"The Theory of Atomic Spectra," surrrrnanzlllg all that was then known about the quantum theory of free atoms; and in 1961, J.S. Griffith published "The Theory of Transition Metal Ions," in which he combined the ideas in Condon and Shortley's book with those of Bethe, Schlapp, Penney and Van Vleck. All this work, however, was done by physicists, and the results were reported in a way which was more accessable to physicists than to chemists. In the meantime, Carl J. Ballhausen had been studying quantum theory with W. Moffitt at Harvard; and in 1962 (almost simultaneously with Griffith) he published his extremely important book, "Introduction to Ligand Field Theory." This influential book was written from the standpoint of a chemist, and it became the standard work from which chemists learned the quantum theory of transition metal complexes. While it treated in detail the group theoretical aspects of crystal field theory, Carl J. Ballhausen's book also emphasized the limitations of the theory. As he pointed out, it is often not sufficient to treat the central metal ion as free (apart from the influence of the charges on the surrounding ligands): - In many cases hybridization of metal and ligand orbitals is significant. Thus, in general. a molecular orbital treatment is needed to describe transition metal complexes. However, much of the group theory developed In connection with crystal field theory can also be used in the molecular orbital treatment.

Over the last twenty years, developments of the ab initio metho dologies and of the computing capacities have progressively turned quantum chemistry into a predictive tool for molecular systems involving only light elements. The situation appears less advanced for systems containing transition metal elements where specific difficulties arise, like those 1inked to the quasi-degeneracy of the lowest atomic states. Correlation effects, which are important only for quantitative accuracy in the treatment of molecules made of light elements, need sometimes to be considered even for a qualitative des cription of transition metals systems (like the multiple metal-metal bond). The treatment of atoms of a high atomic number has necessited the development of model potential methods. These difficulties ex acerbate for systems containing several trans ition atoms a correct description of the dichromium molecule Crz still represents a challenge to quantum chemists. Yet many advances have been made recently in the theoretical treatment of these systems, despite the fact that our understanding still remains disparate with a variety of models and methodologies used more or less successfully (one-electron models, explicitly correlated ab initio methods, density functional formalisms). For these reasons, a NATO Advanced Research Workshop was organized to review in detail the state-of-the-art techniques and at the same time the most common applications. These encompass many fields including the spectroscopy of diatomics and small aggregates, structure and reactivity problems in organometallic chemistry, the cluster surface analogy with its implications for heterogeneous catalysis and the description of extended structures."

The calculation of cross sections and rate constants for chemical reactions in the gas phase has long been a major problem in theoretical chemistry. The need for reliable and applicable theories in this field is evident when one considers the significant recent advances that have been made in developing experimental techniques, such as lasers and molecular beams, to probe the microscopic details of chemical reactions. For example, it is now becoming possible to measure cross sections for chemical reactions state selected in the vibrational rotational states of both reactants and products. Furthermore, in areas such as atmospheric, combustion and interstellar chemistry, there is an urgent need for reliable reaction rate constant data over a range of temperatures, and this information is often difficult to obtain in experiments. The classical trajectory method can be applied routinely to simple reactions, but this approach neglects important quantum mechanical effects such as tunnelling and resonances. For all these reasons, the quantum theory of reactive scattering is an area that has received considerable attention recently. This book describes the proceedings of a NATO Advanced Research Workshop held at CECAM, Orsay, France in June, 1985. The Workshop concentrated on a critical examination and discussion of the recent developments in the theory of chemical reaction dynamics, with particular emphasis on quantum theories. Several papers focus on exact theories for reactions."

This treatment of molecular and atomic physics is primarily meant as a textbook. It is intended for both chemists and physicists. *It can be read without much knowledge of quantum mechanics or mathematics, since all such details are explained-. It has developed through a series of lectures at the Royal Institute of Technology. The content is to about 50 % theoretical and to 50 % experimental. The reason why the authors, who are experimentalists, went into theory is the following. When we during the beginning of the 1970's measured photo electron spectra of organic molecules, it appeared to be impossible to understand them by use of available theoretical calculations. To handle hydrocarbons we ( together with C. Fridh ) constructed in 1972 a purely empirical procedure, SPINDO [1] which has proved to be useful, but the extension to molecules with hetero atoms appeared to be difficult. One of us ( L.A.) proposed then another purely ~~E!E!~~! EE2~~~~E~ ( Hydrogenic Atoms in Molecules, HAM/1, unpublished), in which the Fock matrix elements f5..y were parametrized using Slater's shielding concept. The self-repulsion was compensated by a term "-1". The ~~2~~_~ff2E~, HAM/2 [2] , started from the total energy E:. of the molecule. The atomic parts of L used the Slater shielding constants, and the bond parts of E. were taken from SPINDO. The Fock matrix elements Fpv were then obtained from E in a conventional way.

The development and computational implementation of analytical expres sions for the low-order derivatives of electronic energy surfaces and other molecular properties has undergone rapid growth in recent years. It is now fairly routine for chemists to make use of energy gradient information in locating and identifying stable geometries and transition states. The use of second analytical derivative (Hessian or curvature) expressions is not yet routine, and third and higher energy derivatives as well as property (e.g., dipole moment, polarizability) derivatives are just beginning to be applied to chemical problems. This NATO Advanced Research Workshop focused on analyzing the re lative merits of various strategies for deriving the requisite analyti cal expressions, for computing necessary integral derivatives and wave function parameter derivatives, and for efficiently coding these expres sions on conventional scalar machines and vector-oriented computers. The participant list contained many scientists who have been instrumen tal in bringing this field to fruition as well as eminent scientists who have broad knowledge and experience in quantum chemistry in general."

In 1980. a distinguished group of scientists gathered In Washington. D. C. for an International Symposium on Aging and Cancer. Among the recommendations of this Symposium was to convene a future meeting to discuss the molecular basis for Interrelationships between aging and cancer when the appropriate scientific knowledge was available. That same year. the 13th Jerusalem Symposium on Quantum Chemistry and Biochemistry entitled .Carcl nogenesls: Fundamental Mechanisms and Environmental Effects.. was held. attended by some 50 International authorities In this field. At this meeting. It became clear that the fundamental process of carcinogenesis 15 Intimately associated with differentiation. which must also be mechanistically related to aging. It was therefore proposed that the next Jerusalem Symposium on Cancer could provide the appropriate forum for the study on the Interrelationship among cancer. aging and differentiation. The Impressive advances In our knowledge of the nature of the genome through molecular genetic and physical chemical techniques have now provided the opportunity to examine the Interrelationships between these complex biolo gical processes. Through the Isolation. cloning and rearranging of genes we are able to dissect and manipulate the genome In a fashion that was unanticipated only a decade ago. At the same time. the Increase In longevity and the Increased numbers of Individuals entering the last decades of life where cancer Incidences are highest raise the profound and practical question of whether aging and cancer are linked through common mechanisms."

At the American Chemical Society meeting in Philadelphia, Pennsylvania, U.S.A., a symposium was organized entitled, "Comparison of Ab Initio Quantum Chemistry with Experiment: State-of-the-Art." The intent of the symposium was to bring together forefront experimen talists, who perform the types of clean, penetrating experiments that are amenable to thorough theoretical analysis, with inventive theore ticians who have developed high accuracy ab initio methods that are capable of competing favorably with experiment, to assess the current applicability of theoretical methods in chemistry. Contributions from many of those speakers (see Appendix A) plus others selected for their expertise in the subject are contained in this volume. Such a book is especially timely, since with the recent develop ment of new, more accurate and powerful ab initio methods coupled with the exceptional progress achieved in computational equipment, ab initio quantum chemistry is now often able to offer a third voice to resolve experimental discrepancies, assist essentially in the interpre tation of experiments, and frequently, provide quantitatively accurate results for molecular properties that are not available from experiment."

I get by with a little help from my friends The Beatles: Sgt. Pepper This book should have been in Danish. Any decent person must be able to express himself in his mother's tongue, also when expounding scientific ideas and results. Had I stuck to this ideal, the book would have been read by very few people, and, indeed, appreciated by even fewer. Having it publ ished in English gives me a chance to fulfill one ambition: to be read and judged by the international scientific community. Another reason is that the majority of my professional friends are regrettably unread in Danish, just as I am in Hebrew, Finnish and even Italian. I want to deprive them of the most obvious excuse for not reading my opus. Like a man I admired, I will first of all thank my wife. In his autobiography, Meir Weisgal, then President of the Weizmann Insti tute of SCience, wrote about his wife: "In addition to her natural endowments - which are considerable - she was a more than competent part-tim secretary." He wrote on, and so shall I. The book has been edited by my wife. So if the reader finds the layout pleasant as, in actual fact, I myself do, Birgit is to be praised. If there are blemishes, I am to be blamed for not having caught them."

Stereochemistry is the part of chemistry that relates observable prop erties of chemical compounds to the structure of their molecules, i. e. the relative spatial arrangement of their constituent atoms. In classical stereochemistry, the spatial arrangements relevant for interpreting and predicting a given chemical property are customarily described by geometric features/ symmetries in some suitably chosen rigid model of the molecule The solution of stereochemical problems involving single molecular species is the danain of the geometry based approaches, such as the methods of classical stereochemistry, molecular mechanics and quantum chemistry. The molecules of a pure chemical compound form generally an ensemble of molecular individuals that differ in geometry and energy. Thus it is generally impossible to represent a chemical compund adequately by the geo metry of a rigid molecular model. In modern stereochemistry it is often necessary to analyze molecular relation within ensembles and families of stereoisomers and permutation isomers, including molecules whose geometric features are changing with time. Accordingly, there is definitely a need for new types of ideas, concepts, theories and techniques that are usable beyond the scope of customary methodology. This is why the present text was written."

The present Volume of Lecture Notes in Chemistry fulfils one of the stated aims of the Series, that of disseminating results discussed and evaluated at recent scientific international conferences; in our case a Satellite Meeting of the well-known Conference Series on the Physics of Electronic and Atomic a:ollisions, the XIIIth ICPEAC, which took place in Castelgandolfo, near Rome, from 23 to 25 July 1983. Since the Satellite Meeting attracted a widely international and in- terdisciplina~y audience whose general consensus was one of warm appro- val for the scie'ntific level achieved during it, we hope that the pre- sent collection of essays will be met by similar success, thus warran- ting our having asked the participants to work still further for us. Before turning to their efforts, however, it is only just to thank the Italian National Research Council (Chemistry Committee and Physics Committee), the University of Rome, the C.N.R. Tnstitute H.A.I. of the Rome Research Area (Montelibretti) and the E.N.E.A. Organisation for their financial aid, which made the Castelgandolfo Meeting possible. We warmly acknowledge the professional expertise of the staff at Villa Montecucco and for their collaboration we are grateful to: Rita Abbasciano, Catherine Cajone, Lucilla Crescentini, .Roberta Fantoni, An- tonio Montani, Amedeo Palma, Rosario Platania, Maurizio Venanzi.

At a time when computerized laboratory automation is producing a da ta explosion, chemists are turning to applied mathematics and statistics for the tools to extract useful chemical information from data. This rush to find applicable methods has lead to a somewhat confusing body of literature that represents a barrier to chemists wishing to learn more about chemometrics. The confusion results partly from the mixing of chemical notation and nomenclature with those of statistics, applied mathematics and engineering. Additionally, in the absence of collaboration with mathematicians, chemists have, at times, misused data analysis methodology and even reinvented methods that have seen years of service in other fields. The Chemometrics Society has worked hard to solve this problem since it was founded in 1974 with the goal of improving communications between the chemical sciences and applied mathe matics and statistics. The NATO Advanced Study Institute on Chemometrics is evidence of this fact as it was initiated in response to a call from its membership for advanced training in several areas of chemometrics. This Institute focused on current theory and application in the new field of Chemometrics: Use of mathematical and statistical methods, Ca) to design or select optimal measurement procedures and experiments; and Cb) to provide maximum chemical information by analyzing chemical data. The Institute had two formal themes and two informal themes."

The NATO Advanced Study Institute on "Quantum Chemistry of Polymers; Solid State Aspects" lIIas held at the MARITIM Congress Hotel Braunlage/Harz in the Federal Republic of Germany from July 25 - August 5, 1983. We lIIish to express our deep gratitude to the NATO Scientific Affairs Division, the main sponsor of the Institute, and to the National Foundation for Cancer Research, Bethesda, Maryland for their substantial support. We sincerely thank Dr. Craig Sinclair, Director of the NATO Advanced Study Institutes program as lIIell as the IIIhole Advanced Study Institute/Advanced Research Workshop Advisory Board of the NATO Scientific Affairs Division, IIIho have honored us by holding their external annual meeting during this School in Braunlage. We are very much indebted also to Dr. Mario Di Lullo, Director of the Advanced Research Workshop program of the NATO Scientific Affairs Division IIIho together lIIith Dr. Sinclair has given a very informative lecture about the NATO ASI/ARW programs. Special thanks are due to Mr. Franklin Salisbury, Executive Director of the National Foundation for Cancer Research, to Mrs. Tamara Salisbury, Deputy Director of the National Foundation for Cancer Research and to Dr. Mary Hennen Aldridge, President of the National Foundation for Cancer Research, IIIho also honored the School lIIith their presence.

The bond diagrammatic representation of molecules is the foundation of MOVB theory. To a certain extent, this kind of representation is analogous to the one on which "resonance theory" is based and this fact can be projected by a comparison of the various ways in which MOVB theory depicts a species made up of three core and two ligand MO's which define two subsystems containing a total of six electrons and the ways in which "resonance theory" (i. e. , qualitative VB theory) depicts a six-electron-six-AO species such as the pi system of CH =CH-CH=CH-CH=O. The 2 different pictorial representations are shown in Scheme 1 so that the analogies are made evident. First of all, the total MOVB diagrammatic representation of the 6/5 species is obtained by a linear combination of three complete bond diagrams, as in Al, which describe the optimal linear combination of!l! MOVB Configuration Wavefunctions (CW's). By the same token, a total VB diagrammatic representation of the 6/6 species can be obtained by writing a "dot structure", as in Bl, and taking this to mean the optimal linear combination of all VB CW's. Next, we can approxi mate the MOVB wavefunction of the 6/5 species by one complete (or detailed) bond dia gram" (A2). No simple VB representation analogy can be given in this case. Alterna tively, we can approximate the MOVB wavefunction by a linear combination of compact bond diagrams, as in A3, in the way described before.

The Fourth International Congress in Quantum Chemistry under the auspices of the International Academy of Molecular Quantum Science in Menton, France was arranged at Uppsala University, Uppsala, Sweden, during the period June 14 - 19, 1982, in close collaboration with the University of Florida. The previous congresses were held in Menton 1973, New Orleans 1976, and Kyoto 1979, and the 1985 congress is tentatively planned to be held in the province of Quebec, Canada. The Congress consisted of six symposia in various areas of quantum chemistry, solid-state theory, and quantum bi ology. The meeting was attended by about 450 scientists from 45 different nations, and a total of more than 300 scientific papers were presented. Even the poster contri butions were given some plenary time. These proceedings contain the text of the plenary lec tures as well as the chairmen's introductions, whereas the contributed papers will be published in the International Journal of Quantum Chemistry, (John Wiley & Sons, New York) in the regular January - April 1983 issues."

The Fifteenth Jerusalem Symposium reflected the high standards of the former international scientific meetings, which convene once a year at the Israel Academy of Sciences and Humanities in Jerusalem to discuss a specific topic in the broad area of quantum chemistry and biochemistry. The topic at this year's Jerusalem Symposium was intramo lecular dynamics, a subject of central interest for theoreticians, che mists and biologists. During the last two decades, there has been remarkable pro gress in our understanding of time dependent phenomena. The development and application of the modern techniques of quantum mechanics and sta tistical mechanics to excited-state dynamics and to chemical and biophy sical systems constitutes a fast developing current research area. The main theme of the Symposium was built around a conceptual framework for the elucidation of photophysical and photochemical phenomena in atoms, molecules, van der Waals complexes and clusters, condensed phases, poly mers and biological supermolecules. The interdisciplinary nature of this research field was deliberated by intensive and extensive interactions between scientists from different disciplines and between theory and experiment. This volume provides a record of the invited lectures at the Symposium."

The aim of this chapter is to discuss in detail the Monte Carlo algorithms developed to compute the sequence distributions in polymers. Because stereoregular polymers constitute a unique form of copolymer, the stereosequence distributions in vinyl homopolymers and the sequence distributions in copolymers can be computed using the same algorithms. Also included is a brief review of probabilistic models (i. e. , Bernoulli trials and Markov chains) frequently used to compute the sequence distribtuion. The determination of sequence distributions is important for the under- standing of polymer physical properties, to compute the monomer reactivity para- meters and to discriminate among polymerization mechanisms. 2. 2. Short review of analytical models, Monte Carlo algorithms and computer programs. l A Bernoullian model was developed by Price. Within this model the probability of a given state of the system is independent of the previous state and does not condition the next state. The Bernoullian behaviour has been shown 24 to describe cls-trans distributions among 1, 4 additions in polybutadienes - , 5 the comonomer distribution in ethylene-vinyl acetate copolymer , and configura- 6 tional distributions in polystyrene , poly (vinyl chloride)7, poly (vinyl alcohol)7 Consider the binary copolymerization:;1,J=1,2 (1) where - MI* , I = 1,2, is an ionic or radical polymeric chain end, and M, J = 1,2, J is a monomer. Because the final state (i. e.

The third and last volume of this treatise IS concerned with important applications of the quantum~theory of chemical reactions to chemisorption, catalysis and biochemical reactions. The book begins with an important paper devoted to the theoretical background of heterogeneous catalysis. It is followed by two papers showing typical applications of wave mechanics to the analysis of chemisorption. Catalysed gas-solid reactions are chosen to illustrate gas, organic solid state reaction and some aspects of the mechanism of the FISCHER-TROPSCH synthesis are presented. The second part of the book is devoted to biochemical applications of quantum chemistry. Two papers are concerned with the quantum theory of enzyme activity. Two others present recent progress of quantum pharmacology. Finally an important contribution to the theory of intermolecular forces is made in the view of possible applications to biochemical problems. vii R. Daudel, A. Pullman, L. Salem, and A. Viellard reds.), Quantum Theory o/Chemical Reactions, Volume III, vii. Copyright (c) 1982 by D. Reidel Publishing Company. THEORETICAL BACKGROUND OF HETEROGENEOUS CATALYSIS J.E.Germain Laboratoire de Catalyse Appliquee et Cinetique Heterogene L. A. 231 du Centre National de la Recherche Scientifique Universite Claude Bernard Lyon I, E.S.C.I.L. 43 Boulevard du 11 Novembre 1918, 69622 Villeurbanne Cedex. Heterogeneous Catalysis is a surface Kinetic phenomenon by which a chemical reaction between molecules of a fluid phase is accelerated (activity) and oriented (selectivity) by contact with a solid phase (catalysts, without change of the solid.

The lattice dynamics of molecular crystals has undergone an enor mous progress in these last twenty years or so. The experimental and theoretical advances have been realized by two different approaches. From one side molecular spectroscopists have been primarily interested in the vibrational properties of the molecules themselves subjected to the perturbing influence of the crystal environment. From the other side the lattice dynamical theory familiar in solid state physics for atomic lattices has been extended to molecular arrays. Although the overlap between the two approaches has been considerable the reference material is rather scattered in specialized papers. The purpose of this book is to partly fill this gap and to discuss the lattice dynamical theory of molecular crystals in a compact and specialized form. As such, the book is not intended exclusively for researchers and specialists in the field but also for graduate students entering an activity in solid state mo lecular spectroscopy."

The aim of these notes is to offer a modern picture of the pertur bative approach to the calculation of intermolecular forces. The point of view taken is that a perturbative series truncated at a low order can provide a valuable way for valuating interaction energies, especial ly if one limits oneself to the case of intermediate- and long-range distances between the interacting partners. Although the situation corresponding to short distances is essen tially left out from our presentation, the problems which are within the range of the theory form a vast and important class: a large var iety of phenomena of matter, in fact, depends on the existence of in teractions among atoms or molecules, which over a substantial range of distances should be classified as weak in comparison to the interactions occurring inside atoms or molecules. We are aware of the omission of some topics, which in principle could have been included in our review. For instance, a very scarce at tention has been paid to the analysis of problems involving interacting partners in degenerate states, which is of particular relevance in the case of interactions between excited atoms (only a rather quick presen tation of the formal apparatus of degenerate perturbation theory is in cluded in Chap. III). Interactions involving the simultaneous presence of more than two atoms (or mOlecules) have not been considered, with the consequent non-necessity of considering nonadditive effects which characterize the general N-body problem."

The 14th Jerusalem Symposium continued the tradition of the pleasant and exciting meetings which once a year gather distinguished scientists, the world's most renowned experts in specific fields of quantum chemistry and biochemistry, in the impressive surroundings of the Israel Academy of Sciences and Humanities. The subject discussed this year - Intermolecular forces - is one of the utmost interest for all molecular sciences. I wish to thank all those who made this meeting possible and contributed toits success: the Baron Edmond de Rothschild whose continuous generosity guarantees the perenniality of our venture, t e Israel Academy of Sciences and in particular its Vice-President, Pr fes sor Yoshua Jortner for his devoted contribution to the organization and holding of this meeting, the high authorities of the Hebrew Uni versity of Jerusalem and in particular the Rector Meshulamfor their constant support and Dr. Pierre Claverie for his efficient help in the preparation of the program. Mrs Abigail Hyam and Mrs MyriamYogev must be thanked for their contribution to the efficiency and success of the local arrangements. Bernard Pullman ix B.Pullman ed.}, IntermolecularForces, ix. Copyright (c)1981byD.ReidelPublishingCompany. INTERMOLECULAR FORCES: WHAT CAN BE LEARNED FROM AB INITIO CALCULATIONS? Advan der Avoird Institute of Theoretical Chemistry, University of Nijmegen, Toernooiveld, Nijmegen, The Netherlands. 1. INTRODUCTION Various experiments, suc as elastic or rotationally inelastic molecular beamscattering(1,2 and spectroscopic studies of so-cafled Van der Waals molecules(3,4), have been designed especially to provide information about the Van der Waals interactions between molecules."

Analytical chemistry of the recent years is strongly influenced by automation. Data acquisition from analytica instruments - and some times also controlling of instruments - by a computer are principally solved since many years. Availability of microcomputers made these tasks also feasible from the economic point of view. Besides these basic applications of computers in chemical measurements scientists developed computer programs for solving more sophisticated problems for which some kind of "intelligence" is usually supposed to be necessary. Harm less numerical experiments on this topic led to passionate discussions about the theme "which jobs cannot be done by a computer but only by human brain ? . If this question is useful at all it should not be ans wered a priori. Application of computers in chemistry is a matter of utility, sometimes it is a social problem, but it is never a question of piety for the human brain. Automated instruments and the necessity to work on complex pro blems enhanced the development of automatic methods for the reduction and interpretation of large data sets. Numerous methods from mathematics, statistics, information theory, and computer science have been exten sively investigated for the elucidation of chemical information; a new discipline "chemometrics" has been established. Three different approaches have been used for computer-assisted interpretations of chemical data. 1. Heuristic methods try to formu late computer programs working in a similar way as a chemist would solve the problem. 2."

1. 1 STATEMENT OF THE PROBLEM Quantum chemistry judged not from the ever present possibility of unex pected developments but on the basis of the achievements in the last fifty years, is predominantly limited to attempts to solve for the energy and expectation values of wave functions representing, in the limit, an exact solution to the Schroedinger equation. Because of well-known dif ficulties in system with more than about 50 electrons, the adopted ap proximations are generally rather crude. As examples of quantum chemical approximations we mention the total or partial neglects of electron correlation, the neglect of relativistic effects, the use of subminimal basis sets, the still present neglect of inner-core electrons in semi-empirical methods, the acceptance of the Born-Oppenheimer approximations, and so on. In general, the larger the system, in terms of the number of electrons, the cruder the approxima tion. In a way, the present status of quantum chemistry might appear as nearly paradoxical. Indeed, for small systems, where very accurate ex periments are often available, and therefore, there is not a great need to obtain (from quantum chemistry) predictions of new data but rather, a theoretical interpretation of the existing data, we find increasi gly powerful and reliable quantum chemical methods and techniques."

Since the discovery of quantum mechanics, more than fifty years ago, the theory of chemical reactivity has taken the first steps of its development. The knowledge of the electronic structure and the properties of atoms and molecules is the basis for an un derstanding of their interactions in the elementary act of any chemical process. The increasing information in this field during the last decades has stimulated the elaboration of the methods for evaluating the potential energy of the reacting systems as well as the creation of new methods for calculation of reaction probabili ties (or cross sections) and rate constants. An exact solution to these fundamental problems of theoretical chemistry based on quan tum mechanics and statistical physics, however, is still impossible even for the simplest chemical reactions. Therefore, different ap proximations have to be used in order to simplify one or the other side of the problem. At present, the basic approach in the theory of chemical reactivity consists in separating the motions of electrons and nu clei by making use of the Born-Oppenheimer adiabatic approximation to obtain electronic energy as an effective potential for nuclear motion. If the potential energy surface is known, one can calculate, in principle, the reaction probability for any given initial state of the system. The reaction rate is then obtained as an average of the reaction probabilities over all possible initial states of the reacting artic1es. In the different stages of this calculational scheme additional approximations are usually introduced."