Advances in CHEMICAL PHYSICS

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1 Advances in CHEMICAL PHYSICS Edited by I. PRIGOGINE Center for Studies in Statistical Mechanics and Complex Systems The University of Texas Austin, Texas and International Solvay Institutes Université Libre de Bruxelles Brussels, Belgium and STUART A. RICE Department of Chemistry and The James Franck Institute The University of Chicago Chicago, Illinois VOLUME 126 AN INTERSCIENCE PUBLICATION JOHN WILEY & SONS, INC.

3 ADVANCES IN CHEMICAL PHYSICS VOLUME 126

4 EDITORIAL BOARD BRUCE J. BERNE, Department of Chemistry, Columbia University, New York, New York, U.S.A. KURT BINDER, Institut für Physik, Johannes Gutenberg-Universität Mainz, Mainz, Germany A. WELFORD CASTLEMAN, JR., Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania, U.S.A. DAVID CHANDLER, Department of Chemistry, University of California, Berkeley, California, U.S.A. M. S. CHILD, Department of Theoretical Chemistry, University of Oxford, Oxford, U.K. WILLIAM T. COFFEY, Department of Microelectronics and Electrical Engineering, Trinity College, University of Dublin, Dublin, Ireland F. FLEMING CRIM, Department of Chemistry, University of Wisconsin, Madison, Wisconsin, U.S.A. ERNEST R. DAVIDSON, Department of Chemistry, Indiana University, Bloomington, Indiana, U.S.A. GRAHAM R. FLEMING, Department of Chemistry, University of California, Berkeley, California, U.S.A. KARL F. FREED, The James Franck Institute, The University of Chicago, Chicago, Illinois, U.S.A. PIERRE GASPARD, Center for Nonlinear Phenomena and Complex Systems, Brussels, Belgium ERIC J. HELLER, Institute for Theoretical Atomic and Molecular Physics, Harvard- Smithsonian Center for Astrophysics, Cambridge, Massachusetts, U.S.A. ROBIN M. HOCHSTRASSER, Department of Chemistry, The University of Pennsylvania, Philadelphia, Pennsylvania, U.S.A. R. KOSLOFF, The Fritz Haber Research Center for Molecular Dynamics and Department of Physical Chemistry, The Hebrew University of Jerusalem, Jerusalem, Israel RUDOLPH A. MARCUS, Department of Chemistry, California Institute of Technology, Pasadena, California, U.S.A. G. NICOLIS, Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Brussels, Belgium THOMAS P. RUSSELL, Department of Polymer Science, University of Massachusetts, Amherst, Massachusetts DONALD G. TRUHLAR, Department of Chemistry, University of Minnesota, Minneapolis, Minnesota, U.S.A. JOHN D. WEEKS, Institute for Physical Science and Technology and Department of Chemistry, University of Maryland, College Park, Maryland, U.S.A. PETER G. WOLYNES, Department of Chemistry, University of California, San Diego, California, U.S.A.

5 Advances in CHEMICAL PHYSICS Edited by I. PRIGOGINE Center for Studies in Statistical Mechanics and Complex Systems The University of Texas Austin, Texas and International Solvay Institutes Université Libre de Bruxelles Brussels, Belgium and STUART A. RICE Department of Chemistry and The James Franck Institute The University of Chicago Chicago, Illinois VOLUME 126 AN INTERSCIENCE PUBLICATION JOHN WILEY & SONS, INC.

6 Copyright # 2003 by John Wiley & Sons, Inc. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, , fax , or on the web at Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) , fax (201) , permreq@wiley.com. Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information on our other products and services please contact our Customer Care Department within the U.S. at , outside the U.S. at or fax Wiley also publishes its books in a variety of electronic formats. Some content that appears in print, however, may not be available in electronic format. Library of Congress Catalog Number: Printed in the United States of America

7 CONTRIBUTORS TO VOLUME 126 DAVID M. BISHOP, Department of Chemistry, University of Ottawa, Ottawa, Canada ALFREDO CÁRDENAS, Department of Computer Science, Cornell University, Ithaca, New York, U.S.A. BENOÎT CHAMPAGNE, Department of Chemistry, University of Ottawa, Ottawa, Canada. Permanent address: Laboratoire de Chimie Théorique Appliquée, Facultés Universitaires Notre-Dame de la Paix, Namur, Belgium WILLIAM T. COFFEY, Department of Electronic and Electrical Engineering, School of Engineering, Trinity College, Dublin, Ireland CLIFFORD E. DYKSTRA, Department of Chemistry, Indiana University Purdue University at Indianapolis, Indianapolis, Indiana, U.S.A. RON ELBER, Department of Computer Science, Cornell University, Ithaca, New York, U.S.A. AVIJIT GHOSH, Department of Computer Science, Cornell University, Ithaca, New York, U.S.A. YURI P. KALMYKOV, Centre d Etudes Fondamentales, Université de Perpignan, Perpignan, France MARTIN H. MÜSER, Institut für Physik, Johannes Gutenberg-Universität, Mainz, Germay. Current address: Department of Applied Mathematics, University of Western Ontario, London, Ontario, Canada. MARK O. ROBBINS, Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, Maryland, U.S.A. HARRY A. STERN, Department of Computer Science, Cornell University, Ithaca, New York, U.S.A. SERGEY V. TITOV, Institute of Radio Engineering and Electronics of the Russian Academy of Sciences, Fryazino, Moscow Region, Russian Federation MICHAEL URBAKH, School of Chemistry, Tel Aviv University, Tel Aviv, Israel v

9 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, Advances in Chemical 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 comprehensive analyses of subjects 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 STUART A. RICE vii

11 CONTENTS Intermolecular Interaction: From Properties to Potentials and Back 1 By Clifford E. Dykstra Calculations of Nonlinear Optical Properties for the Solid State 41 By Benoît Champagne and David Bishop Bridging the Gap Between Long Time Trajectories and Reaction Pathways 93 By Ron Elber, Alfredo Cárdenas, Avijit Ghosh, and Harry A. Stern Itinerant Oscillator Models of Fluids 131 By William T. Coffey, Yuri P. Kalmykov, and Sergey V. Titov Statistical Mechanics of Static and Low-Velocity Kinetic Friction 187 By Martin H. Müser, Michael Urbakh, and Mark O. Robbins Author Index 273 Subject Index 287 ix

13 INTERMOLECULAR INTERACTION: FROM PROPERTIES TO POTENTIALS AND BACK CLIFFORD E. DYKSTRA Department of Chemistry, Indiana University Purdue University at Indianapolis, Indianapolis, Indiana, U.S.A. CONTENTS I. Introduction II. Contributing Elements of Intermolecular Interaction A. Distinction from Chemical Bonding B. Types of Elements C. Pairwise Additivity and Cooperativity D. Functional Forms and Uniqueness in Potentials III. Ab Initio Interaction Energies and Surfaces A. Basis-Set Completeness and Superposition B. Electron Correlation Effects C. Perturbative Analysis D. Representing Ab Initio Surfaces IV. Developing Model Interaction Potentials A. Interaction-Specific Versus Transferable Potentials B. Ab Initio Determination of Potential Elements 1. Ab Initio Evaluation of Properties 2. Perturbative Partitioning C. Models for Parameters Used in Interaction Potentials D. Interaction Potential Models V. Calculational Aspects of Property-Based Potential Models VI. Intermolecular Influence on Electronic Structure A. Electronic Structure Changes, Property Changes, and Property Surfaces B. Bridging Quantum Mechanical Treatment to Models of Surroundings VII. Toward More Detailed Response Features VIII. Conclusions Acknowledgments References 1

14 2 clifford e. dykstra I. INTRODUCTION The subject of intermolecular interaction, and specifically the weak noncovalent attraction among molecules, is fascinating because it comprises a chemistry of its own, one in which whole, essentially intact molecules are the building blocks instead of atoms. Clusters of molecules exist via the attractive interactions; and there are, or likely will be, rules for cluster structure akin to the structural rules for the bonding of atoms. The subject is a sizable piece of molecular physics, one that has been reviewed in different ways for about a half-century, if not longer, and a number of those reviews and monographs [1 17] provide a useful context for this report. An always-present research objective in the study of intermolecular interaction is developing interaction potentials, because these encapsulate the understanding we have of the fundamental aspects of interaction. Also, interaction potentials are the tools for the next level of study of this chemistry, namely, the dynamics of clusters and energetics of bulk systems. It is model interaction potentials that are the focus of this review, not the whole of intermolecular interaction phenomena. Intermolecular interaction potentials have application at the junction of molecule-building-block chemistry and atom-building-block chemistry. Studying the influence of surrounding molecules or solvent molecules on chemical reactions or other atom-building-block phenomena requires knowledge of the weak interaction of the surrounding molecules with the reactive species. This brings forth an important issue for the industry of intermolecular interaction potential construction, that of level of detail. A level of detail for an interaction potential that may be tractable for the intricate dynamics of a twomolecule cluster probably won t be tractable for the study of an extended aggregation of molecules that is, a solvated system. Detail translates into accuracy, even if not directly; hence, the question in front of anyone pursuing the construction of intermolecular interaction potentials is, What level of accuracy is needed? There is no single answer, of course, because the potentials are used in ways ranging from those that require the highest attainable accuracy to those that require, or seem to require, merely a coarse form of the overall effect. In the history of interaction potentials, and likely for the immediate period ahead, what is learned from working at the detailed level drives, influences, or provides the knowledge base for everything less detailed. It is a logical progression of simulation technology. For the purposes of a review, there is some organizational advantage in selecting for the focus one certain level of detail, such as one of the extremes of highest accuracy or of being simplest for computation. Rather than that, the objective here is to look at interaction potentials from the perspective of differing levels of accuracy and the type of understanding that aids the progression from the detailed to the practical.

15 intermolecular interaction 3 In a rough sense, molecules do not change on weak intermolecular interaction; and the subject, as normally defined, excludes anything as abrupt as the breaking or forming of a chemical bond. Again, it is essentially intact molecules that are the building blocks. Hence, it is reasonable that the intrinsic properties of isolated, intact molecules offer physical insight to intermolecular interaction and also offer a means, not necessarily a complete means, for constructing interaction potentials. Also at hand as a means for surface construction but usually more laborious is direct quantum mechanical determination. Perhaps best of all is to do both by drawing on ab initio calculations to study the isolated constituent molecules and also to explore the role of properties in subtle electronic structure responses due to weak interaction. An interesting outcome of starting with molecular properties to understand weak interaction energetics is that property changes often can be put on an equivalent footing. That is, property surfaces for clusters can often be constructed along with potential surfaces using some of the same elements. In that sense, the construction of intermolecular interaction potentials can yield back property information akin to that which may have gone into the potentials. This is important for gathering insight into the physical basis and electronic structure features of weak interaction; and in turn, it is important for the advantageous extraction of coarse potentials from the best detailed potential information available. This review is meant to focus on those property connections and hopefully to offer, thereby, a perspective that augments other recent reviews of weak interaction, two of which give emphasis to potential construction [16,17]. The subject, especially in the context of considering the progression from detailed to coarse, could be extended to include continuum representations of surrounding molecules. We won t take that extension; it is better a subject on its own. Furthermore, it is distinct from the notion of analyzing interactions using intrinsic molecular properties as much as possible. The objectives, then, are to take a fundamental view of constructing potentials, one that allows for a range of accuracy and a wide range of applications and one that exploits property information. This requires integrating some topics that are easily review subjects on their own. Consequently, certain major development areas in weak interaction do not have the in-depth discussion that usually goes with reviews of weak interaction and hydrogen bonding [1 17], instead going only as far as needed to connect with the area of potential construction. The ultimate applications of the sort of intermolecular interaction potentials that are considered here are (i) detailed quantum dynamical treatment of rotation, vibration, and tunneling of small clusters, (ii) aggregation energetics, structures, and properties for clusters with up to hundreds of molecules, and (iii) molecular dynamics simulation for solvents in biomolecular and reactive problems. Were one to take those three in order as defining a kind of axis of detail, work from my group to date would be a distribution peaked somewhere past (i) and

ADVANCES IN CHEMICAL PHYSICS

ADVANCES IN CHEMICAL PHYSICS Edited by I. PRIGOGINE Center for Studies in Statistical Mechanics and Complex Systems The University of Texas Austin, Texas and International Solvay Institutes Université