ELECTRON TRANSFER- from ISOLATED MOLECULES to BIOMOLECULES Part 2

ELECTRON TRANSFER- FROM ISOLATED MOLECULES TO BIOMOLECULES Part 2

Edited by JOSHUA JORTNER School of Chemistry Tel Aviv University Tel Aviv, Israel and M. BIXON School of Chemistry Tel Aviv University Tel Aviv, Israel ADVANCES IN CHEMICAL PHYSICS VOLUME 107 Series Editors I. PRIGOGINE STUART A. RICE Center for Studies in Statistical Mechanics Department of Chemistry and Complex Systems and Thc University of Texas The James Franck Institute Austin. Texas The University of Chicago and Chicago, Illinois International Solvay Institutes Universite Libre de Bruxelles Brussels, Belgium

AN INTERSCIENCELe@ PUBLICATION JOHN WILEY & SONS, INC. NEW YORK CHICHESTER WEINHEIM BRISBANE SINGAPORE TORONTO

ELECTRON TRANSFER-FROM ISOLATED MOLECULES TO BIOMOLECULES Part 2

ADVANCES IN CHEMICAL PHYSICS

VOLUME 107 EDITORlAL BOARD

BRUCE,J. BERNE,Department of Chemistry, Columbia University, New York, New York, U.S.A. KURTBINDER, Institut fur Physik, Johannes Gutenberg-Universitat Mainz, Mainz, Germany A. WELFORDCASTLEMAN, JR., Department of Chemistry, The Pennsylvania State University. University Park, Pennsylvania, U.S.A. DAVIDCHANDLER, Department of Chemistry, University of California, Berkeley, California, U.S.A. M. S. CHILD,Department of Theoretical Chemistry, University of Oxford, Oxford, U.K. WILLIAMT. COFFEY,Department of Microelectronics and Electrical Engineering, Trinity College, University of Dublin, Dublin, Ireland F. FLEMINGCRIM, Department of Chemistry, University of Wisconsin, Madison, Wisconsin, U.S.A. ERNESTR. DAVIDSON,Department of Chemistry, Indiana University, Bloomington, Indiana, U. S. A. GRAHAMR. FLEMING;Department of Chemistry, The University of Chicago, Chicago, Illinois, U.S.A. KARLF. FREED,The James Franck Institute, The University of Chicago, Chicago, Illinois, U.S.A. PIERREGASPARD, Center for Nonlinear Phenomena and Complex Systems, Brussels, Belgium ERICJ. HELLER,Institute for Theoretical Atomic and Molecular Physics, Harvard- Smithsonian Center for Astrophysics, Cambridge, Massachusetts, U.S.A. ROBINM. HOCHSTRASSER,Department of Chemistry, The University of Pennsylva- nia, Philadelphia, Pennsylvania, U.S.A. R.KOSLOFF, The Fritz Haber Research Center for Molecular Dynamics and Depart- ment of Physical Chemistry, The Hebrew University of Jerusalem, Jerusalem, Israel RUDOLPHA. MARCUS,Department of Chemistry, California Institute of Tech- nology, Pasadena, California, U.S.A. G. NICOLIS,Center for Nonlinear Phenomena and Complex Systems, Universite Libre de Bruxelles, Brussels, Belgium THOMASP. RUSSELL,Department of Polymer Science, University of Massachusetts, Amherst, Massachusetts DONALDG. TRUHLAR;Department of Chemistry, University of Minnesota, Min- neapolis, Minnesota, U.S.A. JOHND. WEEKS,Institute for Physical Science and Technology and Department of Chemistry, University of Maryland, College Park, Maryland, U.S.A. PETERG. WOLYKES;Department of Chemistry, School of Chemical Sciences; Uni- versity of Illinois, Urbana, Illinois, U.S.A. ELECTRON TRANSFER- FROM ISOLATED MOLECULES TO BIOMOLECULES Part 2

AN INTERSCIENCELe@ PUBLICATION JOHN WILEY & SONS, INC. NEW YORK CHICHESTER WEINHEIM BRISBANE SINGAPORE TORONTO This book IS printed on acid-free paper @

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Library of Congress Catalog ilrrcmbev 58-9935 ISBN 0-471-2529 1-3

10 9 8 7 6 5 4 3 2 CONTRIBUTORS TO VOLUME 106

ISRAELABECKER, School of Chemistry, Tel Aviv University. Ramat Aviv, Tel Aviv, Israel DAVIDN. BERATAN,Department of Chemistry, University of Pittsburgh: Pittsburgh, Pennslyvania M. BIXOX,School of Chemistry, Tel Aviv University, Ramat Aviv, Tel Aviv, Israel H. L. CARRELL,Institute of Cancer Research, Fox Chase Cancer Center, Philadelphia, Pennsylvania PINGYUNCHEN, Department of Chemistry, The University of North Carolina at Chapel Hill, Chapel Hill, North Carolina VLADIMIRCHERNYAK, Department of Chemistry, University of Rochester, Rochester, New York ORICHESHNOVSKY, School of Chemistry, Tel Aviv University, Ramat Aviv, Tel Aviv, Israel MATTHIJSP. DEHAAS, IRI, Delft University of Technology, Mekelweg 15: 2629JB Delft, The Netherlands CAROLINEE. H. DESSEXT,Sterling Chemistry Laboratory, Yale University, New Haven, Connecticut CHRISTOPHERDURNELL, Department of Chemistry, University of Chicago, Chicago, Illinois G. R. FLEMING,Department of Chemistry, University of Chicago, Chicago, Illinois R. MICHAELGARAVITO, Department of Biochemistry, Michigan State University, East Lansing, Michigan STEVENGOODMAN, Department of Chemistry, University of Chicago, Chicago, Illinois GITTEIVERSEN, Department of Chemistry, Technical University of Denmark, Building 207, Lyngby, Denmark MARKA. JOHNSON,Sterling Chemistry Laboratory, Yale University, New Haven, Connecticut JOSHUAJORTNER, School of Chemistry, Tel Aviv University, Ramat Aviv; Tel Aviv: Israel

V vi CONTRIBUTORS TO VOLUME 106

YURIS I. KHARKATS,The A.N. Frumkin Institute of Electrochemistry, Russian Academy of Sciences, Leninskij Prospect 3 1, Moscow, Russia ALEKSANDRM. KUZNETSOV,The A.N. Frumkin Institute of Electro- chemistry, Russian Academy of Sciences, Leninskij Prospect 3 1, Moscow, Russia MATTHEWJ. LAKG, Department of Chemistry, University of Chicago, Chicago, Illinois DONALDH. LEVY,Department of Chemistry and The James Franck Institute, University of Chicago, Chicago, Illinois R. A. MARCUS,Noyes Laboratory of Chemical Physics 127-72, California Institute of Technology, Pasadena, California THOMASJ. MEYER,Department of Chemistry, The University of North Carolina at Chapel Hill, Chapel Hill, North Carolina SHAULMUKAMEL, Department of Chemistry, University of Rochester, Rochester, New York MARSHALLD. NEWTON,Department of Chemistry, Brookhaven National Laboratory, Box 5000, Upton, New York AKIRA OKADA, Department of Chemistry, University of Rochester, Rochester, New York KRISTINM. OMBERG,Department of Chemistry, The University of North Carolina at Chapel Hill, Chapel Hill, North Carolina MICHAELN. PADDON-ROW,School of Chemistry, University of New South Wales, Sydney, Australia SPIROSS. SKOURTIS,Department of Natural Sciences, University of Cyprus, 1678 Nicosia, Cyprus NORMANSUTIN, Chemistry Department, Brookhaven National Laboratory, P.O. Box 5000, Upton, New York JENS ULSTRUP, Technical University of Denmark, Department of Chemistry, Building 207, Lyngby, Denmark JAIS W. VERHOEVEN,Laboratory of Organic Chemistry, University of Amsterdam, Nieuwe Achtergracht 129, Amsterdam, The Netherlands JOHNM. WARMAN,IRI, Delft University of Technology, Mekelweg 15, Delft, The Netherlands BAS WEGEWIJS,Laboratory of Organic Chemistry, University of Amsterdam, Nieuwe Achtergracht 129, Amsterdam, The Netherlands NIEN-CHUC. YANG,Department of Chemistry, University of Chicago, Chicago, Illinois SONG-LEIZHANG, Department of Chemistry, University of Chicago, Chicago, Illinois CONTRIBUTORS TO VOLUME 107

BIMAWBAGCHI, Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore, India PAULF. BARBARA,Department of Chemistry, University of Minnesota, Minneapolis, Minnesota, MINHAENGCHO, Department of Chemistry, Korea University, Seoul, Korea W. DAVIS,Department of Chemistry and Materials Research, Nortwestern University, Evanston, Illinois B. D. FAINBERG,School of Chemistry, Tel aviv University, Ramat Aviv, Tel Aviv, Israel OLEFARVER, Institute of Analytical and Pharmaceutical Chemistry, Royal Danish School of Pharmacy 2 Universitetsparken, Copenhagen, Denmark GRAHAMR. FLEMING,Department of Chemistry, University of Chicago, Chicago, Illinois HAROLDL. FRIEDMAN,Department of Chemistry, State University of New York at Stony Brook, Stony Brook, New York N. GAYATHRI,Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore, India SHELBYHATCH, Department of Chemistry, University of Princeton, Princeton, New Jersey ROBIN M. HOCHSTRASSER,Department of Chemistry, University of Pennsylvania, 23 1 South 34th Street, Philadelphia, Pennsylvania D. HUPPERT,School of Chemistry, Tel Aviv University, Ramat Aviv, Tel Aviv, Israel M. KEMP,Department of Chemistry and Materials Research, Northwestern University, Evanston, Illinois SONJAKOMAR-PANICUCCI, Peptide, Inc. Cambridge, Massachusettes Y. MAO,Department of Chemistry and Materials Research, Northwestern University, Evanston, Illinois NOBORUMATAGA, Institute for Laser Technology, 1-8-4 Utsubo-Honmachi, Nishi-Ku. Osaka, Japan vii ... Vlll CONTRIBUTORS TO VOLUME 107

GEORGEMCLENDON, Department of Chemistry, Princeton University, Princeton, New Jersey HIROSHIMIYASAKA, Department of Polymer Engineering and Science, Kyoto Institute of Technology, Matsugasaki, Sakyo, Kyoto, Japan V. MUJICA,Universidad Central de Venezuela, Facultad De Clenclas; Escuela de Quimica, Apartado, Caracas, Venezuela A. NITZAN:School of Chemistry, Tel Aviv University, Raniat Aviv, Tel Aviv, Israel ERICJ. C. OLSON,Department of Chemistry, University of Minnesota, Minneapolis, Minnesota J. N. ONUCHIC,Department of Physics, University of California at San Diego, La Jolla, California ISRAELPECHT, Department of Immunology, The Weizmann Institute of Scihce, Rehovot, Israel FERKAKDO0. RAINERI, Department of Chemistry, State University of New York at Stony Brook, Stony Brook, New York M. A. RATNER,Department of Chemistry and Materials Research, North- Western University, Evanston, Illinois J. J. REGAN,Beckman Institute, California Institute of Technology, Pasadena, California A. ROITBERG,National Institute of Standards and Technology, Bio- technology Division, Building 222, A-353, Gaithersburg, Maryland HITOSHISUMI, Institute of Materials Science, University of Tsukuba, Tsukuba, Ibaraki Japan KLAASWYNNB, Femtosecond Research Centre, Department of Physics and Applied Physics, University of Strathclyde, 107 Rottenrow, Glasgow, United Kingdom KEITAROYOSHIHARA, Institute for Molecular Science, Nyodall; Okazaki, Japan INTRODUCTION

Few of us can any longer keep up with the flood of scientific literature: even in specialized subfields. Any attempt to do more and be broadly educated with respect to a large domain of science has the appearance of tilting at windmills. Yet the synthesis of ideas drawn from different subjects into new, powerful, general concepts is as valuable as ever, and the desire to remain educated persists in all scientists. This series, Advunces in Chenzicul Physics, is devoted to helping the reader obtain general information about a wide variety of topics in chemical physics: a field that we interpret very broadly. Our intent is to have experts present comprehenisve analyses of subjets of interest and to encourage the expression of individual points of view. We hope that this approach to the presentation of an overview of a subject will both stimulate new research and serve as a personalized learning text for beginners in a field.

I. PRIGOGINE STUARTA. RICE

CONTENTS TO VOLUME 106

ELECTRONTRANSFER PAST AND FUTURE 1 R. A. Marcus

ELECTRONTRANSFER REACTIONS IN SOLUTION:A HISTORICAL PERSPECTIVE 7 Norman Sutin

ELECTRONTRANSFER-FROM ISOLATED MOLECULESTO BIOMOLECULES 35 M. Bixon and Joshua Jortner

CHARGE TRANSFERIN BICHROMOPHORICMOLECULES IK THE GASPHASE 203 Donald H. Levy

LONG-RANGECHARGE SEPARATION IN SOLVENT-FREE DONOR-BRIDGE-ACCEPTORSYSTEMS 22 1 Bas Wegewijs and Jan W. Verhoeven

ELECTRONTRANSFER AND CHARGESEPARATION IN CLUSTERS 265 Caroline E. H. Dessent, Israela Becker, Mark A. Johnson, and Ori Cheshnovsky

CONTROL OF ELECTRONTRANSFER KINETICS: MODELS FOR MEDIUMREORGANIZATION AKD DONOR-ACCEPTORCOUPLING 303 Marshall D. Newton

THEORIESOF STRUCTURE-FUNCTIONRELATIONSHIPS FOR BRIDGE-MEDIATEDELECTRON TRANSFER REACTIONS 377 Spiros S. Skourtis and David N. Beratan

FLUCTUATIONSAND COHERENCE IN LONG-RANGEAKD MULTICENTERELECTRON TRANSFER 453 Gitte Iversen, Yuris I. Kharkats, Aleksandr M. Kuznetsov, and Jens Ulstrup xi xii CONTEXTS TO VOLUME 106

LANCZOSALGORITHM FOR ELECTRONTRANSFER RATES IN SOLVENTSWITH COMPLEXSPECTRAL DEXSITIES 515 Akiru Okada, Vladimir Chevnyak, and Shaul Mukanzel

SPECTROSCOPICDETERMINATION OF ELECTRON TRANSFER BARRIERSAND RATECONSTANTS 553 Kristin M. Omberg, Pingyun Chen, and Thomas J. Meyer

PHOTOINDUCED ELECTRONTRANSFER WITHIN DONOR-SPACER- ACCEPTORMOLECULAR ASSEMBLIES STUDIED BY TIME-RESOLVED MICROWAVECONDUCTIVITY 57 1 John M. Warman, Matthijs P. De Haas, Jan W. Verhoeven, and Michael N. Paddon-Row

FROMCLOSE CONTACT TO LOSG-RANGEINTRAMOLECULAR ELECTRONTRANSFER 603 Jan W. Verhoeven

PHOTOINDUCEDELECTRON TRANSFERS THROUGH 0 BONDS IN SOLUTION 645 Nien-Chu C. Yang, Song-Lei Zlzang, Matthew J. Lung, Steven Goodman, Christopher Durnell, G. R. Fleming, H. L. Carrell, and R. Michael Garavito

AUTHORINDEX 667

SUBJECTINDEX 707 CONTENTS TO VOLUME 107

PREFACE xi

IYTERPLAY BETWEENULTRAFAST POLAR SOLVATION AND VIBRATIONAL DYNAMICSIN ELECTRONTRANSFER REACTIOXS: ROLEOF HIGH-FREQUEXCY VIBRATIONAL MODES 1 Biman Bagchi and N Gayathri

SOLVEKTCONTROL OF ELECTROYTRANSFER REACTIONS 81 Fernando 0. Raineri and Harold L. Friedman

THEORETICALAND EXPE,RIMENTALSTUDY OF ULTRAFAST SOLVATIONDYNAMICS BY TRANSIENTFOUR-PHOTON SPECTROSCOPY 191 B. D. Fainberg and 1). Huppert

COHERENCEAND ADIABATICITYIN ULTRAFASTELECTRON TRANSFER 263 Klaus Wynne and Robin M. Hochstrasser

ELECTRONTRANSFER AND SOLVENT DYNAMICSIN TWO- AND THREE-STATE SYSTEMS 31 1 Minhaeng Cho and Graham R. Fleming ULTRAFASTINTERMOLECULAR ELECTRON TRASSFER IN SOLUTION 371 Keitaro Yoshihara

ELECTRONTRANSFER IY MOLECULESAND MOLECULARWIRES: GEOMETRYDEPENDENCIE, COHERENT TRANSFER, AND CONTROL 403 V.Mujica, A. Nitzan, Y.Mao, W.Davis, M. Kemp, A. Roitberg, and M. A. Ratnev

ELECTRONTRANSFER AND EXCIPLEXCHEMISTRY 43 1 Noboru Mataga and Hiroshi Miyasaka ... Xlll xiv CONTENTS TO VOLUME 107

ELECTRON-TRANSFERTUBES 497 J. J. Regan and J. N. Onuchic

COPPERPROTEINS AND MODELSYSTEMS FOR INVESTIGATING INTRAMOLECULARELECTRON TRANSFER PROCESSES 555 Ole Farver and Israel Pecht

APPLYINGMARCUS’S THEORY TO ELECTRONTRANSFER IN VIVO 59 1 George McLendon, Sonja Komar-Punicucci, and Shelby Hutch

SOLVEKT-FLUCTUATIONCONTROL OF SOLUTIONREACTIONS AND ITS MASIFESTATIONIN PROTEINFUNCTIONS 60 1 Hitoshi Sumi

EXPERIMENTALELECTRON TRANSFER KINETICS IN A DNA EA-VIRONMENT 647 Paul F. Barbara and Eric J. J. Olson

AUTHORINDEX 677

SUBJECTINDEX 709 PREFACE

Remarkable progress has been made in the elucidation of the processes of energy acquisition, storage, and disposal in large molecules, clusters, condensed-phase, and biophysical systems, as explored from the micro- scopic point of view. The broad area of nonradiative dynamics, from isolated molecules to biomolecules, plays an important role in the development of modern chemistry. Electron transfer processes constitute a landmark example for intramolecular, condensed-phase, and biophysical nonradiative dynamics. Nonradiative electron transfer phenomena encompass electron transfer and hole transfer between localized states, involving intramolecular, intracluster, condensed phase, interfacial. and protein medium charge separation, migration. recombination, and localization, as well as electron and hole transport between a large number of constituents. Radiative charge transfer absorption, fluorescence, and resonance Raman processes in Mulli- ken charge-transfer complexes and donor-acceptor molecules are concur- rently of considerable interest. The sweep and grandeur of electron transfer phenomena are reflected in the broad spectrum of diverse systems, encom- passing a multitude of scientific disciplines, which involve isolated solvent- free supermolecules in supersonic jets; elemental. polar, ionic, and metal clusters in cluster beams; ions, complexes, organic and inorganic supermolecules, and solvated electrons in polar and in nonpolar solvents; metal, semiconductor, and superconductor electrodes in solution; surfaces and interfaces involving thin films, adsorbants and surface states; crystalline and amorphous semiconductors, molecular crystals, polymers, and bio- polymers; and biological systems pertaining to respiratory and enzymatic protein systems. DNA repair, and the primary charge separation proceses in photosynthesis, which ensure the efficiency and robustness of the central life-sustaining processes on Earth. Exploration of the ubiquitous electron transfer processes in chemistry, physics, and biology constitutes an interdisciplinary research area, blending concepts and experimental techniques from a wide variety of fields. The very considerable recent advances stem from concurrent progress in experiment and in theory. On the experimental front, considerable progress was made with the advent of femtosecond lasers, allowing for real-time interro- gation of intramolecular and intermolecular electron transfer dynamics on the time scale of nuclear motion. Major impact was exerted by modern xv xvi PREFACE experimental approaches for the preparation and characterization of elemental isolated molecule and cluster systems, by advances in chemical synthesis of donor-acceptor supermolecules, and by the growing sophisti- cation of biochemical synthesis with the application of genetic engineering methods and of chemical engineering for the preparation of well-charac- terized biophysical systems. The theoretical arsenal rests on the seminal Marcus electron transfer theory with the incorporation of electronic and nuclear quantum effects. the theory and simulations of radiationless processes, wave-packet dynamics, coherence effects. cluster dynamic size effects, nonadiabatic condensed-phase dynamics and nonlinear optical effects, which provide the conceptual framework for intramolecular, cluster. condensed-phase. and biophysical electron transfer dynamics. The chapters assembled in these volumes, which describe many of the experimental and theoretical results now in hand. promote the goal of establishing a unified description of the broad spectrum of chemical, physical, and biological electron transfer phenomena. In spite of tremendous progress and impact, the field may not yet be mature enough to permit a compilation of a definite treatise. Instead, the authoritative contributions assembled in these volumes reflect, in our opinion, the kind of information that will underline the development of an integrated approach to electron transfer phenomena, from isolated molecules to biomolecules, on time scales from those appropriate for “conventional” chemical processes (i.e., seconds to picoseconds) to ultrafast (femtoseconds) processes, transcendenting the time scale for nuclear motion. The first two chapters are intended to provide an overview of the historical development of the entire field, from the seminal theoretical concepts of Franck and Libby in the late 194Os, which provided the theoretical corner- stone for condensed-phase electron transfer, up to the present time. We are greatly indebted to the pioneers of electron transfer science, Professor Rudoph A. Marcus and Professor Norman Sutin, for contributing these overview chapters. The third introductory chapter is meant to review some of the concepts, problems, ideas, experiments, and the theoretical arsenal in the field. The chapters have been organized in topical groups, the general material being as follows: 1. Overview 2. Isolated Molecules 3. Clusters 4. General Theory 5. Spectra and Electron Transfer Kinetics in Bridged Compounds 6. Solvent Control PREFACE xvii

7. Ultrafast Electron Transfer and Coherence Effects 8. Molecular Electronics 9. Electron Transfer and Chemistry 10. Biomolecules We have followed the general policy of the Advances iiz Cheniical Physics that the authors are given complete freedom as to the size, scope, and format of their contribution. Our point of view is that the person who pioneered the topic is the best judge of the appropriate mode of its presentation. We very much hope that these volumes will offer an overview of the entire field, reflecting the forefront of current research efforts and exploring the perspectives and future of electron transfer research. We are grateful to numerous colleagues and friends whose lively and probing discussions at scientific meetings and during scientific encounters convinced us of the merits of the project. We thank the authors for their willingness to contribute to this endeavor and for their adherence to the timetable. Thanks are due to the editor of Advances in Chemical Physics, Stuart A. Rice. for welcoming and supporting this project. We thank Ms. C. A. Fjerstad and the editorial staff of Wiley Interscience for support of the publication of these volumes. The wide range of subjects touched on in these volumes bears witness of the scope and quality of modern electron transfer research and of the enthusiasm of its practitioners.

JOSHUAJORTSER M. BIXON Tel Aviv, Isruel

ELECTRON TRANSFER-FROM ISOLATED MOLECULES TO BIOMOLECULES Part 2

ADVANCES IN CHEMICAL PHYSICS

VOLUME 107

INTERPLAYBETWEENULTRAFASTPOLAR SOLVATION AND VIBRATIONAL DYNAMICS IN ELECTRON TRANSFER REACTIONS: ROLE OF HIGH-FREQUENCY VIBRATIONAL MODES

BIMAN BAGCHI

Solid State and Structural Chenzistrj Unit, Indian Institute of Science, Bangalore 560012, India Jawaharlal Nehru Center for Advanced Scientgc Research, Bangalore

N. GAYATHRI

Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore 560012, India

CONTENTS

I. Introduction 11. Early Theoretical Models: Prediction of Strong Dependence of Electron Transfer Rate on Solvent Polarization Relaxation 111. Role of Vibrational Modes in Weakening Solvent Dependence A. Sumi-Marcus Theory: Role of Classical Intramolecular Vibrational Modes B. Jortner-Bixon Theory: Role of High-Frequency Vibronic Reaction Channels C. Hybrid Model of Barbara et al.: Crossover from Solvent to Vibrational Control IV. General Theoretical Formulation of Multidimensional Electron Transfer A. Model B. Equation of Motion on the Reactant and Product Surfaces C. Solution by Green's Function Technique D. Calculation of the Average Rate for a Delocalized Sink E. High-Frequency Modes in the Dynamics of Electron Transfer

Electron Transfev: From Isolated Molecules to Biomolecules,Pavt Two, edited by Joshua Jortner and M. Bixon. Advances in Chemical Physics Series, Volume 107, series editors I. Prigogine and Stuart A. Rice. ISBN 0-471-25291-3 1999 John Wiley & Sons. Inc. 1 ”7 BIMAN BAGCHI AND N. GAYATHRI

V. Comparison of Theory with Experiment: Betaine in Aprotic Polar Solvents VI. Comparison of Theory with Experiment: Betaine in Protic Solvents VII Non-Marcus Free Energy Gap Dependence VIII. Effects of Ultrafast Solvation on the Rate of Adiabatic Outer-Sphere Electron Transfcr Reactions in Water, Acetonitrile, and Methanol A. Model B. Theoretical Formulation I. Barrier-Crossing Rate 2. Rate of Energy Diffusion C. Numerical Calculations 1. Calculation of the Rate in Water 2. Calculation of the Rate in Acetonitrile 3. Calculation of the Rate in Methanol D. Conclusions IX. Nonexponentiality in Electron Transfer Kinetics X. Future Problems XI. Conclusions Acknowledgments References

I. INTRODUCTION

Electron transfer reactions in solution are often coupled to both intramolecular vibrational relaxation and polar solvation dynamics [ 1-41. The coup- ling to solvent relaxation is easy to understand, especially for electron transfer in a polar liquid, as the electric field of the charge itself is strongly coupled to solvent polarization. This solvent polarization plays a central role in the definition of both the reaction coordinate and the reaction energy surface of an outer-sphere electron transfer reaction. On the other hand, the realization that the intramolecular vibrational modes and their dynamics can play an important role in the electron transfer reactions came somewhat later. Interestingly, the currently held consensus that the vibrational energy relaxation plays a greater role in many photoinduced electron transfer reactions than the solvent polarization relaxation is exactly opposite to what was believed even a decade ago. Although our understanding of the details of electron transfer reaction remains imperfect in most cases, it is becoming clear that both vibrational energy and solvent polarization relaxations are important. Another new development in this field is the discovery that polarization relaxation in many common dipolar liquids contains an ultrafast component with time constant on the order of lOOfs or even less. The amplitude of this ultrafast component is significant. This raises the interesting question regarding the role of this component in the electron transfer reaction, especially in the presence of the participation of vibrational modes. SOLVATION, VIBRATIONAL DYNAMICS, AND ELECTRON TRANSFER 3

The objective of the present chapter is to articulate the recent theoretical and experimental advances in understanding the dynamics of electron transfer in polar liquids. The emphasis is on understanding the rich dynamical behavior that can emerge from the interplay between ultrafast solvation dynamics and the intramolecular vibrational modes in photoinduced electron transfer reactions. In the conventional one-dimensional form of Marcus theory [l], the reaction coordinate of an electron transfer is the energy gap between the electronic surfaces of the reactant and product. For a symmetric electron transfer, this coordinate is essentially the difference in the solvation energy between the reactant and product states. Therefore, motion along the reaction coordinate can, in principle, be strongly coupled to the solvent polarization fluctuations. In the extreme limit of very slow solvent relaxation, the rate can even be controlled by the rate of solvent polarization relaxation (provided that alternative reaction channels are not available). The first clear theoretical prediction of a dynamic solvent effect in electron transfer was made by Zusman [S], who showed that for slow solvent relaxation the rate of an adiabatic electron transfer reaction is inversely proportional to the longitudinal polarization relaxation time, T~,of the polar solvent. Since the pioneering work of Zusman, there have been a large number of theoretical studies devoted to dynamic solvent effects, and most of the early studies predicted a strong influence of solvent dynamics on electron transfer [6,17- 191. The strong solvent relaxation dependence was predicted not only for the reactions in the normal region but even for the barrierless electron transfer. There are two reasons for this. First, solvent relaxation was assumed to be overdamped, and the dielectric relaxation of the medium was assumed to be Debye-like. These approximations lead to the prediction that solvation dynamics of a charge is single exponential, with the time constant equal to the longitudinal relaxation time, rL.Second, only motion along the classical polarization coordinate was assumed to be relevant in electron transfer. It is now known that both of these assumptions may have only limited validity [20-261. Initial experimental studies to find the predicted solvent relaxation dependence of the electron transfer rate were made only in mid-1980s. These studies seemed to verify the predicted strong dependence of electron transfer rate on T~.Notable among the experimental studies in this phase are the work of Kosower, Huppert and co-workers on napthalene-N,N-dimethyl- amide and related derivatives [7-91, of McManis and Weaver on self- exchange reactions in metallocenes [10,38], and of Barbara et al. on bi- anthryl [11,12]. All these studies found solvent relaxation dependence of the electron transfer rate to varying degrees. 4 BIMAN BAGCHI AND N. GAYATHRI

In contrast to this older picture, more recent systematic studies on rela- tively clean photoinduced electron transfer reactions have revealed rather a different picture. Experimental results from Yoshihara's group have shown that in some cases of low (or zero)-barrier electron transfer, the rate can be 50-100 times larger than 1/'~~[49]. Experiments by Barbara and co-workers found that the electron transfer rate in betaine-30 in glycerol triacetate (GTA) decouples almost completely from solvent polarization relaxation [43]. It should be pointed out here that betaine-30 is deep into the Marcus inverted regime [43,44,72]. The foregoing experimental studies, in turn: led to interesting theoretical developments, particularly on the role of intramolecular vibrational modes in electron transfer. Sumi and Marcus presented an elegant formulation [14] which showed that if relaxation along the vibrational coordinate (Q) is much faster than relaxation along the polarization coordinate (X),the effects of this coordinate can be included via a position-dependent intrinsic reaction rate of electron transfer. Sumi et al. [15,16] showed that this model can give rise to rich dynamical behavior: such as nonexponential kinetics and frac- tional rId dependence, which is sometimes observed in experiments. In the treatment of Sumi and Marcus, the vibrational coordinate was treated classically, as it was envisaged as a low-frequency mode, such as torsional motion. Subsequently, Jortner and Bixon [73,20-221 developed a detailed treatment of the role of intramolecular vibrational modes in photoinduced electron transfer. These authors pointed out that the high-frequency modes of the product surface can effectively open up new reaction channels via Franck-Condon overlap with the ground and/or excited vibronic levels of the reactant. Thus an electron transfer reaction that is classically in the Marcus inverted regime can occur as a barrierless reaction with much greater rate than was possible otherwise. In the next phase of development, the back electron transfer reaction in betaine-30 played an important role. It was observed that in this case the electron transfer rate was lo6 times larger than that predicted by Sumi- Marcus theory. Naturally, the role of the high-frequency mode was invoked to explain this result. However, the difficulty persisted because no existing theory could explain the crossover from the solvent-dependent relaxation at low viscosities to solvent independence at high viscosities. To explain this rather anomalous result, Barbara et al. proposed that a minimal model of electron transfer should consist of a solvent polarization mode (X),a low- frequency classical vibrational mode (Q), and a high-frequency vibrational mode [43]. This model was termed the hybrid model, as it combines the ideas of Sumi and Marcus and those of Jortner and Bixon. The theoretical analysis of this model will form a major part of this chapter. SOLVATION, VIBRATIONAL DYSAMICS, AND ELECTRON TRAKSFER 5

Theoretical studies carried out in our group indicate that both the ultrafast solvation and vibrational modes can combine to give rise to highly interesting dynamical behavior in photoinduced electron transfer reactions in solution [41,77:78]. An important new outcome is that the dynamic solvent effects in electron transfer are weakened not only because of the participation of the high-frequency modes but also because ultrafast solvation in polar liquids makes the reaction channels from the high-frequency vibrational modes easily accessible. The ultrafast solvation can also significantly alter earlier conclusions on solvent dynamic effects on high-barrier adiabatic reaction. Recent studies have shown that ultrafast solvation can dramatically enhance the rate of barrier crossing over the rate expected if these modes were absent. In fact, one again finds that the ultrafast solvation leads to a weakening of the effects of solvent relaxation on adiabatic electron transfer reaction, and in most cases a significant ultrafast component can lead to the transition-state theory result. In fact, the main theme of this chapter is that the presence of the ultrafast component in solvation can lead to a significant enhancement of the electron transfer rate and can; in addition, lead to a marked weakening of dependence on solvent polarization relaxation time T~.It appears that this ultrafast component serves a twin purpose. First, even a modest ultrafast component is enough to trigger the electron transfer. Second, this component reduces the frictional resistance significantly. Both of these aspects are discussed in detail in this review. The organization of the remainder of the chapter is as follows. In the next section we describe predictions from the early theoretical models and com- pare them with experimental results. In Section I11 we discuss the role of intramolecular vibrational modes in electron transfer reactions. This section includes a discussion of the Sumi-Marcus and Jortner-Bixon theories. In Section IV we present the general theoretical formulation necessary to describe electron transfer reactions in a multidimensional potential energy surface. In Sections V and VI we discuss the results of solvent effects on the back electron transfer reaction in excited betaines in aprotic and protic solvents, respectively. In Section VII we discuss the free energy gap dependence of photoinduced electron transfer reactions, with particular emphasis on non-Marcus energy gap dependence. In Section VIII we present the results of theoretical studies on the effects of ultrafast solvation observed in water, acetonitrile, and methanol on a simple adiabatic electron transfer reaction. Section IX contains a review of recent work on nonexponentiality in the time evolution of electron transfer reactions in polar media. Section X contains a list of future problems that may be worth pursuing. Section XI concludes with a brief discussion. 6 BIMAN BAGCHI AND N. GAYATHRI

11. EARLY THEORETICAL MODELS: PREDICTION OF STRONG DEPENDENCE OF ELECTRON TRANSFER RATE ON SOLVENT POLARIZATION RELAXATION

Outer-sphere electron transfer reactions are rather unique in the sense that a large activation energy is often involved, although no chemical bonds are broken or formed. The activation energy comes from interaction of the charge of the electron with solvent polarization as the former moves from one stable solvated position to another stable position. A key to the great success of Marcus theory is proper formulation of this solvent-dependent reaction coordinate. This reaction coordinate in Marcus theory is a collec- tive coordinate. The nature of the reaction coordinate is best under- stood by considering a symmetric self-exchange reaction, such as M2+ + M3+ * M3+ + M2+. The relevant change is in the solvent polarization around the reaction system. The reaction coordinate is defined by the expression

X = - s drAD(r) . P(r) (2.1) where AD(r) is the change in the bare electric field (the electric displacement vector) of the reaction system due to charge transfer and P(r) is the solvent polarization. The free energy surface when plotted against this reaction coordinate shows parabolic dependence on X, one for each state. Note that X serves as an unambiguous reaction coordinate only when the activation barrier from solvent polarization is large and dominant. In many cases of photoinduced electron transfer reactions, the activation energy is nearly zero. In such cases, other coordinates, such as the intramolecular vibrational modes, also become relevant and one needs to think in terms of a multidimensional reaction energy surface. When the initial state is neutral and the final state is a charge transfer state, the reaction coordinate is essentially the solvation energy of the charge transfer state. Even when the initial state is charged, the reaction coordinate is essentially the energy of interaction between the electric field of the ion- dipole with the solvent polarization. Therefore, the dynamics along the reaction coordinate is largely controlled by the same dynamics as probed by solvation dynamic experiments. It was thus realized quite early that solvation dynamics of polar species can greatly influence and in some cases even dominate the rates of electron transfer reactions. Initial theoretical treatments analyzed the solvent influence on electron transfer with the reaction coordinate in outer-sphere electron transfer reactions as essentially the solvation energy of an ion [l-91. SOLVATION, VIBRATIONAL DYNAMICS, AND ELECTRON TRANSFER 7

The first important work was carried out by Zusman [5] and was based on the one-dimensional Kramers approach [58]. It was assumed that the reactant surface (1) and product surface (2) are both harmonic, and their harmonic frequencies are identical. The surfaces are then described as x2 V,(X)= ~ 4xx

Here X denotes the solvent coordinate, Ax is the solvent reorganization energy [l], and AG is the free energy change of the reaction. A simple schematic representation of the diabatic surfaces, VR(X)and Vp(X).is shown in Figure 1. In the initial studies, the electron transfer was only assumed to occur at the point where (according to the Fermi-Golden rule) the energies of the reactant and the product surfaces are equal. For a purely one-dimensional description, this condition is satisfied at X, = AG + Ax, where the two

R - F

I F 0 x, 2h, X Figure 1. General schematic representation of the reactant and product free energy surfaces as harmonic functions of the solvent reaction coordinate (X)for a one-dimensional Marcus model of electron transfer reaction. R and P represent the reactant and product states; respectively. AG is the difference between the free energy minima of R and P states. A, is the Marcus reorganization energy, and X, is the point of intersection at which the electron transfer takes place. 8 BIMAN BAGCHI AND N. GAYATHRI surfaces intersect to form the only reactive point site, referred to as a sink. For symmetric reactions, AG = 0, and as a result, X, = Ax (see Figure 1 for notation). According to the Zusman model, the electron transfer rate in the adiabatic limit is given by the equation

where TL is the solvent longitudinal relaxation time, AG" (= (A, + AG)2/4Xx) the free energy of activation, Ax the solvent reorganization energy [l], and kBT the Boltzmann constant times the absolute tem- perature. T~ is equal to (E,/E~)T~, where 'T~is the dielectric relaxation time; c0 is the static and t, the infinite-frequency dielectric constant of the solvent. Expression (2.4) implies that the electron transfer rate cannot exceed the solvent relaxation rate (1/~~). Since this pioneering work by Zusman, a large number of theoretical studies have been devoted to solvent effects on outer-sphere electron transfer reactions [6,17-371. We can list only a few here. It was mainly to treat the zero- and low-barrier situations that Zusman's model was extended by others. Many of these treatments address related issues, and the results are often similar. All these studies employ essentially a one-dimensional description of the reaction potential energy surface with the solvation energy of an ion-pair as the reaction coordinate. They all lead to the prediction of strong solvent dependence of the electron transfer rate. Calef and Wolynes [6] studied in detail the dynamic solvent effects on an adiabatic electron transfer reaction and showed that under certain circumstances, the transfer of charge between two centers can be modelled as a one-dimensional diffusion over a barrier. The rate was found to be inversely proportional to the longitudinal relaxation time, T~.In an elegant paper by Efrima and Bixon [19], a stochastic solvent model was employed to describe the dynamics of the polarization fluctuations of the solvent. In this study, a careful analysis of the kinetics of an electron transfer reaction reveals that the effect of solvent dynamics can assume considerable significance only in the case of an adiabatic reaction. Later, an elegant extension of the formulation of Zusman has been presented by Hynes [18]. In this work, Hynes described the dynamical influence of slow. non-Debye polar solvent relaxation on the electron transfer rate in terms of frequency-dependent friction acting on the reaction coordinate and demonstrated that the Zusman model Markovian description along the reaction coordinate can be generalized to include non- Markovian dynamics. A notable feature of Hynes' work is the derivation of