressure dependence of the rate constants frequently requires a temperature different from that used for the determination of partial molar volumes of reactants and products (generally room temperature). Therefore, the activation volumes have to be extrapolated to room temperature or the reaction volumes, correspondingly, to the temperature of reaction. The measurement of the temperature dependence of activation volumes requires a large collection of experimental data. An example is the Diels-Alder dimerization of isoprene, which has been reported in the literature [ 121. With the modern thermostated densimeters it is much easier to determine the ternperaturc dependence of partial molar volumes and, hence, of reaction volumes. From these data El'yanov extrapolated a generally applicable equation shown in Table 2.3 (footnote a) to describe the temperature dependence of activation and reaction volumes. The temperature dependence obtained experimentally for isoprene dimerization is in accord with the El'yanov equation. Accordingly, the partial molar volumes of the pericyclic transition states, which

I

45

46

Tab. 2.3.

I

2 The Ejiect of Pressure on Organic Reactions: Basic Principles and Mechanistic Applications

Volume data o f selected Did-Alder reactions showing (0= A V # : A V ) ratios smaller than unity

(0 < 1). Reaction

Solvent

0.0-

40

-23.7

AVZ"

AV2p

Ob

-22.2

-33.0

0.67

Re$

n-BuC1

n-BuBr

O+,i' -

T["C]

70

-42.0

70

-33.0

35.0

47.8

0.73

-27.5

-44.9

0.61

30

-32.7

-32

-36.7

0.87

n-BuC1

40

-30.1

-28.3

-33.5

0.84

13

MeC02Et

10

-30.2

-32.2

-36.1

0.89

15

n-BuBr

25

-37

0.85

16

CHIC11

82

0.88

17

n-BuC1

58

0.88

17

0.97

18

0.96

19

QE

E = C02CH3

o+e,-

E

31.5

-43

31.5

-34.6

~

39.5

E

(11)

y+p'o:$

MeCN

65

\

0

0

"In cm3 mol-I; AV,? determined from the pressure dependence of the rate constant at temperature AVZ determined from the temperature of the activation volumes or extrapolated dependence from AV; by using the El'yanov equation AVZ = A V , f / [ l l 4 . 4 3 lo-' K-'(T - 25 "C)![20]. "@ = A V S :AVzs.

39.1

-41.6

-34.1

-35.3

-38.8

-36.9

2.2 Cycloadditions Tab. 2.4.

I

47

Volume data of selected Diels-Alder reactions showing (0= A V t : A V ) ratios larger than unity

(0> 1). ~

Reaction

Solvent

(4)

\

[+

OMe

AVL

: AVzs.

AV25"

Ob

-36.9 -37.3 -35.9 -36.4 -35.8 -35.4 -38.1

-38.3 -35.9 -34.5

0.96 7.04 1.04

35

-38.5 -39.0 -37.5 -38.0 -37.4 -37.0 -39.8

-36.8 -35.5 -33.4

0.97 0.99 1.14

30

-41.3

-40.4

-35.5

1.14

13

35

-44.7

-42.8

-31.9

1.22

19

35

-32.0 -53.6 -45.4 -43.7 -43.7

-30.6 -51.3 -43.5 -41.2 -41.8

-32.4 -32.2 -35.5 -28.2 -30.4

0.94 1.6 1.23 1.46 1.37

22

35

-37.2

-35.6

70

-37.0

-30.8

-28.6

1.08

23

70

-41.0

-34.2

-32.3

1.06

23

70

-36.5

-30.4

70

-35.0

-29.2

0

cm3 mol-I; AV: determined from the pressure dependence of the rate constant at temperature T; AVZ determined from AVr by extrapolation with the use of the El'yanov equation A V g = AV?/[l + 4.43 lo-' K-'(T - 25 "C)] 1201. b@ =

AV;'

0

Q- 0, 0

AV;'

Re$

21

0

0

0

~

T["C]

19

23

-29.7

0.98

23

48

I

2 The Effect of Pressure on Organic Reactions: Basic Principles and Mechanistic Applications

can be derived from the activation volumes within the scope of transition-state theory, are approximately equal to or even smaller than those of the corresponding cycloadducts. This finding is surprising and seems to be contradictory to the generally accepted relationship betwecn molecular structure and its volumes. In the transition state the new bonds between diene and dienophile are only partially formed. According to quantum mechanical calculations the lengths of the partially formed CJ bonds in the pericyclic transition structures are in the range between 2.1 and 2.3A [24, 251. Thus the van der Waals volumes, V,, calculated for thc pericyclic transition structures by the use of quantum-mcchanical methods are generally larger than those calculated analogously for the corresponding cycloadducts (Tables 2.7, 2.8 and Scheme 2.6). Further insight into the relationship between the volume of activation and reaction and the mechanism of pericyclic reactions such as Diels-Alder reactions could be gained with the investigation of the effect of pressure on competing [4 21 and [2 21 or [4 21 and [4 + 41 cyloadditions. In competitive reactions the difference between the activation volumes can be directly derived from the pressure-dependence of the product ratio. All [ 2 + 21 or [4 + 41 cycloadditions listed in Tables 2.5 and 2.6 doubtlessly occur in two steps via diradical intermediates and can, therefore, be used as internal standards of the activation volumes expected for stepwise processes. Thus a relatively simple measurement of the pressure dependence of the product ratio should give important information about the mechanism of the competing [4 21 Diels-Alder cycloadditions. The results of these investigations are summarized in Tables 2.5 and 2.6. In the thermal dimerization of chloroprene (l),the activation volumes of two [4 21 cycloadditions leading to 2 and 3 were found to be smaller than those of the third 14 21 and the [2 21 cycloadditions leading to 4, 5, and 6 , rcspectively. Steward 1261 explained these results in terms of concerted Diels-Alder reactions competing with stepwise [2 21 cycloadditions. According to its larger (less negative) activation volume, the third Diels-Aldcr adduct 4 should also be formed in a non-concerted process. Similarly it can be concluded from the pressure dependence of the dimerization of 1,3-cyclohexadiene (7) that the endo-Diels-Alder dimer 8 and the [6 + 41-ene product 9 are formed concertedly whilc the exo-DielsAlder adduct 10 and the [2 21 cyclodimers 11 and 12 arisc via diradical intermediates. According to the activation volume data the Diels-Alder dimerization of 1,3butadiene [39] and o-quinodimethane (Table 2.5, entries (3) and (4), respectively) fall into the same class of concerted processes as those discussed for 1 and 7. while the Diels-Alder dimerization of hexamethylbis(methy1ene)cyclopentane seems to occur in stepwise fashion. According to the activation volume data summarized in Table 2.6 only the Diels-Alder reaction of 1,3-butadiene with a-acetoxyacrylonitrile seems to proceed concertedly while all other Diels-Alder and homo-Diels-Alder adducts are probably formed in stepwise processes comparable to the corresponding competitive 12 21 cycloadditions. Stereochemical investigations of the chloroprene and 1,3-butadiene dimerization using specifically deuterated derivatives confirm the conclusions drawn from activation volume data. In the dimerization of (E)-1-deuteriochloroprene(17) the diastereomeric Diels-Alder adducts 18a-Dz and

+

+

+

+

+

+

+

+

+

+

2.2 Cycloadditions

I

49

Tab. 2.5. Activation volumes AV# (cm3 mol ’), given in parentheses, and differences in activation volumes AAV’ (cm3 molk’) of competing [4 21 and [2 21 or [4 41 cyclodimerizations.

+

14

Reaction

+

+

+ Z]-cycloadducts

[Z + 21 or [4 + 41

* CI

1

0

AAVf

Ref:

cycloadducts ( A V i j

W ’ )

0

L-+ GI

5

6

(-22)

(-22)

70.5‘C

r-

7

-

10 (-22)

9a) (-32)

8 (-28)

119’C

/’-&

600 - 5300 bar

14

13

(-38.4)

15

16

(-20.9)

(-34.0)

80 ‘C 2 l a l -

m-o’

I

30

(- 15.8)

(-15.5)

+

a[6 41-ene reaction. bAV’ (8) - AV#(11). c A V # (9) - AVf (11). dAVt(lO) -AVi(12). eAV”(14) - AVf(15). ‘AVf(14) AVt(16). ~

181>-D2(Scheme 2.3) are formed in a (59:41) ratio. The non-stereospecific course provides clear-cut evidence that this Diels-Alder dimerization proceeds in stepwise fashion, as suggested from the activation volumes most likely passing through a diradical intermediate where rotation about C-C single bonds can substantially compete with the ring-closure reaction. The [2 21 cyclodimerization leading to a mixture of 19a-D2,19b-D2,and 19c-DZalso occurs non-stereospecifically as expected.

+

50

I

2 The EIfect of Pressure on Orgonic Reactions: Basic Principles and Mechanistic Applications

Activation volumes A V f (cm3 mol '), given in parentheses, and differences in activation volumes AAV# (cm3 mol ' ) of competing [4 21 and [2 21 or [4 41 cyclodimerizations.

Tab. 2.6.

[4

Reaction

+

(1)

+

+

+

+ Z]-cycloadducts

+

[2 21 or 14 cycloadducts

NCToAc

\

1 bar-9

+ 41

AAVf

Re$

-11.5

31, 32

OAc

kba

Q;

'c

*cl

0

32, 33

;

1 bar-10 kba

=a 1 bar-7

kbar

40 "C 1 bar-4

kbar

F

F F

3

-2

0

+ cI

35, 36

,

-0.7

(6)

34,35

38

5 1 bar-5 kba

CI

The Diels-Alder dimerization of Z,Z-1,4-dideuterio-l,3-butadiene occurs with 97% cis-stereoselectivity at atmospheric pressure (1 bar) and >99 % stereospecifity at high pressure (6.8-8 kbar). These findings provide good evidence for the stereospecific Diels-Alder mechanism in competition with a small amount of the nonstereospecific reaction, which can be almost completely suppressed by high pressure, and confirms the conclusion drawn from the different activation volumes found for the [4 21 and [ 2 21 cyclodimerization of 1,3-butadiene. From the pressure dependence of product ratio (endo:exo) it can be extrapolated that the endo-Diels-Alder reaction shows a slightly more negative activation volume than the corresponding em-reaction (AAV# z -2.5 cm3 mol although both reactions are evidently pericyclic. According to these data the difference between the activation volumes of competing pericyclic and stepwise cycloadditions (via diradical intermediates) is about AAV# = AV#(pericyclic) - AV#(stepwise) % -10 cm3 mol This is only found for reactions involving non-polar diradical intermediates and is not observed for polar zwitterionic intermediates. In the latter case the volume of activation of the zwitterionic intermediate can be more negative than that of a competing pericyclic reaction due to the solvent-dependent effect of electro-

+

+

'.

2.2 Cycloadditions CI

D 18a-D, 59

D 18b-D, 41

17-D

DE : DZ : Do

94.2: 2.2 : 3.6 93.7: 2.6 : 3.7 (recovered material)

p [bar]

1 1 6800 8000 Scheme 2.3.

T[~C]

138 120 120 120

19a-D,

19b-D,

19c-D,

48

34

18

[cis : trans]

[endo : ex01

97 : 3 97 : 3 299:99:<1

56 : 44 60 : 40 73:27 71 :29

Dimerization o f chloroprene [40]and Z,Z-l,4-dideuterio-l,3-butadiene [28].

Pericyclic Diels-Alder reactions:

AV*= -25 to 4 5 cm3mol-’, A V = -30 to -45 crn3mol-’

O = A V * / A V S I (orevenzl) MV* = A V ’ (pericyclic) - A V * (stepwise) = -10 cm3mo~-’ Volumes of activation and reaction (A!-’#, AV) of pericyclic Diels-Alder reactions. Comparison of the pericyclic processes with the corresponding stepwise processes involving diradical intermediates.

Scheme 2.4.

I

51

52

I

2 The Efect of Pressure on Organic Reactions: Basic Principles and Mechanistic Applications

striction. Scheme 2.5 shows the competing [4+ 21 and [2 7 21 cycloadditions of 1,l-dimethylbutadiene with tetracyanoethylene (TCNE) as one example [ 9. 351. In toluene the activation volume of the [2 + 21 cycloaddition is found to be more negative than that of the [4+ 21 Diels-Alder cycloaddition whereas in butyronitrile reverse results are found. #

-

“NCG C N CN

Toluene:

M V * = +3.5crn3.rno~-’

Butyronitrile:

M V ’ = 4 . 0crn3.rnol~’

NC CNCN

J

The solvent-dependent effect o f pressure on the competing [4 21 and (2 21 cycloadditions o f tetracyanoethylene (TCNE) and 1,2-dimethylbutadiene a t 40 “C (9, 351.

Scheme 2.5.

+

+

One question that needs to be addressed is: why are the activation volumes of pericyclic cycloadditions smaller (more negative) than those of the corresponding stepwise reactions involving diradical intermediates? In the past it was assumed that the simultaneous formation of two new 7~ bonds in a pericyclic [4 21 cycloaddition leads to a larger contraction of volume than the formation of one bond in the stepwise process. The interpretation presented [28] is limited by the scope of Eyring transition state theory where the activation volume is related to the transition state volume, as mentioned above, and does not incorporate dynamic effects related to pressure-induced changes in viscosity [41].An extensive discussion of reaction rates in highly viscous solvents can be found in Chapter 3. For the pericyclic and stepwise cycloadditions of ethene to 1,3-butadiene (the prototype of Diels-Alder reactions) the molar volumes, the van der Waals volumes, Vw, and the packing coefficients, q, of the ground and transition structures shown in Table 2.7 were calculated following the method of Nakahara et al. [44]in order to uncover the effect of different bonding on the transition-state volumes. The packing coefficient, y ~ , of cyclohexene is significantly larger than that of the three isomeric hexadienes. Generally, y~ is found to be larger for cyclic compounds than for the corresponding acyclic ones. From the data listed in Table 2.7 the van der Waals volume of the Diels-Alder reaction [28, 44,451 can be calculated to be,

+

2.2 Cycloadditions

I

53

Molar volumes, V, van der Waals Volumes, V W , and packing coefficients, ti, calculated for acyclic and cyclic ground and transition structures needed for the explanation of the pressure effect on the Diels-Alder reaction of 1,3-butadiene with ethene. Tab. 2.7.

Compound

CH2zCH2 CH2 =CH-CH=CH2 CHZ=CH-CH~-CHZ-CH=CH~ CHZ-CH-CH~-CH=CH-CH~ CHz=CH-CH CH-CHz-CH3

0 7

vw/v

d

V = M/d"

VW0.b

'I =

0.6880 0.7000 0.7050

59.9c 83.2' 119.4 117.7 116.5

25.5 44.8 63.9 63.9 63.8

0.4257 0.5385 0.5354 0.5443 0.5475

0.8102

101.4

59.1

0.5829

109.1d

63.8

0.5829

118.7e

64.4

0.5424

120.4e

65.3

0.5424

i.54A

aIn cm3 mol-'. For the calculation of van der Waals volumes Cartesian coordinates resulting for ground structures from molecular mechanics calculations [42], and for transition structures from ab initio calculations [24], the following van der Waals radii were used: Rw(H) = 1.17A; Rw(C) = 1.80A. Calculated with volume increments [ 431. dWith the packing coefficient of cyclohexene ( q = 0,5829). 'Calculated with the average of the packing coefficients determined for the three isomeric hexadienes ( q = 0.5424).

+

with AVw = (59.1 - (25.5 44.8)) = -11.2 cm3 mol-', only roughly one-quarter of the experimentally accessible volume of reaction (AV = 101.4 - (59.9 + 83.2) = -41.4 cm3 mol-I). Consequently, a significant part of the observed AV results from the higher packing of the cyclic product rather than from the changes in bonding. The difference between the van der Waals volumes of activation calculated for the pericyclic and stepwise reaction (AAV: = AV: (pericyclic) - AV: (stepwise) = -6.7 - (-5.0) = -1.7 cm3 mol-l) is small and inconsistent with the experimental value (AAV# z -10 cm3 mol-'). In order to explain the experimental AAV# one has to assume [28] that the packing coefficient of the pericyclic transition state is similar to that of the cycloadduct . The difference between the activation volumes calculated for the pericyclic and stepwise cycloaddition using the packing coefficient of cyclohexene ( q = 0.5829) for the pericyclic transition structure (AVz (pericyclic) = -109.1 - (59.9 83.2) = -34.0 cm3 mol-') and the average of the packing

+

54

I

2 The Efect of Pressure on Organic Reactions: Basic Pn'nciples and Mechanistic A p p h t i o n s

coefficients of the three hexadienes = 0.5424) for the acyclic transition structure of the stepwise cycloaddition (AV#(stepwise)= -120.4 - (59.9 + 83.2) = 22.7 cm3 mol-') is, with AAV# = -11.3 cm3 mol-', in good accord with the experimental findings. Therefore, the analysis of activation volumes seems to provide important information regarding whether the transition-state geometry is cyclic or acyclic. The second question that needs to be addressed is, why are the activation volumes of some pericyclic Diels-Alder reactions smaller (more negative) than their reaction volumes so that the ratio 0 = AVf/AV > 1, This surprising result could be confirmed by three independent studies. In the two earlier studies Jenner et al. and Isaacs et al. found the ratio AV'/AV in the Diels-Alder reaction of furan with acrylonitrile [4G] and that of N-benzoylpyrrolewith N-phenylmaleic imide [ 471 to be larger than unity (0 = 1.06 and 1.37, respectively). The cycloadducts isolated from both reactions undergo smooth retro Diels-Alder reactions showing negative volume of activation (AVz = -2.0 and -8.3 cm3 mol respectively) in agreement with the value 0 > 1 determined for each forward reaction. In a more recent investigation F.-G. Klarner and V. Breitkopf observed that the retro Diels-Alder reactions of dihydrobarrelene and its 2-cyano derivative and of the endo-Diels-Alder adduct between dimethylfulvene and N-phenylmaleic imide are slightly decelerated by pressure showing positive volumes of activation whereas the retro Diels-Alder reactions of the endo and exo [4 + 21 cycloadducts between naphthalene and maleic anhydride and that of the exo adduct between dimethylfulvene and N-phenylmaleic imide are accelerated by pressure showing a negative volume of activation (Scheme 2.6) [48]. Grieger and Eckert [21, 491 considered two explanations of the ratio @ > 1 in the Diels-Alder reaction of isoprene with maleic anhydride: a larger dipole moment of the transition state or secondary orbital interactions which can only occur in endo Diels-Alder reactions. The findings that the difference between the activation volumes of many endo and ex0 Diels-Alder reactions is small (AAV# < 1-2 cm3 mol-l) and that the activation volume of retro Diels-Alder reaction of the endo cycloadduct between dimethylfulvene and N-phenylmaleic imide is positive and that of the retro Diels-Alder reaction of the corresponding exo cycloadduct is negative (Scheme 2.6), rule out that secondary orbital interactions are important and induce a larger contraction of the volume of the endo transition state. The following conclusions were drawn from the results obtained for the retro Diels-Alder reactions shown in Scheme 2.6. The packing of the entire ensemble consisting of solute and solvent and its reorganization during the course of reaction, and not the changes of the intrinsic molecular volumes of the reactants to the products during the course of reaction are most important for the magnitude of the activation and reaction volumes. The packing coefficients of the pericyclic transition states resemble those of the corresponding cycloadducts as already assumed for the explanation of the different activation volumes of pericyclic and stepwise cycloadditions [50]. In the retro Diels-Alder reactions showing AV# < 0, the packing coefficients of the transition states are calculated to be larger than those of the corresponding cycloadducts. This has been found particularly in the relatively polar systems bearing cyclic anhydride or imide functions (Scheme 2.6).

',

2.2 Cycloadditions

In these cases the size of the activation volumes obviously depends not only on the effective packing probably caused by the restriction of vibrations and rotations in the transition state, but also on the transition-state polarization enhanced by the polar groups leading to a further decrease in volume which is not observed in the less polarized cycloadducts. Blake and Jorgensen [ 511 have assumed similar effects to explain the acceleration of Diels-Alder reactions in water. Catalytic and solvophobic promotion of high pressure addition reactions will be discussed in Chapter 11. In so called homo Diels-Alder reactions, in which double bonds are replaced by three-membered rings or two n-bonds of the reactive 1,3-diene are bridged by an sp3-hybridized group, a powerful pressure-induced acceleration and hence highly negative activation volumes comparable to those of the ordinary Diels-Alder reactions have been observed. Examples of the pressure effect on homo-Diels-Alder reactions are shown in Scheme 2.7. The reaction of homofuran with fumaronitrile (Scheme 2.7, entry (8))[52] seems to be an exception in which the activation volume is significantly less negative than those in other cases. With the use of fumaronitrile and maleonitrile ( ( E ) - and (Z)-NC-CH= CH-CN) as dienophiles it was es-

R = H: 105.3 'C, AV*= +3.1, AV= +47.6 VwIV: 70.71118.7 q: 0.596

74.01121.8 0.608

R = CN: 105.6 ' C , AV*= +2.5, AV= +44.8

v W i v : 81.31123.3 1): 0.659

84.01125.8 0.674

87.0'C,AV*=-l.l (exoand endo),AV=+36.5(exo), AV=+36.2(endo) ex0 endo VwIV: 121.7l168.7 121.7/169.0 q: 0.721 0.720

Scheme 2.6.

ex0 endo 125.11167.6 125.11167.9 0.746 0.745

'='

Activation and reaction volumes determined experimentially and calculated van der Waals volumes and packing coefficients of retro-Diels-Alder reactions [48]. All volumes (in cm3 mol-') related t o the temperature of reaction.

=

eo

I

55

56

I

2 The Efect of Pressure on Organic Reactions: Basic Principles and Mechanistic Applications

87.0 ‘C,A V L = +4.6,A V = +21.5

VwIV: 162.5/238.1 q: 0.682

165.41242.7 0.681 + e N - P h

‘0

121.7 ‘ C , AV*=-5.2, A V = +25.2

VwlV: 162.5/240.0 9: 0.677

165.4/234.8 0.704

All volumes (in cm3.mol-’) related to the temperature of reaction. Scheme 2.6.

(continued)

tablished that the reaction occurs stereospecifically with retention of configuration in the dienophiles and non-stereospecifically with respect to the ratio (endo: em). The relatively small pressure effect was explained in terms of a “late” transition state (with respect to the bond reorganization in the homofuran) in which the central cyclopropan bond has already been extensively cleaved and the bonding to the dienophile is still weak. 2.2.2 Complex Reactions and Synthetic Applications

The reaction of furanobenzocyclophane (20) with dicyanoacetylene (DCA) (Scheme 2.8) illustrates that the effect of pressure and that of a catalyst can be complementary [SS]. At 160 “C and 1 bar the reaction of 20 with DCA leads to the dicyanosubstituted furane (22) (20 %) and oxepin (24) (1 %). In a kinetically controlled reaction of 20 with DCA at 9 kbar and 20 “C the thermally unstable Diels-Aldcr adduct 21, the precursor of 22, is formed as the only product which undergoes a smooth retro Diels-Alder reaction at 1 bar and 20 “C producing the starting materials 20 and DCA. At 160 “C the retro Diels-Alder reaction of 21 leading to 22 and acetylene is obviously competitive with the non-productive reaction leading to 20

2.2 Cyc/oadd;t;ons

I

57

x=x (1)

(2)

E-CEC-E

Solvent h)

Ph-H

(cN)~c=c(cN)~ Ph-Me

T [ T ] AVr* *

(4) (6) (7)

CH2=CH-CN HCEC-E b) E-C-C-E h, c, E-NEN-E

(8)

(€)-CN-CH=CH-CN

(5)

CHC1, CIICI, CHCI, CHCI,

(CD,),CO

AVX'

Ob

Ref [53]

90

40.5

-32.0

-35.5

0.89

4o

-30.0

-32.8

-28.1 -30.7

-32.9 -36.2

0.85 [531 0.94

113

45.0

-32.4

-29.5

1.10 [17]

90 90 40.5 50

-32.0 43.5 -37.3 -28.2

-24.9 -33.8 -34.9 -25.4

-29.1 -38.8 -39.4 -29.6

0.86 0.87 0.89 0.90

70

-10

MeCN

EtOAc

A V Z ~ 'a

[54] [54] [17] [54]

[521

a) see footnotes a) and b) in Table 2.3; b) E = COzMe; c) E = C02Et Scheme 2.7.

Volume data o f selected homo-Diels-Alder reactions.

and DCA. At GO "C and 8.5 kbar or at room temperature in the presence of LiC104 as catalyst 20 reacts with DCA to produce the [ 2 21 cycloadduct 23 which isomerizes to the oxepin 24 at 160 "C. The reactions of the strained benzene derivative 25 with DCA were originally studied with the aim of synthesizing planar cyclooctatetraene derivatives which are interesting compounds with respect to the question of their antiaromaticity [ 561. The cyclooctatetraene derivative, 29 (Scheme 2.9) synthesized by photolysis of the barrelene derivative 26, however, turned out to be non-planar [57]. But the synthesis and the reactions of barrelene derivative 26 are interesting with respect to the utility of high pressure to control the course of reaction. The reaction of 25 with DCA at 1 bar and 127 "C produces the (1: 1) Diels-Alder adduct 26 (yield, 49 %) and the unexpected dark blue (2: 1) adduct 27 (yield, 14 %). At high pressure (9 kbar, 83 "C) 27 is the major product even after the low conversion of 36 % of the

+

58

I

2 The Effect of Pressure on Organic Reactions: Basic Principles and Mechanistic Applications

NC

A F"

CN

k3J

- HCECH

22

21

'I'

NC

\

CN

20

23

24

Scheme 2.8. Competitive and consecutive reactions of furanobenzocyclophane 20 with dicyanoacetylene (DCA).

starting material 25. The observation, that the isolated (1: 1) adduct 26 reacts with DCA at 1 bar and 127 "C leading to 27, indicates that 26 is an intermediate in the reaction 25 + 2 DCA + 27. At 12 kbar 26 reacts with DCA readily at room temperature producing the homo-Diels-Alder adduct 28 which smoothly undergoes a rearrangement to 27 already at room temperature, so that 28 is also an intermediate in the reaction of 26 with DCA; 28 can be detected only by the use of high pressure. The dihydronaphthalene derivative 27 is an interesting compound regarding to its intense color and intramolecular dynamics [57]. Another example, which demonstrates that pressure is a useful parameter to control consecutive reactions, is the addition of DCA to benzodicyclobutene (30) which gives benzocyclobutene (31) at 1 bar and 125 "C as the only product [57]. At 11 kbar the reaction between DCA and 30 occurs readily at 53 "C producing the primary Diels-Alder adduct 31 in addition to 32. Isolated 31 rearranges to 32 slowly at 53 "C. Attempts to catalyze the reaction between 30 and DCA by means of Lewis acids such as AICl3 or TiC14 (analogous to the Diels-Alder reaction of DCA with parent benzene) failed. The cycloadditions of cyanoacetylene (Scheme 2.10) are good examples of the utility of high pressure to accelerate sluggish reactions and to control the course of complex reactions. In contrast to DCA cyanoacetylene is only a moderate dienophile reacting, for example, with 1,kyclohexadiene at 1 bar only at a temperature of ca. 100 "C at which the primary Diels-Alder adduct (2-cyanobicyclo[2.2.2]octa2,s-diene) is not thermally stable and undergoes a retro Diels-Alder reaction, producing benzonitrile and ethene [58, 591. The reaction is highly accelerated by pressure and occurs at 9 kbar and 50 "C. Under these conditions the primary Diels-Alder adduct is stable and can be isolated in good yields. A similar effect of pressure was observed in the trimerization of cyanoacetylene leading to 1,2,3- and 1,2,4-tricyanobenzenes as major products at 1 bar and 160 "C [58, 591. At 12 kbar

2.2 Cycloadditions (1) 1 bar, 127 C

25

&+& 27

I

26

v

26

20 'C, t1/2 = 20 d

20

26

acetone 29

1 bar, 125 'C: 11 kbar, 53 'C:

Scheme 2.9.

32 is the only product 31 is the major product

The effect of pressure on cycloadditions o f DCA to strained benzene derivatives

the trimerization occurs readily at 40 "C giving the thermally labile 2,3,5-tricyanoDewar-benzene which isomerizes to 1,2,4-tricyanobenzeneupon heating to a temperature L 50 "C. The results using high pressure provide good evidence that the thermal trimerization of cyanoacetylene occurs by a sequence of reactions consisting of the [2 21 cyclodimerization in the first step leading to the highly reactive 1,2-dicyanocyclobutadienefollowed by Diels-Alder cycloaddition of cyanacetylene to the cyclobutadiene producing the Dewar-benzene derivatives which aromatize to the observed benzene derivatives via orbital-symmetry forbidden electrocyclic ringopening.

+

I

59

60

I

2 The Efect of Pressure on Organic Reactions: Basic Principles and Mechanistic Applications

1

.

12 kbar, 40"C,48h

+-CN

CN

NC

CN CN

16 Scheme 2.10.

:

:

6

1

Trimerization o f cyanoacetylene.

The reaction of cyanoacetylene with furan leads preferentially to the (2: 1) adduct 36 at 160 "C and 1 bar (Scheme 2.11). In analogy to the trimerization o f cyanoacetylene and the addition o f cyanoacetylene to [2, 21 paracyclophane [58, 591 the 1,2-dicyano-1,3-cyclobutadiene was assumed also to be the intermediate in this reaction. From the investigation of the pressure effect on the reactions of furan with cyanoacetylene and isolated oxanorbornadiene (33) with cyanoacetylene, both leading to the (2 :1) adducts 36 and 37, it could be concluded, that oxanorbornadiene (33) (the Diels-Alder adduct) and not the 1,2-dicyanocyclobutadieneis an intermediate in the reaction between furan and cyanoacetylene. The investigation of the pressure effect on the reaction between the furanobenzocyclophane (20) and cyanoacetylene led to similar results [55].

0

CN

33

CN 34

/CN 12 kbar,40 'C

&CN

-k I

CN 36 Scheme 2.11.

35 0

&'" /

NC

37

Addition o f cyanoacetylene to furan at various pressures.

2.2 Cycloadditions

In the past decade thc utility of high pressure has been demonstrated for many syntheses involving Diels-Alder reactions as key steps (see Chapters 9 and 11)We will describe here only fcw selected examples in order to illustrate the utility of high pressure in organic syntheses. An interesting example is the pressure-induced reaction of buckminsterfullercne CGOwith 1,3,5-cycloheptatriene [ 601. Generally C ~ reacts O as an electron-deficient dienophile or dipolarophile in numerous Diels-Alder or 1,3-dipolar cycloadditions and 1,3,5-cycloheptatriene as a diene. The reaction with CGOis a rare example where both adducts derived from the norcaradiene as well as the cycloheptatriene are observed.

Pressure-induced Diels-Alder reaction of cycloheptatriene + norcaradiene with C ~ as O dienophile.

Scheme 2.12.

The effect of pressure on hetero-Diels-Alder reactions is comparable to that on the aforementioned Diels-Alder reactions leading to carbocyclic products. The reactions are strongly accelerated by pressure showing highly negative volumes of activation (Scheme 2.13). The Diels-Alder reactions of unreactive dienes such as pyrazole [61-631 and oxazole 1641 derivatives (Scheme 2.13, entries (1-5)) are accelerated by high pressure which allows the temperature of reaction to be lowered so that the thermally labile cycloadducts and the 3,4-di-(trimethylsilyl)furane, respectively, can be isolated. The macrocycles shown in Scheme 2.14 can be synthesized by repetitive, highly stereoselective Diels-Alder reactions between the tetramethylene-substituted norbornane or 7-oxanorbornane derivatives as bis-dienes and the benzoanclated norbornadiene derivatives as bis- or tris-dienophiles, containing only 0x0 or methano bridges syn to one another. Whereas in each case the first reaction leading to the acyclic all-syn-configurated bis- or tris-diene occurs at atmospheric pressure, the subsequent inter- and intramolecular Diels-Alder reactions only succeed at high pressure. Obviously, the inter- as well as intramolecular Diels-Alder reactions are accelerated by pressure. The macrocycles are of interest in supramolecular chemistry because of their well-defined cavities of different sizes depending on the arene spacer-units. If the 0x0 (or methano) bridges are not exclusively Syn to one another either in the bis-dienophiles or bis-dienes (Scheme 2.15) or if the bis-diene is too large for the formation of a macrocycle, then the pressure-induced repetitive Diels-Alder reactions (proceeding again highly stereoselectively) produce rigid ribbon-type oligomers on a nanometer scale. The ethano-bridged bis-diene reacts less stereoselectively than the methano- or oxo-bridged bis-dienes [69]. It forms, with oxabenzonorbornadiene as the dienophile, a (2 : 1)cycloadduct and with bis-dienophiles, the ribbon-type oligomers with long chain lengths. A more flexible ribbon-type

I

62

I

2 The Efect of Pressure on Organic Reactions: Basic Principles and Mechanistic Applications

0

(1)

t 14 kbar neat E = C02Me AV*= -18.8 crn3.rnol

’, A V = -30

crn3mo~-’

(4)

N--

a-12% Ar

Ar = o-X-CsH4,X = F,CI, Br, Me

1 bar, 300 ‘C: 8 kbar, 150 ‘C: Scheme 2.13.

76

:

24

only product

The effect of pressure on hetero-Diels-Alder reactions.

structure can be obtained by repetitive Diels-Alder reactions of the difuranocyclooctane as the bis-diene and dimethyl acetylenedicarboxylateas the bis-dienophile. The cage compound is formed in an undesirable side-reaction [70]. The extension of the spacer-unit of a bis-diene can be achieved by the pressure-induced DielsAlder reaction of the bis-diene with allenylchloromethylsulfone followed by basic HC1 and SO2 elimination [71]. High pressure can be also useful in tandem reactions consisting of a Diels-Alder [4 21 cycloaddition followed by a 1,3-dipolar[3 21 cycloaddition (see Chapter 10) or a Claisen-Ireland rearrangement, which is shown in Scheme 2.16. High pressure highly accelerates the Diels-Alder reaction which is the rate-determining step. Thus, pressure has a strong effect on the overall reaction [72]. The consecutive reactions of quadricyclane and norbornadiene, respectively, consisting of a homoDiels-Alder reaction with dimethylacetylenedicarboxylatefollowed by a Diels-Alder

+

+

2.2 Cycloadditions

R

X

X

Y

8-10 kbar

50-125'C yield: 2969%

rn = n = 0, R = H: X = Y = 0, X = 0, Y = CH2; X = Y = CH2, R = OMe: n = rn = 0,n = rn = 1, n = 1, rn = O

(2)

0

0

0

+ acyclic isornere (1:l) ratio 8.1 %

(3)

0

12 kbar

t

0W

0

O

Scheme 2.14. Synthesis of macrocycles by means of pressureinduced repetitive Diels-Alder reactions.

I

63

64

I

2 The Effect of Pressure on Organic Reactions: Basic Principles and Mechanistic Applications

H

H 45.5 %

I"

'm+ lr m ' > SOPCH$~

(3)

//

i

1) 25 'C,15 kbar 2) KOtBU, THF

[711

\ '

Scheme 2.15. Synthesis o f ribbon-type oligomers by means of pressure-induced repetitive Diels-Alder reactions.

reactions of the primary adduct with 1,3-diene leading to polycyclic compounds are more efficient at high pressure, so that in some reactions the final bis-adducts can be observed only at high pressure [73]. 2.2.3

1,3-Dipolar [3

+ 21 Cycloadditions

1,3-Dipolar cycloadditions usually occur stereospecifically with retention of configuration in the dipolarophiles, and their rates are relatively insensitive to solvent polarity [ 7 4 . These results have been taken as an evidence for a concerted process. Only few exceptions are known where the non-stereospecific course of the reaction suggests a stepwise mechanism [75]. Activation and reaction volumes had been measured in the early 1980s for a selection of reactions with diazoalkanes, nitrones and alkyl azides as dipoles and electron-deficient or neutral alkenes as dipolarophiles. They were generally in the range of AVf = -(21 f 3) cm3 mol-' and AV = -(25 2) cm3 mol-' [76]. The relatively large ratios (AVz : AV) have been regarded as an indicator of a pericyclic mechanism. The absolute values of AV and AV# for 1,3-dipolar cycloadditions, however, are about 5 to 10 cm3 mol-', smaller than those of Diels-Alder reactions. No clear explanation has been given for this difference. But one can assume that one reason might be the dependence on ring size in the volume changes during cyclizations. According to the information ob-

2.2 Cycloadditions

X

R = H: 85 'C, 3 kbar: 88 % 100 'C, 1 bar: 100 %

CH2:

70 ' C , 3 kbar:

70 %

CHZCH2:

100 ' C , 9.5 kbar: 100 % (1 bar: 1 %)

0:

30 'C, 9.5 kbar: 86 % (1 bar: 0 %)

CHz

/I

CH-cH:

R = E: 90 'C, 1 bar: 100 % E = COzMe Scheme 2.16.

CHz: CHZCH2:

100 'C, 9.5 kbar: 66 % (1 bar: 0 %)

70 ' C , 3 kbar:

80 % (1 bar: 50 %)

100 'C, 9.5 kbar: 95 % (1 bar: 0 %)

The effect of pressure on tandem reactions.

tained later, the decrease in volume seems to be larger for the formation of a sixmembered ring rather than a five-membered ring [ 771. At 12 kbar and 25 "C benzylazide undergoes a regioselective 1,3-dipolar cycloaddition with a substituted methyl methoxymethacrylate, whereas at 1 bar and 80 "C a (1: 1) mixture of the two regioisomeric cycloadducts is formed (Scheme 2.17, entry (1))[78]. In the pressure-induced cycloaddition of nitrones with electrondeficient alkenes, alkynes and nitriles, the yields and selectivities of the cycloadducts are improved over those achieved at 1 bar and higher temperatures. The silyloxazolineresulting from the pressure-induced reaction of benzylphenylnitrone with trimethylsilylacetylene can be used for the synthesis of p-lactam antibiotics [ 791. The 1,3-dipolar cycloadditions of nitrones with electron-rich enolethers are less influenced by pressure. Moderate pressure of ca. 2 kbar and a Lewis-acid catalyst provided the optimum conditions for some of these reactions. The first step in the reaction of diazomethane with 1-phenylphosphole (Scheme 2.17, entry (3)) is certainly the addition of diazomethane to the phosphorus (R3P CHzNz -+ R3P= N-N=CH2) followed by hydrolysis leading to the highly reactive l-phenylphosphole1-oxide which reacts with diazomethane in the fashion of a 1,3-dipolarcycloaddi-

+

I

65

66

I

2 The Effect of Pressure on Organic Reactions: Basic Principles and Mechanistic Applications

tion to form the monoadduct and subsequently the bis-adduct [SO]. (In the absence of water none of the cycloadducts are formed). Apparently, high pressure has a strong rate-enhancing effect on the first addition of diazomethane to the phosphole and also on the 1,3-dipolar cycloaddition, so that the overall reaction is almost completed at 12 kbar within 12 h compared to 10 day at 3-5 bar where the monoadduct is formed, preferentially.

E'

E = C02Me

(*)

80 'C, 1 bar, 30 %:

50

50

25 'C. 12 kbar, 83 %:

4

>95

~n,fi,8

SiMea 1 25'C.gkbarBn\N'o

Rn

3 - 5 bar, 10 d, conversion: 100 %

60

40

12 kbar, 12 h, conversion: 80 %

>99

Scheme 2.17.

n

Pressure-induced 1,3-dipolar cycloadditions.

2.2.4

[2

+ 21 Cycloadditions

+

[2 21 Cycloadditions involving ketene derivatives as one or both reaction partners are assumed to be rare examples of concerted [r: r,'] cycloadditions [Sl]. The activation volumes determined for the [2 + 21 cyclodimerization of diphenylketene [82] and the [2 21 cycloadditions of diphenylketene to various enolethers [S3] gave values of -30 cm3 mol-I and -22 to -52 cm3 mol-', respectively, and were highly negative. Thus, the effect of pressure leads to a powerful acceleration of these [2 21 cydoadditions comparable to that with Diels-Alder reactions, a characteristic which is useful for synthetic purposes. For example, various p-lactams can be easily synthesized by pressure-induced [2 21 cycloaddition of alkyl and aryl isocyanates and enolethers [ 841.

+

+

+

+

2.2 Cycloadditions

I

67

Dolbier and Weaver investigated the effect of pressure on the stereo- and regioselectivity in a certainly stepwise [2 + 21 cycloaddition of 1,l-difluoroallene to (Z)-p-deuteriostyrene involving a diradical intermediate (Scheme 2.18, entry (1)) [85]. In order to explain the pressure-induced increase in stereoselectivity corresponding to AAV# = A V # ( Z ) - AV#(E) = -2.6 and -2.8 cm3 mol-' (provided that there is a linear relationship between ln(Z/E) and pressure up to the very high pressure of 13 kbar), the authors concluded that at high pressure the ring-closure in the diradical intermediate leading to the (Z)-configured methylenecyclobutane derivatives, are favored over bond rotation which is a prerequisite for the formation of (E)-configuredmethylencyclobutanes. The activation volumes of stepwise [ 2 + 21 cycloadditions in non-polar systems proceeding via diradical intermediates are negative but significantly less negative than those of pericyclic Diels-Alder reactions as already mentioned. An example is the cyclodimerization of 1,3-butadiene (Table 2.5, entry (3)) [SO]. The activation volume (AVz -20.9 cm3 mol-') of the [2 t 21 cyclodimerization leading to truns-1,2-divinylcyclobutaneis less negative by -17.5 cm3 mol-' than that of the competing Diels-Alder [4 21 cycloaddition (AV" = -38.4 cm3 mol-') leading to 4-vinylcyclohexene so that the [2 + 21 cyclodimerization can be almost completely suppressed by the use of high pressure. The semicyclic 1,3-diene system of the 3methylenecyclohexene (Scheme 2.18, entry (2)) is confined strictly to a transoid conformation. Thus, its reactions are limited to the 12 21 cyclodimerization. The thermally-induced cyclodimerization of 3-methylenecyclohexene, however, cannot be observed because of the unfavorable position of the equilibrium which is on the side of the starting material even at high pressure (at 7.5-8.0 kbar and 25-60 "C: syn and anti-cyclodimers5 1 %). Starting from the photochemically accessible synand anti-cyclodimers the activation and reaction volumes of the mutual syn-anti interconversion and the ( 2 + 21 cycloreversions were determined [86]. From these data the activation volumes of the 12 21 cyclodimerizations which are not directly observable, can be calculated and are found to be comparable to those determined for the [2 + 21 cyclodimerization of chloroprene ( 2 3 "C: AVf = -22 cm3 mol-') [26], 1,3-cyclohexadiene(70.5 "C:AVf = -22 and -18 cm3 mol-' for the formation of the syn- and anti- [2 21 cyclodimer, respectively) [27], and 1,3-butadiene [SO]. The finding, that volumes of activation of the mutual syn-anti interconversion and the [2 21 cycloreversion of the cyclodimers of 3-methylene-cyclohexene dimers are positive and of the same order of magnitude, is good evidence that the cyclobutane ring-opening, leading to the corresponding diradical intermediate, occurs in the rate-determining steps of both reactions. The [ 2 21 cycloaddition of tetracyanoethene (TCNE) to vinylethers shows a powerful pressure-induced acceleration resulting in highly negative activation volumes (for example AV' = -55.0 cm3 mol-l, AV = -31.9 cm3 mol-' (25 "C, CH&) for the cycloaddition of TCNE to ethylvinylether) [87]. Detailed mechanistic studies [88] have led to the conclusion that these reactions proceed in a stepwise manner passing through interceptable dipolar intermediates. The observation, that the activation volumes are generally more negative than the corre=1

+

+

+

+

+

+

68

I

2 The Effect of Pressure on Organic Reactions: Basic Principles and Mechanistic Applications

1.8 kbar 57.1 13.0 kbar 59.5

- MV':

-

AVf

@ @ @ @ @ @

+14.2 +13.1

+12.4 +13.2 -26.0(calc.) -24.2 (calc.)

: :

29.0 10.1

:

:

12.2 28.9

- 2.6

: :

1.7 1.5

- 2.8

AV +1 .o -1 .o

+38.4 +37.4 -38.4 -37.4

+

Scheme 2.18. The effect of pressure on stepwise [2 21 cycloadditions and cycloreversions (all volumes i n cm3 rnol ').

sponding reaction volumes (0= AV#/AV > 1) has been confirmed by the finding that [ 2 21 cycloreversion of a TCNE-vinylether cycloadduct is also accelerated by pressure and, hence, its activation volume is also negative [89]. Due to the effect of electrostriction the partial molar volumes of the dipolar intermediate and the polar transition states in its formation are smaller than those of the reactants (TCNE and vinylether) and the cycloadduct. This powerful effect of pressure on polar cycloadditions has been used in the synthesis of various dicyanoalkoxy-substituted cyclobutane derivatives [90].

+

2.2.5

[6

+ 41 and [8 + 21 Cycloadditions

The dependence of the orbital symmetry allowed [6

+ 41 cycloaddition of tropone

with 1,3-dienes on pressure was first studied by le Noble and Ojosipe [911 and they reported extremely small absolute values of AV# and AV. A reinvestigation by Takeshita and his coworkers [92] showed, however, that the activation and reaction

2.2 Cycloadditions

I

69

volumes of these cycloadditions are in the same order of magnitude as those of Diels-Alder reactions. Dogan [ 351 confirmed this finding with a study of the reaction between 1,3-butadiene and tropone in which a [6 41 cycloaddition competes with a 14 21 Diels-Alder reaction. The activation volume of the overall reaction was again found to be highly negative (Scheme 2.19). But the ratio between the [ 6 + 4 ] and [ 4 t 21 cycloadduct turned out to be almost pressure independent which means that the difference between the activation volumes (AAV') is almost zero and, hence, the activation volumes of both reactions are of the same value.

+

+

AV*"'

CPr-Ph; 80 'C

P+41

product ratio

(p = 0.9 kbar) (p=6.9 kbar)

10.0 10.8

Ref.

AVa'

-37.6

-36.1

[92]

-33.1

-34.9'

[92]

[4+21

: :

1 1

M V * ') = AV' [6+4] - AV' [4+2] = 4 . 3

a) in crn3.rnol-'; b) a t 80°C; c) 60°C [93];d) at 50°C. Scheme 2.19.

Cycloadditions with tropone.

+

Tropone can also react as a tetraene component in [8 21 cycloadditions induding the C=O double bond. Tropone reacts e.g. with 1,l-diethoxyethene (at 120 "C, 10 h, 1 bar) to give the corresponding [4 21, [8 21, and [6 41 cycloadducts in yields of 1.1,9.1 and 3.1 %, respectively (conversion of tropone: 16 %). At 3 kbar, 120 "C, only the 14 21 and [8 21 cycloadducts were formed in yields of 13 and 17 %, respectively (conversion of tropone: 30 %) [94]. Tropone reacts with 2,3dihydrofuran in a similar fashion leading to the corresponding [8 21 and [4 21 cycloadducts. The product ratio is again pressure dependent [95]. The heptafulvene derivative 38 shown in Scheme 2.20 undergoes a [8 21 cycloaddition leading to methyl-azulene-1-carboxylate(40) after elimination of C02 and ethanol from the undetectable primary cycloadduct, 39. The [8 21 cycloaddition competes with [4 21 cycloadditions. The study of the pressure effect on the competitive reactions has shown that the formation of the 14 21 cycloadduct (41) is reversible even at

+

+

+

+

+

+

+

+

+

+

+

70

I

2 The Effect of Pressure on Organic Reactions: Basic Principles and Mechanistic Applications

10 kbar, and that 41 is not directly converted to 40. Thus, the formation of 40 can only occur via the intermediate [8 + 21 cycloadduct (39) [9G].

_/OEt

-

I..-

0

0

E= COzMe

+Ao

I

OEt

I 41

30

40 Scheme 2.20.

[8+ 21 and 14 + 21 cycloaddition of 38 with ethoxyethene 1961.

2.2.6 Cheletropic Reactions

Cheletropic reactions were defined by Woodward and Hoffmann to be processes in which two 0 bonds directed to the same atom are formed or cleaved in one step [97].The addition of a singlet carbene to an alkene is an example of a non-linear cheletropic reaction. Turro, Moss and coworkers generated phenylhalogenocarbenes (Ph-C-X: X = F, C1, Br) by flash photolysis of the corresponding diazirines and studied the pressure-dependence of their addition to tetramethylethene and (E)-2pentene at room temperature up to 2 kbar (Scheme 2.21, entry (1))[98]. The activation volumes (AVf = -10 to -18 cm3 mol-') were found to be less negative (by about 20 to 30 cm3 mol-I) than those found for Diels-Alder reactions. This result can be explained by the interdependence of the effect of pressure and ring size (uide inf7a). The addition of SO2 to 1,3-dienes (Scheme 2.21, entry (2)) is an example of a linear cheletropic reaction. The activation volume for the reaction between SO2 and 2,3-dirnethyl-1,3-butadiene was found by Isaacs and Laila to be more negative than the reaction volume of many comparable Diels-Alder reactions [ 991. For that reason one may speculate that in the rate-determining step the Diels-Alder adduct (the six-membered ring sulfinic ester) is formed followed by a rearrangement to the observed five-membered ring sulfone. The cheletropic addition of PhPBr2 to 1,3-dienes leading to the corresponding phospholes after basic HBr elimination of the primary adduct, can be dramatically accelerated by high pressure [loo]. In the analogous reaction of PhPC12 with 1-vinyl-cyclobutenethe time of reaction can be reduced from 2 months to 16 h by raising the pressure from 1 bar to 7 kbar (Scheme 2.21, entries (3) and (4))[loll.

2.3 Pericyclic Rearrangements

[951 X = F,CI. Br

AVf=-10tO-18

0 = 1.06

(3)

R'

R2

75-77%

R', R2 = H, CH3

7 kbar, 16 h, 75 % :

50

:

50

Scheme 2.21. The effect of pressure on cheletropic reactions. ( A V ' , A V in cm3 mol-'; 0 = AV#/AV).

2.3

Pericyclic Rearrangements

Many pericyclic rearrangements show a pressure-induced acceleration which is characterized by negative volumes of activation [l: 71. The effect of pressure on rearrangements is usually smaller than that on intermolecular cycloadditions and may be explained by the larger packing coefficients of the pericyclic transition states compared to those of the corresponding acyclic ground states as already discussed for the pericyclic and stepwise cycloadditions. 2.3.1

Sigmatropic [3.3] Shifts: Cope and Claisen Rearrangement

On the basis of stereochemical and kinetic investigations and quantum-mechanical calculations, most Cope rearrangements are regarded as being pericyclic processes [25, 102, 1031. The van der Waals volumes calculated for the parent 1,s-hexadiene

I

71

72

I

2 The Eflect offressure on Organic Reactions: Basic Principles and Mechanistic Applications

and the pericyclic transition state [77, 1041 are approximately the same (Scheme 2.22). This is understandable since in the symmetrical transition state bond breaking and making have proceeded to the same extent so that the effects of the two processes on the van der Waals volume compensate each other and thus no great overall effect of pressure on the Cope rearrangement is to be expected. However, it is reasonable to assume that the pericyclic transition state exhibits a larger packing coefficient than the acyclic ground state. Therefore the activation volume is expected to be negative. The activation volume of the degenerate Cope rearrangement of 1,shexadiene can be estimated to approximately -10 cm3 rno1-l if the packing coefficient determined for cyclohexene [44] is used as the unknown packing coefficient of the pericyclic transition state.

vw

63.9

63.6

V

1 1 9.4

109.1

A V ' = -0.3

A V =-10.3

All volumes are given in cm3-mol-'. The structural parameters necessary for the calculation of the van der Waals volume for the transition structure (TS) were taken from ab initio calculations [25,102]. The partial molar volume for the TS was calculated from the equation:

V (TS) = Vw (TS) / q (cyclohexene); q = Vw / V = 0.5829 (cyclohexene).

Partial molar volume ( V ) , van der Waals volume (Vw) and the volumes o f activation and reaction ( A V # , A V ) of the Cope rearrangement of 1,s-hexadiene. Scheme 2.22.

In fact, negative activation volumes of the expected size (AV# = -7 to -13 cm3 mol-') were found for several Cope rearrangements and related Claisen rearrangements (Scheme 2.23) [ 104-1081. The only exception is the activation volume of the Claisen rearrangement of the neat parent allylvinylether (Scheme 2.23. entry (4))which was determined to be AV# = -18 cm3 mol (1051. A new measurement of the pressure-dependent kinetics of this rearrangement in solution led to an activation volume of AV# = -10.3 cm3 mol-' [l09], which is of similar size to those determined for the other Cope and Claisen rearrangements. With the concept of cyclic interaction, introduced here, we can understand why the degenerate Cope rearrangement in bullvalene, investigated by Merbach, le Noble and coworkers [ 1101 with pressure- and temperature-dependent N M R spectroscopy, showed no significant pressure effect (AV+ = -0.5 cm3 mol-') (Scheme 2.23, entry (11)).As a result of the rigid bullvalene skeleton no such cyclic interaction appears in the transition state.

2.3 Pericyclic Rearrangements

'"*

[crn3.rno~-']

Ref.

4.7

[lo51

-9.7

[lo61

HO

(3)

6"

160'c 130.4'C, neat:

-18.0

128.9'C, nonane:

-10.3

:tip l ; , ; ; sT

Ph

cis, trans

-

#

meso

,-&+ Ph T S (boat)

Scheme 2.23.

-8.8

Ph

lrans. lrans

Volumes of activation (in cm3 mol ') o f Cope and Claisen rearrangements.

The utility of high pressure in the elucidation of reaction mechanisms can be also demonstrated by the example of the racemization and diastereomerization in 1,3,4,6-tetraphenyl-1,5-hexadiene (Scheme 2.24) indicating that a pericyclic Cope rearrangement competes here with a dissociative process involving free-radical intermediates [ 1111. Optically active tetraphenylhexadiene undergoes a facile racemization at temperatures just above room temperature. At 90 "C rucemic tetraphenylhexadiene shows a mutual interconversion to the meso diastereomer. Whereas the racemization may be the result of a pericyclic Cope rearrangement involving a chair-like transition state, the mutual diastereomerization cannot be explained by one or a sequence of Cope rearrangements involving chair- or boat-like transition states. The effect of pressure allowed an unambigous mechanistic conclusion. The observation, that the racemization is accelerated by pressure and, thus, exhibits a negative volume of activation, is good evidence for a pericyclic Cope mechanism in this case. The finding that the diastereomerization is retarded by pressure, ex-

I

73

74

I

of Pressure o n Organic Reactions: Basic Principles and Mechanistic Applications

2 The E'ect

Ph

-9.1

[I071

-12.8

[lo81

-13.4

[lo71

-11.3

[112]

-0.5

[110]

Ph

rac.

cis

(11)

Scheme 2.23.

(continued)

cludes a pericyclic mechanism or a cyclization by one-bond closure in the ratedetermining step and suggests a homolytic bond cleavage in the rate-determining step leading to the 1,3-diphenylallyl radicals as intermediates which can recombine to the two observed diastereomers. 2.3.2

Electrocyclic Rearrangements

The electrocyclic ring opening of heavily substituted cyclobutene derivatives which was investigated by Plieninger et al. [113],shows negative volumes of activation of

2.3 Pericyclic Rearrangements

I

75

racemization

Ph-Ph

optically active

90'~-

P h A P q-

diastereomerization

-phc Ph

Ph

Ph

meso

racernization: A V * = -7.4 cm3-mol-'

meso-,

rac:

A V " = +13.5cm3.rnol-'

rac + meso: A V * = +I 1.5 crn3.rno~-' Activation volumes of the racemization of optically active 1,3,4,6-tetraphenyl-l.S-hexadiene and the mutual interconversion o f the meso into the racemic diasteromer. Scheme 2.24.

different size depending on the substitution pattern, contrary to the expectation of positive activation volumes resulting from the ring opening. This result indicates that, for example, steric effects contribute substantially to the observed negative activation volumes, overcompensating for the increase in volume expected from ring opening. Clear-cut examples showing both effects are the isomerization of parent [114] and hexamethyl-Dewar benzene [114. 1151 leading to benzene and hexamethylbenzene, respectively (Scheme 2.25, entry (1)).The isomerization of the parent Dewar benzene is retarded by pressure (20 "C: AVf = t 5 cm3 mol-') whereas that of the hexamethyl derivative is accelerated by pressure (140 "C: AVf = -12 cm3 mol-', AV = -22 cm3 mol-'). Evidently, the steric crowding of the six methyl groups in the planar hexamethyl benzene is greater than that in the non-planar hexamethyl Dewar benzene overcompensating for the volumeincreasing effect of ring opening. In the ring opening of 2,3,5-tricyano Dewar benzene leading to 1,2,4-tricyanobenzene [ 591, the two effects obviously compensate each other so that this rearrangement is almost pressure-independent (51.3 "C: AV# zz 0 cm3 mol-'). In the transition state of the electrocyclization of (Z)-1,3,5-hexatriene to 1,3cyclohexadiene (Scheme 2.25, entry (2)), a new six-membered ring develops analogous to that in the Cope rearrangement [ 771. The electrocyclization is accelerated by pressure, showing a negative activation volume of AV# = -10.8 cm3 mol-' which is similar to those of the Cope rearrangements. From the volume data listed in Scheme 2.25 entry (2), the packing coefficient of the transition state is calculated to be approximately equal to that of the cyclic product and differs significantly from that of the acyclic reactant. This result again provides good evidence for the assumption that the packing coefficients of pericyclic transition states resemble those of the corresponding cyclic ground states.

76

I

2 The Efect of Pressure on Organic Reactions: Basic Principles and Mechanistic Applications

2.24 A AV*=-10.8 AV =-14.8 Vw:

61.2

58.6

57.0

V: 118.7

107.9

103.9

: 0.516

0.543

0.549

11

Electrocyclic rearrangements of substituted Dewar benzene derivatives and (Z)-1,3,5-hexatriene. All volumes are given in c m 3 moI-’. Scheme 2.25.

2.3.3

Intramolecular Diels-Alder Reactions

In intramolecular Diels-Alder reactions, two new rings are formed. There are examples of relatively large pressure-induced accelerations comparable to the acceleration observed in intermolecular Diels-Alder reactions which can be exploited for preparative purposes [11G, 1171. All the systems studied hitherto contain polar groups and are, therefore, not very suitable for the analysis of the relationship between pressure effects and ring formation. The activation volume of the intramolecular Diels-Alder reaction appears to depend heavily on the type of solvent used as shown in Scheme 2.26, which indicates that effects other than ring formation, for example electrostriction, may also affect the size of the activation volume (see Chapter 9). In order to analyze the effect of ring size and ring number on the volume changes, the activation and reaction volumes of intramolecular Diels-Alder reactions in the non-planar pure hydrocarbon systems (E)-1,3,8-nonatriene (42) [ 1041 and (E)-1,3,9-decatriene (45),[77] were determined (Table 2.8). The packing coefficients g of the transition states are calculated to be equal to or even larger than those of the corresponding bicydic products and are comparable to the packing coefficients calculated for the electrocyclic ring closure of (Z)-lJ,S-hexatriene leading to 1,3-cyclohexadiene(Scheme 2.25, entry (2)). The absolute values of the acti-

2.3 Pericyclic Rearrangements

I

77

I

meta Ortho A V t = - 3 3 . 1 ; A V = - 3 0 (CHzClz)

A V * = - 1 3 . 4 ; A V = - 1 5 (CH3CN)

meta A V * = -32.1 (CHzC12)

AVt=-12.1

(CHFN)

Pressure dependence o f intramolecular DielsAlder reactions (AV", A V in cm3 rnol-'). Scheme 2.26.

vation volumes of intramolecular Diels-Alder reactions are approximately twice as large or even larger than those determined for the Cope rearrangements or the electrocyclization of 1,3,5-hexatriene to 1,3-cyclohexadiene (Scheme 2.25). From this it was extrapolated that each additional five- or six-membered ring formed in the rate-determining step of a pericyclic reaction contributes about -10 to -15 cm3 mol-' to its activation volume. A particularly instructive example is the thermolysis of (Z)-1,3,8-nonatriene(48) in which an intramolecular Diels-Alder reaction competes with a sigmatropic 1,shydrogen shift (Scheme 2.27) [ 1041. The use of high pressure leads to a significant acceleration of the overall reaction and allows a reversal of the selectivity. At 150 "C and 1 bar the 1,S-hydrogen shift passing through a monocyclic transition state is the preferred mechanism. At 7.7 kbar the intramolecular Diels-Alder reaction is the favored process, evidently due to its bicyclic transition state. The difference in the activation volumes of the two processes extrapolated from the pressure dependence of the product ratio (AAV# 5 -10 cm3 mol-') is comparable to that observed for pericyclic rearrangements involving monocyclic and bicyclic transition states. 2.3.4 Ene Reactions

With the concept introduced in the previous section, the pressure effects on Alder ene reactions related to sigmatropic 1,s-H shift, can also bc explained. These reactions show a powerful pressure-induced acceleration in rate. In many cases (Table

78 Tab. 2.8.

I

2 The Effect of Pressure on Organic Reactions: Basic Principles and Mechanistic Applications

Volume data of the intramolecular Diels-Alder reactions of nonatriene (E)-42 and decatriene (E)-45.

Reaction

AV

Fy]+Jj) 8

-24.8

AV

-

32.0

0

0.78

,

cis- 43' 87.0 156.1 0.557

153.2-C n-hexanc

*

cis- 44 83.3 148.9 0.559

(€)- 42

vw

v

91.6 180.9 0.506 trans- 43'

87.0 156.1 0.557

-

i!;l

0.87

-45.4

0.83

-37.4

0.94

trans- 44

83.4 152.4 0.547

:4 0

4 r- '$7\'

-28.5

C D '

-37.6

-

172.5 'CI n-heptane

cis- 46' 97.7 164.4 0.594

cis- 47 93.8 156.7 0.599

(€)- 45

Vw 102.8 v 202.0 q 0.509 trans- 46'

97.7 167.0 0.585

trans- 47

93.8 164.6 0.570

All volumes are given in cm3 mol-' and related to the reaction temperatures at 153.2 and 172.5 "C, respectively, 7 = Vw/V is the packing coefficient and 0 = AVz/AV, the ratio of activation volume to reaction volume.

2.3 Pericyclic Rearrangements

I

79

150.2 ‘C, 24 h, n-Pentane:

1 bar: 80.2 % (2)-48, 13.7 % 49, 6.1 % cis-50 7.7 kbar: 5.5 % (Z)-48, 18.2 % 49, 76.4 % cis-50

M V ’ = A V F (2-48 + cis-50) - A V * = (2-48 + 49) 5 -10 crn3.rnoI-’ Scheme 2.27.

Pressure dependence o f the therrnolysis of (2)-48.

2.9, entries (1) and (2)) the absolute values of activation volumes were found to be larger than those of the corresponding reaction volumes and, hence, the ratio (AVf : AV) is larger than unity (0> 1) comparable to the Diels-Alder reactions listed in Table 2.4. This result was taken as an evidence of the pericyclic nature of the ene reactions. The van der Waals volumes of reactants, transition structure and product were calculated for the prototype of the ene reaction between propene and ethene (Scheme 2.28). The structural parameters necessary for this calculation were taken in the case of reactants and products from force-field calculations (MM2) and in the case of the transition structure from ab initio calculations [24, 251. In this case the van der Waals volume of the transition structure was calculated to be smaller than that of the product [ 1211 and, hence, the ratio (V$ : Vw) larger than unity. With the reasonable assumption that the packing coefficient of the transition structure is, at least equal to, but probably larger than that of the product, one can predict that the ratio between activation and reaction volume (AVf : AV) is also larger than unity. In the case of ene reactions between cycloalkene or alkenes and diethyl azodicarboxylate (DEAD) (e.g. Table 2.9, entry (3)), the ratio (AVz : AV) was found to be smaller than unity (0< 1).This result can be considered as an indication of a stepwise process in which a pericyclic transition state is not involved. Stephenson and Mattern, however, observed that the ratios SIR and kH/kD in the ene reaction with DEAD as enophile shown in Table 2.9 entry (4),were roughly equal, which was explained in terms of a concerted ene reaction. To explain this discrepancy Jenner and coworkers proposed a mechanism comparable to the formal ene reactions of alkenes with singlet oxygen or triazolindiones as enophiles forming in the first step three-membered rings between the alkenes and one center of the enophile prior to hydrogen transfer. To clarify the mechanism of the ene reaction with DEAD, it

80

I

2 The Efect of Pressure on Organic Reactions: Basic Principles and Mechanistic Applications Tab. 2.9.

Volume data o f selected ene reactions

n-Pro & -28.4

-27.0

1.05 118

-35.0 -31.3

-29.4

1.06

-52.0 -39.6

-35.4

1.12

-39.0

(1) n-Pr

110’C

E

(2) 52.2 ‘C

96,4 ‘c,

E

E’ E’

E’

E

S

SIR N

kH/kD N

120

U

R

3

cm3 mol-I; AV? determined from the pressure dependence of the rate constant at temperature T; AV; determined from the temperature of-the activation volumes or extrapolated by using the El‘yanov equation AVZ : AV{/[l 7 4.43 lo-’ K-’(T - 25 “C); [ZO]. b0= AV; ; AV,,.

~~~

Vwa’

35.1

25.6

54.6

55.8

-6.1

-5.3

1.15

Val

76.2

59.9

94.105

108.6

-(42-31)

-27.5

1.5- 1.13

qc)

0.4606

0.4273

0.58 - 0.52

0.5193

a In cm3 mol-’; = AV#/AV; ‘ 7 = Vw/V, for the calculation o f the partial molar volume of the transition state ( V # = V$/q#); the unknown packing coefficient 7 # was assumed to be within the range of the ene product and cyclohexane. van der Waals volumes of reactants, transition structure [24, 251 and product calculated for the prototype of the ene reaction between propene and ethene. Scheme 2.28.

2.3 Pericyclic Rearrangements

would be desirable to study the effect of pressure on the rate of the reaction studied by Stephenson and Mattern [ 1201. 2.3.5 The Relationship Between Activation or Reaction Volume and Ring Size

The first evidence for the relationship between ring size and volume data came from the observation, that the ring enlargement of cis-1,2-divinylcyclobutaneto 1,5-cyclooctadiene (AV = - 12.8 cm3 mol-l) and truns-l,2-divinylcyclobutaneto 4-vinylcyclohexene and 1,5-cyclooctadiene (AV = -9.6 and -17.4 cm3 mol-l, respectively) showed highly negative reaction volumes [ 1071. This means that the ring enlargement from a four- to a six- and finally eight-membered ring is accompanied by a substantial contraction in volume. The volumes of reaction calculated for the hypothetical cyclizations of 1-alkenes from their partial volumes (AV = V(cycloa1kane) V(1-alkene)) confirm this trend (Table 2.10) 1771. They decrease continuously from the formation of the three-membered ring (AV = -5.5 cm3 mol-') up to the formation of the 10-membered ring (AV = -32.3 cm3 mol-') and then, seem to be constant for the larger rings, whereas the van der Waals volumes of reaction (AVw) are approximately equal, with the exceptions of the formation of cyclopropane, cyclobutane and cyclopentane, and cannot explain the dramatic decrease found for the volumes of reaction. Therefore, this ring sizedependent dccrease in volume observed for the cyclizations of the 1-alkenes to the cycloalkanes results from the different packing of the cyclic and open-chained compounds rather than from the changes in their intrinsic molecular volumes. A simple explanation may come from the assumption that the empty space between the single molecules, which can be attributed to the so-called void volume and expansion volume required for thermally-induced motion and collision of the molecules in the liquid state as already pointed out by Asano and le Noble in 1973 [ 51, is reduced by the ring closure of an open chain largely due to the restriction of rotational degrees of freedom during the cyclization. Apparently, the larger the ring, the more degrees of freedom are restricted resulting in the observed ring sizedependent volume contraction. An upper limit of this effect seems to be the formation of cyclodecane. The increasing conformational flexibility in rings larger than CloHzo obviously requires a larger volume, which compensates the volume contracting effect of ring-closure so that the volume of reaction observed for the formation of these larger rings remains constant. It is interesting to note that the AV-values do not correlate with any other thermodynamic parameter such as enthalpy, entropy, or Gibbs enthalpy of reaction included in Table 2.10 for the formation of cyclopropane to cyclooctane. From these parameters the entropy of reaction should reflect best the restriction of the degrees of freedom as is assumed to occur in the explanation of volume contractions. The entropy of reaction decreases from the formation of cyclopropane to that of cyclohexane, but increases again for the formation of the larger rings, cycloheptane and cyclooctane, which can be explained with the increasing conformational flexibility of rings larger than cyclohexane. A better but not a linear correlation is found between the entropies of for~

I

81

2 The Effect of Pressure on Organic Reactions: Basic Principles and Mechanistic Applications Tab. 2.10. Volume of reaction, AV, van der Waals volumes of reaction AVw, enthalpies, entropies, and Cibbs enthalpy of reaction calculated for the hypothetical cyclizations o f 1-alkenes t o cycloalkanes by means of the corresponding thermodynamic parameters [76].

AVwa

AVRE

ASc

ACb

-1.7

-5.5

7.86

-7.0

9.95

-2.5

6.6

6.43

-10.3

9.50

-13.1

-9.56

-0

-3.8

-14.7

-13.46

-0

-4.4

-16.5

-19.47

-4.7

-21.2

-13.41

-19.6

-7.57

-4.9

-25.6

-9.88

-18.8

-4.28

-4.7

-30.9

-4.6

-32.3

-4.7

-32.8

-4.7

-32.3

-4.6

~-27.6

-0 --u A

"rn3 molt'. V(n-alkene) calculated by the use o f Exner increments [43]. V (cycloalkane) determined from density measurements in n.

hexane. bkcal mol-I. Ccalmolt' Ktl.

AHb

-21.0

-13.21

2.3 Pericyclic Rearrangements

I

83

-w -0

5

''..S4)

18-..

.................. ........................................................ ~

....*..

~-..(5) :: -...

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

12:

.................................................. 0 : L .... (6)

..,...

p

...

LC 4

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

,4:

Y

..-

(7)...............

-*.-....(8) *-...

10 1

,

~

l

l

l

~

l

l

l

[

.

I

,

(

.

,

I

4

mation of the cycloalkanes related to each CH2 group (ASrO(CH2)= AS;(CH,),/n) and the packing coefficients, ~(CHZ),,, which are identical to those related to each CH2 group (Figure 2.1) [77].According to the non-linear correlation the entropy parameter responds to conformational flexibility in medium-sized rings at an earlier state than the volume parameter. In the homologous sequence of n-alkanes, however, the entropy of formation per CH2 group (ASrO(CH2)= 9.5 cal mol-' K-') as well as the packing coefficient per CH2 group (q(CH2) = Vw(CH,)/V(CH2) = 10.4/16.2 = 0.64) remains constant with the increasing number o f atoms in the chain. Provided, that the activation volumes depend similarly on the ring size, the formation of larger rings should be dramatically accelerated by pressure. The intramolecular Diels-Alder reactions of (E)-1,3,8-nonatriene (42)and (E)-1,3,9decatriene (45), in which either a new five- and six-membered ring or two new sixmembered rings are formed, seems to be the first example of evidence for this assumption (Table 2.8). Furthermore, this ring-size effect explains why the activation volume of the formation of a three-membered ring in cheletropic reactions of carbenes with alkenes (Scheme 2.21) and of five-membered rings in 1,3-dipolar cycloadditions, are substantially less negative than those in the formation of sixmembered rings in Diels-Alder reactions (for example, the cheletropic addition of fluorophenylcarbene to tetramethylethylene: AVz = -17 cm3 mol-1 [98], the 1,3dipolar cycloaddition of diphenyldiazomethane to ADM: AVf = -23.2 cm3 rnol-l, AV = -26.8 cm3 mo1-l [122], and the Diels-Alder reaction o f 2,3-dimethylbutadiene to ADM: AVz = -34.1 cm3 mol-'; AV = -38.8 cm3 mol-1 [17] (ADM, methyl acetylene-dicarboxylate).

84

I

2 The E’ect

of Pressure on Organic Reactions: Basic Principles and Mechanistic Applications

2.4

Free-Radical Reactions 2.4.1

Homolytic Bond Dissociations

A volume expansion is expected for homolytic bond dissociations as already pointed out in the Introduction. This expectation has been confirmed for several homolytic bond cleavages showing positive activation volumes near AVf = +10 cm3 mol-’ [123]. The analysis of the pressure effect on the cleavage of azo compounds is however, complicated by the possibility of one- and two-bond scission processes [ 1241. The benzylic and benzhydrylic 1,Cshifts in the substituted pyridiminiumoxides (Scheme 2.29, entry (1))[ 1251 illustrate the utility of high pressure for the distinction between a pericyclic and dissociative mechanism comparable to the rearrangement of 1,3,4,G-tetraphenyl-l,S-hexadiene which has already

r,

meso+rac:AVf=+(10.7f4.8)

rac -+ meso : AVf = + (8.5 & 3.4)

AV‘ = + (37.5 zk 0.4) A H f = (44.7 i 1.9) kcalmol-’ ; A S * = (33.7 & 4.8) kcalmol-’

The effect of pressure on homolytic bond dissociations (all volumes in crn3 mol-’). Scheme 2.29.

2.4 Free-Radical Reactions

I

85

been referred to. The negative activation volume determined for the benzylic shift is good evidence for a pericyclic rearrangement whereas the positive activation volume determined for the benzhydrylic shift is in accord with the C-0 bond cleavage in the rate-determining step. The large difference between activation volumes observed for rearrangements proceeding via homolytic bond cleavage and recombination of the resulting free-radical intermediates (AVf = +6 to +13 cm3 mol-') on the one hand, and for the thiophenol-trapped dissociation of 3,4diethyl-3,4-diphenylhexane(AVz = +35.7 cm3 mol-') on the other, is notable and may be indicative of the reactions of caged or solvent-separated radical pairs, respectively [ 1261. 2.4.2

Quinone Oxidations (Hydrogen Transfer Reactions)

The oxidation of hydroarenes to arenes by quinones such as 2,3-dichlor0-5,6dicyano-1,4-quinone (DDQ) is frequently used for the synthesis of aromatic compounds. Brower et al. have already shown that the dehydrogentaion 1,4-cyclohexadiene to benzene [ 1281 or tetraline to naphthalene [ 1291 by thymoquinone is accelerated by pressure giving a negative volume of activation ((AVz = -33 (75 "C) and -28 (175 "C) cm3 mol-', respectively). A similar effect of pressure has been observed for the oxidation of leuco crystal violet with p-chloranil ((AV+ = -25 cm3 mol (21 "C) [130]. The pressure-dependent kinetic isotope effect of this reaction (29 "C: kH/kD = 11.5 (1 bar) and 8.2 (1.5 kbar)) indicates that hydrogen transfer occurs in the rate-determining step. The large k H / k D value at 1 bar and it pressure dependence was attributed to a quantum mechanical tunneling. Four mechanisms have been proposed for the quinone oxidation of hydroarenes [131]: (1) hydrogen atom transfer leading to a pair of free radicals in the ratedetermining step followed by fast subsequent reactions such as disproportionation or single-electron transfer (SET) finally producing the observed arene and hydroquinone; (2) direct hydride transfer leading to a pair of ions from which the observed products can be formed by proton transfer; ( 3 ) single-electron transfer followed by proton transfer producing the same radicals as direct hydrogen atom transfer; and (4) pericyclic hydrogen transfer which is limited to systems where vicinal C-H bonds are to be cleaved. More recent investigations by Ruchardt et al. [131] provided good evidence that the DDQ oxidation occurs via atom transfer (Scheme 2.30, mechanism (l)), comparable to other uncatalyzed transfer hydrogenations. Mechanism (1)as suggested by Ruchardt is further supported by the pressure dependence of the DDQ oxidation of various hydroarenes (Table 2.11) [132]. The finding, that the activation volumes are not significantly dependent on the solvent polarity, excludes the possibility of direct hydride transfer via mechanism (2). In this case a strong effect of electrostriction is expected due to the production of charged species in the ratedetermining step. Accordingly, the activation volume of the same reaction should be more negative in the less polar solvent (dielectric constant: E = 4.5 (MTBE), 6.03 (AcOEt), 35.9 (MeCN) [133]). However the opposite is found in experimental data

86

I

2 The Effect of Pressure on Organic Reactions: Basic Principles and Mechanistic Applications

0.

OH

"'$f

+

0

R'

R'

+ OH

00

00

R" :2: C r ; " l

R'

0

Scheme 2.30. Mechanistic alternatives o f quinone dehydrogenations of hydroaromatic compounds. (1) Hydrogen atom

transfer, (2) direct hydride transfer, (3) single electron transfer, and (4) pericyclic hydrogen transfer.

(assuming that any solvent effect is indicated in these data). Pericyclic hydrogen transfer (mechanism (4)) can only occur in formal 1,3-dienes such as 1,2-dihydronaphthalene or 9,10-dihydrophenanthreneand should show a significantly more negative activation volume because of the pericyclic transition state than the hydrogen atom transfer of 1,4-dihydronaphthalene or 9,10-dihydroanthracene proceeding through acyclic transition states. But this is not the case which indicates that all reactions shown in Table 2.11 proceed with the same mechanism via hydrogen atom transfer. Further mechanistic support comes from the primary kinetic isotope effect observed for the DDQ oxidation of 9,lO-dihydroanthracene. The strong pressure dependence of the isotope effect may be attributed to a tunneling component of hydrogen transfer comparable to that observed by Isaacs et al. for the p-chloranil oxidation of leuco crystal violet [ 1301. The strongly pH-dependent activation volumes of the quinone oxidations of ascorbic acid (vitamine C) in water or methanol studied by Isaacs and van Eldik [134] are significantly less negative than those found for the oxidation of hydroarenes indicating different mechanisms. The results were explained by a rapid and reversible single electron transfer from the deprotonated anion of ascorbic acid to the quinone followed by a hydrogen atom transfer (see Scheme 2.31).

2.4 Free-Radical Reactions 187

The activation volumes in cm3 molk of the oxidation o f hydroarenes to the corresponding arenes by 2,3-dichloro-5,6-dicyano-l.4-quinone (DDQ) [132].

Tab. 2.11.

Hydroarene

T ("C) A V # (MTBE)"

1,4-Cyclohexadiene 25.1 9,lO-Dihydroanthracene 25.1 9~9,10,10-Tetradeutero-9,10-dihydroanthracene 25.1 9,9-Dimethyl-9,10-dihydr~anthracene~ 39.9 9,lO-Dihydrophenanthrene 39.9 24.9 1,4-Dihydronaphthalene 39.9 1,2-Dihydronaphthalene 64.9 Tetralin'

-24.4 -25.9 -35.7' -20.0 -25.1 -24.8 -25.3

-

A V # (MeCN/AcOEt)b

-29.5 -26.9 -

-22.9 -29.4 -28.9 -28.4 -26.7

Methyl-t-butylether. "acetomtnle and ethylacetate (1 : 1). 'kH/kD 10.8 (1bar) and 5.0 ( 3 kbar). the product is 10,1O-dimethyl-9-anthrone. ethe product is 1,2-dihydronaphthalene. a

0

OH

n

OH

R' = R2 = H : AV* = -20 (unbuffered), -16 (pH = 2), -4 (pH = 4.87) R' = CI, R2 = CN : AV' = -16 (unbuffered)

pH and pressure dependence of the oxidation of ascorbic acid (vitamine C) with quinones. Scheme 2.31.

2.4.3

Free RadicaI Cyclizations

f i e effect of pressure on the competing reactions of the free radicals 5-hexenyl and 6-heptenyl (Scheme 2.32, n = 1 and 2, respectively) were investigated in order to determine whether the cydization of free radicals showed a similar ring sizeiependence at high pressure as the cyclizations described in Sect. 2.3.5. Although the overall reaction of 5-hexenyl and 6-heptenyl is retarded by raising the pressure, :he ratio of the cyclization products (exo-trig and endo-trig) is not significantly pressure-dependent [ 1351. That means that the difference between the activation Jolumes of these cyclization reactions is nearly zero, showing no ring size depen-

88

I

2 The Effect of Pressure on Organic Reactions: Basic Principles and Mechanistic Applications

dence. This finding can be explained by the assumption that in both transition states the rotational degrees of freedom of all former C-C single bonds are restricted and, hence, the expansion volumes, which were postulated to be important for the ring-size effect, do not differ from each other. I t is noteworthy that the pressure effect on the ratio between the cyclization products and the hydrogen atom transfer product ( ( k l k z ) / k 3 ) is also small. Evidently, the bimolecular hydrogen atom transfer has a similar activation volume as the monomolecular cyclizations. A11 volumes are expected to be highly negative.

Br

+

Bu3SnH AlBN

+v

Chlorobenzene I Benzene

exotrig

endotrig

i

I

Q - Q + k2) I k3

P LW

ki I kz

n = 1:

1 1000 5000

91.8 12.2 98.1 11.9 91.9 12.1

85.3 I 14.1 80.41 19.6 11.8 122.2

n=2:

1 1000 5000

82.1 I 11.3 83.41 16.6 80.1 I 19.3

20.2 119.8 16.9 183.1 16.0 I 84.0

(ki

The effect o f pressure on the cyclization of 5-hexenyl and 6-hepteny1, respectively. Transition structures of the endo-trig and exo-trig cyclization. Scheme 2.32.

2.5 Ionic Reactions

Reactions, in which ionic species are generated, show a large volume contraction and, hence a powerful pressure-induced acceleration which can be exploited for synthetic purposes. Among the nucleophilic substitutions and additions (such as

2.5 lonic Reactions

the aliphatic and aromatic SN reactions [ 1361, peptide formation (from esters) [ 1371, or the addition of nucleophiles to electron-deficient alkenes [ 1381 or oxiranes [ 139]),the Menschutltin-type S N reactions ~ are particularly worth mentioning. It is well established that the solvent-dependent activation volumes of the alkylation of pyridine derivatives are highly negative ( A V f = -20 to -50 cm3 mol-l) [GI. Stoddart et a]. used this high-pressure reaction to construct several catenanes [ 1401 and rotaxanes [ 1411 which are of interest as supramolecular devices. The [ 3lcatenanes (Scheme 2.33) can be synthesized in one step at high pressure (25 "C, 12 kbar, 5

1

1

l.DMF/12kbar/ ca. 20°C I 5 d 2. NHaPFe / H20

r\ r

0

?r? 0

0

1

1 0

0

4 PFC

0

0

iJ i i i i ?

Scheme 2.33.

0

0

0

0

Synthesis of catenanes by pressure-induced alkylation of pyridines

I

89

90

I

2 The Effect of Pressure on Organic Reactions: Basic Principles and Mechanistic Applications

days) in reasonable yields of 31-33 %, whereas the yield of those catenancs in the reaction at 1 bar is only ca. 1 % and below after 9 weeks [142]. The rotaxanes shown in Scheme 2.34 were only obtained in the high-pressure reaction [141].

",l '. .,, . .

I,

I)DMF/lZkbar/20'C 2) NH4PF4/ H 2 0

+

' ~

u

'd'

t '0'

o-t

+

8 PFS

8 PFC

Scheme 2.34.

Synthesis of rotaxanes by pressure-induced alkylation of pyridines.

2.6

Concluding Remarks

It has been demonstrated that cyclizations are accompanied by a contraction of volume. The magnitude of this contraction depends on the number and size of the rings involved and is a result of the different packing coefficients of cyclic and acyclic structures rather than of the changes in their intrinsic molecular volumes during the cyclization. This effect is most important in cycloadditions and pericyclic rearrangements and explains the pressure-induced acceleration and the resultant negative activation volumes of these reactions. In reactions in which charged species are generated, the effect of electrostriction also leads to a substantial contraction of volume and, hence, to a rate enhancement at high pressure. The utility of high pressure with respect to these two effects has been described for the elucidation of reaction mechanisms and for organic synthesis.

References 191

Acknowledgments

We are grateful to the Deutsche Forschungsgemeinschaft and the Fonds der Chemischen Industrie for financial support of our work. F.-G. K. thanks the coworkers mentioned in the references for their committed and skillful collaboration, and Ms I. Reiter and Ms H. Wo11 for their skilled assistance with the preparation of the manuscript, the tables, and schemes.

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10 (a) R.

11

12 13 14 15

16 17

18

19 20

21 22 23 24

92

I

2 The Efect of Pressure on Organic Reactions: Basic Principles and Mechanistic Applications 25

26 27

28

29

30

31 32

33

34 35 36

37

38 39

K. N. I j O U K , Y. LI, I. D. EVANSECK, Angew. Chem. Int. Ed. Engl. 1992, 31, 682. C. A. STEWARD JR.,J. Am. Chem. SOL. 1972. 94, 635. F.-G. K L ~ R N EB. R ,M. J . DOGAN,0. ERMER,W. v. E. DOERING,M. P. COHEN,Angew. Chem. Int. Ed. Engl. 1986, 25. 110. U. DEITERS,F . C . K L ~ R N EB. R, KRAWCZYK, V. RUSTER,J. Am. Chem. SOL.1994. 116, 7646. (a) W. R. ROTH, S. B. P., Chem. Ber. 1981, 114, 3741; (b) M. BARTMANN, PhD Thesis, Ruhr-Universitat Bochum, 1980. J. BARAN,H. MAYR,V. RUSTER,F . 4 . KLXRNER, J. Org. Chem. 1989, 54, 5016. C. J. LITTLE,]. Am. Chem. SOC.1965, 87, 4020. V. RUSTER,Diploma Thesis, RuhrUniversitat Bochum, 1987; PhD Thesis, Ruhr-Universitat Bochum, 1991. (a) P. D. BARTLETT, K. E. SCHMELLER, J. Am. Chem. SOC.1968, 90, 6077; (b) J. S. SWENTON,P. D. BARTLE~T, J. Am. Chem. SOC.1968, 90, 2056. D. KAUFMANN, A. DE MEITERE, Angew. Chem. Int. Ed. Engl. 1973, 12, 159. B. M. I. DOGAN,P h D Thesis, RuhrUniversitat Bochum, 1984. M. R. D E CAMP;R. H. LEVIN,M. 1. JONES,Tetrahedron Lett. 1974, 15, 3575. (a) H . E. SIMMONS,J.Am. Chem. SOC. 1961, 83, 1657; (b) H. D. MARTIN,S. KACABU, H. J. SHIWEK,Tetrahedron Lett. 1975, 41, 3311. w. 7. LE NOBLE,R. MUKTHTAR,]. Am. Chem. SOC.1974, 96, 6191. The surprisingly small activation volume found for the formation of the very minor [4 41 cyclodimer 16 in the 1,3-buta&ene dimerization seems to be inconsistent with a stepwise mechanism. The small ratio 0 = AVvz/AV = 0.54 which is substantially smaller than that of the formation of 1 4 , O = 0.79, and almost equal to that of the formation of 15, 0 = 0.59, may indicate that 13 is formed via a stepwise [4 + 41 cycloaddition

+

passing through a (Z,Z)-configured diradical intermediate. 40 F.-G. K L ~ R N EV. R , RUSTER,B. ZIMNY, D. HOCHSTRATE. High Press. Res. 1991, 7, 133. 41 (a) L. N . KOWA,D. SCHWARZER, J. TROE,J. SCHROEDER, J. Chem. Phys. 1992, 97,4827; (b) M. A. FIRESTONE, M. VITALE,J. Org. Chem. 1981, 46, 2160. 42 PCMODEL, Serena Software, 1992. 43 0. EXNER,in Organic High Pressure Chemistry, W. J. LE NOBLF(Ed.), Elsevier, Amsterdam, 1988, 19-49. 44 Y. YOSHIMURA, J. OSUCI,M. NAKAHARA, Bull. Chem. SOC.Jpn. 1983, 56, 680. 45 R. A. FIRESTONE, G. M. SMITH,Chem. Ber. 1989, 122, 1089. 46 G. JENNER, M. PAPADOPOULOS, J. RIMMELIN,J. Org. C k m . 1983, 48, 748. 47 A. GEORGE,N. S. ISAACS,]. Chem. SOC., Perkin Trans. 2 1985, 1845. 48 F.-G. K L ~ R N EV. R , BREITKOPF,Eur. J. Org. Chem. 1999, 2757-2762. 49 R. A. GRIEGER,C. A. E C K E R T , Chem. ~. Soc., Faraday Trans 11970, G6, 2579. 50 F.-G. K L ~ R N E R B., KRAWCZYK, V. RUSTER,U. K. DEITERS,J. Am. Chem. SOC.1994, 116, 7646-7657. 51 J. F. BLAKE, W. L. JORGENSEN, /. Am. Chem. SOC.1991, 113, 7430-7435. 52 F.-G. K I ~ R N E R D., SCHROER,Chem. Ber. 1989, 122, 179. 53 G . JENNER, M. PAPADOPOULOS, Tetrahedron Lett. 1982, 23. 4333. 54 G . J E N N E R , M. PAPADOPOULOS, NouueauJ. de Chimie 1983, 7, 463. 55 v. BREITKOPF, P. BUBENITSCHEK, H. HOPF, P. G. JONES,F.-G. KLXRNER,D. SCHOMBURG, B. WITULSKI,B. ZIMNY, Liebigs Ann. Chem. 1997, 127 and unpublished results. 56 (a) G. I. FRAY,R. G. SAXTON,The Chemistry of Cyclooctatetraene and its Deriuatiues, Cambridge University Press, Cambridge, 1978 (b) P. G. WENTHOLT,D. A. HROVAT,W. T. BORDEN, W. C. LINEBERGER, Science 199G, 272, 1456-1459; (c) K. K. BALDRIDGE, J. S. SIEGEL,J. Am. Chem. SOC.2001, 123, 1755-1759; (d) A. M. MATSUURA, K. KOMATSU, J. Am. Chem.

References 193 SOC.2001, 123, 1768-1769; (e) F.-G. 68 P. R. ASHTON, I. F. STODDART.].Am. K L ~ R N EAngew. R, Chem. Int. Ed. Engl. Chem. SOC.1993, 1 15, 5422-5429. 2001 40, 3977-3981. 69 S. WEGENER, K. MULLEN, 57 F.-G. K L ~ R N E RR. , EHRHARDT. H. Macromolecules 1993, 26, 3037. R. BOESE,D. BLXSER, K. BANDMANN, 70 M. POLLMANN, K. MULLEN,].Am. N. HOUK,B. R. BENO,Chem. Eur.]. Chem. SOC. 1994, 116, 2318. 1999, 5, 2119. 71 R. M. GRAHAM, L. A. PAQUETTE,]. 58 H. HOPF,B. WITULSKI, Pure Appl. Org. Chem. 1995, 60, 5770. Chem. 1993, 65, 47. 72 J. VELKER, J.-P. ROBLIN, A. NEELS, A. 59 V. BREITKOPF,H. HOPF?F.-G. TESUORO. H. STOECKLI-EVANS, F.-G. K L ~ R N E RB. : WITULSKI, B. ZIMNY? K L ~ R N E7.6. R , GEHRKE, R. NEIER, Liebigs Ann. Chem. 1995, 613. Synlett 1999, S l , 925-929. 60 J.-F. LIN, N.KETO, A. MORI,H. 73 G. J E N N E R , High Press. Res. 1996, 15, R. ISOBE,Bull Chem. SOC. 51-57. TAKESHITA, ]pn. 1994, 67, 1507. 74 (a) R. SUSTMANN, Heterocycles 1995, 61 W. ADAM,C. BARNEVELD VAN, J.-S. 40, 1-18; (b) A. PADWA (Ed.), 1,3GEHRKE, F.-G. KLLRNER,J . Chem. SOC., Dipolar Cycloaddition Chemistry, Wiley Perkin Trans. 2 1999, 2723-2728. Interscience, New York, 1984. 62 K. EXNER,D. HOCHSTRATE; M. KELLER, 75 R. HUISGEN, G. MLOSTON, E. F.-G. KLXRNER, H. PRINZBACH, Angew. LANGIIALS,]. Am. Chem. SOC.1986, Chem. Int. Ed. Engl. 1996, 35, 2256108, 6401-6402. 2259. 76 (a) V. M. ZHULIN,Z. G. MAKAROV, M. 63 S. HUNIG,P. I
94

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2 The Effect of Pressure on Organic Reactions: Basic Principles and Mechanistic Applications

W. R. DOLBIER, S . L. WEAVER,].Org. Chem. 1990, 55. 711. 86 (a) B. KRAWCZYK. P h D Thesis, Universitat Essen, 1996: (b) W. v. E. DOERING,J. EKMANIS, K. D. BELFIELD, Am. F.-G. KLXRNER.B. KRAWCZYK,]. Chem. SOC.(in press). 87 1. JOUANNE, H. KELM,R. HUISGEN, ]. Am. Chem. SOC.1979, 101, 151. 88 R. HUISGEN, ACC. Chem. Res. 1977, 10, 117. 89 W. 1. LE NOBLE,R. MUHKTAR,]. Am. Chem. SOC.1975, 97, 5938. 90 R. W. M. ABEN,J. GOUDRIAAN, J. M. M. SMITS,H. W. SCHEEREN, Synthesis 1993, 37. 91 W. J. LE NOBLE,B. A. OJOSIPE,]. Am. Chem. SOC.1975, 97, 5939. 92 H. TAKESHITA, S. SUGIYAMA, T. HATSUI,]. Chem. SOC.,Perkin Trans. 2 1986,1491; S . SUGIYAMA, H.TAKESHITA, Bull. Chem. SOC.Jpn. 1987, 60, 977. 93 The partial molar volumes of tropone, 1,3-butadieneand the [6 + 41 cycloadduct were measured by Dogan [35] to be V = 88.8, 83.1 and 153.2 cm3 mol-', respectively, at 21 "C and extrapolated to be 99.8, 87.9, 154.1 cm3 mol-', respectively, at 60 "C using the values give by Takeshita et al. [92] for the reaction of tropone with 2,3-dimethylbutadiene. 94 H. TAKESHITA, H. NAKASHIMA,S. SUGIYAMA, A. MORI,Bull. Chem. SOC. jpn. 1988, 61, 573. 95 Z. LI, A. MORI, H. TAKESHITA, Y. NAGANO,Chem. Express 1992, 7, 213. 96 A. MORI,Y. NUKII, H. TAKESHITA, T. NOZOE,Heterocycles 1993, 35, 863. 97 R. B. WOODWARD, R. HOFFMANN, Angew. Chem. Int. Ed. Engl. 1969, 8, 781. 98 N. J. TURRO,M. OKAMOTO, I. R. COULD,R. A. Moss, W. LAWRYNOWICZ, L. M. HADEL,J. Am. Chem. SOC.1987, 109,4973. 99 N. S. ISAACS,A. LAILA,~. Phys. Org. Chem. 1994, 7, 178. 100 N. S. ISAACS,G. N. EL-DIN,Synthesis 1989,967; Tetrahedron 1989, 45. 70837092. 101 F.-G. KIXRNER,S. YASLAK, R. DREWES, C. GESENBERG, M. PETER,Liebigs Ann. Chem. 1995, 203-210. 85

102

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105 106

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108 109

K. MOROKUMA, W. T. BORDEN.D. A. HROVAT. J . Am. Chem. SOC. 1988, 110. 4474. (a) D. A. HROVAT,B. R. BENO,H. LANGF, H.-Y. Yoo, K. N. HOUK,W. T. BORDEN,].A m . Chem. SOC.1999, 121. 10529; (b) W. v. E. DOERING,Y. WANG,]. Am. Chem. SOC.1999, 121. 10112-10118; 10967-10975. M. K. DIEDRICH,D. HOCHSTRATE, F.-G. KLXRNER,B. ZIMNY,Angew. Chem. Int. Ed. Engl. 1994, 33, 1079. C. WALLING,J. NAIMAN,]. Am. Chem. SOC.1962, 84, 2628. G. A. STASHINA,E. N. VASIL'VITSKAYA, G. D. GAMELEVICFI, B. S. EL'YANOV, E. P. SEREBRYAKOV, V. M. ZHULIN, Izu. Akad. Nauk SSSR, Ser. Khim. 1986, 329. w. V. E. DOERING,L. BIRLADEANU, K. SARMA,J. H. TELES, F.-G. K L ~ R N E R , j . 4 . GEHRKE, J . Am. Chem. SOC.1994, 116,4289-4297. P. JANSEN,Diploma Thesis, Universitat Essen, 1994. (a) F.-G. KLLRNER,D. MULLER, unpublished results; (b) D. M ~ ~ L L E R . Diploma Thesis, Universitat Essen, 1998. (c) The temperature-dependent kinetic analysis was carried out for this rearrangement in the gas phase between 142 and 173 "C leading to the Arrhenius equation log k = (11.1 0.3) - (29.3 f 0.5) kcal mol-'/RT. In the gas phase the resulting activation enthalpy and entropy, A H f = 28.5 kcal mol-' and ASf = -10.6 cal mol-I K - I , are larger than those in benzene solution (80 "C: A H # = 25.4 kcal mol-' and A S f = -15.9 cal mol-' K-l: J. BURROWS, B. K. CARPENTER, J . Am. Chem. SOC. 1981, 103, 6983). E. M. SCHULMAN, A. E. MERBACH, M. W. I. LE NOBLF. TURIN,R. WEDINGER, ]. Am. Chem. SOC.1983, 105, 3988. W. v. E. DOERING,L. BIRLADEANU, K. SARMA,G . BLASCHKE, U. SCHEIDEMANTEL, R. BOESE,J. BENETBUCHOLZ,F.-G. K L ~ R N E J.-S. R, GEHRKE,B. ZIMNY,H.-G. KORTH,]. Am. Chem. SOC.2000, 122, 193-203. 1 . 3 . GEHRKE,P h D Thesis, Universitat Essen, 1999.

+

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115 116

117 118

119 120 121

(a) R. MUNDLICH.H. PLIENINGER, H. VOGLER,Tetrahedron 1977, 33, 2261; (b) R. MUNDLICH,H. PLIENINGER. Tetrahedron 1978, 34, 887. W. J. LE NOBLE,K. R. BROWER,C. BROWER,C. S., J. Am. Chem. SOC. 1982, 104, 3150. R. MWNDLICH,H. PLIENINGER, Tetrahedron 1976, 32, 2335. (a) L. F. TIETZE,C. Orr, K. GERKE,M. BUBACK.Angm. Chem. Int. Ed. Engl. 1993, 32, 1485; (b) S. JAROSZ,E. Tetrahedron KOZLOWSKA, A. JERZEWSKI, 1997, 31, 10775-10782; (c) Y. ARAKI, T. KONOIKE,]. Org. Chem. 1997, 62, 5299-5309; (d) A. TAHARI,D. UGUEN, Tetrahedron Lett. 1994, 23, 3945-3948; (e) G. GALLEY,M. PATzEL,]. Chem. SOC.~ Perkin Trans. 11996, 2297-2302; ( f ) L. F. TIETZE,A. SCHUFFENHAUER, Eur.]. Org. Chem. 1998, 1629-1637; (9) N. S. ISAACS,P. G. VAN D E R BECKE, /. Chem. SOC.,Perkin Trans. 2 1982, 1205; (h) M. BUBACK,j. ABELN,T. HUBSCH,C. OTT, L. F. TIETLE,Liebigs Ann. 1995, 9; (i) T. HEINER,K. MICHALSKY, K. GERKE,G. KUCHTA,M. BUBACK,A. DE MEIJERE,Synlett 1995, 355; ( 1 ) A. C. BRICKWOOD, M. G. B. DREW,L. M. HARWOOD, T. ISHIKAWA, P. MARAIS,V. MORRISON,].Chem. Soc., Perkin Trans 11999, 913-921; (k) T. HEINER,S. 1. KOZHUSHKOV, K. GERKE,T. HAUMANN, R. BOESE,A. D E MEIJERE, Tetrahedron 1996, 37, 12185-12196; (1) T . BUTZ, J. SAUER: Tetrahedron Asymm.1997, 8, 703714. M. BUBACK,K. GERKE,C. O n , L. F. TIETZE,Chem. Ber. 1994, 127, 2241. G. J E N N E RM. , PAPADOPOULOS, B. S. EL’YANONV, E. M. GONIKBERG,].Org. Chem. 1982, 47,4201. G. J E N N E RR., B E N SALEM, /. Chem. SOC.,Perkin Trans. 2 1989, 1671. L. M. STEPHENSON, D. L. MATTERN, J. Org. Chem. 1976, 41, 3614. Although the new C-C bond is only partially formed in the transition structure, the C-H-C distances are obviously both within the range of van der Waals distances, whereas in the product the non-bonding (=HzC----H-CHj- ) distance is,

122 123

124

125 126 127

128 129 130 131 132 133

according to the most stable geometry, larger than the van dcr Waals distance. G. SWIETON.J. JOUANNE, H. KELM,J. Org. Chem. 1983, 48, 1035. (a) U. B. IMASHEV, V. V. ZORIN,S. M. KALASHNIKOV, S. S. ZLOTSKII,V. M. Z H U L I N D. , L. RAKHMANKULOV, Dokl. Akad. Nauk. S S S R 1978. 242, 140; (b) A. A. LAPSHOVA, G. A. STASHINA,V. V. ZORIN,S. S. ZLOTSKII,V. M. Z H U L I N , D. L. RAKHMANKULDV, Zh. Org. Khim 1980, 16, 1251; (c) M. Y. BOTNIKOV, S. S. ZLOTSKII, V. V. ZORIN,E. K. KRAVETS, V. M. ZHULIN,D. L. RAKHMANKULOV, Izu. Akad. Nauk SSSR. Ser. a i m . 1977, 690; (d) E. V. PASTUSHENKO, M. Y. BOTNIKOV,S. S. ZLOTSKII, v. M. ZHULIN,D. L. RAKHMANKULOV, React. Kinet. Catal. Lett. 1981, 16, 195; (e) M. BUBACK,H . LENDLE,2. Naturforsch. 1979, 34a, 1482; ( f ) Y. KIMURA,Y. YOSHIMURA, M. NAKAHARA, Chem. Lett. 1987, 617. (a) R. C. NEUMAN,C. T. BERGE,G. A. BINEGAR, W. ADAM,Y. NISHIZAWA,]. Org. Chem. 1990, 55,4564; (b) R. C. NEUMAN,G. D. LOCKYER, J. Am. Chem. SOC.1983, 105, 3982; (c) R. C. NEUMAN,M. J. AMRICH,J. Org. Chem. 1980, 45, 4629; (d) V. M. ZHULIN,G. A. STASHINA,E. G. ROZANTSEV, Izu. Akad. Nauk SSSR, Ser. Khim. 1979, 977; (e) Y. OGO: M. KOTIMA,High Temp.-High Press. 1981, 13, 321. W. J. LE NOBLE,M. R. DAKA,1.Am. Chem. SOC.1978, 100, 5961. G. DIERKES,PhD Thesis, Universitat Essen (in preparation). G. KRATT, H.-D. BECKHAUS, C. RUCHARDT,Chem. Ber. 1984, 117, 1748. J. PAJAK,K. R. BROWER,]. Org. Chem. 1985, 50, 2210. K. R. BROWER,].Org. Chem. 1982, 47, 1889. N. S. ISAACS,K. JAVID,E. RANNALA,]. Chem. SOC.,Perkin Trans. 2 1978, 709. C. HOFLER,C. RUCHARDT,Liebigs Ann. Chem. 1996, 183. F. WURCHE,PhD Thesis, Universitat Essen (in preparation). C. REICHARDT, Solvents and Soli>ent E5ects in Organic Chemistry, VCH, Weinheim, 1990.

96

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2 The Effect of Pressure on Organic Reactions: Basic Principles and Mechanistic Applications 134

N.

s. ISSACS, R. VAN ELDIK?/. Chew.

SOC., Perkin Trans. 2 1997, 1465.

C. VEKHAELEN, Diploma Thesis, Universitat Essen, 2001. 136 See e.g. (a) K. MATSUMOTO, S. HASHIMOTO, S. OTANI,]. Chem. Sac. Commun. 1991, 306; (b) T. IBATA, M.-H. SHANG,T. DEMURA,Bull. Chem SOC. Jpn. 1995, 68. 2941; (c) I. BARKPT, M. A. KERR,Tetrahedron Lett. 1999, 40, 2439. 137 (a) F.-G. K L ~ R N EU. R , KALTHOF,J. GANTE./. Prakt. Chem. 1997, 339, 359; (b) T. YAMADA, Y. OMOTE,Y. YAMANKA, T. MIYAZAWA, S. KUWATA, Synthesis 1998. 991-998; (c) T. SHIOIRI,T. IMAEDEA, Y. HAMADA, Heterocycles 1997, 46, 421-442. 138 See e.g. (a) S. PINHEIRO,A. J. GUIGNANT, D. DESMAELE, D'ANGELO,Tetrahedron Asymmetry 135

1992, 3. 1003; (b) G. TENNER, Tetrahedron Lett. 1995, 36, 233. 139 H. KOTSUKI,M. WAKAO,H. HAYAKAWA, T. SHIMANOUCHI, M. SIIITO,/. Org. Chem. 19913, 61, 8915. 140 D. B. AMABILINO, P. R. ASHTON,V. BALZANI,S. E. BOYD,A. CREDI,1. Y. LEE, S. MENZER,1. F. STODDART, M. VFNTURI,D. J. WILLIAMS, J. Am. Chem. SOC.1998. 120. 4295 and 141

142

references cited therein. R. BALLARDINI, V. BALZANI, W. A. E. DELL'ERBA, F. M. DEHAEN, RAYMO.I. F. STODDART, M. VENTURI. Eur. /. Org. Chem. 2000, 591. P. R. ASHTON,S. E. BOYD,C. G. CLAESSENS, R. E. GILLARD, S. MEWZER, J. F. STODDART, M. S. TOILEY, A. J . P. Chem. Eur. /. W ~ I I T ED. , J. WILLIAMS, 1997, 3, 788.

High Pressure Chemistry Synthetic, Mechanistic, and Supercritical Applications

Edited by Rudi van Eldik and Frank-Gerrit Kliirner

0WILEY-VCH Verlag GmbH, 2002

I 3

High-pressure Kinetics and Highly Viscous Media Tsutomu Asano

3.1

High Pressure and Dynamic Solvent Effects

The transition state theory (TST) may be considered to be established in 1941 by publication of a monumental book The Theory of Rate Processes [ 11. In Chapter VIII of the book, the authors discuss solution reactions and conclude “. . . that the ratedetermining step in solution is . . . the formation from the reactants of an activated complex which subsequently decomposes”. Though the authors pointed out the importance of diffusion in bimolecular reactions, they did not consider a possible break down of their two key assumptions, that is, thermal equilibrium between the initial and the transition state and neglecting recrossing, in unimolecular rate processes. The remarkable success of TST in the interpretation of kinetic effects of pressure [2] turned the attention of high-pressure kineticists away from a possible failure of TST and efforts were concentrated on the interpretation of the activation volume AV?’ obtained from pressure dependence of a rate constant k at a constant temperature (Eq. 3.1).

As a result of accumulation of thousands of activation volumes 13-51, high-pressure kinetics is now widely recognized as a powerful tool in the mechanistic investigation of reactions in solution. As long as we remain within the framework of TST however, it is not possible to study the events between the initial and the transition state. In other words, activation parameters, including activation volume, obtained in TST-valid conditions are “static” parameters concerned with the equilibrium constant for the activation step K # . Therefore, if we want to know, for example, whether solvent molecules are rearranged together with the structural transformation of the reactant molecule or the solvation shell rearrangement precedes the chemical transformation, kinetic experiments in which the conditions of TST are invalid have to be undertaken.

97

98

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3 High-pressure Kinetics and Highly Viscous Media

rb

reaction coordinate r

Fig. 3.1. The double-well potential as a function of the reaction coordinate in Kramers’ model. The reactant moves back and forth along the reaction coordinate by Brownian motion and gradually ascends the barrier as shown by the zigzag arrows.

It is surprising that Kramers developed a comprehensive kinetic theory of chemical reactions before the establishment of TST [ 61. He modeled reactions as a movement of a particle caught in a double-well potential over an energy barrier “through the shuttling action of Brownian motion”. Figure 3.1 illustrates his model together with zigzag arrows showing schematically the movement of the particle along the reaction coordinate. The potential around the barrier top is given by

1 V(r) = Eo - -rncoi(r 2

-

rb)

2

(3.4

where rn is the mass of the particle. In this model, chemical transformations are considered to be in concert with thermal fluctuations of solvent molecules and, therefore, only one reaction coordinate was needed. At high solvent viscosities, the model predicts that the rate constant would be inversely proportional to the medium viscosity q (Eq. 3.3).

3.7 High Pressure and Dynamic Solvent Effects

In Eq. (3.3),kTsT is the rate constant expected from TST when the solvent thermal fluctuations are fast enough and the other conditions are the same. High-pressure chemists interested in kinetics were in a good position to measure the viscosity dependence of rate constants, i.e. “dynamic” solvent effects, and to examine the validity of Kramers’ prediction because solvent viscosity of organic liquids increases rapidly with increasing pressure [ 71 and pressures of several hundred McgaPascals (MPa) do not usually result in major mechanistic changes. Unfortunately, however, most of them, including this author, were strongly attracted to activation volume measurements and were satisfied with “naive” analysis of the results as criticized by Troe [ 8 ] . Troe and his coworkers were pioneers in the field of dynamic solvent effect studies and had good reasons for their criticisms. They measured rates of E / Z isomerization of stilbene and 1,4-diphenylbuta-1,3-diene (DPB) at their S1 excited state [9], typical unimolecular rate processes, in gaseous and supercritical fluids as well as in liquids at various pressures and temperatures. The results clearly demonstrated that the rate constant decreased with increasing viscosity in high density media. Similar effects were also observed by other groups. For example, Waldeck [lo, 111 and Hochstrasser [12]studied the photoisomerization of stilbenes in a series of solvents with an identical functional group but with different chain lengths. Fleming and his coworkers (131 as well as Hochstrasser [14], used high pressure as a tool to manipulate the viscosity in their study of stilbene and DPB. There were also important theoretical developments in the 1980s. Grote and Hynes elaborated Kramers’ model by introducing a concept of “frequencydependent friction” [15]. They assumed that friction felt by a reactant during the crossing of an energy barrier decreased with increasing frequency wb of the potential. A fundamentally different model was proposed by Agmon and Hopfield [lG, 171. Their model adopted two independent reaction coordinates, i.e. the chemical coordinate and the medium (solvent) coordinate. The theory was further developed by Sumi and Marcus [18, 191 and also by Basilevsky and Weinberg [20, 211. The difference between the Kramers-Grote-Hynes one-dimensional reaction coordinate (KGH) model and the Agmon-Hopfield two-dimensional reaction coordinate (AH) model can be seen clearly by comparing Figs 3.2a and b. In Fig. 3.2a, solvent rearrangement and chemical transformation cannot take place independently and the diagonal valley connecting the reactant and the product through the saddle point is the reaction coordinate in Fig. 3.1. In Fig. 3.2b, valleys of the reactant and the product are separated by a ridge with a saddle point and solvent rearrangement does not necessarily result in a movement along the chemical coordinate. If a reactant molecule tries to go over the ridge without changing its solvation shell, it will be faced with a high energy barrier. This model may be further simplified as shown in Scheme 3.1.

R

--

Scheme 3.1.

R*-

P

I

99

100

I

3 High-Pressure Kinetics and Highly Viscous Media

reactant

reactant

a

b

Fig. 3.2. Two-dimensional potential energy surface where the two coordinates are fully concerted (a) and where the solvent coordinate is almost independent o f the chemical coordinate

(b).

R and P in this scheme are the reactant and the product, respectively, and R’ represents the reactant molecules with a finite probability of crossing the energy barrier, i.e. reactant molecules in the area of the valley close to the saddle point. It was demonstrated by Sumi [ 191 that in the steady state approximation 1

1

1

kobs

kf

kTST

-- --+-

(3.4)

where the fluctuation-limited rate constant kf is a high viscosity limit of kobs in TST-invalid conditions, and may be considered to be the forward rate constant of the first step in Scheme 3.1. The validity of Eq. 3.4 was supported by exact numerical solutions obtained for the AH model [20, 211. The two models predict significantly different temperature dependence of kobs at a constant viscosity. In the KGH model, the reactant always goes over the same energy barrier in the ratedetermining step. Therefore, the isoviscous temperature dependence must be independent of the solvent viscosity inasmuch as the energy barrier does not show any significant dependence on the measure used to manipulate the viscosity, for example, the external pressure. On the other hand, in the AH model, the isoviscous activation energy is expected to decrease with increasing 7. At low viscosities where the thermal fluctuations of the solvent are fast enough to maintain the thermal equilibrium between the initial and the transition state, kf >> kTsT and

3.2 Selection of Reaction Systems

I

lo’

Thercfore, the activation energy will be approximately equal to the height of the energy barrier at the saddle point, Eo. However. as the thermal fluctuations in the solvent become slower with increasing viscosity, the rate-determining step gradually shifts to the first step in Scheme 3.1 or the movement of the reactant along the reactant valley in Figure 3.2b. As long as the viscosity is kept constant, the rate of solvent thermal fluctuations stays constant and the isoviscous temperature dependence would reflect the energy increase along the valley. Since this increase would never exceed Eo, the isoviscous activation energy is expccted to decrease with increasing viscosity in the AH model. The above discussion strongly suggests that it would bc possible to examine which model describes real reaction systems more accurately by checking the isoviscous temperature dependence of kobs at various viscosities starting from the TST-valid region. Applying high pressure seems to be practically the only one way to conduct such experiments because the solvent viscosity can be changed continuously and considerably without affecting reaction systems seriously [22]. It is true that the shape of the potential energy surface depends on the external pressure. However, the dependence can be estimated from the pressure effects on the rate constant in the TST-valid viscosity region. Fast reactions of electronically excited molecules such as photo-induced isomerization of stilbene is not suitable for this purpose, because the reaction is too fast to guarantee the validity of TST. Namely, neither kTST nor its pressure dependence can be estimated experimentally.

3.2 Selection of Reaction Systems

Reactions suitable for the kinetics aiming at the purpose mentioned above needs to satisfy one condition. The TST must be valid for a fairly wide range of pressure and temperature. Furthermore it is desirable that the reactant can be generated in situ and the reaction can be followed spectroscopically to obtain reliable rate constants. As the first set of reactions, thermal ZIE isomerization of three N-benzylideneanilines (benzaldehyde anils), i.e. N-[4-(dimethylamino) benzylidene]-4-nitroaniline (DBNA), N-[4-(dimethylamino)benzylidene]-4-ethoxycarbonylaniline (DBEA), and N-[4-(dimethylamino)benzylidene]-4-bromoaniline (DBBA), and two push-pull substituted azobenzenes, i.e. 4-(dimethylamino)-4’dimethylamino)-2-methoxy-4-nitroazobenzene nitroazobenzene ( DNAB) and 4’-( (DMNAB) as shown in Scheme 3.2 were selected. All of the forward reactions are “slow” thermal reactions of molecules in their ground So state and the half-lives were in the range of milliseconds to seconds, slow enough to guarantee the validity of TST in common solvents under “normal” conditions, because all the time scales of solvent thermal motion that may affect the reaction rate, i.e. vibrations, molecular rotations, and translational diffusion, are in nano- to picoseconds. The reaction mixture was contained in a glass/quartz bulb connected to a hypodermic syringe cut in the middle by means of a PTFE coupler [23]. The Z-isomers were generated by irradiating the solution from the

102

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3 High-Pressure Kinetics and Highly Viscous Media

$3b

Me2N

py jfN

A

X = CH, Y = 4-NO2 X = CH, Y = 4-COOEt X = CH, Y = 4-Br X = N , Y =4-N02 X = N, Y = 2-Me0 and 4-N02

Me2N

DBNA DBEA DBBA DNAB DMNAB

Scheme 3.2.

outside of the high-pressure vessel through sapphire window(s) and their decay was monitored spectroscopically. In all of the cases studied, the reaction followed the first-order rate law and, thus, the rate constants could be determined unequivocally [24]. The compounds were stable even under UV irradiation and the measurements could be repeated when necessary. Selection of the solvent was another problem. Since it was expected that a high viscosity would be required to invalidate TST in these reactions, three viscous liquids with different functional groups were chosen, namely, 2,4-dicyclohexyl-2methylpentane (DCMP) as a non-polar solvent, glycerol triacetate (GTA) as a polar aprotic solvent, and 2-methylpentane-2,4-diol(MPD) as a protic solvent. All these solvents have a branched molecular structure and, therefore, the shear viscosity q increases much more rapidly with increasing pressure than in common solvents. The pressure effects on q of MPD are shown in Fig. 3.3. As can be seen from this figure, the pressure dependence of q could be approximately expressed by 2 0

I n 1

. a c

a

/

25'C

0

35'C

0

40'C

A

45'C

a

GOT

I

Cn 0

-

0

-1

-2

-3

0

100

200

300

400

500

P lMPa Fig. 3.3.

Pressure dependence o f viscosity o f M P D at various temperatures

3.3 Z/E lsomerization of N-Benzylideneanilines

I

103

Tab. 3.1. Shear viscosities at 0.1 MPa (rlo/Pa.s) and its pressure coefficients (n/GPa- ' ) for the three viscous liquids at various temperatures.

T/'-C

DCMP

-10

-5 0 5 10 15 20 2s 30 35 40

GTA

MPD

110

a

4%

a

70

a

1.16 0.546 0.281 0.156 0.0928 0.0584 0.0387 0.0267 0.0192 0.0142 0.0115

57.2 53.2 49.6 46.5 43.7 41.2 39.0 37.0 35.3 33.7 32.5

0.247 0.146 0.0921 0.0608 0.0419 0.0299 0.0221 0.0168 0.0131 0.0104 0.00841

46.2 41.8 37.9 34.4 31.3 28.5 25.9 23.6 21.6 19.6 17.9

0.574 0.324 0.194 0.122 0.0805 0.0553 0.0393 0.0288 0.0217 0.0167 0.0132

30.8 28.3 26.1 24.1 22.4 20.7 19.3 17.9 16.7 15.6 14.6

where qo is the viscosity at 0.1 MPa and ci is its pressure coefficient. In order to estimate the viscosities at the reaction temperatures, temperature dependence of qo and z were estimated by means of two empirical equations? Eqs 3.7 [25] and 3.8, where vo is a kinematic viscosity in centistokes at 0.1 MPa and p1-p4 are the parameters to be adjusted.

qo values

were obtained by multiplying vo with the density po. The values thus obtained are listed in Table 3.1 [ 2 G ] .

3.3

Z/E lsomerization of N-Benzylideneanilines

The isomerization of N-benzylideneanilines had been shown to be effected by the nitrogen inversion via the activated complex 3.1 where the N-phenyl group is in conjugation with the nitrogen lone pair [28]. H

\

104

I

3 High-pressure Kinetics and Highly Viscous Media

3.5

3.0

0

2.5 -

o

n

GTA AcOMe

0

2.0

I

1

I

I

I

PIMPa A comparison o f pressure effects on the rate of thermal Z / E isomerization of DBNA i n GTA and in AcOMe at 25 "C. Fig. 3.4.

The polarity of the reactant might decrease slightly during activation because of the rehybridization of the nitrogen 1291 and it, in turn,might result in a slight volume increase. On the other hand, increased rotational restriction of the phenyl group connected to the imino nitrogen in the activated complex may cause a small volume decrease. As a result, the activation volume for this isomerization is expected to be a small positive or small negative value. Kinetic measurements in various solvents [30] met this expectation. Figure 3.4 illustrates the pressure dependence of the isomerization rate of DBNA in GTA and methyl acetate (AcOMe) at the same temperature. Methyl acetate has a similar functional group to GTA and its dielectric constant (6.7 at 25 "C) is close to that of GTA (6.0 at 21 "C). As expected from the structural similarity in the two solvents, the rate constants were similar at 0.1 MPa [31]. Furthermore, the rate was little affected by an increase in pressure throughout the whole pressure range in AcOMe and at P < 200 MPa in GTA, strongly suggesting the validity of TST even at viscosities as high as 1 Pa s (= 1000 cP). However, a strong pressure-induced retardation was observed at higher pressures in the latter solvent. Since the reaction is a one-step isomerization, there is little possibility of a shift of the rate-determining step in the usual sense and this retardation is difficult to rationalize within the framework of TST. The most reasonable explanation is that the reaction was retarded by an increase in the solvent viscosity because the same retardation was not observed in AcOMe.

3.3 Z/E lsornerization of N-Benzylideneanilines

I

105

’I 0

e e 0

20’C

0

15’C

0

1O’C

A

5’C

O’C

6

I

-5‘C I

I

I

This view is supported by the results in Figs 3.5-3.7. In these figures, results at different temperatures are shown for the isomerization of DBNA in the three viscous solvents [32-341. In all of these cases, the higher the reaction temperature, the higher the pressure required to observe the pressure-induced retardations. This is reasonable because the viscosity decreases with increasing temperature and we were convinced that these retardations were in fact dynamic solvent effects observed for “slow” thermal reactions for the first time [35]. We are now in a position to examine viscosity dependence of the rate constant. The results obtained for DBNA in DCMP are plotted against viscosity in Fig. 3.8. It is obvious that the isoviscous temperature dependence stays almost constant at lower viscosities but decreases with increasing viscosity in the TST-invalid viscosity region. Similar tendencies were observed for all of the anils in all three of the viscous solvents studied and these results strongly suggest that the present reaction systems cannot be adequately described by the KGH model. The solvent coordinate has to be treated separately from the chemical coordinate as assumed in the AH model. In other words, a reorganization of the solvation shell takes place prior to crossing the energy barrier without inducing a major structural change in the reactant. If the AH model is applicable to the present reaction systems, the fluctuation-limited rate constant k f obtained from Eq. 3.4 would give a linear Arrhenius plot because solvent rearrangement requires thermal activation. Estima-

106

I

3 High-Pressure Kinetics and Highly Viscous Media

r------

3'5

PIMPa Fig. 3.6. Pressure effects on the rate of thermal Z/E isomerization of DBNA in CTA at various temperatures.

-.

2.5c1 o o o o o o o o ~ o

<'

u)

0 0

o n

0 0 0 0 0

n

0 0

0 0 0 0 0 0 0 0

m

0 -

0

0 0 0 ~ . O ~ \ A A A A A A A O ~ O O A A 0 0 o o 3 8 8 m m m m m A A A 0 8 8 8 A 8 1.5-

m

8 8

1.0-

0

10'C

0

0 'C

0

O'C

A

-5'C

8

0.5

0

-1O'C I

I

I

I

100

200

300

400

c

3.3 Z/E lsornerization of N-Benzylideneanilines

-2.0

0

2O'C

0

15'C

0

1O'C

A

5%

m

O'C

e

-5'C

I

I

I

I

0.0

2.0

4.0

6.0

t

log (q/Pa s) Fig. 3.8. Plots of log kobs against log 7 for the thermal Z/E isomerization of DBNA in DCMP at various temperatures.

tions of kTsT under TST-invalid conditions were performed by linearly extrapolating log kobs against pressure because the kinetic effects of pressure in the TST-valid region were small. The k f values thus obtained satisfied our expectation as can be seen from examples in Fig. 3.9. Although the quality of linearity vaned from one system to another, no systematic deviation from the expected linearity was observed. It has been reported by many groups that the rate of isomerization at the S1 state is inversely proportional to a fractional power of the solvent viscosity 1391. Those measurements were almost certainly performed at TST-invalid viscosities. Therefore, the observed rate constant would have been fluctuation limited. This consideration suggests a similar viscosity dependence of our kf (Eq. 3.9).

Several plots of log k f against log 9 are given in Fig. 3.10. The slopes of the plots in Fig. 3.10 were around -0.7 and, hence, smaller than unity as expected. Again, in all of the cases studied similar linearity was observed. On the basis of these results, we concluded that the AH model is a better description of our "slow" reaction systems. Now the next step is to examine whether it is possible to obtain further information on the extent of correlation of the two coordinates. Figure 3.10 gives an important hint on this point. The isoviscous tem-

I

107

108

I

3 High-Pressure Kinetics and Highly Viscous Media

0.0035

0.0034

0.0036

0.0037

0.0038

IITIK Fig. 3.9. Isobaric Arrhenius plots for the fluctuation-limited rate constant kf in the thermal Z/E isomerization of DBNA in DCMP at various pressures.

A

0 0

3h

7

r A? Y

0

0 -

20

1-

0-

-1 -

0 O C D A

0

0

25 'C

0

20 'C

0

15 'C

A

10 'C

5 'C

2

3

4

5

log( qlPa s) Fig. 3.10. Viscosity dependence of the fluctuation-limited rate constant kf in the thermal Z / E isomerization of DBNA and DBBA in CTA a t various temperatures.

3.4 Z/E lsomerization of Push-Pull Substituted Azobenzenes

perature dependence of k f is quite small. Actually it is too small to estimate the isoviscous activation energy with sufficient accuracy. This is also true of other systems. Only in the case of DBNA and DBEA in DCMP, could we estimate (with difficulty) the values to be 20-30 kJ mol-'. What these findings indicate is that the slope of the reactant valley is relatively gentle probably because the correlation of the solvent and the chemical coordinate is weak as shown in Fig. 3.2b. This is reasonable because any significant changes in solute-solvent interactions may not be required to achieve the rehybridization of the imino-nitrogen atom.

3.4

Z/E lsomerization o f Push-Pull Substituted Azobenzenes A similar but mechanistically different isomerization of two push-pull substituted azobenzenes shown in Scheme 3.2 was also studied. Although it is possible for azobenzenes to isomerize by the same nitrogen-inversion mechanism as the Nbenzylideneanilines [40], rotational isomerization via a highly dipolar activated complex 3.2 becomes predominant [41, 421 in polar solvents provided that the compound contains a strongly electron-donating dialkylamino group as in DNAB and DMNAB.

Me2N+

3.2

Because of the increased solvation, the partial molar volume of the reactant decreases in the activation step (AVf << 0). This reaction gives us an opportunity to study whether the correlation between the two coordinates becomes stronger when electrostriction is reinforced during the activation step. Figure 3.11 illustrates the effect of pressure on the isomerization rate of DNAB in common and viscous solvents. As expected from the mechanism, the reaction was strongly accelerated in aprotic as well as in protic solvents. The activation volumes were -21 and -22 cm3 mol-' in ethanol and methyl acetate, respectively. Similar pressure-induced accelerations were also observed in MPD and GTA at lower pressures. However, the direction of the pressure effect was reversed at higher pressures. Figures 3.12 and 3.13 illustrate pressure effects observed for DNAB in the two solvents. The results for DMNAB were qualitatively identical. Pressure-induced retardation clearly occurred at higher pressure when the reaction temperature was raised. The results leave little doubt about the validity of TST at low pressures and its failure at higher pressures in the rotational isomerization of push-pull substituted azobenzenes in GTA and MPD [43]. The observed rate constants are plotted against g in Figs 3.14 and 3.15. The results in GTA (Fig. 3.14) were qualitatively different from those in MPD

I

109

110

I

3 High-PressureKinetics and Highly Viscous Media

A

200

0

0

EtOH

0

MPD

0

AcOMe

600

400

1 10

800 P/M Pa

Comparisons of pressure effects on the rate of thermal Z / E isomerization of DNA6 in common and viscous solvents at 15 "C.

Fig. 3.11.

2

-

o

. 2 m

1-

so

0

v

(51

0 -

o

~

o

no

7

[,O

0 0

o o o o o o o o o o o o 0 o o o

0

A

()

A A A

A

40'C

0

25°C

0

15'C

A

-2

0

0

0 0 0

0

A

0

o

0

A

I,

-1 -

~

0

O

A A A A

0"o

~ 0

A

5'C I

I

I

I

200

400

600

800

11

3.4 Z/E isornerization of Push-Pull Substituted Azobenzenes

2.5

i n

0.5

,,I1l,

o.o[;

-5-c

-0.5

m;

I

0

100

200

300

400

500

600

1

700

PlMPa Fig. 3.13. Pressure effects on the rate o f thermal Z/E isomerization of DNAB in MPD a t various temperatures.

0

-2.5

15’C

A

5°C

I

I

I

I

0.0

2.5

5.0

7.5

log( q/Pa s) Fig. 3.14. Plots o f log kobs against log q for the thermal Z/E isomerization of DNAB i n CTA at various temperatures.

10.0

I

ll1

112

I

3 High-Pressure Kinetics and Highly Viscous Media

2-

. -

7

0)

01

n

so 0,

0 -

1-

‘m

f8

0-

-1

log( q/Pa s) Plots of log kobsagainst log q for the thermal Z/E isornerization of DNAB in MPD at various temperatures.

Fig. 3.15.

(Fig. 3.15). In GTA, the isoviscous temperature dependence almost disappears at the TST-invalid viscosity region. In MPD, however, a large proportion of the isoviscous temperature dependence still remained even at 1 x lo5 Pa s. The results in MPD suggest that the two coordinates are partially correlated and the fluctuationlimited rate constant k f would show temperature dependence even at a constant viscosity. The kobs values at TST-valid pressures were fitted to either one of the following empirical three-parameter equations [28, 441 to estimate the TST-expected rate constants.

k In 2 = a~

+ b I n ( l + cP)

(3.10)

k0.l

(3.11)

As in the N-benzylideneanilines, kf gave linear isobaric Arrhenius plots and satisfied Eq. 3.9. The values for DNAB are plotted against q in Figs 3.16 and 3.17. Obviously, the isoviscous temperature dependence of kf was small in GTA. However, significant temperature dependence was clearly seen in MPD as shown in Fig. 3.17. The isoviscous activation energies Eaf and E ~ T were ~ T estimated for DNAB and DMNAB and they are listed in Table 3.2. The E a f and E U T ~values T in Table 3.2 suggest that the reactant molecules climb more than half of the potential energy barrier during the solvent rearrangement

3.4 Z/E lsornerization of Push-pull Substituted Azobenzenes

0

-

0

r

P

0

2-

0

Y m

v

-0

0 0 00

0

1-

A

0

0 A0

0 OA

0

0-

O A

0

40’C

0

15‘C

O

25’C

0

A

5‘C

A

1

-1

2

3

I

1

1

1

4

5

6

7

8

log( q/Pa s) Fig. 3.16.

Viscosity dependence of kf in the thermal Z/E isomerization of DNAB in CTA.

0 00 v

3-

m

-0

“oe

0

35%

0

25’C

0

15’C

A

5%

0% 0 0 OOO

0

2-

-5.c

OOO 00 A ‘0 A OO A

r

m

n

A

mm

1-

‘m

~ A

B

0

0

I

1

1

2

4

6

8

log( q/Pa s) Fig. 3.17.

Viscosity dependence of kr in the thermal Z / E isornerization of DNAB in MPD.

I

113

114

I

3 High-Pressure Kinetics and Highly Viscous Media

Isoviscous activation energies calculated from kr (Eaf/kJ mol-’) and k ~ s ~ (EaTSr/kJ mol-’) for the thermal Z/E isomerization o f DNAB and DMNAB in MPD.

Tab. 3.2.

w a

10 102 103 104

5

DMNAB

DNAB

4

EaTST

56 & 6.2 50 k 4.4 45 & 3.1 45 k 0.8

69 f 0.8 69 i 1.3 69 i 3.1 69 2.0

EaTST

58 k 3.7 54 i 2.6 50 & 1.9 46 & 1.8

70 k 0.2 71 0.5 72 f 0.6 70 k 1.9

around the Z-isomer in MPD. Considering the absence of such energy increases in GTA, the hydroxyl groups on the MPD molecule may be responsible for this behavior. In order to break the nitrogen-nitrogen TC bond heterolyhcally, electron-pair donation by the amino group is essential. Therefore, desolvation of the solvent molecule hydrogen-bonded to the dimethylamino group is a prerequisite for rotation around the N-N bond and also for the preparation of a solvation shell which stabilizes the highly dipolar activated complex 3.2. Considering the fact that the magnitude of the Eaf is much larger than the normal bond energy of hydrogen bonds, mere desolvation is not enough to explain the energy increase. The slope of the reactant valley must be considerably larger in MPD than in GTA probably as a result of a partial correlation of the solvent and the chemical coordinate. In other words, rotational movement around the nitrogen-nitrogen bond takes place as the hydrogen-bonded solvent molecules are desolvated. On the other hand, the results in GTA demonstrate that solvent reorganization takes place without inducing a major structural change in the Z-isomer. From these results, it would be reasonable to expect that we would also observe a similar isoviscous temperature dependence of kobs and kf in other systems, if the solute-solvent interactions are strong enough. In order to examine this possibility, we decided to undertake kinetic measurements on some carbocyanine cations because solute-solvent interactions are much stronger in charged species than in neutral ones.

3.5

Z/E lsornerization o f Carbocyanine Cations

Carbocyanine cations are known to isomerize photochemically in their polymethinic chain. 3,3’-Diethyloxacarbocyanineiodide (DOCI) and 3,3’-diethyloxadicarbocyanine iodide (DODCI) are among the most extensively investigated compounds and the cations are believed to exist in solution in the all trans extended structure. After irradiation one of the carbon-carbon double bonds undergoes Z/E-type isomerization and unstable photoisomeric cations are formed as illustrated in Schemes 3.3 and 3.4 [45].

3.5 Z/E lsomerization of Carbocyanine Cations

I

115

DOC cation

Scheme 3.3.

DODC cation

Scheme 3.4.

Pressure effects on the rate of these thermal return processes were investigated in ethanol and MPD [46]. The results for DOC1 are shown in Fig. 3.18. The isomerization rate in ethanol clearly demonstrates that the activation volume was close to zero in this solvent. This is in accordance with the Laser-Induced

-1 0

35'C

0

25'C

0

15'C

A

5'C

-2 0

200

400

600

P lMPa

Fig. 3.18. Pressure effects o n the rate of thermal Z/E isornerization of DOC1 in MPD and ethanol at various temperatures.

116

I

3 High-pressure Kinetics and Highly Viscous Media

Optoacoustic Spectroscopy (LIOAS) measurements reported by Braslavsky and her co-workers [45]. As a result of their experiments, the authors concluded that the partial molar volume of the Z-and E-cation were close to each other. Since the reaction is a unimolecular geometrical isomerization, it is hard to imagine that the volume profile of the reaction has an extreme value and it is reasonable to observe a very small pressure effect if the reaction volume AV is close to zero. In MPD, the rate constant itself was close to that in ethanol and the pressure effect at P < 150 MPa was similarly small. The activation volumes were 0 f 1 cm3 mol-I, a clear indication of the validity of TST at lower pressures. Isomerization, however, was strongly suppressed by an increase in pressure at higher pressures. There is little doubt that applying high pressure moves the reaction into the TST-invalid region of high solvent viscosity. The results obtained for DODCI were qualitatively different from those for DOC1 as shown in Fig. 3.19. The reaction was retarded by an increase in pressure even in ethanol. The activation volume obtained by fitting these results into Eq. 3.10 was 5.8 f 0.8 cm3 mol-*. Usually log k - P plots for a reaction with a positive activation volume become concave-up (which means concave on the upper side) because the compressibility increases with the volume of the system. The plots in ethanol met this expectation and the pressure effect must have been the effect of a volume increase during

A

a

35-c

+

15'C

0

25'C

0 0

0 A

,

1.0!AA5'Cl

0.5

0

200

400

600 PlMPa

Fig. 3.19. Pressure effects on the rate of thermal Z/E isomerization of DODCI in MPD (open symbols) and ethanol (closed symbols) at various temperatures.

3.5 Z/E lsomerization of Carbocyanine Cations

activation. The observed moderately positive activation volumes were again in accordance with the results of the LIOAS measurements [45]. According to Braslavsky, the partial molar volume of the DODCI was smaller by 29 f 12 cm3 molk' in the photo-produced unstable conformer. This unexpected result was rationalized on the basis of the increasing solvation (electrostriction) caused by a charge distribution difference in the two conformers. Therefore, the reaction volume must be positive for the present thermal return and the observation of a positive activation volume is not surprising. Hara and Akimoto [ 381 studied the pressure effect on the same reaction in several I-alkanols including ethanol. In all of the solvents, the reaction was moderately retarded by pressure and the activation volume in ethanol calculated from their results was 4.3 cm3 rnol-' at 30 "C, in a rcasonable agreement with our value. However, the authors interpreted the pressure dependence as a dynamic solvent effect, namely the reaction was suppressed by an increase in the solvent viscosity caused by the applied pressure. Similarly, Fleming and his coworkers [37] measured the isomerization rate in a series of 1-alkanols at 0.1 MPa. The reaction was found to be slightly retarded with the increasing chain length (kEtOH/kDecOH = 2) and this effect was also interpreted as viscosity-induced retardation. Judging from the reaction rate (412 s-' at 25 "C and 0.1 MPa) and the different pressure dependence in ethanol and MPD (vide inju), however, we believe that TST remains valid in common 1-alkanols for this reaction. The solvent effects observed by Fleming cannot be rationalized on the basis of the bulk polarity of the solvent because the activated complex is less polar than the Z-isomer and decreasing the solvent polarity is expected to accelerate the reaction by destabilizing the reactant more than the activated complex. One possible factor which might be responsible for the retarding effect of a longer alkyl chain is the internal pressure. The internal pressure is expected to increase with increasing chain length [47, 481 and if the mechanism is the same as that for external pressure, the reaction may be slower in higher alcohols. Since the rate constant in MPD at 0.1 MPa was close to that in ethanol under the same conditions, it may be reasonably supposed that the atmospheric rate constant was, at least, close to that expected from TST. However, the log kobs- P plots were concave-down for MPD, that is, the magnitude of the pressure effect increased with increasing pressure throughout the whole pressure range. We could not detect any inflection point in the log kobs-P plots. Therefore, deviations from TST must have started at a pressure close to 0.1 MPa. The kobs values were plotted against in order to check the isoviscous temperature dependence and are shown in Figs 3.20 and 3.21. Several activation energies Euobs in isoviscous conditions were estimated from the plots in these figures and they are listed in Table 3.3. The isobaric values in ethanol are also given in Table 3.4 for comparison. Obviously, the isoviscous activation energy decreases with increasing viscosity. Since the isobaric activation energy for DODCI in ethanol shows that the height of the energy barrier is little affected by the external pressure, a decrease in the isoviscous Eaobs cannot be attributed to the pressurc dependence of the shape of the potential energy surface. The most reasonable rationalization may be that the

I

117

118

I

3 High-pressure Kinetics a n d Highly Viscous Media

2 n

9

v

o,

-0

0

35'C

0

25'C

0

15'C

A

-00%

0.5-

"00

000000000~

5 'C -5.c

0

OoOO0

0.0-

0 AAAAAAAA

OO 0

A AA 'AA

-0.5 -

AA A A

-1.o -

A A

-1.5

I 0

-2

2

5

8

log(q/Pa s) Fig. 3.20. Plots of log kobs against log q for the thermal Z/E isomerization of DOC1 in MPD a t various temperatures.

1

3.0

A

A A

0

-

A A

o

o

0

A A

0 A

15'C

A

0

0 Y

0

OO

0

5'C

A

o

0

3.5 Z/E lsornerization of Carbocyanine Cations Tab. 3.3. Isoviscous activation energies calculated from kobs (Ea,b,/kJ Z/E isornerization o f DOC1 and DODCI in MPD.

v/Pa

*

!?Gobs (DOCI)

Eaobs (DODCI)

mol-’) for the thermal

0. I

I

10

102

103

I 04

67.2 52.7

67.6 49.3

66.5 45.8

63.7 42.2

58.8

51.6

rate-determining step shifts from the point of crossing the energy barrier at low pressures/viscosities to the point of solvent reorganization around the reactant at high pressures/viscosities. If this rationalization is correct, the kf values obtained on the basis of Eq. 3.4 would give linear isobaric Arrhenius plots and obey Eq. 3.9. Since the TST-valid pressure range was wide enough in the case of DOCI, the observed rate constant kobs was extrapolated to estimate the kTsT values. However, similar extrapolation could not be performed for DODCI because the TST became invalid at pressures slightly above 0.1 MPa. Therefore, we decided to assume that the static pressure effect in MPD was identical to that observed in ethanol. The rate constants in ethanol were fitted to Eq. 3.10 and the parameters a , b, and c were determined. The kTsT under the TST-invalid conditions were estimated by applying Eq. 3.10 for ethanol to the rate constant in MPD at atmospheric pressure. The kf values obtained gave linear isobaric Arrhenius plots and they were inversely proportional to a fractional power of q. The log kf-log q plots are shown in Figs 3.22 and 3.23. The plots were satisfactorily linear and the slopes were smaller than unity. The linearity was slightly poorer in DODCI probably because k T s l values estimated on the basis of the rate constants in ethanol were used. It is obvious that kf shows temperature dependence even at the same viscosity. The isoviscous activation energies derived from kf are listed in Table 3.5 together with those derived from kTST. Judging from the E ~ ~ / E u Tratios, ~ T the correlation between the solvent and chemical coordinate in the isomerization of the carbocyanine cations was of the same order as that in the azobenzene isomerization in MPD. Considering the significant difference in the isomerization rate and in the pressure range where dynamic solvent effects were observed for the two carbocyanines, it is interesting to examine whether the dynamic solvent effect appears at a similar level in the relative time scales of the solvent and the chemical coordinate. It has earlier been shown [20, 211 that the product kTsT x q can be used in the AH model to describe the balance of the characteristic times of the reaction system and the solvent: the greater the product, the higher the anisotropy of the two time scales as

Tab. 3.4. Isobaric activation energies calculated from kobs (Ea,b,/kJ isomerization o f DODCI in ethanol.

mol-’) for the thermal Z/E

P/ MPa

0.1

150

300

450

600

Eaabs

58.9

59.6

59.9

60.0

60.4

I

119

120

I

3 High-Pressure Kinetics and Highly Viscous Media

3

-

. 5

7

0

35'C

0

25 'C 15 'C

2-

in

5 'C

m

-0

-5'C

1-

0-

-1 -

A

!

I

1

I

I

-2

0

2

4

6

-2

8

log (q/Pa s)

Fig. 3.22. Viscosity dependence of kf in the thermal Z/E isomerization of DOC1 in MPD.

3.5j

00

0

A 7

-r?

5 m

0

0

0

0

o

3.0'

-0

A.

2.5 -

n

D o 0 0 o n

0

O

A 0

O n

0

0 0 0

A

2.0 -

o A

0

0

o

0

0

35 'C 25 'C

1.5-

-1

0

0

15 'C

A

5 'C

0

A

0

A

o A

1

2

3

4

log( q/Pa s ) Fig. 3.23.

Viscosity dependence of kf in the thermal Z / E isomerization of DODCI in MPD

3.5 Z/E lsornerization of Carbocyanine Cations lsoviscous activation energies calculated from kf (€of/kJ mol-') and kTs, (EOTST/kJ mol-') for the thermal Z / € isornerization of DOC1 and DODCI in MPD.

Tab. 3.5.

1 10

lo2 10' 104

41 f 1.0 41 & 1.0 40 f 0.9 39 f 0.7

69 k 0.8 70 k 1.0 71 2 1.2 72 f 1.4

45 f 3.7 42 k 3.2 43 k 2.4 44 f 2.1

*

51 0.2 49 f 0.1 46 k 0.1 44 f 0.1

a result of the slower movement of the solvent. The plots of log(kobs/kTST)against log(kTsT ' 1 7 ) are shown in Fig. 3.24. As expected, the results obtained at different temperatures fall on the same curve when plotted in these coordinates. The quality of aggregation was higher for DOCI than for DODCI probably for the same reason that the linearity was improved in the log kf-log q plot for DOCI. It is interesting to note that the points for the two compounds fall very close to each other despite much faster isomerization and much earlier deviations from TST in DODCI. This fact strongly suggests that the extent of deviation from TST is governed mainly by the relative time scale of the solvent and

0.0

-t;;

-0.2

s; a Yo

3

-0

-0.4

-0.6

I

-0.8

A 35 T

0

-1.o

+

25'C

0 0

15'C

0

A A -1.2

0

A

5 'C I

I

I

I

I

1

2

3

4

5

lo!"Ts+')(dPa

41

Dependence o f log(k,b,/kTsr) on log(kTST . q) in the isomerization of DOC1 (open symbols) and DODCI (closed symbols) a t various temperatures. Fig. 3.24.

6

I

121

122

I

3 High-Pressure Kinetics and Highly Viscous Media

-+

< 0

<

-0.2-

n

P,

0 -

-0.4-

-0.6 -

ABm

0

-0.8-1 -

A

DBNA DBEA

0

DBBA

A

DOC1

m

A

A

DODCl ..L

I

I

I

I

0

2

4

6

I

log( kTST/s-')(v/s-') Fig. 3.25. Dependence of Iog(kobs/kTST) on log(kTST . q) in the thermal Z/E isomerization of N-benzylideneanilines and carbocyanine cations at various temperatures in MPD.

the chemical coordinate in closely related systems. This point can be seen even more clearly in Fig. 3.25 in which the points for the three N-benzylideneanilinesat various temperatures are added to Fig. 3.24. The relative rates at 0 "C and 0.1 MPa were DBBA: DBEA: DBNA = 1: 56: 1600. However, the points added cluster in a higher-anisotropy area than the carbocyanines. Similar aggregation of the points for the three N-benzylideneanilines was also observed in GTA and DCMP. Figure 3.26 shows the plots in DCMP. It may be safely concluded from these plots that the magnitude of a deviation from TST in analogous reactions is determined mostly by the relative time scale of the reaction and the solvent fluctuations. Furthermore, since the plots in Figs 3.25 and 3.26 are similar to the results of numerical simulations [20], they may be taken as evidence of the validity of the model.

3.6

Z/E lsomerization of DNAB in a Polymeric Medium Throughout our analyses, macroscopic solvent shear viscosity q has been assumed to be proportional to the microscopic friction between the reactant and the solvent

3.G Z/E lsomerization of DNAB in a Polymeric Medium

I

123

+

P -o.2-

21

X"

v

-

-0.4-

-0.6-

-0.80

DBNA

0

DBEA

-1 -

0

DBBA

0

-1.2

3

I

I

I

I

4

5

6

7

I

8

I

9

'

logf(kTsT/s-')(rl/Pas)l Fig. 3.26. Dependence of Iog(kabr/kTST) on log(kTST . 17) in the thermal Z/E isomerization of N-benzylideneanilines at various temperatures in DCMP.

during the crossing of the energy barrier. This assumption has some experimental support. For example, rotational relaxation times of neutral as well as charged species are reported to be proportional to 7 [49, SO]. In polymer media, however, it is expected that the macroscopic viscosity may not adequately describe the microscopic frictions and if this is the case, it may be considered to be indirect evidence for the proportionality between the macroscopic viscosity and the microscopic friction in monomeric solvents. In order to pursue this possibility, we measured kinetic pressure effects on the isomerization of DNAB in a commercially available silicone oil [51]. The oil used was KF-54 from Shin-Etsu Chemical and its structure is given below. The average degree of polymerization was 25 and the phenyl :methyl ratio was 1:3. ye

ph

-0-sio-phe

Ph

The pressure dependence of the viscosity of KF-54 obeyed Eq. 3.6. The rate constants observed in GTA and KF-54 at various temperatures and pressures are illustrated in Fig. 3.27.

124

I

3 High-pressure Kinetics and Highly Viscous Media

A

A

0 0

A A

15 5'C

10

It was observed that the reaction deviated from the first-order rate law at high pressures and the measurements were restricted to the pressure range in which the first-order rate law was obeyed. The results in KF-54 look similar to those in GTA. The reaction was accelerated at low pressures because of its negative activation volume. The phenyl group in the polymer chain stabilizes the rotational transition state as does benzene [41]. The reaction rate reached a maximum and then started to decrease with increasing pressure, a clear indication of a shift of the reaction from the TST-valid to the TST-invalid region. It is difficult to judge from Fig. 3.27 whether the polymeric solvent behaves differently from monomeric GTA. However, the difference can be seen clearly by plotting log kobs against log r] as shown in Fig. 3.28. The viscosity which yields the maximum reaction rate, shifts to a lower value with increasing temperature in GTA. In KF-54, however, the maximum viscosity stays almost constant. This behavior suggests the existence of a factor which affects the reaction rate but does not contribute to the macroscopic viscosity. If this second contribution to the microscopic friction decreases with increasing temperature, the behavior shown in Fig. 3.28 is to be expected. This second factor may be related to local segmental rotation of the siloxane chain. However>further experiments are necessary for detailed analysis. At any rate, the results in Fig. 3.28 may be considered as indirect evidence for the validity of our use of q as a measure of microscopic friction.

3.7 Concluding Remarks

I

125

2 0

40'C

0 4

25'C

.

0 0

15'C

so

A A

5'C

h 7

i n 1 n

v

m

0 -

0 A

-1

A

-2

-3 -2

0

2

4

6

8

10

log( q/Pa s) Fig. 3.28. Plots of log kobr against log 7 for the thermal Z/E isomerization of DNAB in CTA (open symbols) and KF-54 (closed symbols) a t various temperatures.

3.7

Concluding Remarks

Kinetics in highly viscous media is a new field of high-pressure kinetics and it gives us information that cannot be obtained by conventional activation volume measurements. From the experiments performed so far, it has now been unequivocally demonstrated that the simple KGH model which uses only one reaction coordinate does not satisfactorily explain the experimental observations, at least in slow unimolecular reactions, of molecules in their So-state. In those reactions, solvent reorganization does not necessarily result in a chemical transformation along the reaction coordinate. When the solvation of the reactant is relatively weak, the solvent molecules are rearranged prior to the chemical transformations to form a solvation shell which stabilizes the activated complex. As demonstrated by the reaction of push-pull substituted azobenzenes in GTA, this independence of the solvent coordinate remains true even if the activated complex is much more polar than the reactant. However, when specific desolvation is required in the reaction mechanism (DNAB and DMNAB in MPD) or the solvation in the initial state is strong (DOC1 and DODCI in MPD), the two coordinates are more or less correlated and the solvent molecules are rearranged together with chemical transformations. Even in such reactions, the energy increase during solvent rearrange-

126

I

3 High-Pressure Kinetics and Highly Viscous Media

mcnt does not reach the value of the activation energy observed under conditions where TST is valid. Namely the reactant goes up to the middle of the energy barrier and if further energy can be obtained from nearby solvent molecules, a large vibration along the reaction coordinate brings the molecule to the product energy surface in a “frozen” solvation shell. It is highly desirable to analyze the experimental results in more detail on the basis of the theoretical model. If the experimental results are correlated with the model quantitatively, we will have a greater understanding of the reaction system. Research along these lines is now in progress [52]. It will also be very fruitful, if calculations using molecular dynamics combined with quantum chemistry can be carried out for the present thermal isomerizations, as was the case for the photoisomerization of stilbene [ 5 3 ] .

Acknowledgments

The author is grateful for financial support from the Ministry of Education, Science, Sports and Culture of Japan, Japan Society for the Promotion of Science, and Nishida Research Fund for Fundamental Organic Chemistry. He is also grateful to coworkers in Oita University, especially to Professor Y. Ohga and Mr T. Takahashi. Helpful comments by theoretical scientists, Professors N. Weinberg (University College of the Frazer Valley), M. V. Basilevsky (Karpov Institute of Physical Chemistry) and H. Sumi (University of Tsukuba) are also greatly appreciated.

References 1 S. GLASSTONE, K. J. LAIDLER, H .

2

3 4

5

6 7

8

EYRING, The Theory of Rate Processes, McGraw-Hill, New York, 1941. S. D. HAMANN,Physico-Chemical Efects of Pressure, Buttenvorths, London, 1957. T. ASANO,W. J. LE NOBLE,Chem. Rev. 1978, 78, 407. R. VAN ELDIK,T. ASANO,W. J. LE NOBLE,Chem. Rev. 1989, 89, 549. A. DRLJACA, C. D. HUBBARD,R. VAN ELDIK,T. ASANO,M. V. BASILEVSKY, W. J. LE NOBLE,Chem. Rev. 1998, 98, 2167. H . A. KRAMERS, Physica, 1940, 7, 284. K. STEPHAN,K. LUCAS, Viscosity of Dense Fluids, Plenum, New York, 1979. j. TROE,Ber. Bunsenges. Phys. Chem. 1991, 95, 228.

9 As a review, J. SCHRODER, J. TROE, 10 11

12

13

14

15 16

Ann. Rev. Phys. Chem. 1987, 38, 163. D. M. ZEGLINSKI, D. H . W A L D E C K , ~ . Phys. Chem. 1988, 92, 692. N. S. PARK,D. H. W A L D E C KPhys. ,~. Chem. 1990, 94, 662. G. ROTHENBERGER, D. K. NEGUS, R. M. HOCHSTRASSER, J . Chem. Phys. 1983, 79, 5360. G. R. FLEMING, S. H . COURTNEY and M. W. BALK,]. Stat. Phys. 1986, 42, 83. M. LEE, G. R. HOLTOM,R. M. HOCHSTRASSER, Chem. Phys. Lett. 1985, 118, 359. As a review, J. T. HYNES,J . Stat. Phys. 1986, 42, 147. N. AGMON,J. J. HOPFIELD,]. Chem. Phys. 1983, 78, 6947.

AGMON, I. J. HOPFIELD,].Chem. Phys. 1983, 79, 2042. 18 H. SUMI,R. A. MARCUS, J . Chem. Phys. 1986. 84, 4894. 19 H. S U M I J, . Phys. Chem. 1991, 95, 3334. 20 M. V. BASILEVSKY, V. M. RYABOY,N. N. WEINBERG, J . Phys. Chem. 1990, 94, 8734. 21 M. V. BASILEVSKY, V. M. RYABOY, N.N. WEINBERG, J . Phys. Chem. 1991, 95, 5553. 22 Using a series of solvents with the same functional group is sometimes adopted as a measure to change the viscosity as discussed above [ 10-121. The viscosity range that can be covered by this method, however, is rather narrow. For example the viscosity of 1-octanol is barely 15 times larger than that of methanol. It is possible to increase the viscosity much more significantly if the alkyl chain is branched or if the number of the functional groups is increased However, any drastic change in the molecular structure can possibly alter the shape of the potential energy surface and it is very difficult to estimate the magnitude of this effect. Furthermore, it is not possible to change the viscosity continuously by changing the solvent. 23 T. ASANO,T. OKADA, ]. Phys. Chem. 1984, 88, 238. 24 For a case of a deviation from the firstorder rate law, see Sect. 3.6. 25 Standard Viscosity-Temperature Charts for Liquid Petroleum Products, D341-74, Part 23, Annual Book of ASTM Standards, ASTM, Philadelphia, 1985. 26 The high pressure viscosity of GTA showed a small upward deviation from Eq. 3.6. In order to consider this non-linearity, an empirical equation proposed by Yasutomi and his coworkers [27] was tested. Unfortunately, however, the function obtained resulted in unreasonably large high-pressure viscosities at low temperatures and, therefore, Eq. 3.6 was also adopted for GTA. 27 s. YASUTOMI,S . BAIR,W. 0. WINTER, Trans. ASME,J . Trib. 1984, 106, 291. 17 N.

28

29

30

31

32 33

34 35

36

37 38 39 40

41

42 43

T. ASANO,H. FURUTA, H.-J. R. CIMIRAGLIA, Y. TSUNO, HOFMANN, M. FUJIO,J . Org. Chem. 1993, 58,4418 and earlier papers cited therein. P. HARBERFIELD, P. M. BLOCK,M. S . Lux, J . Am. Chem. SOC.1975, 97, 5804. T. ASANO,T. OKADA, W. G. HERKSTROETER. J . Org. Chem. 1989, 54, 379. The reason for the small rate difference between the two solvents cannot be rationalized at the present level of knowledge. However, the fact that the rate in GTA was larger than that in AcOMe also supports the absence of dynamic solvent effects in GTA at low pressures. T. ASANO, H. FURUTA,H. SUMI,J . Am. Chem. SOC.1994, 116, 5545. T. ASANO,K. COSSTICK, H. FURUTA,K. MATSUO,H. SUMI,Bull. Chem. SOC. Jpn. 1396, 69, 551. T. ASANO, K. MATSUO,H. SUMI,Bull. Chem. SOC.Jpn, 1977, 70, 239. Several authors [ 36-38] have measured the pressure/solvent dependency of some unimolecular rate processes of ground-state molecules and all of the authors have interpreted the results as “dynamic” solvent effects. However, as a result of our own measurements described in this chapter, we believe that what they observed was “static” pressure/solvent effects. See also Sect. 3.5. J. JONAS, X. PENG,Ber. Bunsenges. Phys. Chem. 1991, 95, 243 and earlier papers cited therein. S. P. VELSKO,D. H. WALDECK, G. R. FLEMING,]. Chem. Phys. 1983, 78, 249. K. HAM,S. AKIMOTO,J . Phys. Chem. 1991, 95, 5811. See Tables 5 and 7 in ref. 5. R. CIMIRAGLIA, T. ASANO, H.-J. Gazz. Chim. Ital. 1996, HOFMANN, 126, 679. T. ASANO, T. OKADA,].Org. Chem. 1986, 51, 4454 and earlier papers cited therein. D.-M. SHIN, D. G. WHITTEN, J . Am. Chem. SOC.1988, 110, 5206. Measurements in DCMP were not carried out because the reaction

128

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3 High-pressure Kinetics and Highly Viscous Media

proceeds via nitrogen inversion in non-polar media. 44 C. A. N. VIANA,J. C. R. REIS,Pure Appl. Chem. 1996, 68, 1541. 45 M. S. CIIURIO, K. P. ANCERMUND, S. E. BRASLAVSKY, J. Phys. Chem. 1994, 98, 1776 and refrences cited therein. 46 J. C. K I M , Y. OHGA,T. ASANO,N. WEINBERG, A. V. GEORGE, Bull. Chem. SOC.Jpn. 2001, 74, 103-111. 47 G . ALLEN,G. GEE,G. 1. WILSON, Polymer 1960, I , 456. 48 M. R. 1. DACK,Chem. SOC.Rev. 1975, 4, 211. 49 N. ITO, 0. KAJIMOTO, K . HAM, Chem. Phys. Lett. 2000, 318, 118.

G . B. D u n , M. I<. SIN G H A. , V. SAPRE, J . Chem. Phys. 1998: 109. 5994. 51 A. S H U K , T. TAKAHASHI. Y. OHGA,T. ASANO,H. SAITO,K. MATSUO,H.-D. L ~ D E M A N2. N ,Naturforrch. 2000. 55a, 616. 52 Y. OHGA,T. ASANO.M. V. BASILEVSKY, N. WEINBERG, 41st High-Pressure Symposium of japan, Kashiwa, Japan, 6-8 November 2000, Abstract 2C09. 53 C. D. BERWEGER, W. F. VAN GUNSTEREN, F. MBLLER-PLATHE, Angew. Chem. Int. Ed. 1999, 38. 2609. 50

II

Mechanistic and Synthetic Applications o f High Pressure

High Pressure Chemistry Synthetic, Mechanistic, and Supercritical Applications

Edited by Rudi van Eldik and Frank-Gerrit Kliirner

0WILEY-VCH Verlag GmbH, 2002

4

Water Exchange on Metal Ions: The Effect o f Pressure Lothar Helm a n d Andre E. Merbach*

4.1

Introduction

The solvent exchange reaction between the first and second coordination shell around a metal ion in solution is the simplest ligand substitution reaction. Environmental issues and the move towards “clean technology” is driving synthetic chemists away from organic-based solvent systems and towards water as the preferred solvent. Furthermore, water is the preferred solvent of nature, and therefore an understanding of the reactivity of hydrated metal ions is of fundamental importance for the understanding of many reactions in chemical and biological systems (Eq. 4.1). The replacement of a water molecule from the first coordination shell is an important step in complex-formationreactions of metal cations as well as in many redox processes. The general chemistry of aqua ions over the Periodic Table of elements, their synthesis, structure and reactivity have been reviewed recently by Richens [ 11. [M(HzO),]‘+

+ nHzO* * [M(HzO*)n]Zf+ nHzO

In water exchange reactions, the reagent and the product are identical, as are the ligand and the solvent: water. The Gibbs free energy change, AG, of the reaction is zero. The observed exchange rate constants cover more than 18 orders of magnitude (Fig. 4.1) from the most labile monovalent alkaline ions to the very inert trivalent transition metal ions Rh3+and Ir3+ [ 2 ] . On the fast exchange side, the mean lifetime of a water molecule in the first coordination shell of Cs+ was estimated to 200 ps [ 31. Cs’ is the largest monovalent metal cation and has therefore the lowest surface charge density. At the other extreme, a water molecule stays for more than 300 years in the first coordination shell of hexaaqua iridium(III), a third-row transition metal ion with a large ligand field contribution to the activation energy. The metal ions are often classified into three groups. The first group is represented by the main group metal ions, varying mainly in ionic radius and electric charge. The number of water molecules in the first coordination sphere range from 4 to 10 or greater 141.The second group consists of the d-transition metal ions, all

132

I

4 Water Exchange on Metal lons: The Effect of Pressure

<

=n,o1 s

n nin

Li'

1010

lo8

lo6

104

lo2

100 102 kn20 J s '

104

lo6

lo8

1 0 ~ ~ >

Fig. 4.1. Mean lifetimes o f a single water molecule in the first coordination sphere of a given metal ion, T H , O , and the corresponding water exchange rate constants, k H 2 0 . The filled bars indicate directly determined values, and the open bars indicate values deduced from ligand substitution studies.

hexa-coordinated with the exception of PdZ+and PtZ+which are square planar and Sc3+ that might be hepta-coordinated (51. Their exchange rate constants are very strongly linked to the occupancy of their d-orbitals. The third group involves the lanthanide and actinide ions which are eight- or nine-coordinated. Their kinetic behavior is mostly influenced by the decrease in ionic radius along the series and the subsequent change in the coordination number. Experimentally, water exchange rate constants are mainly determined from nuclear magnetic resonance measurements [ 6, 71. Other techniques are restricted to very slow reactions (classical kinetic methods using isotopic substitution) or are indirect methods, such as ultrasound absorption, where the rate constants are estimated from complex-formationreactions with sulfate [ 31. The microscopic nature of the mechanism of the exchange reaction is not directly accessible by experimental methods. In general, reaction mechanisms can be deduced by experimentally testing the sensitivity of the reaction rate to a variety of chemical and physical parameters such as temperature, pressure, or concentration. In recent years the application of classical molecular dynamics or Monte Carlo simulations as well as ab initio and DFT calculations have gained significant interest. The performance of the new generation of computers and theoretical approaches now allows calculations, which can provide deeper microscopic insight

4.2 Concepts of Solvent Exchange Reactions

into water exchange processes, to be undertaken. Classical simulations of hydrated metal ions in solution mainly rely on painvise additive, effective interaction potentials obtained from quantum mechanical calculations or from empirical optimization of thermodynamic values like hydration energies or radial distribution functions. This approach limits these simulations to metal ions with filled atomic orbitals, mainly to main group ions and those transition metal ions, where ligand field effects can be neglected (e.g. lanthanides). The advantage of the classical methods is that relatively large systems, containing up to lo3 water molecules can s). Exchange processes can be followed directly be simulated over several ns ( by inspecting trajectories, molecular coordinates and velocities as a function of time. Full quantum mechanical calculations using ab initio self-consistent field (SCF) methods or density functional theory (DFT) are computationally much more demanding and, therefore, mostly restricted to ion-water clusters containing one metal ion and a limited number of water molecules. Different metal-water clusters that can occur along the reaction coordinate of a water exchange process have to be calculated. A comparison of energies and structural parameters such as metaloxygen bond distances in the reactants, transition states and intermediates will help to associate them to different reaction mechanisms. In gas-phase calculations, second coordination sphere, bulk solvent and anions are neglected and, furthermore, contrary to classical molecular dynamics simulations, no real time scale is provided. On the other hand, these calculations are not based on empirical pairwise interaction potentials, in fact calculations on all types of ions, including transition metals, are feasible. A promising method, developed in recent years, is the use of first principles molecular dynamics as exemplified by the Car-Parrinello technique [ 81. In these calculations the interatomic potentials are explicitly derived from the electronic groundstate within the density functional theory in local or non-local approximation. It combines quantum mechanical calculations with molecular dynamics simulations and, therefore, overcomes the limitations of both methods. Actual computers allow only simulations of aqueous solutions of about GO water molecules for several ps ( s). This limit is still at least one order of magnitude shorter than the fastest directly measured water exchange rate, k = 3.5 x lo’ s-l for [Eu(H20)8]*+,i.e. one exchange event every (8 x 3.5 x lo’ s-’)-’ = 36 ps [91. Nevertheless, several publications appeared in the late 1990s on solvated Be2+ [lo], K+ 1111 and Cu2+ [12] presenting mainly structural results. This chapter is essentially an update of our review which appeared two years ago 1131.

4.2

Concepts of Solvent Exchange Reactions

The mechanistic classification accepted for ligand substitution reactions was proposed by Langford and Gray in 1965 [14]. They divided substitution reactions into

I

133

134

I

4 Water Exchange o n M e t a l Ions: The Effect of Pressure

three categories of stoichiometric mechanisms: associative (A) where an intermediate of increased coordination number can be detected, dissociative (D) where an intermediate of reduced coordination number can be detected, and interchange ( I ) Y repwhere there is no kinetically detectable intermediate (Eqs 4.2-4.4). MX, resents an outer-sphere complex. ' '

-X

MX,

+X

+Y

MX,,-l

+Y

(D = dissociative)

(4.2)

(A = associative)

(4.3)

(I = interchange)

(4.4)

-X

MX, F'tY MX,Y MX,

+ MX,-lY

-Y

$

tX

MX,-IY

. . . Y $ MX,_lY.

. .X

Furthermore, they distinguished two major categories of intimate mechanisms: those with an associative activation mode (a), where the reaction rate is approximately as sensitive to variation of the entering group as to variation of the leaving group, and those with a dissociative mode (d), where the reaction rate is much more sensitive to the variation of the leaving group than to the variation of the entering group (Fig. 4.2). Evidently all D mechanisms must be dissociatively and all A mechanisms must be associatively activated. The interchange ( I ) mechanisms include a continuous spectrum of transition states where the degree of bond-making between the incoming ligand and the complex ranges from very substantial (I, mechanism) to negligible ( I d mechanism) [15, 161. For a solvent exchange process, the forward and backward reaction coordinates must be symmetrical. Thus, for an Id mechanism, with weak bond-making of the entering group, the leaving group is also necessarily weakly bound. Inversely, for an I, mechanism, both the entering and the leaving group must have considerable bonding to the metal (Fig. 4.3) [15]. As mentioned above, the proposition of a reaction mechanism is mainly based on the response of the reaction rate to the variation of chemical and physical pa-

evidence for an intermediate of lower coordination number stoichiometric mechanism

evidence for an intermediate of higher coorinatiion number

no evidence for an intermediate

I

D

A

intimate mechanism

A I

I

rate independent of nature of entering

I

1

rate to nature of entering

Fig. 4.2.

Classification o f solvent substitution reactions.

I I

rate dependent of nature of entering group

4.2 Concepts of Solvent Exchange Reactions

I

135

hlechanism

Rate constant

Reaction Coordinate

Metal ion with first coordination sphere Leaving solvent molecule

@

Entering solvent molecule

Fig. 4.3. Representation o f the transition state for the spectrum of solvent o r symmetrical ligand exchange processes,

rameters. The volume of activation, AV# , has become the main tool for the experimental identification of the water exchange mechanism [17-191. AVf is defined as the difference between the partial molar volume of the reactants and that of the transition state at a temperature ?; as shown in Eq. 4.5.

The observed exchange rate, k, is either slowed down or accelerated by increasing pressure, depending on the positive or negative sign of AVz, respectively. It is usually accepted that the activation volume has two contributions: an intrinsic component, AVi$ resulting from changes in bond lengths and bond angles, and an electrostrictive component, AV&, which arises from changes in electrostriction of the solvent outside the first coordination sphere. For solvent exchange reactions differences in electrostriction between the transition state and the reactant can be

136

I

4 Water Exchange on Metal Ions: The Eflect offressure

neglected, hence AVz E AV,Zt. Consequently, the activation volume will be a direct measure of the degree of bond formation or bond breaking in the transition state. The relation between the pressure-induced changes of the observed exchange rates and the underlying solvent exchange reaction mechanisms is shown in Fig. 4.3. An important issue is the prediction of activation volumes for the limiting substitution mechanisms D and A. Swaddle [20, 211 developed a semi-empirical model in which the absolute partial molar volume, AV&, of a hydrated metal ion in water is related to its ionic radius, depending on the coordination number, and the charge of the metal ion. Taking ionic radii from Shannon, this model gives similar absolute limiting values of IAV’I = 13.5 cm3 mol-’ for D and A processes on octahedral di- and trivalent 3d transition metal ions. An extensive compilation of activation and reaction volumes of organic and inorganic reactions in solution can be found in a series of reviews by Asano et al. [ 221.

4.3

Water Exchange from the First Coordination Shell 4.3.1

First Row Transition Metal Ions

Water exchange on first row di- and trivalent transition metal ions has been the subject of extensive experimental studies and has been widely reviewed [IS, 231. Table 4.1 summarizes the experimental first order rate constants and the activation parameters. The sequence of reactivity of the diualent first-row transition metal ions does not correlate with the radii of the ions and is largely independent of the reaction mechanism. The rate constants are sensitive to the electron configuration and semiquantitatively coincide with predictions based on ligand field activation energies and molecular orbital calculations [23, 33, 341. The water exchange mechanism progressively changes from I, to Id as the number of d-electrons increases and the ionic radius decreases. This change is demonstrated most evidently by the change in sign of the activation volume, AVz. The observed progressive mechanistic changeover cannot be explained only in terms of cationic size, the electronic configuration also plays an important role. For a a-bonded octahedral complex, the t2g orbitals are non-bonding, whereas the eg orbitals are anti-bonding. The gradual filling of the t2gorbitals, spread out between ligands, will electrostatically disfavor the approach of a seventh molecule towards a face of the octahedron, and therefore decrease the ease of bond making. Similarly, an increased occupancy of the eg orbitals, directed to the ligands, will enhance the bond breaking tendency. These effects, combined with the steric effects outlined above, explain the sequence of the AV# values. A special case is the very labile hydrated copper ion. Because of its electronic dg configuration, a Jahn-Teller distortion is generally assumed to elongate axially two bonds of the octahedral [ C U ( H ~ O ) ~complex ] ~ + in solution [4, 31, 351 by anal-

M3+ rM (pm) k298 t -1 \s 1 AHZ (kJ mol-I) AS# (JK-' mol ') A V Z (cm3mol-') Mechanism Ref.

64 5.0 x 102 49.0 -27.8 8.9

1,

27

A, 1,

26

v3+

3dZ

Ti3' 67 1.8 x 105 43.4 +1.2 -12.1

3d'

28

1,

Cr3+ 61 2.4 x 10 108.6 +11.5 -9.6

79 8.7 x 10' 61.8 -0.4 -4.1 1, 24

V2+

3d'

Mn3' 64

cr2' 80

3d4

Id

25

1,

25 Fe3+ 64 1.6 x l o 2 64.0 +12.1 -5.4 1, 29, 30

78 4.4 x 106 41.4 721.2 +3.8

Fe2+

3d6

83 2.1 x 107 32.9 +5.7 -5.4

Mn2+

3dS

Id

25

25

Ni2+ 69 3.2 x 104 56.9 f32.0 +7.2

3d8

Id

74 3.2 x lo6 46.9 +37.2 +6.1

C02'

3d7

Rate constants and activation parameters for water exchange on first row transition metal ions [ M ( H 2 0 ) 6 ] " +

M2+ rM (pm) k2" (s-') AHf (kJ mol-I) AS# (1 K-' mol I ) AV# (cm3mol-I) Mechanism Ref.

Tab. 4.1.

73 5.7 x 109 11.6 -19.2 +2.0 I 12, 31

cu2+a

3d9

32

Id

'+

Ga 62 4.0 x l o 2 67.1 +30.1 -5.0

Zn2' 74

3d'O

a

3.

P

138

I

4 Water Exchange on Metal lons. The Effect of Pressure

ogy with its X-ray structure [3G]. The tetragonal distortion reorients randomly very rapidly so that the lifetime of a given distortion (51 5.1 x 10- l 2 s at 298 K) is much shorter than the lifetime of a given coordinated HzO molecule (rH20 = 2.3 x lo-'' s at 298 K). The longer axial bonds facilitate water exchange through a d-activation mode which is consistent with the small positive activation volume (Table 4.1) [37]. Pasquarello et al. [12] have shown recently by a combined experimental neutron diffraction and a theoretical first-principles molecular dynamics study that there is strong evidence for a five-fold coordination of the Cu(I1) aqua ion in aqueous solution. The simulation revealed that the [Cu(H20)5I2+complex undergoes frequent transformations between square pyramidal and trigonal bipyramidal configurations which weaken Cu-water bonds. The ''0 NMR data [31] can successfully be re-interpreted in terms of five-fold coordinated copper with interconversion (rl 5 ps) between square pyramidal and trigonal bipyramidal forms, yielding a water exchange rate of (5.7 0.2) x 109 s-'. The small positive activation volume of f2.0 f 1.5 cm3 mol-' is also fully compatible with an interchange process for water exchange on [Cu(H2O)5I2+. Water exchange on trivalent first-row transition metal ions shows a similar mechanistic behavior as that of the divalent analogues. [Cr(H20)6I3+is the most inert (Table 4.1) as a consequence of its large ligand field activation energy reflected in the large AH1 value. AVi decreases from -12.1 cm3 mol-' ([Ti(H20)6]3+)to -5.4 cm3 mo1-l ([Fe(HzO)6I3+). The activation volume for Ti3+ approaches the limiting value of -13.5 cm3 mol for an A mechanism [20], hence the operation of an A mechanism can be assigned. As the occupancy of the t2g orbitals and in parallel the electronic repulsion towards an entering ligand increase, the activation volumes become less negative, indicating a changeover to less associative, and finally a dissociative activation mode (for Ga3+)as a consequence of the filling of the o anti-bonding e l orbitals. A general problem arising with trivalent metal ions is the occurrence of the conjugate base species, [M(H20)50HI2+, already kinetically active at quite high [H+] concentrations. In all cases studied (M = Cr, Fe, Ga) the lability of the coordinated water is highly increased and the activation volumes are all positive (f2.7, +7.0, +G.2 cm3 mol-' for [Cr(H2O)5OHl2+,[Fe(Hz0)50HI2+, and [Ga(H20)5OHI2+,respectively, Table 4.2). It is worth noting that the associative activation mode found for [Fe(H20)6I3- changes to a dissociative one for [Fe(H20)50H]2 t . In recent years, several authors published ab initio or DFT calculations on gasphase hydrated metal ions. The main goal of the studies was to obtain microscopic insight into water exchange on octahedral complexes. Rotzinger [ 40-431 carried out calculations on di- and trivalent first-row transition metal ions from Sc3+ to Zn2+ using ab initio methods at the Hartree-Fock or CAS-SCF level. All pertinent transition states and intermediates that could occur along the reaction coordinate of an associative, a concerted and a dissociative water exchange process were calculated. In his study, reactants, products, and intermediates were characterized throughout by the absence of any imaginary vibrational frequency, whereas transition states always show a single imaginary frequency [40]. As an approximation, he neglected in the first studies second sphere and bulk water as well as anions. The 1

-

kobs = kl i kz/[H';

[M(H20)50H12+

= kl

rM

(pm)

-1.1 4.1 1.8x 10-4

lo-'

1.4 x

k:98a (m s-l)

AV:

28

Ref

T

ko~K~/iH+].

Mechanism

-3.8 12.7 I

(s-')

AVZ ( c m 3 mol-') AV;,, ( c m 3 mol-')

kOH

P K

( c m 3 mol-l)

Mechanism

AVf ( c m 3 mol-')

61 2.4 x -9.6 1,

k,2g8 (s-')

cr (111)

29, 30

Id

f7.0

f7.8 2.9 1.2 x 105 +0.8

1.2 x 103

1.6 x lo2 -5.4 1,

64

Fe(I11)

39

I

I 38

f1.2 3.5 4.2 x -0.2 f1.5

1.5 x

lo-$

2.2 x 10-9 -4.1 1,

66.5

Rh(111)

-2.1 2.7 5.9 x 10-4 -3.0 +0.9

1.1x 10-6

1,

3.5 x 10-6 -8.3

68

Ru(l1l)

5.7

0.2 4.45 5.6 10-7 1.5 -t 1.3 1 2 ~

1.4 x lo-"

1,

1.1 x 10-10

68

Ir(111)

Rate constants and activation volumes for water exchange o n trivalent hexa-aqua transition metal ions and their conjugate base species.

[M(Hro)6I3+

Tab. 4.2.

32

Id

+6.2

+l.S

f7.8 3.9 1.1x 105

1.4 x 10'

Id

+5.0

4.0 x lo2

62

Ca(lf1)

W

4

-...

VI

z -

6-

4

a 9'

5 6

3.

2

%

S

is-?

Y

$

lu

P

140

I

4 Water Exchange on Metal Ions: The Effect of Pressure

301+m I. mechansim lV(OH2)612'

A mechansim [Ti(0H2)d3'

D or (IJ mechansim "i(OH2)d2'

E A kJ mol-' 60

50 40

t

+61.9...... AG$czp

+43.0

......AG',.,

20

10

0

I'

Q 0 0 @ Q @ Q

000

00000

A

J W

-2 AV'~~,,= -12.1 cm3 mol-'

AV'.,,

= -4.1 cm3mol-'

AV'.,,

= +7.2 cm3mol-'

reliability of his calculations was proved by the agreement of the computed activation energies AE# with the experimental AGf and AHf values (Fig. 4.4). Calculation of the partial molar volumes of the reactants, the transition state and the intermediate is difficult and Rotzinger calculated differences of the sums of all metal-oxygen bond lengths, AC(M-0), which are related to the activation volumes. Figure 4.4 shows that the sign of AC(M-0) is negative and agrees with that of the experimental AVf . For the titanium transition state, as Rotzinger states, reaction water entry undoubtedly dominates the activation process which can clearly be identified as an A mechanism. The transition state for {[V(H20)5. . . (H20)2]2t}f has C2 symmetry and arises from a concerted process. The hypothetical transition states involving electronic low-spin (triplet) states, {[V( H Z O ) ~ #] ,~have ~ } very high energies (242 and 244 kJ mol-') relative to the reactant, excluding spin-change in the water exchange process. The negative value of ACd(M-0) for the transition state shows that bond formation occurs to a larger extent than bond breakage. For water exchange on [Ni(H20)6l2+,only a transition state for dissociative activation could be calculated. The species {[ Ni( H20)s . (HzO).(HzO)]2t}i has C, symmetry and the incoming and leaving water molecules are easily distinguishable. The '

4.3 Water Exchange from the First Coordination Shell

subsequent intermediate [ Ni(H20)5.(H20)2]2+ has ClYsymmetry and is basically a square pyramidal penta-coordinate species, hydrated by two water molecules. The energy difference between transition state and intermediate is small for this dissociative process. The calculated sum of the metal-oxygen bonds increased for both the transition state and the intermediate as compared to the reactant state, leading to a positive of value AC(M-0). An improvement of the calculations is the introduction of dynamic and static electron correlation in the computation of the energies and the second coordination sphere together with bulk solvent as a dielectric continuum in the calculation of energies and geometries [43]. This extended model was applied to the H2Oexchange in [V(H20)(1]2 [Mn(H20)6I2+,and [Fe(H20)6I2+.For each hexaaqua ion associative and dissociative mechanisms were investigated. Starting from a second sphere water molecule forming two hydrogen bonds with the first sphere water molecules, activation energies in agreement with experimental data were obtained. For water exchange in V(I1) and Fe(II), computational data suggest an a and a d activation, respectively, in accordance with experimental data. The model did not allow distinction between a and d activation for Mn(I1) on the basis of energies. The attribution of an associatively activated exchange was made in this case using changes in the sign of the bond length. In summary, the results obtained by Rotzinger on first-row transition metals provided the following picture [41]. Hexacoordinated Sc3+,Ti3+ and V3+ react via an associative A mechanism with relatively long-lived intermediates. The dissociative pathway is only possible for water exchange on Ni2+,Cu2+ and Zn" . For the elements in the middle of the 3d series both associative (IJA) and dissociative (D) pathways can occur. The structure and water exchange mechanism of hexahydrated Ti(III), its hydrolysis, and the water exchange mechanism of analogous hydroxo-aqua complexes have also been studied using DFT calculations by Hartmann et al. [44]. It was found that the water exchange reaction of this complex follows a (almost) limiting A mechanism with an energy of activation of 66.1 kJ mol-'. Only a weak structural influence, indicated by a slight increase in the mean value of the T i - 0 bond lengths of water molecules in the first coordination sphere, is observed when the hydroxo ligand is formed. The water exchange reactions of the corresponding hydroxo-aqua complexes [Ti(H2O),(OH)]2+ and [Ti(H20)5(0H)]'+H20, respectively, were found to proceed via limiting D mechanisms. The energies of activation for the exchange of the water molecule in the trans-position to the hydroxo ligand were calculated to be only 41.0 and 30.1 kJ mol-', respectively. The hydration of the zinc(11) ion was also studied by Hartmann et al. [ 451. Structures and hydration energies were computed using DFT for [ Zn( H z O ) ~ '] with n = 1-6 and for [Zn(H20),]2+.rnH20with n = 5 and rn = 1 , 2 and n = 6 and rn = 1. The structures with water molecules in the second coordination sphere revealed two types of complexes having either one or two hydrogen bonds between first and second sphere water molecules. In agreement with Rotzinger [41]a dissociative D mechanism was found to be most likely for the water exchange in [Zn(HzO)6I2+. +,

I

141

142

I

4 Water Exchange on Metal lons: The Effect of Pressure

Rate constants and activation parameters for water exchange on second- and third. row transition metal ions.

Tab. 4.3.

M ll+ Geometry

4dS

4d6

Ru3+ Octahedral

RuZ+ Rh’t 1 ~ 13 Pd2+ Pt2+ Octahedral Octahedral Octahedral Square Square planar planar 73 66.5 68 64 60 1.8 x 2.2 x 10-9 1.2 x 10-9 5.6 x 10’ 3.9 x 10-4 131.2 87.8 49.5 130.5 89.7 fl6.l +29.3 -26.0 -9.0 +2.1 -0.4 -4.1 -2.2 -4.6 -5.7 Id, D Ia 1, 1, Ia 2 38 39 46 47

68 rM (pm) k2’* (s-I) 3.5 x 10-6 AH# (k]mol I ) 89.8 ASf (1 K-’ mol-I) -48.2 AVf (cm3 mol-’) -8.3 Mechanism 1, Ref. 38

4d6

5d4

4d8

5d8

4.3.2 Second- and Third-Row Transition Metal lons

Experimental data on water exchange on second- and third-row transition metal ions are much more scarce (Table 4.3). For the low-spin t!g hexaaqua ions [Ru(H z o ) ~ ] [ Rh(HzO),] 3+ and [ Ir(H 2 0 ) ~ ] one would a priori predict a dissociative activation mode. The filled t2g orbitals, spread out between ligands, electrostatically disfavor the approach of a seventh molecule towards a face or edge of the octahedron and therefore decrease the ease of bond making. In a first study of the mechanism of substitution in [Ru(H20)~]”;it was shown that the rate constants for the anation reactions of C1-, Br-, and I- were very similar, indicating identical steps to reach the transition state (i.e. dissociation of H 2 0 )[48]. Later, this study was extended to a large variety of ligands possessing various charges and nucleophilicities, and it was clearly demonstrated that the rate determining step of the monocomplex-formation reactions was independent of the nature of the entering ligand. An Id mechanism was therefore suggested for the substitution reactions in [ Ru(H20)6]2+ [49]. However, a variable pressure study of water exchange on this ion gave an activation volume close to zero (AV# = -0.4 cm3 mol-’) and was therefore interpreted as an interchange I mechanism without a predominant “a” or “d’ character [38]. Attempts to compute, at the restricted Hartree-Fock (SCF) level using the selfconsistent reaction field model (SCRF), a transition state for an I mechanism failed and only a D mechanism with a five-coordinate intermediate could be computed [SO]. The impossibility of calculating a transition state for the Id mechanism does not mean that it does not exist: it is just not available within the model in which the second coordination sphere is not treated by quantum chemistry. Therefore, the experimental and theoretical results available today suggest that water exchange on [Ru(H20)6I2+proceeds via a “d activation”, either the Id or D mechanism. This is also in agreement with the high pressure study of the formation of [ Ru(H20)5(DMF)]2+ from the aqua ion, for which the volume of the transition

’+,

’+,

4.3 Water Exchange from the First Coordination Shell

state lies between the volume of the reactant and the volume of the products and where an I d mechanism has been assigned [Sl]. [ Rh(H20)6]3+ and its third-row analog [ Ir(H20)6] ' are the most inert aqua ions known up to now [2].The lifetime of a water molecule in the first coordination shell of Ir3- is 9.1 x lo9 s (at 298 K), which corresponds to about 300 years. The negative activation volumes of Rh3+ and Ir3+ ions suggest the operation of an associative I, exchange mechanism (Table 4.3).Theoretical calculations have allowed the characterization of the seven-coordinate transition state {[Rh(OH2)5. . . (OH2)2l3+}+ corresponding to the I, exchange mechanism for Rh3+ [SO]. Why do Rh3+ and Ir3+ on one hand and Ru2' on the other, undergo water exchange via disparate mechanisms although they are isoelectronic? The charges are different, affecting particularly the M - 0 bond strength. This is manifested by the calculated activation energies for the exchange reactions via the D mechanism: 71.9 kJ mol-' for Ru2+ and 136.6 kJ mol-' for Rh3+ [SO] (Fig. 4.5). Therefore, the strong Rh"'-0 bonds allow water exchange in [ Rh(Hz0)6]3T to proceed via the I, pathway, whereas the same reaction on [ Ru(H20)6]2 + , which has considerably weaker Ru"-0 bonds, follows the I d or D mechanisms.

160 + I 22.3 +114.8

:I. 00000

-2 -1

......AG'.,

A 000

Fig. 4.5. Energies calculated with a polarizable continuum model, differences of the sums of all metal-oxygen bond lengths, AC(M-0), and energy profiles for water exchange on rhodium(ll1) and ruthenium(l1) hexaaqua ions.

+83.0-----5 +7 1.9

00000

I

143

144

I

4 Water Exchange on Metal Ions The Effect of Pressure

The low-spin t& [ R U ( H Z O ) ~is ] ~four ’ orders of magnitude more labile than the tig [ R u ( H ~ o ) 6 ] ~[38] ’ and, according to the same arguments developed above, exchanges water by an I, mechanism. The knowledge of the difference in lability of [ Ru(H20)6]2- and [ Ru(H20)6]3- led to the unequivocal identification of an outersphere mechanism operating in the electron exchange between these two aqua complexes [38]. Water exchange rates of the three M3+ complexes were also measured for the deprotonated species [M(H20)s(H,0)]2f.As for their first row analogs, a substantial acceleration of the water exchange was observed compared to the hexa-aqua complex: k,, = 5.9 x 10- s-l ([Ru(H20),(OH)12+),k,, = 4.2 x lo-’ s-l ([Rh(H20),(OH)]2f),and k,, = 5.9 x s-l ([Ir(H20)5(0H)12+), and also a changeover towards a more dissociative activation or less associative activation mode. The vast majority of square-planar dXtransition metal ions, such as palladium(I1) and platinum(11) undergo ligand substitution through associatively activated mechanisms [ 5 2 ] . Water exchange on [Pd(H20)4l2+[4G] and [Pt(H20)4I2+1471 were studied by I7O N M R (Table 4.3). The mechanistic interpretation of the activation volumes is complicated by the square-planar geometry of the complexes. The axial sites may be occupied by non-bonded water molecules. Bond formation between the metal center and such a water molecule leading to a five-coordinate transition state may result in rather small volume changes. It is therefore difficult to distinguish from AVf values between an associative interchange I, and a limiting associative A mechanism. Density functional theory has been used by Deeth et al. [ 531 to model water exchange on square-planar [ Pd(HzO),] 21 and [ Pt(H z O ) ~2 L]. The calculations strongly suggest that water exchange at these square-planar metal centers proceeds via an associative mechanism, in full agreement with experimental assignments [4G, 471. The agreement in experimental and calculated activation enthalpy is better than 10 kJ mol-* for an I, mechanism, whereas it differs by more than 100 kJ mol-I for an Id mechanism. 4.3.3 Lanthanides

The 15 trivalent lanthanide ions, which may be collectively denoted by Ln3+, represent the most extended series of chemically similar metal ions. The progressive filling of the 4f orbitals from La3+ to Lu3+is accompanied by a smooth decrease in ionic radius with an increase in atomic number as a consequence of the increasingly strong nuclear attraction of the electrons in the diffuse f orbitals. These orbitals are shielded by the surrounding filled 5s and 5 p orbitals, leading to very small crystal field splittings in the lanthanide complexes. Thus the coordination properties of the Ln3+ ions mainly depend upon the steric and electrostatic nature of the ligands. The coordination of the lanthanide(II1) ions in aqueous solution was certainly one of the most controversial questions in lanthanide chemistry. Now it is well established from neutron scattering [54, 551, X-ray scattering [5G-58] and absorption fine structure [ 591, density [GO] and spectrophotometric (611 techniques that the lighter ions ( La3+-Nd3+) are predominantly nine-coordinate and the

4.3 Water Exchange from the First Coordination Shell

heavier ions ( Gd3+-Lu3+) are predominantly eight-coordinate species. The ions Sm3+-Eu3+ exist in equilibria between eight- and nine-coordinate species (Eq. 4.6).

+

[Ln(H2O)sI3+ H2O $ [Ln(H20)9]3+ The change in coordination number is reflected in the absolute partial molar volumes, V2b,, determined in aqueous LnC13 solutions (Fig. 4.6). The calculated absolute partial molar volumes using the semi-empirical model of Swaddle [20, 211 agree well with [ Ln( Hz0)9] 3+ at the beginning and with [ Ln(H20)8]3-' at the end of the Ln3+ series. Rate constants for water exchange on lanthanide(II1) ions can be determined by oxygen-17 NMR relaxation and chemical shift measurements [62, 631. Unfortunately, only eight-coordinate heavy lanthanides (Gd3+to Yb3+) could be studied (Fig. 4.6) due to the less important chemical shift induced by the early lanthanide ions. Powell's results [G4]at high magnetic field allowed the determination of the lower limits for water exchange rates at 298 K on [Nd(H20)9] and [ Pr( H20)9] 3 t . The water exchange rates are closely correlated with the rate, kfq8, of the interchange between an inner sphere water molecule and a SO:- ion from the outer sphere coordination (Fig. 4.6) [65]. The values show a maximum in the middle of the series, corresponding to the crossover region in CNI from nine to eight. For the heavy lanthanides, in addition to variable temperature, variable pressure measurements were performed so that the activation volumes for the exchange process could be determined. The activation volumes are all negative [G3], indicating an associatively activated water exchange mechanism (Fig. 4.6). This observation can be explained in terms of the coordination equilibrium observed in the middle of the series. For the heavy lanthanides, the octa ion is the lowest energy species and the ennea-aqua ion represents the intermediate (or transition state) in the associatively activated water exchange reaction. The exchange rates become faster towards the middle of the series as the difference in the energy between octa- and enneaaqua ions decreases. For the mid-series lanthanides, the octa- and ennea-aqua species are in equilibrium. The transition from one species to the other requires relatively little energy, so that these lanthanides should have the fastest water exchange rates of the series. For the light lanthanides, the ennea-aqua ion is now the lowest energy species. One can expect, therefore, that the octa-aqua ion will be the intermediate (or transition state) in the exchange process, which will proceed via a dissociatively activated mechanism. One would expect to observe an increase in water exchange rates and positive activation volumes from La3+ to Nd3+. Unfortunately, so far it has not proved possible to demonstrate experimentally these predictions for the light lanthanide ions. The absence of crystal field splitting and the shielding of the f orbitals makes classical molecular dynamics (MD) simulations feasible. Hence, for solvents without covalent bonding like water, ion-solvent forces can be well represented by simple Coulomb and van der Waals terms. The polarization of water molecules in the first coordination shell due to the strong electric field of the trivalent ions has

'

I

145

146

I

4 Water Exchange on Metal Ions: The Effect ofpressure

-45

1

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

\€i-coordinate

l ! 9-coordinate

E

h

''

-2 -

-

-4 -6-

-

-8-

-

1

1

1

1

1

1

1

1

1

1

1

1

l

I

I

to be taken into account [GG]. Figure 4.7 shows the distribution of the number of water molecules for three distance regions of three trivalent ions, designated as Nd3+, Sm3+ and Yb3+ obtained from classical MD simulations [GG]. The experimentally observed change in the first shell coordination number CN, from 9 for Nd3+ to 8 for Yb3+could be reproduced. The result for Sm3+reveals that the observed CNI of 8.5 indeed corresponds to an equilibrium between an octa- and enneaaqua ion. Only 9 % of all configurations have a ninth water molecule between the two spheres (Fig. 4.7). An advantage of computer simulations is that they can deliver microscopic

4.3 Water Exchange from the First Coordination Shell

I

147

I

3.1-3.78,

0.0-3.1A 3.1-5.48, '

(1st

1

shell)

(2nd shell)

0.8

.-0 5

0.6

2g 0.4 a

0.2 0

1 0.8

L. Z 0.6

R.52

5g 0.4

17.13

P,

0.2 0 1

-%3 0.60.8 .-

s 0

k 0.4 0.2

0

5

10

15

20

25

number of water molecules Fig. 4.7. Distribution of the number o f H20 molecules in three distance regions for the Simulations, Nd, Sm, and Yb within the polarizable water model. The inserted numbers are the mean number of water molecules in each distance range.

structural pictures of the systems studied. A detailed analysis of the first coordination shell [67] showed that for the light lanthanide ions (Nd3+),the nine water molecules form a tricapped trigonal prism similar to that found by solid state X-ray diffraction studies on [Ln(H20)0]3+ with counterions CF3SO7, EtOSO;, and BrO; [68]. The eight H 2 0 molecules in contact with the smaller heavy lanthanide ions (n3+) form a square antiprismatic geometry with equal ion-oxygen distances. Hydration shells from simulations of Sm3+ are actually a mixture of equal amounts of eight- and nine-fold coordinated ions adopting the geometry of a square antisprim or a tricapped trigonal prism, respectively [67]. Figure 4.8 (bottom) gives an example of the trajectories of the water molecules in the first and

148

I

4 Water Exchange on Metal Ions: The Effect of Pressure

-

--

116

0'50

ili 300

320

340

360 tlps

380

400

Fig. 4.8. Ion-oxygen distance for a 100-ps interval simulation for Sm (bottom). The plot illustrates the equilibrium between eight- and nine-fold coordination. The volume V,,, that is enclosed by the solvent-accessible surface of the [Sm(Hz0)8/9]3+aqua ion is shown as a function of time (top).

second hydration shells for a 100-psinterval and illustrates the equilibrium between the two coordinations. The reaction volume, AVO, for this equilibrium can be estimated using Swaddle's semi-empirical model [20], as about --13.0 cm3 mol-'. From the M D simulations, volumes included in the solvent-accessible Connolly surface [G9], VSa,, can be calculated (Fig. 4.8, top). With V,,, (CN, = 9) = 112.0 cm3 mo1-l and V,,, (CNI = 8) = 101.2 cm3 mol-', a reaction volume of -7.2 cm3 mol-' was calculated [70]. MD simulations performed at different densities ( p = 0.9, 1.0 and 1.1 g cm-3 corresponding to pressures of -244, 0.1 and 188 MPa), showed a change in the mean coordination number from 8.26 to 8.62 due to an increase of configurations with nine coordinated water molecules in the first shell with increasing density (Fig. 4.9). The slope of a plot of ln(K) versus pressure gives a AVO of -8.3 cm3 mol-l [70]. Both volumes calculated in different manners

4.3 Water Exchange from the First Coordination Shell

1

3.1-3.7A

0.0-3.1A (1st shell)

133'i2L$i

0.8 0.6

a 0.4

0.2

0.8

P=1.013 g/cm' 8.48

0.6

c

0.4 4.

0.2

0.8 0.6

a 0.4 0.2

L 0

5

10 15 20 number of water molecules

25

Fig. 4.9. Distribution of the water molecules in three distance ranges around the S m 3 ' ion at three different overall densities. The inserted numbers are the mean numbers of water molecules in each distance range.

from MD simulations agree well with the reaction volume of -10.9 cm3 mol-' measured experimentally for [ Ce(H20)8]3f H 2 0 F? [ Ce(Hz0)9]3+ [ 711. From molecular dynamics simulations, information on water exchange is available for the three regions of coordination. The simulation qualitatively confirmed the lability maximum of the first hydration shell found in the middle of the series [70]. From the trajectories obtained from the simulations, all transitions of water molecules between the first hydration shell and the bulk were identified and grouped into pairs of water molecules that together form a coupled exchange [70]. Similar to the hydration equilibrium of Sm3+, volume profiles for water exchange processes can be obtained using Connolly's method. Volume changes with

+

I

149

150

I

4 Water Exchange on Metal Ions: The Efict of Pressure

5 4

20 3 f “E0

. m 1

$ 0 -1.

I

-

128

‘re1 ’PS Fig. 4.10. Mean activation volume profile AVsas(t)from the water exchanges on Nd3’- (CN = 9, top) and Yb3+ (CN = 8, bottom) after averaging the positive and the negative halves of the profile.

respect to the mean volume of an aqua ion in equilibrium plus one isolated water molecule are shown for 10-ps intervals in Fig. 4.10 1701. For [Nd(H20)9]3L (Fig. 4.10 top) the dissociation of a water molecule from the primary hydration shell corresponds to an increase in volume. The picture that emerges from the volume profile for the water exchange on [Yb(H20)s]3+ is more complicated. The entering of a water molecule from the second hydration shell into the region between the first and second spheres leads to a slight increase in volume. This feature of the volume profile indicates that the square antiprismatic octa-aqua ion prepares itself geometrically for the reception of a ninth water molecule before compacting to the transition state that is a tricapped trigonal prism. The only easily accessible divalent lanthanide is europium(I1). Eu2+ is isoelectronic with Gd3+ and very similar in size to Sr2+. Since water exchange on the

4.3 Water Exchangefrom the First Coordination Shell

heavier group 2 elements cannot be directly measured, Eu" may provide insight as a probe in the chemistry of Ca" and Sr". A simultaneous fit of nuclear and electronic relaxation rate data results in k::8 = 4.4 x 10' for the water exchange rate with activation parameters AHf = 15.7 kJ mol-' and A S # = -7.0 J K-' mol-', AV# = -11.3 cm3 mol-' for the volume of activation for exchange, and 2 i 9 8 = 16.3 ps for the rotational correlation time 19, 721. The volume of activation is very large and corresponds to a limiting associative mechanism. This suggests that water exchange for an eight-coordinate ELI& (typically square antiprismatic) would proceed through a nine-coordinate transition state (tricapped trigonal prism), similar to that for [Gd(H20)8]3i[73]. However, the water exchange rate for ELI;) is 5-6 times faster than that for Gd&. 4.3.4 Main Group Elements

There are only a few main group metal ions amenable to a detailed mechanistic study of water exchange: Be2+-,Mg2+,A13+, Ga3+ and In3+. They provide the opportunity to study the influence of size and charge on the mechanism without the complicating effects of the variation of the electronic occupancy in the d-orbitals. All alkali ions and CaZ+,Sr2+and Ba2+ are very labile as a consequence of their relatively low surface charge density. The only direct experimental data on water exchange in some of these ions comes from incoherent quasi-elastic neutron scattering (IQENS) [74-761. IQENS has an observation time scale t&,s 1ns and allows for the calculation of limits for ion to water-proton binding times zi (Table 4.4). Mean lifetimes of H2O in the first shell of Ca2+ and Sr2+ can be estimated to -0.2 ns from the chemically similar EuZLion (see Sect. 4.3.2). The tetrahedrally [ 77-81] coordinated beryllium( 11) and the octahedrally [82-87] coordinated magnesium( 11) show relatively slow water exchange rates from the first coordination sphere and can be measured directly by NMR techniques (Table 4.5). The water exchange reaction on beryllium(I1) is characterized by the most negative activation volume observed for a water exchange process (AV# = -13.6

-

Tab. 4.4. Ion-water proton binding times,

T , ,obtained from IQENS experiments on concentrated aqueous ionic solutions at -298 K [76].

q

< 0.1 ns

ri

> 0.1 ns

T; > 5

Li+

Zn2+

Mg2+

cs+

Nd'+ Dy'+

Al3t

Ca2+

Ni2

cu2+ F-

Cr'+

c1-

Ga3

Ic10;

Fe3'

ns

152

I

4 Water Exchange on Metal Ions: The EJect of Pressure Tab. 4.5.

Water exchange rate constants and activation parameters for water exchange on

[Be(H20)4]2+ and [ Mg(HzO) 612+.

[Be(H20)4]2+

[Mg(H20)6l2+

7.3 x l o s 6.7 x lo5

59.2

+ 8.4

49.1

+31.1

-13.6 6.7

77

A Id,

D

88

cm’ mol -I), which is close to a calculated limiting A V f = -12.9 cm3 mol-’ for an A mechanism (hexaaqua ion) [77]. The water exchange rate for [Mg(H20)6]2’ [88] lies between that of [Co(H20)6]*+and [Ni(H20)6I2+(Table 4.1) and reflects the order of ionic radii of these three ions (Co2+= 74 pm, Mg2+= 72 pm, Ni2+ = 69 pm) [89].The strongly positive activation volume (AVt = +6.7 cm’ mol-’) is intermediate between that obtained for Co2+and Ni2+. Based on the similarity between Mg2+ and these ions, an Id or D mechanism is proposed for H 2 0 exchange. Furthermore, the complex-formation rates [90] are close to the water exchange rate. which is indicative of a metal-water bond rupture as the rate determining step. The trivalent cations A13+, Ga3+ and In3+ have closed shell configurations and differ strongly in their ionic radii (53, 62 and 80 pm, respectively). They form octahedral [M(H20)~]’-subunits in the solid alums CsM1”[SO4I2.12H201911. In aqueous solution the coordination numbers are also six as revealed by X-ray diffraction for Al(II1) [92-941 and In(II1) [95-971, and by NMR measurements for Al(II1) [97-991, Ga(II1)[97, 100-1021 and In(II1) [97]. Rate constants and activation parameters for water exchange in Al(II1) [lo31 and Ga(II1) 132, 1041 have been determined from kinetic 1 7 0 NMR experiments (Table 4.6). Water exchange processes in [AI(H20)6]’+and [Ga(HzO),] are characterized by positive AVt values, which are, however, substantially smaller than anticipated for a D mechanism, and, therefore, an Id mechanism was proposed. Unfortunately, the water exchange rate for In3+ was too fast to be measured, and thus precluded the measurement of an activation volume. The new limits for water exchange rate for In3$ established by using Tb’’ as a paramagnetic shift reagent [105], are about three orders of magnitude higher than the previous estimates [ 1061. Kowall [lo51 modeled water exchange mechanisms on Al’+, Ga’+, and In’+ using ab initio calculations at the Hartree-Fock level. For all three ions, transition states and intermediates have been obtained for a dissociative pathway with structures similar to those found by Rotzinger. The energies of the dissociative transition state are in excellent agreement with the activation enthalpies, AHf, measured for [Al(H20)6]’+ and [Ga(H20)6I3+ (Table 4.6) [103, 321. The energy difference, A!$, between the calculated intermediate and its corresponding transition state is relatively large for Al’’ and Ga’ t , but smaller for In3+.The computation of transition states for an associative exchange mechanism was only successful for In3+.The structures ofthe transition state and the intermediate for [ In(H20)7] are the same as those for [Ti(H2O)7I3’ [40]. Furthermore, the associative pathway requires a much lower activation energy (AEl = $29.1 kJ mol-l) than dissocia-

’+

’+

4.3 Water Exchangefrom the First Coordination Shell Tab. 4.6.

Selected properties of reactants/products, transition states, and intermediates.

Species

Symmetry

AEf a

(kj mol-lj [A1(OH2)6.0H2]3+ linear hydrogen bond {[Al(OH2)5...OH2.OH2l3+}# dissociative transition state [Al(OH2)s.(OH2)2]3 ' pentacoordinated intermediate

CS

0.0

c,

85.4 84.7< f74.7

Experimental C2"

[Ga(OH2)6.OH2I3+ cs linear hydrogen bond {[Ga(OH2)S . . .OH2.OH2I3+}# cs dissociative transition state Experimental [G~(OH~)S~(OH~)~I~~ C2" pentacoordinated intermediate [Ga(OHds40H2)213+ C2" water adduct [Ga(OH2)s.(OH2)2I3+ c2 water adduct

0.0

[ I I I ( O H ~ ) ~ . O3+H ~ ] linear hydrogen bond {[ln(OH2)5- ..OH2.0H2I3+}# dissociative transition state [In(OHz)s.(0H&l3' pentacoordinated intermediate { [ h ~ ( o H...OH2I3+}# ~)~ associative transition state [In(OH2)7l3' heptacoordinated intermediate

CS

0.0

CS

75.2

C2"

69.6

c1

29.1

CZ

19.7

69.1 67.1 54.6

AEfb (kj mol-')

AVJ or AV,

10.7

+5.6 +5.7

( ~ m mo1-l) - ~

+7.1

14.5

+4.8 +5.0 +6.9

5.6

T4.4

17.2 10.3

+4.8 9.4

-5.2 -7.1

"Difference in energy between transition state and linear bound water adduct. Difference in energy between transition state and penta- or heptacoordinate intermediate. CAHf (kJ mol-I).

tive water exchange (AE# = +75.2 kJ mol-I). The calculated activation energy of +29.1 kJ mol-' is in good agreement with the limit I 33.1 kJ mol-l for AGtg8 obtained experimentally [lOS]. Positive activation volumes for water exchange were measured on A13+ and Ga3+ by variable-pressure NMR experiments, and a dissociative mechanism, Id, was assigned. Due to the relatively large energy differences between transition state and intermediate calculated for these clusters, a limiting D mechanism was recently proposed from the calculations [105]. The much lower energy pathway for an a activated mechanism for In3+ together with the presence of a stable seven-coordinate intermediate, allowed the assignment of an A mechanism for HzO exchange in [In(H20),] 3 + . Activation volumes were estimated from the ab initio cluster calcu-

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4 Water Exchange on M e t a l Ions: T h e Effect of Pressure

8

A13+ Ga3+

6

-

4

z2

A

“E “. 0 .

> d

-2

’+ 1x

I

-4

Fig. 4.11. Volume changes (reactants - transition states intermediates) for a dissociative D water exchange (top) and an associative A water exchange (bottom).

lations using the Connolly surface [G9] (Fig. 4.11). The van der Waals radius of oxygen was adjusted to reproduce the experimental AVk for A13+ and Ga3+. The corresponding activation volume for an associative exchange process calculated for In3+ was -5.2 cm3 molt’. The change in mechanism from dissociative (A13-, Ga3+) to associative ( S C ~In3-) ~ , has already been experimentally observed for organic solvent exchange reactions [23]. Swaddle used a More-O’Ferrall type diagram, scaled to the volume as a physical parameter, to visualize the interplay between bond making and bond breaking in simple interchange processes (Fig. 4.12). Based on Swaddle’s semi-empirical model for partial molar volumes of metal ions in solution, Merbach has chosen f13.5 cm3 mol-’ as the limiting value for A and D mechanisms [lG]. The only measurable volume is, however, the activation volume, that is the volume difference between the transition state and the reactant. If, as Swaddle supposes, all water exchange reactions had to be regarded as interchange mechanisms, the transition state would lie on the dashed diagonal in Fig. 4.12a. In this event, A and D mechanisms are considered as the limiting cases for the interchange mechanistic con-

4.4 Water Exchangefrom the Second Coordination Shell

bond making 0

M(H,O),'*

-2

-4

-6

-8

-10

-12

+ 2 H,O

M(H,O)d'

+ H,O

$ Fig. 4.12. Interpretation o f volumes of activation for water exchange on aqueous [M(HzO),]'+ in terms of contributions (cm' mol-') from bond making and bond

breaking: (a) summary of volumes o f activation for metal aqua ions, (b) calculated curves for AI(III), Ga(lll), and In(lll) with use ofthe Connolly volumes.

tinuum and are, therefore, following the edges of the square diagram. However, from Rotzinger's [40,411 and Kowall's [ 1051 calculations, intermediates with increased and decreased coordination numbers have been identified and a different view of the square diagram was defined [105]. For concerted mechanisms (I), the single transition state lies, as before, on the AV diagonal axis. However, for stepwise mechanisms, the intermediate is situated on the diagonal while the two transition states lie symmetrically off the diagonal. The intermediates must not necessarily lie on the corner of the square, which means that the absolute value of the volume difference between intermediate and ground state can be significantly smaller than 1+13.51 cm3 mol-I. From calculated structures, Kowall et al. [lo51 derived volume changes for the transition states, AV:, and for intermediates, AVc. These values are then used to draw reaction trajectories into the square diagram (Fig. 4.12b). As one would expect, transition states are about half way between the reactant and the intermediate.

4.4

Water Exchange from the Second Coordination Shell

Information on the second coordination shell of water molecules around cations is much poorer than that regarding the first shell [4]. Properties of solvent molecules in this coordination shell are often very similar to those of the bulk, making their investigation extremely difficult. The analysis of radial distribution functions, g(r ) ,

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4 Water Exchange on Metal Ions: The Effect of Pressure

at long r distances, is difficult and much less reliable. The main source of structural information comes from neutron scattering 11071 and X-ray diffraction [ 1081111 experiments on aqueous solutions. For cations with strong second shell solvation, such as the trivalent A13+,Cr3+,or Rh3+,information can be obtained from far infrared spectroscopy 11121. Computer simulations performed in close relation to experimental studies can deliver more insight into the microscopic structure and dynamics of solvent molecules in the second coordination shell [113, 1141. From MD simulations it can be concluded that for trivalent ions (Cr3-, lanthanides) in general, first shell water molecules form two hydrogen bonds to second shell water oxygens. In that way the number of second shell water molecules (CNII) is roughly twice that ofthe first shell coordination number (CN,). For [Cr(H20)6] a mean second shell number of 12.9 H 2 0 molecule was found and for lanthanides, CN,I-values of 17.61 (for [Nd(H20)9I3+)and 16.74 (for [Yb(H20),13+)were obtained (Fig. 4.7). In an experimental oxygen-17 NMR study Bleuzen et al. I1131 measured an exchange rate constant of k,, = 7.8 x 10' s-l (at 298 K) on Cr3+,corresponding to a lifetime of 128 ps for one water molecule in the second coordination shell. In the same study a lifetime of 144 ps was observed from the molecular dynamics simulation. Based on the simulation, the following picture for an exchange reaction between a second and a third sphere water molecule on [Cr(H20)6I3+could be obtained (Fig. 4.13). In the first instance, a water molecule (no. 4 in Fig. 4.13) enters the second coordination sphere and increases the coordination number temporarily. In a second step the first sphere water molecule (no. I), which is close to the one that is entering, rotates around its oxygen-chromium bond, then one of the hydrogen bonds formed to second sphere waters (no. 3) breaks up and a new hydrogen bond is formed with the entering water molecule. During the rotation the second hydrogen bond is maintained (no. 2 in Fig. 4.13). In the third step the water molecule which has lost its hydrogen bond to the second sphere is itself

'+,

t=-2.5ps

t=Ops

I $L

I

--\

Fig. 4.13. Visualization o f water exchange between the second coordination shell and bulk solvent on [Cr(HzO)&+ obtained from MD simulation: (1) selected first sphere water molecule; (2). (3) second sphere water molecules before exchange; (4) exchanging outer sphere water molecule.

Acknowledgments

lost. The activation mode which can be attributed to this reaction from the MD simulation, is associative. Mufioz-Paez et al. [ 1141 performed extended X-ray absorption fine structure studies on aqueous solutions of Cr3+and Zn2+. They detected second coordination shells in both cases with coordination numbers of 13.3 f 1 (Cr3+)and 11.6 f 1.5 (Zn2+). The same group performed Monte Carlo I1151 and molecular dynamic [11G, 1171 simulations of [Cr(Hz0)6I3+in dilute aqueous solutions using an ab initio Cr3+ hydrate-water interaction potential. They found second shell coordination numbers of -14 from both simulations. Furthermore, from simulations and EXAFS measurements they concluded that chloride ions are situated beyond the second hydration shell. Near infrared experiments on lanthanide( 111) ions showed no well-defined second hydration shell [118].The residence times for water molecules in the second shells around Nd, Sm and Yb are 13, 12 and 18 ps respectively [ 7 0 ] . The slightly higher value for Yb3' can be related to its smaller ionic radius, rion.

4.5

Conclusions

The results reviewed in this chapter demonstrate the usefulness of pressure variation for the elucidation of mechanisms of water exchange reactions on metal ions. Even if the distinction between a limiting and an interchange mechanism, based on the magnitude of the activation volume, is not straightforward, the activation mode, associative or dissociative, can mostly be assigned unambiguously from the sign of AVt. Due to the range of more than 18 orders of magnitude for water exchange rate constants on metal ions, a variety of experimental techniques, mainly nuclear magnetic resonance, have to be applied. High-pressure equipment, such as high-pressure NMR probes, is still not easy to obtain and is therefore not widely used. The concept of activation volumes has also become a valuable tool in studies of exchange reactions by ab initio computer calculations and in classical computer simulations. In these theoretical studies activation volumes can be estimated by bond-length variations or by calculating volume differences using Connolly surfaces. In MD simulations pressure can be applied by variation of the density of the simulated water box. In that way reaction volumes are accessible by following for instance the change in coordination number.

Acknowledgments

The authors gratefully acknowledge financial support from the Swiss National Science Foundation and the Swiss Office for Education and Science (COST Program). Furthermore, we wish to thank the large number of people who have contributed to the work performed in Lausanne.

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4 Water Exchange on Metal lons: The Efect ofpressure

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FRATIELLO, R. R. LEE,V. M. NISHIDA,R. E. SCIIUSTER, J . Chem. Phys. 1968, 48, 3705. J . ]ORGIN, P. s. KNAPP,w. L. FLINT, G. HIGHBERGER, E. R. MALINOWSKY, J Chem. Phys. 1971, 54, 178. w. BOL,G. GERRITO,c. VON PANTHALEON V A N ECK, J . Appl. Crystallog. 1970. 3, 486. R. CAMINITI,G. LICHERI.G . PICCALUGA, G. PINNA,J . Appl. Crystallogr. 1979, 12, 34. R. CAMINITI,G. CERIONI,G. CRISPONI, P. CUCCA,2. Naturforsch. A 1988, 43A, 317. A. BLEUZEN, P:A. PIlTET, L. H E L M A. , E. MERBACH,Magn. Reson. Chem. 1997, 35, 7G5. R. D. SHANNON, Acta Crystallogr. Sect A 1976, 32, 751. M. EIGEN,K. TAMM,2. Elektrochem. 1962, 66, 107. j. K. BEATTIE,S. P. BEST,B. W. SKELTON, A. H. WHITE,J . Chem. Sac. Dalton 1981, 2105. W. BOL, T. WELZEN,Chem. Phys. Lett. 1977, 49, 189. R. CAMINITI,G. LICHERI,G. PICCALUGA, G. PINNA,T. RADNAI,J. Chem. Phys. 1979, 71, 2473. R. CAMINITI,T. RADNAI,2. Naturforsch. A 1980, 35A, 1368. M. MAEDA,H. OHTAKI,Bull. Chem. SOC.Jpn. 1977, SO, 1893. R. CAMINITI,G. PASCHINA,Chem. Phys. Lett. 1981, 82, 487. A. FRATIELLO, R. E. LEE,V. M. NISHIDA,R. E. SCHUSTER, J . Chem. Phys. 1968, 48, 3705. R. E. CONNICK,D. N. FIAT,J. Chem. Phys. 1963, 39, 1349. M. ALEI,J. A. JACKSON, J . Chem. Phys. 1964, 41; 3402. T. J. SWIFT,0. G. FRITZ, F. A. STEPHENSON, J . Chem. Phys. 1967, 46, 406. D. FIAT, R. E. CONNICK,J. Am. Chem. SOC.1966, 88,4754.

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I:RATIELLO, R. E. I.EE,R. E. SCIIUSTER, Inorg. Chem. 1970, 9, 82. D. HUGI-CLEARY. L. H E L MA. , E. MERBACH,Heltr Chim. Acta 1985, 68, 545. D. FIAT, R. E. CONNICK, J . Am. Chem. SOL.1968, 90, 608. TH. KOWALL,P. CARAVAN, H. BOURGEOIS, L. H E L M ,F. P. ROTZINGER, A. E. MKRBACH, J . Am. Chem. Sac. 1998, 120, 6569. G. E. GLASS,W. B. SCHWABACHER, R. S. TOBIAS, Inorg. Chem.1968,7,2471 R. D. BROADBENT, G. W. NEILSON, M. SANDSTROM, J . Phys.: Condens. Matter 1992, 4, 639. M. C. READ.M. SANIXTROM, Acta Chem. Scand. 1992, 46, 1177. R. CAMINITI,G. LICHERI.G. PICCAGUIA, G . PINNA,/. Chem. Phys. 1978, 69, 1. W. BOL, T. WELZEN.Chem. Phys. Lett. 1977, 49, 189. M. MAGINI,J . Chem. Phys. 1980, 73, 2499. P.-A. BERGSTROM, J. LINDGREN,M. C. READ,M. SANDSTROM, J . Phys. Chem. 1991, 95, 7650. A. BLEUZEN, F. FOGLIA,E. FURET,L. HEI.M,A. E. MERBACH, J. WEBER,J . Am. Chem. SOL.1996, 118, 12777. A. MUFJOZ-P~EZ, R. R. PAPPALARDO: E. SANCHEZMARCOS,J . Am. Chem. Sac. 1995, 117, 11710. R. R. PAPPALARDO, J. M. MARTLNEL, E. SANCHEZMARCOS,J . Phys. Chem. 1996, 100, 11748. J. M. MART~NEZ, R. R. PAPPAIARDO, E. SANCHEZMARCOS,K. REFSON,S. D~Az-MORENO, A. MUEOZ-PAEz,J . Phys. Chem. B 1998, 102, 3272. J. M. MART~NEZ, J. HERNANDEZCOBOS,H. SAINT-MARTIN, R. R: PAPPAIARDO, I. ORTEGA-BIAKE, E. SANCHEZMARCOS,J . Chem. Phys. 2000, 112, 2239. P.-A. BERGSTROM, J. LINDGREN, Inorg. Chem. 1992, 31, 1529.

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High Pressure Chemistry Synthetic, Mechanistic, and Supercritical Applications

Edited by Rudi van Eldik and Frank-Gerrit Kliirner

0WILEY-VCH Verlag GmbH, 2002

5 Insights into Solution Chemistry from High Pressure Electrochemistry Thomas W. Swaddle 5.1 Introduction

Just as the effect of pressure P on an equilibrium constant K can be expressed in terms of a volume of reaction AV AV

=

-RT(a In KIdP),,

(5.1)

so one can express the dependence of a rate constant k upon P in terms of a volume of activation A V z :

It is commonly argued that the value of AVf for a particular reaction can give insights into the reaction mechanism, since pressure not only affects bond making or breaking, with their attendant volume changes, but also can “tune” solvent properties that may influence k. These properties include the density p, static dielectric constant E , optical dielectric constant E , ~(usually equated to the square of the refractive index n), and viscosity 7. The argument presupposes, however, that AVf can be predicted quantitatively for a particular reaction mechanism. The thrust of much of the research in our laboratory over the past two decades has been to develop methods of predicting AVz for reactions of known mechanism for which adequate theoretical models are available, and to test the predictions experimentally. The primary test case has been outer-sphere electron transfer reactions of metal complexes in solution - an ostensibly very simple yet fundamentally important class of chemical and biological processes for which a well-developed kinetic theory is available [ 1-61 and can readily be extended to encompass pressure effects on k [7-lo]. By definition, no bond making or breaking is involved in outer-sphere electron transfer processes and, as we shall see, intramolecular reorganization does not normally affect AVz for such processes appreciably, so that AV# reflects in large measure the tuning of solvent properties by pressure. A particular virtue of pressure-tuning is that kinetically relevant solvent proper-

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ties can be varied without changing the chemical identity ofthe solvent. Efforts to learn about solvent effects on reaction rates by comparing values of k measured in a range of solvents are dogged by the possibility that the microscopic modes of solvation of the reactants may be quite different in chemically different solvents: in other words, it may not be appropriate to regard the solvent merely as a dielectric continuum. Resort to mixed solvents to vary (say) the dielectric constant of the medium is arguably an even worse choice, since it is highly unlikely that the components of a mixed solvent will be equally effective at solvating a particular reactant, and some (usually unknown) degree of fractionation of the solvent in the solvation sheath relative to the bulk liquid is almost inevitable. Much of our earlier work on pressure effects on the kinetics of electron transfer reactions focused upon the rate constants k,, and corresponding volume of activation AVL for seljkchange reactions (5.3)

which are simplest to interpret because there is no net chemical change (so that AVex and the free energy of reaction AGex are both zero). For such reactions, an acceptable understanding of AVf has been achieved [9] and forms the basis for analyzing pressure effects on outer-sphere redox processes that involve net chemical change (“cross” reactions). For this purpose, it is necessary to determine the reaction volume AV12 of the cross reaction, and this is most readily obtainable from the pressure dependence of the electrode potentials of the contributing half-reactions relative to some common electrode. Thus, we have been led ineluctably into highpressure electrochemical measurements. Furthermore, practical limitations on the number of self-exchange reactions that can be studied experimentally at high pressures has prompted us to attempt to measure the rate constants k,l and associated volumes of activation AVZ of the corresponding electrode reactions instead, and to consider the relationship between the kinetic parameters of the two classes of reactions. Important insights into the mechanisms of electrode reactions corresponding to the reaction shown in Eq. (5.3) have resulted, and comprise the main theme of this chapter. As a preparatory step, however, it is necessary first to summarize what has been learned about pressure effects on the kinetics of bimolecular self-exchange reactions.

5.2

Pressure Effects on the Kinetics o f Self-Exchange Reactions 5.2.1 Principles

The rate constant k,, for an outer-sphere self-exchange reaction may be expressed in terms of its free energy of activation AG; through the equation:

k,, = K p ~ e c ~exp(-AGz/RT) ~e,

(5.4)

5.2 Pressure Effects on the Kinetics of Self-Exchange Reactions

Here, K is the electronic transmission coefficient ( K = 1 for adiabatic electron transfer) and vex the nuclear frequency factor, whereas K& is the equilibrium constant for assembly of a precursor state and effectively includes any coulombic work and medium (Debye-Hiickel) terms [ 4,51. Following the approach taken by Stranks [7], the observed volume of activation AVZ for a simple, adiabatic, outersphere, bimolecular electron transfer reaction can be represented as AVZ

=

-RT(d In k,,/dP),

= AVI$

+ AV& + AV&, + AV&

(5.5)

in which the terms on the right-hand-side represent the respective contributions of internal reorganization of the reactants (usually taken to mean bond length changes), the reorganization of the solvent, the coulombic work of assembling the precursor complex, and the pressure dependence of the ionic activity coefficients (Debye-Huckel terms). Stranks [7] showed that AVl$ is -0.6 cm3 mol-l for most rigid complexes, that is, barely outside the experimental uncertainty in AVZ ; this is because, as the two reactants distort to reach a common nuclear configuration to allow electron transfer to occur, the increase in volume of the oxidant almost cancels the decrease in volume of the reductant. In the simplest treatment, the other terms are given by

+ = [RTz(z+ l)C11/2/(l + B U I ' ~ ~ ) ~In] ~/dP),(3 [(~ + 2 B ~ 1 ' / ~-) p)]

A V ~ = , ~[N*Z(Z l)e2/4n~oaj(a~-'/aP)T

(5.7)

AV&

(5.8)

where a is the separation between the two M centers (usually taken to be the sum of the effective radii r,, and r,,d of the oxidant and reductant), a, B, and C are the Debye-Hiickel parameters, I is the ionic strength, is the isothermal compressibility of the solvent, and the other symbols have their usual meanings in SI. It turns out that AVg, and AV&, are opposite in sign and usually fortuitously cancel each other quite closely for practical values of I(O.1to 0.5 mol L I ) , at least in water. In non-aqueous solvents of low dielectric constant, however, AV&, and AV& can become numerically very large (for example, about f 5 0 cm3 mol-' in acetone) so that the calculation of AV: becomes unstable [9, 101. Furthermore, for any realistic combination of solvent parameters, AV& is predicted to be negative and to be the dominant term in Eq. (5.5). A more detailed version of the Stranks approach would incorporate the notion due to Sutin [4, 51 that electron transfer within the precursor assemblage {MLFfl)+,ML,Z+)occurs over a reaction zone of thickness Sa rather than on "hard-sphere'' contact of the reactants. In that case, cr must be treated as pressuresensitive, compressing along with the solvent. It turns out, however, that allowance for compression of cr in Eqs (5.6) and (5.7) can be neglected for adiabatic reactions because it is almost exactly cancelled by a term AV& representing the effect of compression on the pre-exponential part of the expression for I$!ec[9] (the exponential part generates AV&,). Electron transfer, however, could be non-adiabatic -

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that is, the electronic coupling between the precursor and successor states could be weak enough for the electronic transmission coefficient K to become significantly less than 1. In that case, an exponential dependence of k,, on 00 - u (where go is the value of u for which electron transfer would be adiabatic) would result, such that there would be a significant additional negative non-adiabatic contribution AV& to AVZ . In summary, the key predictions of Eqs (5.5)-(5.8) are: (1) that AVsfR is usually the dominant part of AV: , and (2) that AV& (and hence AV): will be negative for simple outer-sphere electron transfer reactions in solution, regardless of whether electron transfer is fully adiabatic - with the caveat that predictions of the magnitude of AVZ are unlikely to be reliable for solvents of low E. 5.2.2

Experimental Observations with Aqueous Media

At the outset, it should be noted that Eqs (5.5)-(5.8) predict that IAVZ 1 should become numerically smaller with rising pressure because the isothermal compressibilities of solvents (and therefore also the pressure derivatives of properties such as E and n [S-lo]) decrease with rising pressure. In practice, plots of In k,, against pressure usually appear to be linear functions of P within the observational uncertainty over the usual experimental pressure range of 0-200 MPa. In this chapter. theoretical values of AV: are calculated for the mid-range pressure of 100 MPa, and the experimental AVZ values are, in effect, averaged to this pressure. Figure 5.1 shows that Eqs (5.5)-(5.8) reproduce the observed AVZ well in several cases (abbreviations: Figure 5.2). Agreement is less good for the C o ( d i a m ~ a r ) ~ + / ~ + couple, although the diprotonated form conforms well to expectations despite a rather wide error bar and the very high charges (5+/4+) [14]; solutions containing the 3+/2+ couple were buffered with morpholine/CF3SOjH, and it is suspected that some interaction with the buffer was occurring (perhaps significantly, the electrochemical transfer coefficient y for this couple was only 0.27 rather than the 0.4-0.5 normally found for the complexes considered in this chapter [lG]). In contrast, Table 5.1 lists cases in which Eqs (5.5)-(5.8) appear to fail. In each instance, however, reasons for the failure are recognizable. Thus, AVZ for the conjugate base pathway for the Fe(a~l)~+/’+ self-exchange is about 12 cm3 mol-’ more positive than expected for an outer-sphere mechanism because it is evidently of the inner-sphere type involving expulsion of a water ligand from the first coordination sphere of Fe(H20);+ to form an FeeOH-Fe bridge, and the AVZ value can be accounted for rather precisely on this basis [12]. The strongly negative AV: value for the cation-independent pathway for the Mn0,”- exchange remains enigmatic, but seems to reflect the very small sizes of the reactants, which approach the molecular dimensions of solvent water [ 191; what is important is that the Na+and K+-catalyzed pathways show much more positive AVZ values. Alkali-metal cation (M’) catalysis of anion-anion self-exchange reactions is dominant to the extent that Mf-independent pathways are ordinarily undetectable for the cyanometalate couples listed in Table 5.1 [20, 211, and the M+-mediated pathways show

5.2 Pressure Eflects on the Kinetics of SeFExchange Reactions I

I

I

I

I

I

Co(ttcn)z

Co(act)

3+/2+

3+/2+

I

-12

-8

-10

-6

-4

Calculated activation volume/cm

0

-2 3

rnol

-1

Fig. 5.1. Comparison o f observed AV: values with those calculated from Eqs (5.5)-(5.8). Diagonal line represents perfect agreement. phen 1,lo-phenanthroline; other ligand abbreviations a s in Fig. 5.2. Data from references [ll-15). 7

ttcn

tacn

Fig. 5.2. Ligand systems: act = azacapten; diamsar = diarninosarcophagine; sep = sepulchrate; ttcn = 1,4,7trithiacyclononane; tacn = 1,4,7-triazacycIononane.

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5 lnsights into Solution Chemistryfrom High Pressure Electrochemistry Tab. 5.1. Experimental values of AV: that deviate markedly from the predictions AVL (calc) of Eqs (5.5)-(5.8).

Couple

AV: (exptj (cm3 mol-’)

AV; (calcj (cm3 mol-’)

Fe(HzO)sOH’+/Fe(aq)’+ Co(en):+/*’ Co(phen):MnO;/’MnO;‘*- (K+) Mn0,”- (Na+) Fe(CN):-I4 ( K + ) O~(CN);-’~ (K+) M ~ ( c N ) ~ - /(K+) ~MO(CN);-’~- (Et4N’) W(CN)i-’4- (K’) W(CN):-l4- (Me4N+) W(CN);-l4- (Et4N’)

-11 k 0.4 -16.5 k 0.P 4 7 . 6 k 0.7 17 f 2J

-

a

-1 1 1 k1 +14.7 k 0.6

-6 -6 -6 -6

12 17 18 19 19 19 20 21 21

k 0.6

-6

21

-6

21

~

l k l +3*1 +19

-8.2

+22+1 -7.4 -6.2

k 0.5 k 0.5

10

Ref:

-5 -2 -9

-6

-6

21

-6

21

Pressure dependent - average value, 0-200 MPa.

much more positive AVZ values than are expected for simple bimolecular electron transfer. These anomalies cannot be ascribed to ion-pairing - the AV: values are too positive to be accounted for solely on the basis of pressure-induced break-up of (supposedly) more reactive ion pairs. Besides, for cation-cation couples at least, ion-pairing seems to diminish reactivity in electron transfer [22]. A clue to the origin of the relatively positive AVZ values for cyanometalate couples with alkali-metal cations M+ is that the corresponding reactions in tetraalkylammonium media are similarly catalyzed by %N: but have negative AV; of about the magnitude expected from theory (although this last fact is fortuitous because the model does not consider mediation by a third body). Since M+(aq) ions have a definite first coordination sphere of water ligands but R4N+(aq) do not, one can infer that all cations facilitate electron transfer between anions by providing a region of positive potential to assist tunneling of the electron, but that the alkalimetal cations must be at least partially dehydrated first. Indeed, the relative effectiveness of various M+ as catalysts (Li+ < Na+ < Kt < Rbf < Cs+) follows their ease of dehydration - that is, it correlates with the (negative) heats of hydration of M+ [ 231. This interpretation also provides an explanation for the lack of significant counter-ion catalysis in cation-cation outer-sphere electron transfer reactions: involvement of an anion with two reacting cations would actually hinder tunneling by the negatively charged electron electrostatically, and there is evidence that this is the case [22]. The anomalous, strongly ne ative AV: values in Table 5.1 for the low-spin/highspin Co”!/“ couples Co(en):i’2+ and Co(phen)ifi2+ (and, on the basis of indirect evidence, for tris(bipyridyl)cobalt(III/II) [24] and Co(EDTA)-/Co(HEDTA)OH; [25]) contrast sharply with those for the low-spin/low spin Co(ttcn);”’- couple

5.2 Pressure Effects on the Kinetics of Self-Exchange Reactions

and the cage complexes C ~ ( a c t ) ~ + (low-spin/low-spin), /~+ C o ( ~ e p ) ~ + /and ~+, Co(diamsarH2)'+i4+ (low-spin/high-spin)(Fig. 5.1), for which AV,, is well represented by Eqs (5.5)-(5.8). There are basically two possible explanations for the anomaly. One (which we favored rather arbitrarily in our earlier publications 18, 17, 18, 251) is that electron transfer occurs directly between high-spin Co" and lowspin Co"' but is non-adiabatic by virtue of the simultaneous large change in spin multiplicity - in other words, that the electron transfer is "spin forbidden", much as are intramolecular electronic excitations involving spin state changes. As noted in Sect. 5.2.1, non-adiabaticity implies an exponential dependence of k,, on E ( G ~- a ) , where a is a distance scaling parameter, and would contribute a markedly negative amount AV,f, = -2ap~RT/3 to AVZ; a reasonable value of a of about 19 nm-' would be required to account for the observed values. This explanation, however, fails because it is inconceivable that electron transfer in the low-spin/ high-spin CO"'/" cage complexes could be adiabatic (as is evidently the case) if that in the smaller Co(en):+'2+ complexes, from which they are derived, were nonadiabatic [ 14, 261. The alternative is that a spin-change equilibrium (presumably in the Co" species) precedes electron transfer; such equilibria are rapidly established [ 271, and, if the Co(terpy);+ (terpy = terpyridine) high-spin/low-spin equilibrium [28] is typical, can contribute AVSpin -10 cm3 mol-' to AVZ - that is, account for the deficit in AV: . The spin pre-equilibrium model, however, begs the question as to why the Co cage couples should conform to the predictions of Eqs (5.5)-(5.8) even in lowspin/high-spin cases. The answer seems to be that flexible chelate complexes such as the tris(bidentate) Co(en):+ and Co(phen):+ or even the sexadentate Co( HEDTA)OH, are subject to substantial Jahn-Teller-relateddistortions and associated volume decreases on going from high to low spin states, whereas these distortions are suppressed in the c o cage complexes. To test this idea, we have recently examined 1291 the pressure dependence of the visible absorption spectrum of aqueous Fe(diamsarH~)~+ [ 30-331, for which the high-to-low spin equilibrium constant (0.34) is uniquely suitable for this purpose (although the 0 2 sensitivity of the iron(I1) complex poses severe experimental difficulties). The low-spin form of the complex has a ligand-field absorption maximum at 569 nm, at which the absorbance of the high-spin form is negligible. No change in the compression-corrected molar absorbance at 569 nm could be detected within the experimental uncertainty over the pressure range 0-294 MPa, implying AVspin = 0.0 k 0.2 cm3 mol-'. Unfortunately, direct determination of AVL for the Fe(diamsarH2)' +I4 self-exchange reaction is not feasible, but high-pressure electrode kinetics (see below) indicate that it is close to the theoretical value of about -5 to -6 cm3 mol

-

'.

5.2.3

Experimental Observations with Non-aqueous Media

For self-exchange reactions of multiply charged complexes in non-aqueous solvents of low dielectric constant, Eqs (5.5)-( 5.8) become numerically unstable because of runaway values of the Coulombic and Debye-Huckel terms, as noted

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in Sect. 5.2.1. Moreover, for multiply charged solutes, ion pairing will also become important, with unpredictable kinetic consequences (although mild retardation by ion pairing, resulting in a negative contribution to AVL, seems likely for cation-cation exchanges [ 221). If, however, one reactant is electrically neutral and the other is singly charged, the terms AVZ,, and AV& become zero, ion pairing becomes minimal (and affects only the ionic reactant), and Eqs (5.5)(5.8) can be expected to perform well. Then, since AV,< is typically small, AVL can be identified with AV&. This seems to be the case for the Ru(hfac);’- selfexchange (hfac- = hexafluoroacetylacetonate ion), for which AVL in methanol, acetone, and acetonitrile is well accounted for by either Eq. (5.6) [34] or a model that takes the size of solvent molecules into account through the Mean Spherical Approximation (MSA) [ 351. Thus, the Ru(hfac)y’- self-exchange evidently proceeds by an adiabatic outer-sphere electron transfer, without significant involvement of ion pairing, in these three solvents at least - a significant point to which we will return later - although in chloroform there were indications of ion-pairing, as might be expected in view of the very low dielectric constant of this solvent [ 341. Practical problems including solubility and redox stability have so far limited comparisons of kinetic pressure effects in aqueous and non-aqueous media to just one couple - the Fe(phen),3+/2- self-exchange reaction [ll],for which AVL was found to be -2.2 cm3 mol-’ in aqueous HzS04, in excellent agreement with the prediction of Eqs (5.5)-(5.8) (Fig. 5.1), and -5.9 cm3 mo1-l in acetonitrile (cf. -6.8 cm3 mol-l predicted using an estimated pressure dependence of the refractive index for acetonitrile [8] and ignoring possible ion pairing). As explained in Sect. 5.4.2, these results rule out any significant influence of solvent dynamics in the self-exchange reactions studied to date at high pressures. 5.2.4

Approaches Involving Electrochemistry

The AVZ data of Fig. 5.1 that are satisfactorily accounted for by Eqs (5.5)-(5.8) are fewer in number than the anomalous cases of Table 5.1. This is a rather unsatisfactory situation, even though most of the anomalies can be explained away - indeed, deviations from the predictions of Eqs (5.5)-(5.8) can often provide important mechanistic information. More AVZ data are clearly desirable, but the prospects for further successful experiments are poor. The measurements of AVZ summarized in Fig. 5.1 and Table 5.1 were obtained at high pressures by radiochemical tracer methods for the slowest reactions [12, 17, 251, N M R linebroadening techniques for the faster cases [11, 13, 15, 19-22, 341, and stopped-flow circular dichroism [ 13, 14, 181 for moderately rapid reactions of reactants that could be prepared as resolved enantiomers. There are, however, many selfexchange reactions that are inaccessible to these techniques. For example, rates of electron transfer in couples where both reactants have unpaired electrons generally cannot be studied by NMR methods, while other couples that undergo electron transfer at intermediate rates may not be resolvable into optical isomers or be amenable to radiochemical sampling procedures under pressure.

5.2 Pressure Efects on the Kinetics of Self-Exchange Reactions

In principle at least, two further indirect methods exist for determining AV.: Both involve high-pressure electrochemistry. One is the measurement of the pressure dependence of the rate constant k,] for electron transfer in a given couple at an electrode, but it is not immediately clear how k,, and the corresponding volume of activation AVZ relate to k, and AVL , respectively, for the self-exchange reaction of the same couple. This is a major theme of this chapter, and is pursued in detail below. The other method involves invocation of the "cross relation" of Marcus [5], which expresses the rate constant kl2 for the oxidation of, say, A by Bt in terms of its equilibrium constant K12 and the rate constants k l l and k22 for the respective At/A and B+/B self-exchange reactions:

where

Here, Z is the frequency factor (assumed to be the same for all the reactions) and are the work terms (assumed to be the same for the self-exchange and the forward and reverse cross reactions). For the cross reaction, K12 can be obtained from the difference AE' in the standard electrode potentials for the two self-exchange reactions: w,i

In

~ 1 = 2

~FAE'/RT

(5.11)

where n is the number of (moles of) electrons transferred (almost always 1 in the present context). The volume relationship corresponding to Eq. (5.9) [3G] is then

+ AVZ + AVi2)/2] + X

(5.12)

AV;

= [(AVZ

X

-(RT/2)(8 lnf/dP)r

(5.13)

-nF(8AEo/dP),

(5.14)

=

AV12 =

For low driving potentials AE', f can be approximated to 1 and X can be neglected. In practice, Eq. (5.12) is accurate with the inclusion of X if AE' is small or moderate, as in the reduction of aqueous Fe(H20)2+ by Co(ttcn);+ (AE' = 0.28 V) [3G] or ofCo(phen);+ by Ru(en):+ (AE' = 0.19 V) [15],but fails for large driving potentials, as in the reduction of Fe(H20);' by Co(sep)2- (AE' = 1.03 V) and of Co(bpy);+ by Co(sep)'+ (AE' = 0.66V) [24]. Where Eqs (5.12) and (5.13) fail, the Marcus cross relation itself (Eqs (5.9) and (5.10)) also fails. The emerging picture is that selfexchange reactions in water are generally adiabatic, but cross reactions may become increasingly non-adiabatic as one goes to higher and higher driving potentials AE'. Alternatively (perhaps equivalently), some of the assumptions implicit in the Marcus theory (e.g. that the precursor and successor states may be treated as harmonic oscillators) may fail at high AE'.

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Thus, the cross-reaction approach, judiciously applied, can deliver AV: data that are otherwise inaccessible. The converse, however, may be more important - that is, if an adequate database of AVZ values is available, then only the easily measurable pressure dependence of AEo is needed to apply Eqs (5.12)-(5.14) to predict AVZ for numerous cross reactions (algebraic summation of partial molar volumes of all the relevant solute species is an alternative route to AVI,, but such data are rarely available or relevant to practical reaction media). Comparison of predicted and experimental AV; data could then provide mechanistic insights. Thus, highpressure electrochemical measurements are central to further progress in this field.

5.3

Electrochemical Measurements at High Pressure

The techniques of electrochemistry at high pressure have recently been reviewed [37, 381, and need not be reconsidered in detail here. In essence, the electrochemical cell consists of a Teflon body containing a working electrode (usually an Au or Pt wire or a glassy carbon fiber), a counter-electrode(typically Pt wire), and a reference electrode (usually either a AgC1-coated Ag rod in a compartment containing 4 mol L-l KC1 solution, or an Ag/Agf electrode consisting of a Ag rod in AgC104 solution). The reference electrode has a Vycor frit mounted in a free piston to allow for ionic contact and compression of the solution in the reference compartment, and the cell as a whole also has a free piston to accommodate compression of the reaction medium. The cell is mounted in a pressure vessel with electrical feed-throughs that are soldered to the electrode connections. Hydrostatic pressure is applied with a suitable electrically insulating liquid (usually clean mixed hexanes) which in turn is isolated from the hydraulic oil of the pump with a free-piston separator vessel to minimize contamination. Pressure is monitored on either side of the separator with either electronic or Bourdon gauges, calibrated against a standard deadweight gauge. The temperature of the pressure vessel is controlled with thermostated water circulating in an aluminum jacket. Some 3050 min are required for thermal equilibration of the pressure vessel and its contents at 25.0 "C, either initially or after the pressure is raised or lowered, so that a cycle of pressure measurements lasts several hours and the chemical stability of the system under examination must be accordingly high. Success in high-pressure electrochemical measurements depends largely on having clean, reproducible working electrode surfaces, which are therefore polished with fine alumina and sonicated in clean solvent before assembly of the electrochemical cell. Before a sequence of measurements at each pressure, the electrodes are cleaned electrochemically by cycling the applied potential several hundred mV either side of the potential of the couple of interest (preferably to the point of hydrogen evolution, in aqueous media). Electrode potentials relative to the particular reference electrode are conveniently measured as the half-wave potential E1p in cyclic voltammetry (CV) [IS, 16, 20, 24, 36-48] or cyclic staircase voltammetry [49-51]: or by differential pulse voltamme-

5.4 Homogeneous Versus Heterogeneous Electron Transfer

try (DPV) [ 5 2 ] . In principle, electrode reaction rate constants k,, can be estimated from the peak-to-inverse-peak voltage separation in CV [ 5 3 , 541, but our experience has been that the peak separation is neither sufficiently accurately measurable nor reproducible. Good reproducibility and precision in k,l can, however, be obtained using alternating current voltammetry (ACV), which involves imposing a small ( 25 mV) AC pertubation of angular frequency w on a DC voltage ramp, and recording the maximum in-phase and gO"-out-of-phasecurrents (at voltage Emax)as the DC voltage is swept through the redox potential. From the observed Emaxand Ell2, the electrochemical transfer coefficient y can be calculated. If Em, = Ell2, as is most often the case, then y = 0.5. From the ratio of the two currents, properly corrected for uncompensated resistance, a phase angle a, can be calculated, whence (for the simplest case where y = 0.5) k,l can be obtained from the linear plot of cot a, against 40): cot a, = 1

+ ( D o112D,112/2)112~112/kel

(5.15)

where Do and DRare respectively the diffusion coefficients of the oxidized and re112 112 duced forms of the reactants. For practical purposes, Do D, may be replaced by a mean diffusion coefficient D, which can be obtained from the maximum current of a cyclic voltammogram using a couple of known D as a standard. Once thermal equilibrium is achieved at a selected pressure in a cycle of measurements, multiple cyclic voltammograms are run to check the reproducibility and integrity of the system and to measure D, and then AC voltammograms are taken repeatedly until reproducibility is obtained. The pressure dependences of Ell2, In D, and In kel then give AV,,, (the volume of reaction of the couple relative to the particular reference electrode), AV& (the volume of activation for diffusion of the reactants), and AV:, respectively (cf. Eqs (5.2) and (5.14)). It is our practice to accept only those variable-pressure cycles of measurements of E1p, D and k,l for which the initial and final low-pressure data agree to within the experimental uncertainty, although, in some isolated cases in which measurements show a slow but constant rate of drift, provisional AVZ values may be extracted by correcting for the drift. Figure 5.3 shows some typical results for Ell2 and In k,, in an aqueous system; as explained below, the pressure dependence of D for aqueous systems at 25 "C is negligible in the 0-200 MPa range. Further details of the experimental procedure and associated calculations are given elsewhere [lG, 24, 40, 41, 551.

5.4 Homogeneous Versus Heterogeneous Electron Transfer 5.4.1 Aqueous Solutions

Marcus [56-59] has shown that the free energy of activation AG; for an electrode reaction can be expected to be one-halfof that (AGZ) for the corresponding selfexchange process, so that, from Eq. (5.4), we have for adiabatic electron transfer

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5 Insights into Solution Chernisttyfrom High Pressure Electrochernistrv 0.54

I

I

1

I

I

I

I

0

50

100

150

200

V Y

1.

”,

0.52

d \ 0,

6 v)

’

0.50

>

h

I-

9

0.48

-2.0

--

-2.2

I

Lo

E 0

-2.4

\ A? v

5 -2.6 -2.8

Pressure/MPa Fig. 5.3. Pressure dependences of In k,, (by ACV) and E l p (by CV) for the W(CN)i-’4- couple (2 mmol L-’) at a Pt wire electrode i n in aqueous KCI (0.5 mol L-’) a t 25.0 “C (411.

( K = 1):

(5.16) where Zex and Zel are the pre-exponential factors taking the place of K&cilexand I$&ve~ respectively in Eq. (5.4) and its equivalent for electrode reactions. This relation may be intuitively understood by recognizing that two reactant species undergo internal and solvational reorganization to a common intermediate configuration to allow electron transfer to occur in the case of (bimolecular) self-exchange in homogeneous solution, but only one has to reorganize to that configuration in the corresponding heterogeneous electrode reaction. Marcus [ 561 pointed out that “=” should be replaced by ‘ ‘ 2 ” in Eq. 5.16 if the reactant center-electrode distance is more than half the metal-metal separation (r for the homogeneous electron transfer reaction (due, perhaps, to a layer of adsorbed solvent or other molecules on the electrode surface). Hush [GO] independently arrived at conclusions

5.4 Homogeneous Venus Heterogeneous Electron Transfer

similar to those of Marcus, but cautioned that the role of image charges in the electrode is not clear in solutions with practical supporting electrolyte concentrations which substantially reduce (or almost eliminate) the diffuse double layer potential. In addition, the measured rates of electrode reactions are notoriously sensitive to the nature and history of the electrode surface. Thus, it is not surprising that plots of In k,, vs. In k,,, which might be expected to be linear with slope 0.5 on the basis of Eq. (5.16) if Zel and Z,,were approximately constant from one reaction to another, may be severely scattered with a “slope” (insofar as it can be defined) as low as 0.1 [16]. Cannon [ G l ] , however, did find a loose correlation between some In k,l and In k,, data that leveled out (either because of the incursion of diffusion control or of incompletely compensated resistance [62]) as k,, approached 1 cm SKI. In sharp contrast, a plot of AV: against AVZ for almost all aqueous reactions for which both parameters are currently available shows an excellent linear correlation of slope 0.50 f 0.02 and negligible intercept [I61 (according to a recent reinvestigation [20], the Fe(CN)i-/4- case may be anomalous and should be excluded). For convenience, we refer to this relationship as the “fifty-percent rule”. The evident equivalence between AV; and AV: / 2 implies that the pre-exponential factors Zel and Z,, for aqueous systems are effectively independent of pressure. Such is known to be the case for Z,,, from experience with the success of Eqs (5.5)-(5.8) for self-exchange reactions, and presumably it also applies to Zel because the nature of a given electrode and its surface are virtually independent of pressure, even though the pre-exponential factor may differ widely from one electrode to another. Zel could, however, be influenced by solvent dynamics, but, as demonstrated in Sect. 5.4.2, this would not be apparent in AVZ values for dilute aqueous systems at near-ambient temperatures. Little is known about the effects of pressure on the electrical double layer [G3], but compaction of the diffuse double layer by the high concentrations of supporting electrolytes used in our experiments means that double-layer contributions to AVZ can be expected to be small. In any event, the close equivalence between AV: and AV: /2, regardless of the medium, indicates that double layer effects in aqueous systems can be empirically neglected as far as pressure effects are concerned. It also implies that the metal center-electrode separation can indeed be taken to be simply one-half of 0 for the bimolecular electron transfer [56]. Thus, if there is an adsorbed layer of solute or solvent on the electrode, it either acts as a conducting surface or can otherwise be ignored for our purposes. The fifty-percent rule implies that AVZ for aqueous electrode reactions can be predicted from Eqs (5.5)-( 5.8). Thus, for the Fe(diamsarH~)’+/~+ couple, for which we saw in Sect. 5.2.2 that there is a detectable spin equilibrium but with AVspin = 0.0 _+ 0.2 cm3 rnol-’ 1291, one can predict AVZ = 0.5AV: = -2.9 cm3 mol-’ (neglecting the possibility of a small positive contribution on the order of 0.3 cm3 mol-’ from internal rearrangement). ACV measurements [29] on Fe(diamsarH2)’+I4+ (1 mmol L-’) in aqueous HC104/NaC104 (0.1/0.4 mol L-’) on a Pt electrode at 25.0 “C gave k,, = 0.08 cm s-’ and AV: = -2.4 0.5 cm3 rnol-’. These data are consistent with rapid adiabatic electron transfer from the low-spin isomer (which

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5 Insights into Solution Chemistryfrom High Pressure Electrochemistry

comprises about 25 % of the total Fe), and the AVSpm and AV: values confirm the postulate in Sect. 5.2.2 that cage complexes conform to the predictions of Eqs (5.5)-( 5.8) because distortions associated with spin-state changes are suppressed. 5.4.2 Non-aqueous Media

The foregoing rather tidy picture of pressure effects on outer-sphere electron transfer in aqueous systems is based on the supposition that transition state theory (TST), upon which the Marcus approach is based, is applicable to both homogeneous and heterogeneous electron transfer reactions. In other words, it is assumed that the transition states are present in minute concentrations in equilibrium with the reactants in their initial states. This is probably a valid assumption for homogeneous (bimolecular) electron transfer, but evidence has been accumulating to the effect that solvent dynamics (solvent “friction”) may limit the rates of some (or even all) electrode reactions. In simple terms, the expectation is that coupling of solvent motions to the passage of the reactants through the transition state may act to diminish the pre-exponential factor Zel, which can then be expected to show an approximate proportionality to thefluidity of the solvent - that is, to the reciprocal of its viscosity I.‘ (The relevant solvent parameter is actually the longitudinal relaxation time TL, but Zel K ?-’ can be substituted for proportionality to r;’ for Debye solvents at least.) In that case, if kTsT is the rate constant expected for an electrode reaction on the basis of transition state theory, the rate constant kso observed under solvent dynamical control is given by

Such phenomena have been reported for electrode reactions of Cr(EDTA)-/2- and Fe(CN)i-/4- in which the viscosity of the solvent (water or dimethyl sulfoxide) is varied by the addition of dextrose or sucrose [ 64-66]. Solvent friction has also been invoked in reductions of thiophenecarboxylatopentaamminecobalt( 111) complexes [67] and of metallocenes [68, 691 at Hg electrodes in organic solvents. Of particular interest in the present context are studies by Murray et al. [70, 711 of the reduction kinetics of C~(bpy);+/~+ in a variety of organic solvents, in which k,, was found to be proportional to I/?, to l/tL,and to the mean diffusion coefficient D of the reactants over a huge range (11 orders of magnitude) of k,]. Such studies, however, rely upon changing the chemical identity of the solvent in order to vary q ,7, and D,with the attendant risk that specific solvation phenomena or (in the case of mixed solvents) differential solvation may be responsible in part for the observed effects. This particular conundrum may avoided by the use of high pressures to “tune” the solvent properties, because the viscosity of normal liquids rises sharply and exponentially with increasing pressure (Fig. 5.4). A striking exception to this generalization is the viscosity of water at nearambient temperatures. Water may be considered to consist of a mixture of transient ice-I-like structures and free water molecules; break-up of the former by

5.4 Homogeneous Versus Heterogeneous Electron Transfer 3.5

oo 3.0 m

c x .-

2.5

v)

0 V

.-

u)

>

2.0

> .c U 0)

CE

1.5

1 .o 0

50

100

150

200

Pressure/MPa Fig. 5.4. Pressure dependence o f some typical solvents, based on data from references [72] (water, 25 "C), [73] (acetonitrile and N,N-dimethylformamide, 30 "C),[74] (acetone, 30 "C). and [75] (methanol, 30 "C).

increasing pressure results in a decrease in viscosity, whereas the free molecules behave as expected for a normal liquid. Thus, at temperatures near the freezing point, v] first falls and then rises as the pressure is increased, whereas around 25 "C these opposing trends cancel almost exactly, resulting in a near-independence of q on pressure in the range 0-200 MPa considered here (Fig. 5.4). Consequently, any dependence of k,l on solvent dynamics will be reflected in a markedly positive contribution to AVZ for outer-sphere electron transfer reactions in typical organic solvents, but none at all when water is the solvent at near-ambient temperatures. The fifty-percent rule for activation volumes, then, is fortuitously valid for aqueous systems even if solvent dynamics govern Zel. Indeed, AVZ for Co(bpy)i+/2+in aqueous NaCl is strongly negative (Table 5.2), and closely similar in magnitude to AVZ for the analogous couples Co(phen):+/2i (-9.1 cm3 mol-') and Co(en):+/2i (-8.3 cm3 mol-l) [ 161. Since AVZ values for the latter two couples follow the fiftypercent rule, one can infer that the (as yet unmeasured) AVZ for Co(bpy):+'*+ is -17 f 1 cm3 mol-l. For non-aqueous systems, however, AVZ for Co(bpy):+"+ is strongly positive and comparable to AV& (= -RT(d In DlaP),), at least for the three solvents for which good, reproducible, high-pressure electrochemical measurements could be made (Table 5.2). From the Stokes-Einstein relation D = kgT/cxrq,

(5.18)

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5 lnsights into Solution Chemistryfrorn High Pressure Electrochemistry Tab. 5.2.

Kinetics of the Co(bpy);”*’ electron transfer reaction at a platinum electrode”.

Solvent

~

Ell2 (mv) AV~~II k:l (cm s-l) DO c m 2 SKI) AV: (cm3 mol-l) AV& (cm3 mol-’)

~~

___

~

(125)p (26.8 f 0.9)e 0.172 6.06 -8.6 f 0.4 0.37 0.03

4f.g 15.9 0.4‘ 0.198 10.6 9.1 k 0.3 8.8 f 0.1

+

0‘ 12.3 k 1.0‘ 0.070 9.41 10.2 f 0.7 11.1 f 0.1

-52f‘ 14.0 f 0.4‘ 0.0160 1.40 12.2 k 0.9 15.6 f 0.4

aData from ref. [24]; 1.0 mmol L-’ Co; 25.0 “C; transfer coefficient y = 0.5 in all cases. b0.20 mol L-’ NaCI. <0.20 mol L-’ Bu4NC104. Propylene carbonate. Reference electrode Ag/AgCl/(4 mol t KC1). ‘Reference electrode Ag/(0.013 mol L-’ AgC104-0.20 rnol L-’ Bu4NC104-CH3CN). g-85 10 mV vs. Fe(C5H5):”.

’

where c is a constant (6 and 4,respectively, for the sticking and slipping limiting models of diffusion) and r is the hydrodynamic radius of the reactant, it follows that AV& measured from high-pressure CV may be equated to the volume of activation AVACfor viscous flow of the solvent (= RT(3 In r / / 3 P ) T ) . In the simplest solvent-dynamical interpretation, then, we can expect (5.19)

Since AV& is large relative to the expected values of AVGTST) (that is, AVZ/2, which can be either measured or calculated from Eqs (5.5)-(5.8)), we can expect AVZ and AV& to be similar in sign and magnitude if solvent friction is indeed important and Zel i s roughly proportional to l/a. Because the TST-based Eqs (5.5)-(5.8) in combination with the fifty-percent rule predict negative values for AV; in the absence of special mechanisms such as cation catalysis of anion-anion electron transfer, the observation of positive AVZ values is a very strong indication of the incursion of solvent dynamics, especially when (as in the C~(bpy):+’~+case) a negative AV; is found for the same electrode reaction in aqueous media. We have used this last criterion in an attempt to detect solvent dynamical influences in homogeneous electron transfer (self-exchange) reactions [ll].Because solvent friction is most likely to emerge when the internal reorganizational barriers to electron transfer are lowest, the reaction chosen was the Fe(phen):+’2+ self-exchange, which is a fast low-spin/low-spin reaction with negligible change in Fe-N bond lengths and also can be followed in both aqueous and acetonitrile solutions. For the reaction in aqueous H2S04,AVL was found to be -2.2 cm3 mol-’, in excellent agreement with the TST prediction (Eqs (5.5)-

5.4 Homogeneous Versus Heterogeneous Electron Transfer

(5.8)), but in acetonitrile AVL was more negative (-5.9 cm3 mol-') than for water,

again in good agreement with the predictions of TST but ruling out rate control by solvent dynamics. Solvent friction, then, does not show up even in one of the most favorable bimolecular electron transfer reactions - unfortunately, there are exceedingly few self-exchange reactions for which AVk can be measured in both aqueous and organic media. In sharp contrast, Matsumoto [7G] has studied pressure effects on the Fe(phen)i+'2t reaction at a Pt electrode in acetonitrile containing 0.5 mol L-' tetrabutylammonium perchlorate, and found AV: +15 cm3 mol l , cf. AV: = -1.G cm3 mol-' in 0.1 mol L-' aqueous NalS04 and the negative values for self-exchange given above. It may be concluded that solvent dynamics dominate electrode kinetics in non-aqueous media even when the corresponding selfexchange reactions clearly conform to the TST model. One serious obstacle to interpretation of kinetic data in non-aqueous solvents having dielectric constants substantially lower than that of water is that ion pairing is almost inevitable, at least for the more highly charged couples such as C~(bpy);+'~+. Pyati and Murray [70] considered but rejected the possibility that their attribution of the kel-y correlation for this couple to solvent dynamical influences was vitiated by ion-pairing. Nevertheless, by going to a couple with large partners, one electrically neutral and one singly charged, one can reduce ionpairing to the absolute minimum and also completely remove the Coulombic and Debye-Hiickel contributions to AV: . We have therefore examined the electrode kinetics of the Ru(hfac)!'- couple at high pressures in acetonitrile, acetone, and methanol (for which AVZ data were already available [34]), and propylene carbonate (PC; efforts to extend the investigation to other polar solvents were unsuccessful) (551. The results are summarized in Table 5.3, and can be interpreted in detail following consideration of the background to Eqs (5.17) and (5.19).

-

Tab. 5.3.

Electrochemical characteristics of Ru(hfac)y'- at a Pt wire electrodea.

Solvent

CH3CNb

(CH3)zCOc

CH30Hd

Ell2 (mVf) AVceII' k,9 ( c m s-') AV: (cm3 mol-') AV& (cm' mol-I) AVZ (cm' mol-'g) AV: (calc)h

431 f 2 -24.8 k 0.8 4.0f 0.1 8.4& 0.5 12.1 0.7 -5.5 f 0.1 9.0f 0.7

414 f 2 -19.8 & 0.2 2.44 0.07 12.4 f 0.7 15.4f 0.7 -6.1 f 0.3 12.0f 0.7

364 2 -18.3 & 0.8 4.1 & 0.1 9.9 f 0.4 14.7k 0.7 - 5.8 k 0.3 11.4 k 0.7

*

+

aData from reference r551; lRul = 2.0-3.5mmol L-I, reference electrode Ag/(O.Ol moi L''-AgC104-0.20 rnol L-' Bu4NC104-CH3CN), 25.0 "C. Supporting electrolyte 0.20mol I>-' [Bu4N]C104. c0.20rnol L-' [Bu4N]PF6. d0.50 rnol L-' [Bu4N]C104. '0.50 rnol L-' [ B u ~ N J P F ~ . 'Relative to Ag/(O.Ol mol L AgC104-0.2 mol L-' Bu.+NC104-CH,CN), g Reference [ 34). "Calculated from Eq. (5.23)for the mid-range pressure of 100 MPa.

'

*

PCe

369 f 2 -13.0 f 0.5 2.26 f 0.03 11.2 f 0.3 18.5f 0.2 -

-

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5 Insights into Solution Chemistryfrorn High Pressure Electrochemistry

The question of the possible role of solvent dynamics in controlling the rates of chemical (and particularly electrochemical) reactions has been widely considered 168, 77-85]. There are basically two approaches to solvent-dynamical interpretation of the data of Table 5.3. One, originated by Kramers as long ago as 1940 [SG] and later developed by Grote and Hynes [87], regards the motion of the solvent as coupled to the reaction coordinate in a one-dimensional manner analogous to Brownian motion, assisting the reactant(s) to climb the activation barrier but: in the case of strong coupling, also hindering their passage across the barrier top, resulting in several crossings and re-crossings before moving on to product configurations. The other approach, introduced by Agmon and Hopfield [88, 891 and developed further by Sumi, Marcus and Nadler [90-921 and subsequently by Basilevsky, Ryaboy and Weinberg 193, 941, represents the activation process as a freeenergy surface with the reaction coordinate (in effect, a low-frequency intramolecular vibration of the reactant( s)) represented along one dimension and diffusive solvent motions along another coordinate orthogonal to it. These alternative views have been summarized succinctly by Asano [ 771 (see also Chapter 3 ) . For adiabatic electrode reactions with a negligibly small internal reorganization energy AG;, the Kramers-Grote-Hynes model leads to (5.20)

v,l = ~ ; ' ( A G & / ~ K R T ) ' ' ~

where AC& is the contribution of solvent reorganization to AG;. If the solvent behaves as a Debye liquid (that is, one in which molecules can be treated as spheres rotating in cavities in a continuous dielectric) of Debye relaxation time 7 D , and VM is the effective hard-sphere molar volume of the solvent molecules, q can be obtained (at least approximately) from '7 ;

=

(E/E,~)TD~= ( E / E , , , ) R T / ~ V M ~

(5.21)

Thus, the dominant variable in the pre-exponential factor of the expression for k,, (cf. Eq. (5.4)) is q, giving rise to the approximate proportionality (5.17) and so to equation (5.22): A V i = A V & . + RT(a In q / d P ) , = AV&,

+ AV&

= AVA,

+ AV&

(5.22)

A more precise version of Eq. (5.22) for the theoretical value AVZ(ca1c) of AVZ includes a term Q representing the small, largely self-canceling pressure dependences of the factors other than q in Eqs (5.19) and (5.20). For the Ru(hfac)t' couple in the solvents listed in Table 5.3, Q is only -0.3 to -0.4 cm3 mol-'. Furthermore, since AV& is the value of AV: that would be expected in the absence of solvent friction, we can use the fifty-percent rule to estimate it as AVZ /2: AV: (calc) = (AV: /2)

+ AV& + Q

(5.23)

5.4 Homogeneous Venus Heterogeneous Electron Transfer

Table 5.3 shows that AV$(calc) agrees with the experimentally observed AVZ to within the experimental uncertainty for the Debye solvents acetone and acetonitrile, and comes surprisingly close for methanol which, because intermolecular hydrogen-bonding contributes several frequencies to the apparent rL, is not considered to be a Debye liquid. Unfortunately, there are insufficient data for application of Eq. (5.23) to the Ru(hfac)y'- electrode reaction in propylene carbonate, which is also regarded as a non-Debye liquid. In any event, the implication is that the fifty-percent rule applies to volumes of activation for electrode reactions but its effect is swamped by solvent dynamical contributions. The applicability of Eq. (5.23) to the Ru(hfac)!'- electrode reaction may be questioned on the basis that AG& is only slightly less than AG&. The Sumi-Marcus approach (901, however, does cover cases in which AG$ is not negligible, and we find that replacement of the parameter Q by one derived by differentiation of Eqs (8.6) and (8.7) in reference [90] with respect to pressure, results in no significant change in AV:](calc), within the experimental uncertainty. There is also the possibility, raised by Weaver and co-workers [95], that the Ru(hfac);/- electrode reaction may be non-adiabatic (li << l),but in that case one would expect v , ~to be proportional to r;" where 1 2 0 2 0, with 0 reaching 1 only when the reaction is fully adiabatic [92, 961. In fact, the results of Table 5.3 imply that 0 is close to 1, and in any event non-adiabaticity is expected to make a substantial negative contribution to AVZ, whereas the problem is to explain why AV: is so positive 1551. Clearly, AV: information for other O/- or +/0 couples in non-aqueous media are needed to vindicate the arguments leading to Eq. (5.23), but there is very little AVZ information for such systems. For the Fe(qS-CsH5)2f/' self-exchange reaction in aceonitrile, Hunt and co-workers reported AVZ = -7 cm3 mol-l [97], but efforts [98] to obtain AV; for the electrode reaction have been thwarted by excessive drift of the apparent k,l over the time span of a series of pressure measurements. It is, however, clear that AVZ is markedly positive for the Fe(qS-C~H5)i/' electrode reaction in acetonitrile, consistent with Eq. (5.23) in at least a qualitative way. Recent studies also reveal AVZ values of +6 and +ll cm3 mol-' for the Mn(CN-chex):+/+ electrode reaction in CH3CN and acetone, respectively [ 7 G ] , whereas for the corresponding self-exchange reaction AV: = -17 and -20 cm3 mol-' [99]. For this Mn"/' couple, the interpretation of the volumes of activation is likely to be complicated by ion-pairing and medium effects, but these and all other data collected to date point to a striking qualitative difference between self-exchange and electrode reactions: the respective volumes of activation differ unambiguously in sign, and AV: for the electrode reactions shows some relation to AV&. The only likely explanation (since none of these reactions seems to be diffusion-controlled) is that the electrode reactions are subject to solvent dynamical effects, but the selfexchange reactions are not. The reason for this difference is not yet certain but may be due in large part to the fifv-percent rule, as applied to the respective free energies of activation. Thus, AG: is expected to be just one-half of A G Z , which itself is not normally very high, and the incursion of solvent dynamical effects is expected for reactions with a low internal free-energy barrier.

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5 Insights into Solution Chemistryfrorn High Pressure Electrochemistry

5.5

Conclusions

For simple outer-sphere self-exchange reactions of transition-metal complexes in both aqueous and polar organic solvents, AVZ is dominated by AV& and hence is expected to be negative, regardless of whether electron transfer is fully adiabatic. In cases in which this expectation is not realized, there is usually an identifiable departure from a simple outer-sphere mechanism attributable to inner-sphere pathways, cationic catalysis of anion-anion electron transfer, or structural distortions associated with spin multiplicity changes. Thus, AVZ can serve as a rnechanistic criterion. For bimolecular outer-sphere electron transfer reactions involving net chemical change (“cross” reactions), the volume of activation AVZ can be successfully predicted from Eqs (5.12)-(5.14) if AVZ for the two constituent self-exchange couples is known (or can be estimated from Eqs (5.5)-(5.8)) and the pressure dependence of the difference AE in their electrode potentials is measured by high-pressure electrochemistry. Such predictions may fail if AE is too large, or if the reaction mechanism is other than simple outer-sphere. Thus, measurements of AVL combined with high-pressure studies of AE can also provide mechanistic criteria for redox reactions in homogeneous solution that involve net chemical change. The relationship between the rate constants k,l for an electrode reaction and k,, for the corresponding self-exchange electron transfer reaction is not obvious because k,l can be strongly influenced by the nature and history of the electrode surface and by solvent dynamic effects if present. Electrode properties, however, are not expected to be sensitive to pressures in the 0-200 MPa range. Moreover, the signature of solvent dynamical effects is a dependence of reaction rate on solvent viscosity, but the viscosity of water is effectively independent of such pressures at near-ambient temperatures. Consequently, for typical aqueous electrode reactions, AV: = O S A V . , regardless of any involvement of solvent dynamics, and so AVZ can be predicted from transition state theory (TST) according to Eqs (5.5)(5.8). On the other hand, for non-aqueous solvents, viscosities rise sharply and approximately exponentially with pressure, so that any dependence of k,l (or k,) on solvent dynamics will be reflected in a markedly positive contribution to AV: (or AVZ). For couples such as Ru(hfac)!/- in which one of the reactants is electrically neutral, ion pairing and related effects in polar organic solvents are negligible, so that AVZ in organic solvents should be given to a good approximation by the sum of a moderately negative TST contribution and a strongly positive solventdynamical contribution represented closely by the activation volume AV& for reactant diffusion. For the self-exchange reaction of Ru(hfac);/ - in organic solvents, AVZ is negative and conforms closely to predictions based on TST, so that the TST contribution to AVZ can be identified with O.SOAV2. This accounts very well for the positive AVZ values found for the Ru(hfac):’- system in organic solvents. Thus, the fifty-percent rule evidently also applies to AVZ for electrode reactions in non-aqueous media but its effect is swamped by solvent dynamical contributions,

References

so that AVZ is invariably positive. This last remark is also valid for electrode reactions of 2+/+ and 3+/2+ couples, but the possibility of ion pairing prohibits detailed interpretation other than to note that AV: runs roughly parallel to AVZE

~761. High-pressure kinetics indicate the absence of solvent dynamical effects in outer-sphere bimolecular self-exchange reactions in non-aqueous media, even in the most favorable experimentally accessible case (the Fe(phen):+” couple) - on the contrary, expectations based on TST alone are generally met, and AVZ is negative. At the same time, AVZ is invariably positive for electrode reactions in organic solvents, signaling rate control by solvent friction. Solvent dynamics dominate electrode kinetics in non-aqueous media even when the corresponding self-exchange reactions clearly conform to the TST model. In short, pressure effects reveal that electrode reactions are subject to solvent dynamical effects in non-aqueous media at least, but the corresponding self-exchange reactions are not, regardless of the solvent.

’

Acknowledgments

I thank my co-workers, whose names appear in the references, for their many superb contributions, the Natural Sciences and Engineering Research Council of Canada for financial support of our work, Dr N. Weinberg for illuminating discussions, and the Alexander von Humboldt Foundation for a Research Award.

References 1 R. A. MARCUS,]. Chem. Phys. 1956, 24, 2

3 4

5

6

7 8 9

10

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5 lnsights into Solution Chemistryfrom High Pressure Electrochemistry ZAHL,K. VAN ELDIK, T. W. Inorg. Chem. 2002, 41, in SWADDLE, press. 21 P. D. METELSKI. T. W. SWADDLE? Inorg. Chem. 1999, 38, 301. 22 S. WHERIAND, Coord. Chem. Rei?. 1993, 123, 169. 23 Y. MARCUS, [on Properties, Marcel Delker, Inc., New York, 1997, Chapter 8. 24 Y.Fu, A. S. COLE,T. W. SWADDLE,]. Am. Chem. Soc. 1999. 121, 10410. 25 W. H. J O L I F Y , D. R. STRANKS, T. W. SWADDLE, Inorg. Chem. 1992, 31, 507. 26 J . K. BEATTIE, H. ELSBERND,Inorg. Chim. Acta 1995, 240. 641. 27 J. K. BFATrTE, Adc. Inorg. Chem. 1988, 32, 2. 28 K. A. BINSTEAD, J. K. BEATTIE, Inorg. Chem. 1986, 25, 1481. 29 C. FEUORCHUK, M. MATSUMOTO, T. W. SWADDLE, unpublished studies. 30 L. L. MARTIN, K. S. HAGEN,A. HAUSER, R. L. MARTIN,A. M. SARGESON,]. Chem. SOC.Chem. Comm. 1988, 1313. 31 L. L. MARTIN, R. L. MARTIN,K. S. MURRAY, A. M. SARGESON, Inorg. Chem. 1990, 29, 1387. 32 L. L. MARTIN, R. L. MARTIN, A. M. SARGESON, Polyhedron 1994, 13, 1969. 33 A. M. SARGESON, personal communication. 34 H. DOINE,T. W. SWADDLE, Inorg. Chem. 1988, 27, 665. 35 H. D. TAKAGI, T. W. SWADDLE, Chem. Phys. Lett. 1996, 248, 207. 36 M. R. GRACE, H. TAKAGI, T. W. SWADDLE, Inorg. Chem. 1994, 33, 1915. 37 T. W. SWADDLE, in High Pressure Techniques in Chemistry and Physics, W. B. HOLZAPFEL, N. S. ISAACS,(Eds), Oxford University Press, Oxford, 1997, p. 343. 38 T. W. SWADDLE, P. A. TREGLOAN, Coord. Chem. Rev. 1999, 187, 255. 39 H. DOINE,T. W. WHITCOMBE; T. W. Can.]. Chem. 1992, 70, 81. SWADDLE: 40 Y. Fu, T. W. SWADDLE, Chem. Comrnun. 1996, 1171. 41 Y. Fu, T. W. SWADDLE, Inorg. Chem. 1999, 38, 876. 42 M. BIIAI,2. Natuforsch. 1991, 46a, 1108. 20 A.

M. MA~SUMOTO, T. TARUMI, I. TAKAHASHI, S. FUNAHASHI, T. NODA, 2.Natuforsch. 1997. H. D. TAKAGI, 52b, 1087. 44 M. T. CR~JAAES. H. G. DRICKAMER, L. R. FAULKNER,]. Phys. Chem. 1996, 100, 16613. 45 J. GOLAS, H. G. DRICKAMER, L. R. FAULKNER, ]. Phys. Chem. 1991. 95, 10191. 46 M. T. CRUAAES, H. G. DRICKAMER, L. R. FAUI-KNER,]. Phys. Chem. 1992, 96, 9888. 47 M. T. CRUAAES, K. K. RODGERS:S. G . SLIGAR,].Am. Chem. SOC.1992, 114, 9660. 48 M. T. C R U A ~ ~H. E SG, . DRICKAMER, L. R. FAULKNER, Langmuir. 1995, I 1, 4089. 49 I. 1. SACHINIDIS, R. D. SHALDERS, P. A. TREGLOAN, 1. Electroanal. Chem. 1992, 327, 219. 50 J. I. SACIIINIDIS, R. D. SHALDERS, P. A. TREGLOAN, Inorg. Chem. 1994, 33, 6180. 51 J. I. SACIIINIDIS, R. D. SHALDERS, P. A. TREGLOAN, Inorg. Chem. 1996, 35, 2497. 52 7. S U N ,1. F. WISHART, R. VAN ELDIK, R. D. SIIAIDERS, T. W. SWADDLE,]. Am. Chem. SOC. 1995, 117, 2600. 53 R. S. NICHOLSON, I. SHAIN,Analyt. Chem. 1964, 36, 706. 54 R. S. NICHOLSON, Analyt. Chem. 1965, 37, 1351. 55 J. ZHOU,T. W. SWADDLE, Can.]. Chem. 2001, 79, 841. 56 R. A. MARCUS, Can.]. Chem. 1959, 37, 155. 57 R. A. MARCUS,].Phys. Chem. 1963, 67, 853. 58 R. A. MARCUS,].Chem. Phys. 1965, 43, 679. 59 R. A. MARCUS, Electrochim. Acta 1968, 13, 995. 60 N. S. HUSH,Electrochim. Acta 1968. 13, 1005. 61 R. D. CANNON, Electron Transfer Reactions, Buttenvorths, London, 1980, pp. 220-222. 62 D. MILNER, M. J. WEAVER,]. Electroanal. Chem. 1985, 191, 411. 63 G. HILLS,]. Phys. Chem. 1969, 73, 3591. 43

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High Pressure Chemistry Synthetic, Mechanistic, and Supercritical Applications

Edited by Rudi van Eldik and Frank-Gerrit Kliirner

0WILEY-VCH Verlag GmbH, 2002

6

Pressure Effects on the Photoreactions of Transition Metal Complexes Peter C. Ford” and Leroy

E. Laverrnan

6.1

Introduction

In this chapter, the focus will be on the application of high pressure techniques in the study of the photochemical behavior of transition metal complexes (coordination, organometallic and bio-inorganic) in solution. We will present a systematic treatment of pressure effects on the nature of excited states (ES) and on the photophysical and photochemical processes that lead to ligand substitution, electron or energy transfer and thermal reactions of reactive intermediates generated by ES reactions. Selected examples will be presented in detail to illustrate how pressure effects can provide valuable mechanistic insight when combined with other quantitative studies. Figure 6.1 is a simple Jablonski diagram that introduces the sequence of events subsequent to a spin allowed electronic excitation of a molecule. This will define the processes that must be considered when elucidating photoreaction mechanisms. Initial excitation (hv) from the electronic ground state (GS) is vertical (FranckCondon Principle), so the first electronic excited state (ES1) is initially prepared with the geometry of the ground state. Thus, ESI is prepared in a vibronic excited state, and the first deactivation process is vibronic relaxation. In Fig. 6.1, ESI is shown to decay by several competing processes including chemical reaction to form a product ( P I ) with rate constant fluorescence (q)or non-radiative decay directly to the ground state, or by non-radiative internal conversion (kit) or intersystem crossing (kist) to a lower energy state ES2, (if the ES has the same or different spin multiplicity, respectively). The quantum yield of a particular process arising from ESI (Qi) would thus be defined by the ratio of decay rate constants,

(x)

q,

If only unimolecular processes are involved then ES1 decays according to an exponential function and the lifetime of ESI is defined as

6. 7 Introduction

ES2

krl'

Fig. 6.1.

Generalized Jablonski diagram.

Therefore Eq. (6.1) can be rewritten as

If ES2 has a different spin multiplicity from that of ES1, the efficiency of its formation is the intersystem crossing quantum yield

ES2 has its own decay processes including radiative (kr, termed phosphorescence) and non-radiative deactivation (k"), unimolecular reaction to product(s) (kp) and bimolecular quenching by energy or electron transfer (b) to another species. For this model the ES2 lifetime is defined by

However, the quantum yield is defined slightly differently since the efficiency of intersystem crossing has to be taken into account.

I

185

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6 Pressure Effects on the Photoreactions of Transition Metal Complexes

The purpose of outlining the decay pathways for this simple model (Fig. 6.1) is to emphasize that hydrostatic pressure can affect rates of the individual processes. Pressure can also affect energies of excited states relative to the ground state as well as relative to each other. Understanding pressure effects on photoreactions requires careful evaluation of all parameters that may be affected. Lastly it should be emphasized that the primary photoproducts formed directly from the excited states might themselves be very reactive species. These may react subsequently to give stable products by unimolecular or more complex mechanisms. Continuous photolysis experiments which use low intensity excitation generate only small steady state concentrations of excited states and reactive intermediates, so only stable products or a steady state phenomenon such as luminescence are generally observed. Flash photolysis techniques, which prepare transient species in non-steady state concentrations, often allow direct observation of such species. 6.1.1

Pressure Effects on Excited State Energies

For metal centered ligand field (LF) transitions, the magnitude of the pressure induced spectral shifts will depend markedly on the symmetries of the orbital transitions. For a hexa-coordinate transition metal complex having an approximate Oh symmetry, transitions between the t2g(d,) and the eg (do*)orbitals are energetically related to the magnitude of LF strength as represented by the octahedral splitting parameter Ao. At high pressure, A. increases owing to stronger metalligand overlap from bond compression. For example, this is reflected in the blue shifts of about +25 cm '/I00 MPa for the ligand field bands of a variety of nickel(I I) complexes [ 13. A qualitative energy level diagram for the ligand field states of an octahedral chromium(II1) ion is shown in Fig. 6.2. The dominant bands in the absorption spectrum are ground state quartet to excited state quartet transitions, since the quartet to doublet transitions are spin forbidden. Under high pressure, solid [Cr(NH3)6]C13[2] demonstrated blue-shifts for the Q1 + Qo (+53 cm-'/100 MPa) and Q2 + QObands ( t 3 6 cm-'/100 MPa). In contrast, both absorption and emission transitions between the QOground state and the lowest energy doublet state Do display very small red shifts with pressure. For example, the Do + QOemission from the Cr(II1) center of ruby (694.2 nm at ambient pressure) shifts to the red by -0.7 cm-l/lOO MPa. The sharpness of this emission line and the linear nature of its response up to 20,000 MPa has proved extremely useful as an internal calibration of very high pressures in diamond anvil cells. Modest red shifts ( - 3 to -5 cm-'/100 MPa) were seen for the doublet emission (Do --+ Qo) and absorption (Do + Qo) bands for the Cr(NH3);' ion in aqueous solution [3]. The different pressure sensitivities of the doublet and quartet bands can be rationalized in terms of orbital parentages. The quartet excited states have (t2g)2(eg)1 configurations and must involve distortions of the M-L bond lengths owing to the

6.1 Introduction

I

187

"\ QO

Fig. 6.2. Generic energy level diagram for a strongfield Cr(lll) complex. PI is phosphorescence from the double Do and F1 the fluorescence from the quartet Q1.

nature of eg orbitals. In contrast, both the ground and doublet states have ( t ~ ) configurations, ' so there is little distortion between the QOand Do states. Although emission from Cr(II1) in an octahedral field usually displays sharp lines from the spin-forbidden Do + QO transition, broad band Q1 + QO fluorescence may be seen when the field is sufficiently weak [4]. Different sensitivities of the quartet and doublet ligand field state energies to pressure are illustrated by a diamond anvil cell investigation of the 22-K emission spectrum of solid (NH4)3[CrF~] (51. At ambient pressure, broad fluorescence at ,,v = 12,984 cm-l (Eoo = 14,319 cm-') is the only feature seen. Raising P to 7.1 GPa shifts vmax to 13,605 cm-' (Eoo = 14,855 cm-'). Raising P further leads to disappearance of the fluorescence and appearance of the sharp doublet emission at 14,896 cm-'. Thus the increased pressure tunes the QOstate above the Do state. Ligand localized nn* ES are common to complexes having large aromatic ligands. Absorption and emission bands attributed to nn* states shift to the red with increasing P [6]. For example, fluorescence maxima from the ligand centered states of the tetraphenyl porphyrin complexes Mg(TPP) and Zn(TPP) display shifts ranging from -34 cm-'/100 MPa in methanol to -94 cm-'/100 MPa in chloroform with

188

I

6 Pressure Effects on the Photoreactions of Transition Metal Complexes

increasing pressure [7]. Phosphorescence bands are less pressure sensitive than fluorescence bands owing to the lower polarizability of triplet states. Metal to ligand charge transfer (MLCT) absorption and emission bands have been examined as a function of pressure for the ruthenium(I1) complex Ru(bpy)i+ and related Ru(I1) and Os(I1) species [&lo]. In acetonitrile, small red shifts were seen for MLCT absorption and emission maxima with increasing P (- -20 cm-’/ 100 MPa over 300 MPa), and it was argued that the small shifts result from pressure induced decreases in the ligand R ‘ orbitals compensated by lower d, orbital energies from increased M-L overlap [9]. Similar shifts were seen in diamond anvil pressure studies (3-7 GPa) of the emission from solid [Ru(bpy)3I2+salts [lo]. Pressure-induced solvent freezing has been shown to have remarkable effects on the spectra of the rhenium(I) complex ReBr(C0)3(phen)and the copper(I) cluster Cu414py4.The former displays strong MLCT emission 1111; the latter displays a strong emission from a “cluster centered” (CC) excited state assigned as having mixed d-s metal-centered and iodide-to-copper charge transfer character [ 121 in ambient temperature fluid benzene. For each, the emission spectrum is markedly dependent on the rigidity of the medium, a behavior termed the “rigidochromic effect” [ll].Since benzene freezes readily at relatively low pressure (Pf = 72 MPa at 25 “C), the rigidity of benzene solutions can be sharply changed by raising P above this value. The broad emission maximum of Cu414py4 :;1( = 690 nm) was unaffected by raising pressure as long as the benzene solution remained fluid, but above 72 MPa there was a dramatic shift ;in: 1 to 575 nm (Fig. 6.3) [13]. In the same context, pressure-induced freezing of a benzene solution of ReBr(C0)3phen shifted ; : 1 from 610 nm at 0.1 MPa to 546 nm at P > 72 MPa [13]. One explanation of rigidochromic effects is the reduced ability of solvent to reorient in the frozen state to facilitate the most favorable electrostatic interaction with an ES. Alternatively, ab initio and experimental results suggest that the CC” state of Cu414py4 is quite distorted from the ground state [12b]. Thus, the hypsochromic shift of solvent freezing by raising P may result from restrictions imposed by a rigid solvent cavity. A recent review [ 141 summarizes some other high pressure (diamond anvil) studies of vibrational and electronic spectra of metal complexes. 6.1.2 Pressure Effects on Excited State Kinetics

The two most common parameters measured in photochemistry are the quantum yield @i for a specific process, and the lifetime t of the excited state. The quantum yield is operationally defined as the moles of product formed (or starting species reacted) per einstein of light absorbed by the system at a particular wavelength of irradiation (&). In this context, the pressure effect on the quantum yield gives an “apparent activation volume”, i.e. AV; = -RT[d(ln @i)/dP], from a plot of In @i vs. P. To elucidate a mechanism, one must first consider the states initially formed by photoexcitation as well as other ES eventually populated by internal conversion and intersystem crossing. Although not always the case, many metal complexes, when

G. 1 Introduction

I

500

600 700 800 Wavelength (nm)

900

Fig. 6.3. Emission spectra of Cu4I4py4in benzene a t 298 K a t ambient pressure and 75 MPa. Both spectra have been normalized to an arbitrary maximum intensity of 1.O (redrawn from ref. 13).

-

excited, undergo efficient relaxation (QiSc 1.0)to a lowest energy excited state (LEES) from which the various chemical processes lead to photoproducts. In such systems, one can apply transition state theory and consider pressure effects in terms of the excited state mechanisms. For the model shown in Fig. 6.1, the quantum yield for a specific pathway would be

and the apparent activation volume would be AV! = AVL

+ AV:

(6.8)

where AV! = RT[d(ln r)/dP)T and AVL is defined above. However, it is generally preferable to use Eq. 6.7 to determine ki for each set of conditions and to determine AV! from a plot of In ki vs. P. Radiative rates: For most transition metal complexes in solution, emission quantum yields are small, thus radiative decay is only a minor component of the overall deactivation mechanism. Limited studies show pressure effects on k, to be small, a few percent over the hydrostatic pressure ranges of principal interest here and these effects can largely be attributed to solvent perturbations [15, 161. The relatively small values of k, for most luminactive metal complexes in fluid solutions, suggest that such modest changes will not have much impact on interpretations of pressure effects on lifetimes or quantum yields.

I

189

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I

6 Pressure Efects on the Photoreactions of Transition M e t a l Complexes

Non-radiative deactivation rates: In contrast, nonradiative deactivation (kI,) often constitutes the major pathway by which metal complex excited states decay. For large molecules non-radiative deactivation is largely due to intramolecular processes determined by vibrational and electronic factors. Vibronic coupling between electronic states has been analyzed in terms of two limiting cases. In the weak coupling limit, the relative displacement of the ES potential surfaces is small. and k, is predicted to increase exponentially as the difference in energy (AE) between the ES and the GS decreases (“the energy gap law”). In the strong coupling limit, there is a large displacement of the ES surface (at least one normal mode) relative to the ground state such that the surfaces cross not far from the minimum of the higher state [ 171. Accordingly, strong coupling deactivation should show Arrhenius type temperature dependence while weak coupling should be essentially temperature independent. Strong coupling may also be associated with ES reactions, especially unimolecular reactions such as ligand substitution. In such a case there should be correlation between pressure effects seen for the reaction pathway k, and the strong coupling component of k,. Pressure can affect k, in other ways, for example, it may raise or lower an ES energy by compression of the complex or by perturbation of the solvent dielectric constant. According to the energy gap law, k, should respond to -AE exponentially [18]. Such behavior was observed by Salmon and Drickamer 1151 who investigated the MLCT phosphorescence spectra, lifetimes and quantum yields for the rhenium( I) complexes ReC1(C0)3phen and ReCl(C0)3(4,7-Ph2phen) in different solvents. By systematic variation of solvent properties with applied P, they demonstrated a linear relationship between ln(k,) and -AE indicative of a weak-coupling mechanism for non-radiative deactivation. The effects were small in dimethylformamide and acetonitrile but were larger in m-xylene, reflecting the sensitivity of the MLCT states to the greater compressibility of the latter solvent. Another example can be drawn from the emission properties of two dinuclear d8 complexes the diplatinum(I1) ion Pt,(POP);- (POP = p-q2-H2P20;-) [19] and the diiridium( I) ion Ir2pz2(COD)2 (pz = p-q2-pyrazolate, COD = q4-1,4-cyclooctadiene) [20]) (Fig. 6.4). In both complexes the metal centers have square planar coordination with the bridging ligands holding the two square planes in a cofacial configuration. The LEES has been assigned as having d(o,&) + p(obM)orbital parentage in each case leading to a stronger M-M bond in the excited state than in the ground state [21]. Both species are strong emitters in ambient temperature fluid solutions [ 221. Hydrostatic pressure up to 300 MPa had no effect on the absorption and emission spectra ;:1( = 511 nm) of Pt2(POP):- in ambient temperature aqueous solution. There was a modest decrease in the phosphorescence lifetime from z = 8.8 ps at 0.1 MPa to 7.6 ps at 300 MPa and a corresponding 13 % decrease in the phosphorescence quantum yield (@ = 0.55, @)r3O0 = 0.48). Since the intersystem crossing to the LEES was estimated to be unity in both cases, these data demonstrate that pressure has little effect on k, (Eq. 6.9) [22], consistent with the relative insensitivity of the refractive index of water to pressure [23].

G. 7

HO P

Introduction

\*/

Fig. 6.4. Drawing of Pt2(p-q2-H2P205)j- and I r 2 p ~ 2 ( C O D ) 2 (pz = p-q2-pyrazolate, COD = q4-l ,4-cyclooctadiene) (from ref.

20).

In the absence of photoreaction, the shortened lifetime at 300 MPa must be largely due to increases in the non-radiative deactivation rate constant. Since @isc 1, then:

-

(6.10)

qoo/e

This gives = 1.34 f 0.03, from which an apparent activation volume for the non-radiative deactivation path can be calculated to be -2.4 f 0.5 cm3 mol-'. In acetonitrile, a AV: value of -0.2 cm3 mol-I was determined [22]. Similar analysis of the emission properties of I r z p ~ ~ ( C 0 D demonstrated )~ again that k, was little affected by pressure to 300 MPa. The absorption maxima shifted (from 49G to 500 nm), but there was no shift in the emission band ;1 ( = 663 nm). However, unlike Pt2(POP)t-, t increased with P from 0.24 ps at 0.1 MPa to 0.42 ps at 300 MPa, thus the AVA for I r z p ~ ~ ( C 0 D has ) ~the positive value 1-4.7 cm3 mo1-l in acetonitrile [22]. That the ES of these d8-d8dinuclear complexes have shorter M-M bonds than the respective ground states suggests that k, should display a positive AV: along the deactivation trajectories. The positive AV: value for Ir2pz2(COD)2is consistent with this expectation, but the small negative AV: value for Pt2(POP)t- suggests modest contraction rather than expansion accompanying non-radiative deactivation. The contrasting photophysical behaviors may be attributed to structural differences. The volume changes between the flexible butterfly structure of Ir2pz2(COD)2 and its ES may be larger than for the tetrabridged Pt2(POP): ion. For the latter, shortening of the Pt-Pt bond may be compensated by ES lengthening of others, perhaps Pt-P bonds, thereby minimizing overall volume changes. However, an alternative (but not mutually exclusive) interpretation would be that the small AV: value for Pt2(POP):- is indicative of a weak coupling deactivation mechanism. This is indeed consistent with the temperature independence of k, for Ptz(POP)t~

I

191

192

I

G Pressure Effects on the Photoreactions of Transition Metal Complexes

under these conditions [22]. In contrast, k d for I r z p ~ ~ ( C 0 D shows ) ~ markedly temperature-dependent behavior consistent with a strong coupling mechanism due to a molecular distortion leading to deactivation. Non-radiative deactivation involving a second excited state: A somewhat different situation is presented by the ruthenium( 11) complex Ru(bpy):'. In ambient temperature, fluid solution this species shows little unimolecular photochemistry and modest emission quantum yields (mr < 0.3) [9]. Initial pressure studies on the MLCT luminescence from Ru(bpy)if in 18 "C aqueous solution saw little change [24]. However, detailed studies by Fetterolf and Offen [9, 251 demonstrated a remarkable temperature dependence for AV:, which rises from +2.9 cm3 m o t at 15 "C to f8.7 cm3 mol-' at 45 "C in acetonitrile and from -1.5 cm3 mol at 2 "C to +7.5 cm3 mol-' at 70 "C in aqueous solution [26]. This behavior is best explained in terms of the proposed mechanism [27] where a key pathway for [R~(bpy);'];~ deactivation involves thermal promotion from the MLCT LEES to a ligand field state -3600 cm-' higher (Fig. 6.5). The large AV! associated with the thermally promoted pathway may be the consequence of two contributions, a larger partial molar volume for the 'LF state than for the 3MLCTstate, and second, a AVt for the 3LF owing to a strong-coupling mechanism.

-'

Fig. 6.5. Model describing proposed mechanism for decay of the MLCTexcited state of Ru(bpy):+ and related complexes. Emission occurs from the lowest energy excited state 'MLCT. At low temperature, nonradiative

deactivation occurs predominantly from this but a t higher temperature, the state predominant pathway is via thermal promotion to the higher energy 3LF state followed by rapid deacviation (k:).

(ky)

G.1

Introduction

I

193

The Ru(phen):+ analog shows similar behavior, while the osmium(11) analog Os(phen):' does not 191. The much higher ligand field splitting for Os(I1) complexes positions the lowest 'LF state at an energy too high relative to the 'MLCT state to be a significant contributor to the non-radiative deactivation pathways. Ambient temperature emission intensities and lifetimes from Ru(bpy);+ and Ru(bpy)z(py);+ salts in solutions of poly(4-vinylpyridine) (PVP) and poly (acrylic acid) (PAA) have been studied at pressures to 7 GPa in a diamond anvil cell [lo]. For Ru(bpy):', emission intensities and lifetimes decreased monotonically by -65 % and -50 % in PAA and PVP, respectively, as P was raised from 0.1 MPa to 7 GPa. This modest effect (AV; (apparent) -1 cm3 mol-') was attributed to increases in k, according to energy gap law considerations as the 3MLCTemission shifts to lower energy. Volume changes related to photophysical properties can also be deduced from time-resolved photoacoustical calorimetry (PAC) studies [ 281. This technique has been used with the Ru(11) complexes Ru(bpy):+, cis-Ru(bpy)z(CN)z and Ru(bpy)(CN);- [29, 301. Analysis of such data was used to calculate enthalpy and volume changes induced by the formation and decay of MLCT excited states in aqueous solutions. For Ru(bpy);+ formation of the 3MLCT state is associated with a modest contraction (AVI\?LCT= -3.6 & 0.3 cm3 mol I), which was rationalized in terms of slight decreases (-0.001 A) in Ru-N bond lengths in the ES [29]. The AV for decay is the same magnitude, but of opposite sign ($3.4 f 0.4 cm3 mol-') [30]. In sharp contrast, positive values of AVMLCT (+14.9 and +5.2 cm3 mol-1 respectively) were determined for MLCT excitation of cis-Ru(bpy)z(CN)2 and Ru(bpy)(CN):- [ 301. These were rationalized in terms of reduced basicity of coordinated cyano groups in the MLCT state resulting in net desolvation. As a consequence, the AVMLCT of Ru(bpy)(CN):- was shown to be markedly pH dependent [ 3OCl.

-

Excited state tuning with pressure: The influence of pressure on metal complex excited state energies, either by changes in the intrinsic properties of the complex, or by modification of the solvation properties, provides an opportunity to tune the excited state energies. Such tuning generally has only modest effects on unimolecular photophysical kinetics over the hydrostatic pressure ranges used in most kinetics studies (0.1-400 MPa), ifthe LEES is a single state or a collection of thermally-equilibrated states with similar orbital parentages. However, much greater effects would be expected if several excited states of dissimilar orbital parentages are involved in determining the radiative and/or non-radiative pathways as described above for the Ru(bpy)p ion. ES tuning effects on photophysical properties are quite evident in the luminescence spectrum of the iridium(II1) complex ion Ir(Mephen)2Cl; (Mephen = 56dimethyl-1,lO-phenanthroline) in ambient-temperature dimethylformamide. This displays dual emission from thermally equilibrated 3MLCT and 3LF states. Increased pressure (300 MPa) leads to enhanced MLCT emission (550 nm) at the expense of the LF emission (720 nm) with little or no shift of peak maxima (Fig. 6.6) [31]. The spectral changes were attributed to shifts in the relative populations

194

I

G

Pressure Effects on the Photoreactions of Transition Metal Complexes

NANOMETERS

500 I

700 900 110 I

I

I

I

I

I

300 MPa

z

0 fn

W

a

c M-'(

I 0- 3,

Fig. 6.6. Emission spectra of Ir(Mephen)zCIz in DMF a t 0.1 MPa and 300 MPa showing the increase in the MLCTemission intensity a t the expense of the longer wavelength LF emission a t the higher P (redrawn from reference 31).

owing to partial molar volume differences between the two ES in thermal equilibrium (Fig. 6.7), since emission lifetimes and spectra are independent of the excitation wavelength. The apparent volume difference of +4.2 cm3 mol-' was calculated according to Eqs. (11) and (12) by assuming that the ratio of the radiative rate constants is pressure independent. This indicates that the LF state is larger by 4.2 cm3 mol-I than the ground state. (6.11)

AV!pp = -RT

d ln(ky/k?) dP

+ AVeq z AVeq

(6.12)

Lifetime measurements for Ir(Mephen)*Cl: in DMF solution show that pressure decreases the deactivation rates, and a linear ln(kd) vs. P plot gives the AV: value +4.0 0.2 cm3 mol-', where kd = T-'. This would suggest, according to Fig. 6.7, that deactivation is largely occurring via thermal promotion to the LF excited state followed by non-radiative decay via the pathway. High spin/low spin equilibria: Pressure effects on the distribution of electronic states have also been investigated for d6 iron(I1) complexes of the type FeL:*, where L is a polydentate nitrogen donor ligand. For certain L such as p y m (Fig. 6.8), the

6 7 Introduction

I

195

Fig. 6.7. Scheme for luminescence from two emitting states o f different orbital parentages in equilibrium.

energy difference between the high spin (quintet)/low spin (singlet) electronic configurations is small. As solids, these species may undergo a phase transition from the quintet to the more strongly colored singlet as T is lowered. In certain cases, irradiation at low T converts the singlet to the quintet which persists indefinitely under these conditions in a process termed the LIESSTeffect [32]. For some FeL? the two electronic states are in thermal equilibrium in solution (Eqs 6.13 and 6.14), and the relative concentrations of the two states can be tuned by hydrostatic pressure. Values of AV as large as +16 cm3 rno1-l have been reported, depending upon the ligand and the solvent [ 331. kis

[FeL;'] g [FeL;'] (LS) krl (HS)

(6.13) (6.14)

Fig. 6.8.

Drawing of 2(2-pyridy1)imidazole (pyim)

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G Pressure Efects on the Photoreactions of Transition Metal Complexes

The pressure effects on spin relaxation dynamics for these iron(11) complexes have been examined using laser flash photolysis techniques. For Fe(pyim):+ the two spin states are in equilibrium with a K = 0.56 in 298 K acetone with a partial molar volume difference AV = +8.1 cm3 mol-' [34]. Photoexcitation (Aex = 532 nm) leads to transient bleaching of the low spin isomer's MLCT bands followed by first order relaxation to the original spectrum with a 45-ns lifetime. Transient bleaching and subsequent return of the MLCT absorption was attributed to formation of the HS isomer and subsequent spin relaxation. The pressure dependence of the relaxation lifetimes was used to determine the activation volumes of the spin relaxation rates for a variety of FeL:+ in different solvents. It was found that AV!l fell into a remarkably narrow range of values (-5.5 1 cm3 mol-l) and it was concluded that the spin crossover for these species follows a common mechanism via a transition state located midway between the high and low spin states [33]. An analogy to Fe(I1) spin isomers can be found in considering pressure effects on the relaxation rates for d8 nickel(I1) complex Ni(dppe)Clz. The latter has a tightly solvated square planar configuration in the ground state but is presumed to have a tetrahedral configuration in its triplet excited state. Flash photolysis studies on the ES relaxation rate gave large negative AV: (-10 cm3 mol-') and AS: (-70 J mol-' K-') values. These data have been interpreted as indicating a transition state for the k, pathway distorted substantially toward the ground state configuration [ 351.

6.2

Unimolecular Excited State Reactions 6.2.1

Ligand Photosubstitution Reactions

Ligand substitution (Eq. 6.15) is commonly observed as the result of photoexcitation. Two excited state reactivity models can be considered. In one the ES responsible for the photochemistry is a bound, thermally relaxed state, in which case? transition state theory treatment is relevant and the individual ki and AV: values for ES decay can be elucidated. The second is ligand labilization from an ES that is unbound along the metal-ligand coordinate, i.e. a dissociative potential energy surface, with a lifetime on the order of vibrational relaxation. Pressure effects on photoreaction efficiencies would then be largely confined to viscosity perturbations and the rigidity of solvent cages around the molecule. [L,M-X] *

+Y

+

LM-Y

+X

(6.15)

When initial excitation is followed by relaxation to a bound lowest energy ES, the quantum yield CD, for ligand substitution from that state would equal @isckst, where k, is the rate constant for ligand substitution from the LEES. Thus the activation volume AV; for k, can be evaluated if the pressure dependencies of Q S , Disc

6.2 Unimolecular Excited State Reactions

and T are separately determined. Such parameterization has been carried out for the photosubstitutions of a limited number of metal complexes; and examples of such studies of rhodium(III), ruthenium( 11) and chromium(111) complcxes and several group VI metal carbonyls will be described here. For a vibronically relaxed bound ES, ligand substitution mechanisms can be discussed in terms of models developed for analogous thermal reactions [ 361. The limiting mechanisms would be the dissociative (D) and associative (A) pathways, where the rate-limiting steps are, respectively, dissociation of the M-X bond or formation of the M-Y bond to form distinct intermediates (Eqs 6.16 and 6.17). The electronic nature of such intermediates is ambiguous, since these species may also be electronic excited states. For example, the cis to trans isomerization concomitant with the photoaquation of C1- from the Rh(II1) complex cis-Rh(NH3)qCl: was successfully explained by a model where C1- dissociation gave a pentacoordinate intermediate in a triplet LF excited state [37, 381. D:

[L,M-XI *

+Y

+

[L,M]*?

+X +Y

A:

[LnM-X]*

+Y

+

[LnM(Y)X]*?+ LnM-Y

+

L,M-Y

+X

+X

(6.16) (6.17)

Lying between the limiting A and D pathways would be the interchange mechanisms (I, or Id). These involve concerted exchange between the first and second coordination sphere without formation of discrete intermediates and with bond formation or breaking being energetically more important, respectively. A truly concerted mechanism would require that the ground and excited state surfaces cross along the reaction coordinate so that intrinsic volume changes AV& along the substitution reaction coordinate also include contributions from the AV between the ES and GS. Based on volume profiles of thermal reactions, the A@,, contribution to AV; would be expected to be negative for an A mechanism and positive for a D mechanism. Qualitatively, thermal I, and Id pathways would show similar patterns, but with the AVint contribution somewhat attenuated (see Chapter 4).The other key contribution to AV: derives from solvation changes, AV;,,, which can easily exceed AV& in magnitude for reactions with charge creation or neutralization and which may be opposite in sign. This is illustrated by Fig. 6.9, which shows the impact of solvation changes during dissociation of an anion. As noted above, the reactive ES may have a different partial molar volume than the analogous GS. Other than the photoacoustic calorimetry experiments described earlier, there is relatively little direct quantitative information on E S volumes. The magnitude of the AV between the GS and the ES will depend on the excited state orbital parentage. For example, there is little distortion upon forming the doublet LF state of an octahedral Cr(II1) complex, so both intrinsic and solvation contributions to AV should be quite small. In contrast, the quartet LF state of Cr(II1) and the triplet LF excited states of Rh(II1) complexes, both formed by metal centered eg(ohL)+ tls(nML) excitation, would be expected to have substantially positive AVint contributions, but again relatively small differences between ground and excited

I

197

198

I

G Pressure Effects on the Photoreactions ofhansition Metal Complexes

I

TS Volume profile diagram showing the contributions of intrinsic and solvational activation volumes to the observed AV; of a hypothetical ligand substitution via limiting D mechanism. Fig. 6.9.

state solvation. In contrast, since charge transfer states involve greater intramolecular dipole changes, larger solvation contributions would be expected to accompany MLCT and LMCT excitation. Rhodium(ll1) complexes: Collaborative studies between van Eldik, Ford and coworkers have led to thorough parameterization of pressure effects on photosolvolysis of the rhodium(111) halopentaammines Rh(NHj)sX2+ (Eq. 6.18) [39-451. For these systems LF excitation is followed by rapid intersystem crossing ((Disc z 1) to the lowest energy LF state 3 E from which reactive (kp),radiative (k,) and nonradiative (kn) deactivation occur competitively (Fig. 6.10) [41,461. Rate constants for individual excited state processes were calculated from phosphorescence quantum yields @, lifetimes T and quantum yields for halide (a,) and ammine (@)A) solvolysis according to ki = Q ~ Tin different solvents over a range of temperatures and pressures [47].

x

2'

2'

(6.18)

+ HZO

A

6.2 Unimolecular Excited State Reactions

I

199

Fig. 6.10. Jablonski type diagram for the lower energy ligand field states o f a CdV Rh(lll) complex such as Rh(NH9):' showing reactive (kp), radiative (k,) and nonradiative (kn) deactivation from the lowest energy triplet state.

The @x and @A values proved to be dramatically solvent dependent. Labilization of CI- from Rh(NH3)5C12' predominates in the very polar solvents water or formamide solutions; NH3 labilization predominates in methanol, DMSO and DMF [48]. These photoreactivity patterns were attributed to the much greater solvent sensitivity of the C1- substitution rates from the ES. Activation volumes for ammine and halide labilization and for non-radiative deactivation are summarized in Table 6.1. Immediately apparent from these data are the large positive AVL values for ammine substitution and the large negative AVL values for halide substitution in all solvents. In order to interpret these data, we shall compare the volume changes predicted for the limiting A and D mechanisms. The A mechanism would proceed via associative attack of solvent S to give a seven-coordinateintermediate Rh(NH3)5(X)(S)'+ ( I 1 ) followed by ligand loss to give the two products. The volume of the transition state lies along the volume profile between the reactants and I1; thus AV; would have a value between 0 cm3 mol-' and the difference V(Ii) - (V(ES) +Vi(S)). Although V(I1) and V(ES) are both unknown, they can be estimated to give a AV for the formation of 11 -15 cm3 mol-' 1421. According to this mechanism, similar negative values would be expected for both AVL and AVL. The positive AVL values found experimentally thus argue against the operation of a common associative

-

200

I

6 Pressure Effects on the Photoreactions of Transition Metal Complexes

Volumes o f activation (in c m 3 molL') calculated from pressure effects on the photoreaction/ photoluminescence properties o f the Rh(lll) complexes Rh(NH3)X2+ in various solvents (data taken from refs. [47] and [48]).

Tab. 6.1.

Complex

Solvent

Rh(NH3)5C12'

H2O Dz 0 FMA DMF DMSO HZO D20

Rh(NH3)5Br2+

AV:!.. @x

-5.2 f 0.4 -4.2 f 0.5 -4.6 f 0.7 -7.8 k 1.8 10.3 f 1.2 -9.4 f 1.5

.-

.?:

/jV$

h

12.7 k 1.2 9.5 f 1.6 4.2 f 0.9 6.3 _+ 0.9 4.4 0.9 4.6 k 0.6 3.5 f 0.5

+

d

(-3.4) 3.5 f 1.1 0.3 k 0.4 1.3 0.2 -1 k 1 (3.5) 4.1 k 0.6 ~

~

Av.? X

-8.6 k 1.6 -7.7 k 1.6 -4.9 f 1.1

-8.9 f 2.7 -6.8 k 1.6 -5.8 f 1.8

AVt

AV i

9.3 k 1.9 6.2 k 2.2 3.9 f 1.3 7.6 f 1.1 3.3 f 1.8 8.1 f 1.2 7.5 f 1.1

(-2.6) -2.6 k 1.0 0.2 0.5 0.7 0.3 -1+1 (+2.5) +2.5 k 1.2

*

mechanism for the excited state substitution pathways. In contrast, a limiting D mechanism leads to two different Rh(II1) intermediates (Eq. 6.19), one being +2 and the other $3 in electrostatic charge. A substantial AV! difference between the halide and ammine photolabilizations would be expected owing to solvation terms. The AVB,, contributions to AV; would be negative owing to charge creation as halide dissociates from Rh(NH3)5XZ+ion to form the Rh(NH3):' plus X-. However, NH3 dissociation should afford no appreciable charge creation, hence minor contributions from AV:ol would be expected.

-c A..

hv

*+ J

s

3+

.A

A

6

A..

I

2'

T

2'

.A

,,RhLA (6.19)

Figure 6.11 presents a volume profile for the photoaquation reactions of Rh(NH3)5C12+according to a limiting D mechanism. The volume changes calculated for the overall photoreactions from ground state to products are +3.9 cm3 mo1-l for ammine aquation (AVA)and -17.8 cm3 mo1-l for C1- aquation (AVcl), the difference largely attributable to charge creation upon C1- aquation. A similar AV (- 22 cm3 mol-*) might be expected to exist between the intermediate species from C1- dissociation and from NH3 dissociation. Notably, the AAVt for these pathways (AV; - AVi) was measured to be 17 cm3 mol-'. An analogous conclusion can be drawn for the Rh(NH3)5Br2+ion in aqueous solution. The difference in the overall AV values for NH3 vs. Br- photolabilization is 19.7 4.1 cm3 mol-l, while the excited state reactions displayed a AAVJ of 14.9 2.8

G.2 Unimolecular Excited State Reactions

I 20 10

1 +3.9

w

I 3 0 0

>

I

-10

TS

\ -17.8

-20

IAH values in cm3 mot-' Fig. 6.11. Volume profile diagram for the competitive photoaquation of NH3 and of CI- from Rh(NH3)SCI2+in aqueous solution via a proposed limiting dissociative mechanism.

cm3 mol-', again pointing to charge creation as defining the differences in the pressure effects for the two excited state reactions. Thus, the pressure data are consistent with earlier studies that point strongly toward a dissociative mechanism for the ligand photosubstitutions of the halopentaamminerhodium(111) complexes [36, 381. Features of the data in Table 6.1 and other data collected elsewhere [39, 42, 451 relate to the non-radiative pathways from the 3LF. For these photoactive Rh(II1) complexes, the pressure dependence of k, generally has the same sign as that for the major photoreaction pathway but a smaller absolute value. This suggests parallel character for k, and a strong-coupling contribution to k,, [49]. Such a pattern would be consistent with a reaction coordinate which approaches the ground state surface in a manner that allows partitioning between ligand dissociation and nonradiative deactivation. Chromium(ll1) complexes: Pressure effects for both the emission and photo-

reaction quantum yields under comparable conditions have now been described for several Cr(II1) complexes in fluid solution including Cr(bpy):+, Cr(NH3);+, Cr(NH3)5(NCS)'+ and the cis and trans isomers of Cr(cyclam)(NHj);+ (cyclam = 1,4,8,11-tetraazacyclotetradecane) [ 3, 50-571. There is a rich and subtle literature regarding the photochemistry of hexacoordinate Cr(111) complexes to which such pressure studies have contributed insight. The first quantitative studies of pressure effects on the photosubstitution reactions of transition metal complexes were reported by Kelm et al. for a series of Cr(NH3)5X2+ ions (X- = SCN-, C1- or Br-) in aqueous solution [SO-521 (Eq. 6.20). These workers measured photoaquation quantum yields as a function of vs. P. Notapressure and determined the apparent AVf values from plots of In bly, the AVf values were substantially negative regardless of whether X- or NH3

I

201

202

I

G Pressure Effects on the Photoreactions

Q1

of

Transition Metal Complexes

\

DO

PRODUCTS

QO

Fig. 6.12. A simplified generalized energy level diagram for the photoreactions of Cr(lll) complexes. Initial excitation leads t o formation of the Franck-Condon quartet state which is followed by relaxation t o the thermally

equilibrated quartet ( Q ,) and doublet (Do) excited states, k,, k, and k, are the decay pathways direct from the doublet, and k; and k6 are the decay pathways from Q1.

was labilized. Owing to charge creation, AVto, contributions to AVL values for halide aquation are likely to be negative regardless of the mechanism. However, the negative AVL values for ammine aquation suggest an associative mechanism

PI.

+

Cr(NH3)5X2++ HzO 5 Cr(NH3)5(HzO)3f X

(6.20)

Figure 6.12 is a generic energy level diagram for chromium(II1) ligand substitutions as possible reactive deactivation pathways. Much of the discussion regarding Cr(111) photoreaction mechanisms has been concerned with the roles of the lowest energy quartet (Q1) and doublet (Do) states. For hexa-coordinate complexes with moderate to strong ligand fields, the LEES is the Do state with a (t2g)3electronic configuration. As noted in Sect. 6.1, Do is relatively undistorted, while Q1 with a (t2g)z(es)' configuration should be considerably more distorted from the ground state structure [58]. It is this distortion that makes Q1 an attractive candidate as the excited state responsible for photosubstitution reactivity. Chromium(II1) photosubstitutions have been discussed [59] in terms of two limiting mechanisms: (1) intersystem crossing from quartet states formed by initial excitation to the doublet manifold followed by reaction from the relatively longlived Do, or (2) reaction from the quartet state(s) via thermally promoted back-

6.2 Unimolecular Excited State Reactions

intersystem crossing from the doublet and/or prompt reaction upon formation via initial excitation. The pitfalls of making too simple an interpretation of pressure effects on the photochemistry of hexacoordinate Cr(111) complexes have been discussed by Endicott and Ryu [GO], who analyzed earlier pressure studies of Cr(NH3);' and Cr(NH3)5NCS2+photochemistry and photophysics. They noted the complications induced by the potential roles of the two states and the possibility of back-intersystem crossing as well as multiple passes through the lower energy state, which make calculation of pressure effects on individual rate constants in Fig. 6.12 subject to considerable ambiguity. Nonetheless, these workers concluded that the pressure effects support an associative mechanism (A or Ia) for ligand labilization regardless of the reactive state responsible. Waltz and coworkers subsequently reexamined pressure, temperature and medium effects on the doublet emission and photoaquation of Cr(NH3);' [56]. Emission lifetimes vary with solvent, and a strong correlation was observed between kd (T-') and the solvent donor character. This was attributed to solvent interactions with the N-H bonds of the coordinated ammines. Corresponding activation energies E,(kd) and activation volumes AV: ranged from 46 kJ mol-l and f4.3 cm3 mol-' in water to 51.5 kJ mol-l and +3.4 cm3 mol-' in HMPA, similar to calculated energy and volume differences between the Do and Q1 states. On this basis, it was concluded that at room temperature and above, non-radiative deactivation occurred primarily via thermally-activated back-intersystem crossing from Do to Q1. The k,, from the latter is much faster owing to strong coupling contributions. Quantum yields for the Cr(NH3);' photosolvolysis reaction (Eq. 6.21) are not solvent sensitive (0.44 in H2O and DMF) and are independent of whether initial excitation is into the Q1 or Do states, as are the activation volumes for photoaquation (-6 cm3 mol-l). These data led Waltz et al. to conclude, in agreement with Endicott and Ryu [GO] and with Angermann et al. [SO], that pressure effects suggest excited state ligand substitution occurs via an associative mechanism.

Cr(NH3)t+

+ H2O 3Cr(NH3)5(H20)3++ NH3

(6.21)

Group VI Carbonyl complexes: In the case of substitution of neutral ligands by

neutral ligands, pressure effects can be better correlated with the intrinsic volume changes associated with the mechanism. One such study dealt with the photosubstitution reactions of the hexacarbonyls M(C0)6 (M = Cr, Mo, W) to give M(C0)sL (Eq. 6.22) and M(CO)qL2, where L is a ligand such as pyridine [ G l ] . For each M, @co decreased with increasing pressure. Under the risky assumption that k, is independent of P, the pressure dependence of @/(I - CJ)can be used to estimate AVJ for the ES reaction. The positive values derived are consistent with a D mechanism for CO release. However, laser flash photolysis techniques have shown that CO loss to form the 5-coordinate intermediate M(CO)5 occurs in less than 1 ps. For this reason, one cannot treat the ligand substitution pathway from the reactive ES in terms of mechanisms elucidated for bound excited states. Instead the positive

I

203

204

I

G Pressure Effects on the Photoreactions of Transition Metal Complexes K,,

= [MLCT']/[LF']

L 1

Fig. 6.13.

Schematic diagram representing the various reaction routes of W(C0)sL complexes.

values of AVL may reflect solvent viscosity effects on the escape of CO from the solvent caged pair [ M(C0)5, CO] generated immediately upon flash photolysis. M(CO),

+ L 5M(CO),L + CO

(6.22)

A different situation is represented by a series of pentacarbonyl complexes W(CO)sL, involving either a LF ( L = pyridine) or a MLCT state (L = 4-acetyl and 4-cyanopyridine) as the LEES [62]. Excitation is followed by rapid internal conversion-intersystem crossing to the lowest excited state, and the proposed model suggests that the observed photochemistry in the MLCT state results from back population to the LF state (Fig. 6.13). Pressure studies demonstrate positive AVf values for each W(C0)sL complex [62], and the larger effects observed for L = 4acetylpyridine and 4qanopyridine (AVL = f9.9 and f6.3 cm3 mol-') are consistent with the volume difference expected between the LF and MLCT excited states. Photosubstitutions of the M(C0)4(phen) complexes (M = Cr, Mo, W, phen = 1,lo-phenanthroline) have received attention because of possible roles played by both LF and MLCT excited states. The working model from the pentacarbonyl complexes would suggest that the photosubstitution proceeds dissociatively from the LF excited state, and that MLCT excitation is followed by thermal back population into the LF state [63]. However, it has also been argued that the MLCT states themselves may be reactive toward associative substitution owing to the more electrophilic nature of the metal center in the ES [64]. In order to probe this, the effect of pressure on Eq. (6.23) as a function of Iirr was studied [65, 661. For L = PEt3 and M = W, negative AVL values were found for 546-nm irradiation of MLCT bands in contrast to positive activation volumes AVLs for ligand substitution when LF bands were excited with 366 nm light. This argues for a D mechanism in the latter case but an A mechanism in the former. Similar behavior was seen for the molybdenum and chromium analogs [67-691.

6 2 Unimolecular Excited State Reactions

M(CO),(phen)

+ L -fac-M(CO),(L)(phen) + CO hu

(6.23)

Ruthenium(l1): Ru(bpy):+ has been the subject of more photochemical studies than any other metal complex, owing partly to interest in using this visible absorber as a “catalyst” for the conversion of radiant energy to chemical potential energy. Its MLCT excited state is relatively long lived ( r 1 1s) in ambient temperature solutions including water. This ES has strongly reducing and oxidizing character thus is susceptible to efficient electron transfer quenching by a number of substrates (see Sect. 6.3.1). Furthermore, it displays little photoactivity toward decomposition under most such conditions, so it can be used for numerous turnovers in electron transfer cycles. Nonetheless, [ Ru(bpy);’]” does undergo some photosubstitution chemistry [ 70-721. For example, in acetonitrile solution containing chloride, the following reaction is observed.

-

+

[Ru(bpy).i+]* C1-

+ CH3CN 2 R u ( ~ ~ ~ ) ~ ( C H +~ bpy CN)C~~

(6.24)

The proposed excited state substitution mechanism is that described above for non-radiative deactivation at higher T, namely, back population of a ’LF state lying above the lowest energy 3MLCT state. This state would undergo dissociation (or solvent associative displacement) of one Ru-N bond to give a monodentate bipyridine intermediate. The role of Clk is attributed to trapping of the coordination site to give Ru(bpy)z(tI’-bpy)Clt, which undergoes further dissociation of bpy. The strong temperature dependences of ligand labilization and of nonradiative deactivation have been rationalized in terms of the reversible thermal promotion to the ’LF state. Fetterolf and Offen [72] carried out pressure experiments for Ru(bpy):+ at several temperatures and solvents and in the presence of both C1- and PF, in order to evaluate this mechanism. The effect of pressure was to slow the photosubstitution with AVL (app) values +12 and +22 cm3 mo1-l determined at 15 and 60 “C, respectively. The large temperature dependence is related to the requirement for ion association between Cl- and the Ru(I1) cation leading to desolvation and a positive contribution from AVto,. A change to the non-ligating PF, counterion reduces the photosubstitution rate in CHjCN considerably and gives only the RU(~PY)~(CH~C product. N ) ~ + In this case, AVL (app) (- 10 cm3 mol-’) is temperature independent, even though the rates are quite temperature dependent. Since this parallels the values seen for k,, one can conclude that AVL (app) largely reflects the 3MLCTto 3LF photophysical process. Ru(phen)3Clz behaved in a similar manner. 6.2.2

Unimolecular Photoredox Decompositions

Charge transfer states are (formally) internal redox processes which are reversed by relaxation to the ground state. However a CT state could also decay by dissociation of the oxidized or reduced ligand resulting in net redox decomposition. An exam-

I

205

206

I

6 Pressure Eflects on the Photoreactions of Transition Metal Complexes

ple is the LMCT excitation of the cobalt(II1) ion Co(NIH3)sBr2', which undergoes photoreduction to give the labile Co2+ center (Eq. 6.25). For this reaction Kirk et al. [73] reported a AV: value of +4.8 cm3 mol-' and suggested the formation of a caged value of radical pair (Co", Br') from the LMCT excited state. Dissociation of this radical pair to products was suggested to account for the positive AVL.

2 Co2+t 5NH3 +products of Br' formation

Co(NH3)5Br2+

(6.25)

Similarly, photolysis of nitroprusside ion Fe(CN)=,NOZ- via MLCT excitation results in the oxidation of the metal and labilization of NO (Eq. 6.26) [74]. The quantum yicld for the production of Fe(CN)5S2- is moderately sensitive to the viscosity of the medium. The values of AVL are significantly positive (+7 to f 8 cm3 mol-') and point to the participation of a cage recombination mechanism. [(CN)5Fe'1(NOf)]3--% [(CN),Fe"',NO){'-

2[(CN)5Fe1"(Sol)]2-+ NO (6.26)

6.3 Bimolecular Pathways For Excited State Deactivation

Bimolecular quenching may occur by energy transfer to another acceptor or by electron or atom transfer to give an oxidized or reduced species. Other bimolecular pathways include reaction of the LEES with another species in solution to form short-lived exciplexes. In the presence of a quencher Q the ES decay rate is defined as: 5-l

= k,

+ k, + k,

+ k,[Q]

(6.27)

and kq can be calculated from (6.28) where 50 is the lifetime in the absence of quencher. Values of AV: are determined in the normal manner from the dependence of k, on P, although modest corrections of [Q] are made for compressibility, the appropriate factor amounting to a few percent over the range 0.1 to 300 MPa depending upon the solvent. The AVfOlcontribution to AV; is especially important in bimolecular quenching by electron transfer processes owing to electrostriction effects resulting from charge creation or annihilation [75]. On the other hand, it is small for energy transfer quenching unless k, approaches the diffusion limit kD. For any bimolecular pathway, pressure induced changes in the solution viscosity become crucial as k, approaches kD, given the simple relationship between kD and the viscosity 11 1761:

kD

= 8RT/2000~

(6.29)

6.3 Birnolecular Pathways For Excited State Deactivation

In this situation, AV;, will be dominated by the pressure dependence of the viscosity regardless of the mechanism. As YI, increases with P, rates slow giving positive values of AV; (and therefore of AV;). For solvents such as acetonitrile and ethanol, AVL is large (19.5 and $7.7 cm3 mol-' respectively), but for water it is small (-1 cm3 mol-l) owing to the relative incompressibility of that medium [77]. Quenching can be envisioned as the reversible formation of a precursor complex between the ES and Q followed by energy or/and electron transfer (Eq. 6.30).

(6.30)

For this model

(6.31)

When kel +ken >> k - D this simplifies to kq = k D , or in more general terms Eq. 6.31 can be rewritten as:

(6.32)

where KA = k D / k - D . 6.3.1

Excited State Electron and Energy Transfer Reactions

An example of this behavior is the bimolecular quenching of the MLCT emission from the 2,9-diphenyl-1,lO-phenanthroline (dpp) complex Cu(dpp)f by different electron and/or energy acceptors such as a series of chromium(111) acetylacetonate (acac-x) derivatives that can quench by either mechanism (Eq. 6.33) [78]. These Cr(acac-x)3complexes display a wide range of reduction potentials (-0.79 to -2.43 V in CHlClz, referenced to the Fci/Fc couple, Fc = ferrocene) dependent on the nature of the substituents. However, their doublet ligand field ES energies are relatively invariant [(12.5 0.4) x lo3 cm-l] [79]. Electronic energy transfer is favorable in each case, since the energy of the MLCT excited state 3[Cu(dpp):]* is -14.5 x lo3 cm-l. The C~(dpp)i+/~[Cu(dpp):];~ couple was estimated as -1.41 V (versus Fc+/Fc) by subtracting the MLCT excited state energy (1.80 V) from the standard potential determined for the ground state [78]. From these data Eq. (6.34) can be used to calculate the free energy change for Eq. (6.33).

I

207

208

I

G Pressure Effects on the Photoreactions of Transition Metal Complexes

3[Cu(dpp):]+c+ Cr(acac-x)3

Cu(dpp)?

+ Cr(acac-x)j

Cu(dpp): i [Cr(acac-x)3]*

(6.33)

AGZl = -{El,2(Cr111/Cr'1)- E 1 / 2 ( C ~ ' 1 / X C ~ 1 ) }

(6.34)

For the unsubstituted acetylacetonate (R = CH3, X = H), AG;, is quite positive (+1.02 V), thus electron transfer quenching would be highly unfavorable, and quenching must be due solely to energy transfer. In this case, a k, of 1.5 x lo7 M-'s-' was observed in dichloromethane [go]. Comparable rates were also seen in CHC13 and THF solutions. In all three solvents AV; is quite small (-0 cm3 mol-'). Since energy transfer leads to little or no charge creation, A&, must be small. Thus, AV!nt must also be small, indicating that neither the MLCT excited state 3[Cu(dpp)z]*nor the doublet ES formed by energy transfer to CrL3 are dramatically distorted from the respective ground state configurations. At more favorable free energy for the redox reaction, k, increases (the turning point being AG:l 0.2 V) consistent with the increasing importance of outer sphere electron transfer as a component of this quenching. Thus for Cr(tfac)3.(tfac is trifloroacetylacetonate), AG;] = 0.23 V and k, = 4.2 x lo7 M-' s-' in dichloromethane. What is much more striking is that AV: becomes significantly negative (-8.1 cm3 mol-'). This was attributed to the solvent electrostriction contribution (AVLol) from charge creation in the transition state of the electron transfer mechanism. The third type of behavior for these systems is seen when the excited state electron transfer becomes much more favorable and k, approaches the diffusion limit. For example, 3[Cu(dpp)2]$cquenching by Cr(hfac)3 (hfac = hexafloroacetylacetonate) has a calculated AGZ, value of -0.62 V, and k, = 0.94 x 10" M-'s-'. In this case, AV; is quite positive ( t 8 . 0 cm3 mol-'), reflecting the role of pressure in tuning the solvent viscosity. Figure 6.14 illustrates the contrasting pressure dependence of the respective k, values in these three quenching experiments. These data as well as k, and AV; values for other quenchers are summarized in Table 6.2. The quenching of the CC" luminescence from the copper(I) clusters Cu414py4 by a series of Cr(acac-x)3and other electron transfer and energy transfer acceptors demonstrated a similar pattern of pressure effects [Sl]. For the [Cu414py4]jrluminophore, energy transfer quenching demonstrated virtually no pressure effect for Q = Cr(acacj3 (k, = 4.7 x lo7 M-l s-l, AV; = -0.3 cm3 mol-'), while a large positive AV; (+6.2 cm3 mol-') for diffusion limited redox quenching (1.2 x 10" M-' s-l ) by Fcf. Large negative values, (-8.2 cm3 mol-') were the case for

-

G.3

Bimolecular Pathways For Excited State Deactivation

Pressure (MPa) Fig. 6.14. Plots of In(k,/k:) vs. P for quenching of '[Cu(dpp)2]>* by C r ( t f a ~ ) ~ (upper), Cr(acac)3 (middle) and Cr(hfac)3 (lower) in dichlorornethane a t 23 "C. For Cr(tfac)j, k, is dominated by an electron

transfer mechanism (A$ - -8.1 c m 3 mol-'); for Cr(acac)g by energy transfer (AV; = -0.1 c m 3 mol-'); and for Cr(hfac)3 by diffusion kd (AV; = +8.0 cm3 mol-').

quenchers such as m-dinitrobenzene, where electron transfer is favorable (AGEl = -0.41 V) but energy transfer is not and k, is significantly less than the diffusion limit. As might be expected one of the earliest pressure effect studies of the quenching of a metal complex excited state involved the aqueous [Ru(bpy)i"]" ion. Kirk and Porter [24] found that the near diffusion limited quenching of aqueous Ru(bpy):+ by o2(1.7 x 109 M-I s - 1 ) showed a very small AV; ($0.5 cm3 mol-I), which was attributed to a modest increase in the viscosity of water over the investigated pressure range. However, a similarly small AV; would have been expected anyway if this quenching were occurring via an energy transfer pathway. Fetterolf and Offen [2G] studied the effect of pressure on the reductive quenching of Ru(bpy)f+ by several aromatic amines. Quenching by N,N-dimethylaniline (DMA) in CH3CN resulted in AV! values between +1.3 and 4 2 . 9 cm3 mol-I while values of 9 to 13 cm3 mol-' were reported for the quenching by the free base benzidine and N,N,N',N'-tetra-methylbenzidine (TMB) in CH3CN and n-BuOH as solvents. These pressure effects can be interpreted in terms of the following mechanism

(6.35)

I

209

210

I

6 Pressure Efects on the Photoreactions of Transition Metal Complexes k,'s at ambient pressure and AVi's for quenching of emission from '[Cu(dpp):]* in dichloromethane (data from ref. [51]).

Tab. 6.2.

Q Cr(hfac)3' p-Dinitrobenzene Cr(tfbzac)3 Cr(W3 Cr(tc-bzac), Cr( br-dbm)g Cr(n - a ~ a c ) ~ p-Chloronitrobenzene Cr(tfac)3 Cr(tc-acac), Cr( br-acac)j Cr(dbm)3 Cr(acac),

Ace, (e")

k4

(V)"

-0.79 -1.18 -1.43 -1.43 (-1.48) (-1.53) (-1.57) -1.58 -1.64 (-1.66) (-1.89) -1.87 -2.43

-0.62 -0.23 -0.02 0.02 (0.07) (0.12) (0.16) 0.17 0.23 (0.25) (0.48) 0.46 1.02

940 1050 200 220 60 4.2 6.3 3.0 4.2 3.4 6.7 6.8 1.5

El/2

(107 M-1

AV8 4

5-1

)

(cm3 rnol-')

+8.0 +6.9 +0.8

+2.1 +3.8 -3.5 -3.8 -20.4 -8.1 -1.4 -2.4 -0.3 -0.1

aE1/l values versus the Fe(cp)T/Fe(cp)2couple in CH2C12; values in parentheses estimated from parameters as discussed in ref. 51. bAC:, = -{E1/Z(Crlll/Crll) - El/z(Cull/qCul)}.e,e is the elementary

charge. Cacac= acetylacetone; dbm = dibenzoylmethane; hfac = 1,1,1,5,5,5hexafluoro-2,4-pentanedione; tflJzac = 4,4,4-trifluorobenzoylacetone; tta = thenoyltrifluoroacetone; tc-bzac = 2-thiocyanato-l-phenyl-1,3butane-dione; br-dbm = 2-bromo-l,3-diphenyl-l,3-propanedione; tfac = l,l,l-tri-fluoro-2,4-pentanedione; n-acac = 3-nitro-2,4pentanedione; tc-acac = 3-thiocyanato-2,4-pentanedione; br-acac = 3bromo-2,4-pentanedione.

for which k, = kD in the diffusion-controlled limit and k, = k,lKA in the activation-controlled limit, where KA = kD/k-D the association constant for the precursor complex. The large positive AV; values observed for the quenching by benzidine and TMB were attributed to pressure effects on solvent viscosity in these nearly diffusion-limited reactions (kq = 3.0 x 10' and 7.6 x lo' M-' s-' , respectively, in 298 K acetonitrile at ambient pressure). For the slower quenching by DMA (k, = 9.1 x l o 7 M-' s-l ) it is likely that the small positive values for AV; largely reflect positive AV:,l contributions to k,, owing to delocalization of the positive charge. Detailed analysis suggested that changes in the dielectric constant of the medium may account .for the observed effects in the latter case [26]. Oxidative quenching by dimethylviologen (MV2+) (Eq. 6.36, k, = 9.5 x 10' M-l s-l in aqueous solution) has been reported to exhibit a modestly negative AV; (-2.6 cm3 mol-') [24]. Interestingly, recent PAC experiments [75] indicate that the overall volume change for Eq. 6.36 is positive. Thus, it appears that the transition state of the electron transfer reaction is dominated by formation of an encounter complex with a smaller volume than the separated reactants most likely due to solvation effects. Separation of the encounter complex into products has a large, positive AV (Fig. 6.15).

6.3 Birnolecular Pathways For Excited State Deactivation

(Di I

+ A')

'7-

Fig. 6.15. Volume profile for the oxidative quenching o f [Ru(bpy)3'+]" by rnethylviologen (MV'') (redrawn from reference 75).

+

[Ru(bpy):+]* MV2+ -+ Ru(bpy):+

+ MV'

(6.36)

A somewhat different type of redox quenching mechanism has been proposed for the reaction of the excited state of the Pt(I1) dimer, Ptz(p - q2-H2Pz05)2-, with organic substrates [82]. The AV; values for quenching of the triplet excited state 3Pti, by a series of benzylic compounds are between -2.6 and -5.7 cm3 mol-' in methanol. These values are consistent with an associative interaction between the benzylic H atom donor and the excited-state complex, presumably at metal atom site trans to the Pt -Pt bond, resulting in H atom abstraction according to Eq. 6.37. In contrast, 0 2 quenching of 3Pt;, is close to diffusion limited (kq = 3.3 x 10' M-' sP1 in ambient methanol) and exhibits a AV; value of +2.8 cm3 mol-' reflecting contributions from pressure-induced viscosity changes.

31't;

+ H-R + HPt2 + R.

(6.37)

6.3.2

Brnnsted Base Quenching

The trans-Rh(cyclam)(CN): ion (cyclam = 1,4,8,11 -tetraazacyclotetradecane) displays luminescence from a ligand field excited state ('LF") in room temperature, aqueous solution with a lifetime (8.1 ps) [83], several orders of magnitude longer than generally observed for rhodium( 111) amines [ 371. This emission is quenched by OH- in solution (Eq. 6.38), a process attributed to amine deprotonation [84] at rates approaching the difFusion limit (k, 10'O M-' s-l). The pressure effects on

-

I*"

212

I

6 Pressure Effects on the Photoreactions of Transition Metal Complexes

this and for analogous quenching of the 3LF;’<emission from Rh(ND3)i+(by ODin D20) were examined by DiBenedetto [39]. The resulting AV; values were positive, f4.1 0.5 and +4.0 f 0.6 cm3 mol-’, respectively. Positive AV?,s, would be predicted by two factors. For reactions which approach diffusion-limited rates, positive AVk are expected owing to the increased solvent viscosity under pressure; however, the relative incompressibility of water makes this contribution very small (<1 cm3 mol-’). A large positive contribution to AVi is also expected from the desolvation accompanying the charge neutralization resulting from proton transfer from the ES to OH-. The change in partial molar volumes AV would be quite large for complete proton transfer, since the AV between OH- and FIzO is -16 cm3 mol and desolvation of the complex ion should give a large and positive AV as well. Thus, the much smaller value of AV; likely reflects a very early transition state for the proton transfer leading to ES quenching.

’

3[trans-Rh(cyclam)(CN):] *

-ki[OH-]

trans-Rh(cyclam)(CN):

(6.38)

6.3.3 Reactions with Lewis Bases to Give an Excited State Complex

The copper(I) complex Cu(dmp): (dmp = 2,9-dimethyl-l,lO-phenanthroline) displays MLCT luminescence in ambient temperature CH2Cl2 solutions [85]. This emission has been shown to be quenched by various Lewis bases (B), and the mechanism proposed is addition of B to the MLCT state at the metal center to give an “exciplex” which decays rapidly (Eq. 6.39). The validity of this mechanism was tested by comparing, in the presence and absence of Lewis base quenchers, the pressure effects on the emission lifetimes of Cu(dmp); with those on the emission lifetimes of the bulkier 2,9-diphenyl-phen analog Cu(dpp): [ 861. The lattice ions should not be as susceptible to reaction of the copper center with B. For both ions, emission quantum yields are small ( <w3) at ambient T and unimolecular photoreactions are not observed, so the pressure sensitivity o f t reflects non-radiative deactivation mechanisms. [Cu(dmp)f]*

1

kn

+

[Cu(dmp), : B+]*

-B

Ik.

Kb[Bl

+ k