Molecular Collision Theory

Activity in any theoretical area is usually stimulated by new experimental techniques and the resulting opportunity of measuring phenomena that were previously inaccessible. Such has been the case in the area under consideration he re beginning about fifteen years aga when the possibility of studying chemical reactions in crossed molecular beams captured the imagination of physical chemists, for one could imagine investigating chemical kinetics at the same level of molecular detail that had previously been possible only in spectroscopic investigations of molecular stucture. This created an interest among chemists in scattering theory, the molecular level description of a bimolecular collision process. Many other new and also powerful experimental techniques have evolved to supplement the molecular be am method, and the resulting wealth of new information about chemical dynamics has generated the present intense activity in molecular collision theory. During the early years when chemists were first becoming acquainted with scattering theory, it was mainly a matter of reading the physics literature because scattering experiments have long been the staple of that field. It was natural to apply the approximations and models that had been developed for nuclear and elementary particle physics, and although some of them were useful in describing molecular collision phenomena, many were not.

This high-level monograph offers an excellent introduction to the theory required for interpretation of an increasingly sophisticated range of molecular scattering experiments. There are five helpful appendixes dealing with continuum wavefunctions, Green's functions, semi-classical connection formulae, curve-crossing in the momentum representation, and elements of classical mechanics. The contents of this volume have been chosen to emphasize the quantum mechanical and semi-classical nature of collision events, with little attention given to purely classical behavior. The treatment is essentially analytical. Some knowledge of the quantum mechanics of bound states is assumed.

The broad field of molecular collisions is one of considerable current interest, one in which there is a great deal of research activity, both experi mental and theoretical. This is probably because elastic, inelastic, and reactive intermolecular collisions are of central importance in many of the fundamental processes of chemistry and physics. One small area of this field, namely atom-molecule collisions, is now beginning to be "understood" from first principles. Although the more general subject of the collisions of polyatomic molecules is of great im portance and intrinsic interest, it is still too complex from the viewpoint of theoretical understanding. However, for atoms and simple molecules the essential theory is well developed, and computational methods are sufficiently advanced that calculations can now be favorably compared with experimental results. This "coming together" of the subject (and, incidentally, of physicists and chemists !), though still in an early stage, signals that the time is ripe for an appraisal and review of the theoretical basis of atom-molecule collisions. It is especially important for the experimentalist in the field to have a working knowledge of the theory and computational methods required to describe the experimentally observable behavior of the system. By now many of the alternative theoretical approaches and computational procedures have been tested and intercompared. More-or-Iess optimal methods for dealing with each aspect are emerging. In many cases working equations, even schematic algorithms, have been developed, with assumptions and caveats delineated.

Chemistry 2e is designed to meet the scope and sequence requirements of the two-semester general chemistry course. The textbook provides an important opportunity for students to learn the core concepts of chemistry and understand how those concepts apply to their lives and the world around them. The book also includes a number of innovative features, including interactive exercises and real-world applications, designed to enhance student learning. The second edition has been revised to incorporate clearer, more current, and more dynamic explanations, while maintaining the same organization as the first edition. Substantial improvements have been made in the figures, illustrations, and example exercises that support the text narrative. Changes made in Chemistry 2e are described in the preface to help instructors transition to the second edition.

Activity in any theoretical area is usually stimulated by new experimental techniques and the resulting opportunity of measuring phenomena that were previously inaccessible. Such has been the case in the area under consideration here beginning about fifteen years ago when the possibility of studying chemical reactions in crossed molecular beams captured the imagination of physical chemists, for one could imagine investigating chemical kinetics at the same level of molecular detail that had previously been possible only in spectroscopic investigations of molecular stucture. This created an interest among chemists in scattering theory, the molecular level description of a bimolecular collision process. Many other new and also powerful experimental techniques have evolved to supplement the molecular beam method, and the resulting wealth of new information about chemical dynamics has generated the present intense activity in molecular collision theory. During the early years when chemists were first becoming acquainted with scattering theory, it was mainly a matter of reading the physics literature because scattering experiments have long been the staple of that field. It was natural to apply the approximations and models that had been developed for nuclear and elementary particle physics, and although some of them were useful in describing molecular collision phenomena, many were not. The most relevant treatise then available to students was Mott and Massey's classic The Theory of Atomic Collisions, * but, as the title implies, it dealt only sparingly with the special features that arise when at least one of the collision partners is a molecule.

Almost 100 years have passed since Trautz and Lewis put forward their collision theory of molecular processes. Today, knowledge of molecular collisions forms a key part of predicting and understanding chemical reactions. This book begins by setting out the classical and quantum theories of atom-atom collisions. Experimentally observable aspects of the scattering processes; their relationship to reaction rate constants and the experimental methods used to determine them are described. The quantum mechanical theory of reactive scattering is presented and related to experimental observables. The role of lasers in the measurement and analysis of reactive molecular collisions is also discussed. Written with postgraduates and newcomers to the field in mind, mathematics is kept to a minimum, and readers are guided to appendices and further reading to gain a deeper understanding of the mathematics involved.

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.

The broad field of molecular collisions is one of considerable current interest, one in which there is a great deal of research activity, both experi mental and theoretical. This is probably because elastic, inelastic, and reactive intermolecular collisions are of central importance in many of the fundamental processes of chemistry and physics. One small area of this field, namely atom-molecule collisions, is now beginning to be "understood" from first principles. Although the more general subject of the collisions of polyatomic molecules is of great im portance and intrinsic interest, it is still too complex from the viewpoint of theoretical understanding. However, for atoms and simple molecules the essential theory is well developed, and computational methods are sufficiently advanced that calculations can now be favorably compared with experimental results. This "coming together" of the subject (and, incidentally, of physicists and chemists !), though still in an early stage, signals that the time is ripe for an appraisal and review of the theoretical basis of atom-molecule collisions. It is especially important for the experimentalist in the field to have a working knowledge of the theory and computational methods required to describe the experimentally observable behavior of the system. By now many of the alternative theoretical approaches and computational procedures have been tested and intercompared. More-or-Iess optimal methods for dealing with each aspect are emerging. In many cases working equations, even schematic algorithms, have been developed, with assumptions and caveats delineated.