The permutation group has gained prominence in the fundamental research in diverse areas of physics and chemistry. Covering all salient developments of the last few years in a single symposium would require weeks, legions of participants and parallel sessions, highlighting the differences in language and communication problems between pure mathematicians, high and low energy physicists and chemists. The symposium held July 1978 at the Centre of Interdisciplinary Studies of the University of Bielefeld focussed on a small area, the pertinence of the permutation group in chemical physics, with the goal to increase and generate a fruitful dialogue between mathe maticians and chemists. In chemistry, concerned with the electronic and geometric structure of molecules as well as elementary chemical reactions, i.e. rearrangements in these structures, the permutation group has its relevance, since with its representations the effects and consequences of exchanging indistin guishable particles, electrons and identical nuclei, can be systematized and classified. This may be exemplified by a brief survey of the lectures presented, which may also serve as a first orientation· to the articles of this volume. In the first two contributions by A. Kerber and J.G. Nourse, the permutation group is used in the counting and systemtaic generation of stereoisomers aiding in the elucidation of possible molecular structures. The dynamics of stereochemistry is considered in the next article by J.G.

This text introduces advanced undergraduates and graduate students to key applications of group theory. Topics include the nature of symmetry operations; applications to vibrating systems, continuum mechanics, and quantum structures; permutation, continuous, and rotation groups; and physical Lie algebras. Each chapter concludes with a concise review, discussion questions, problems, and references. 1992 edition.

This is the first book to provide comprehensive treatment of the use of the symmetric group in quantum chemical structures of atoms, molecules, and solids. It begins with the conventional Slater determinant approach and proceeds to the basics of the symmetric group and the construction of spin eigenfunctions. The heart of the book is in the chapter dealing with spin-free quantum chemistry showing the great interpretation value of this method. The last three chapters include the unitary group approach, the symmetric group approach, and the spin-coupled valence bond method. An extensive bibliography concludes the book.

From December 1985 through March 1986 the text of this book formed the basis of an in-hours course taught by the author at Harry Diamond Laborato ries. Considerable assistance in revising and organizing the first draft was given by John Bruno. The original draft of these notes was based on a collection of lectures delivered at the Universidade Federal de Pernambuco, Recife, Brazil, between 2 November 1981 and 2 December 1981. The visit to Recife was a response to an invi tation of Professor Gilberto F. de Sa of the Physics Department. In the preparation of these notes I made many requests of my coworkers for earlier resul ts and recollections of our early work. Among those consul ted were Donald Wortman, Nick Karayianis, and Richard Leavitt. Further, a number of .suggestions from my Brazilian colleagues helped make the lectures more clear. Particular among these were Professor Oscar Malta and Professor Alfredo A. da Gama both of whom I wish to thank for their help. Encouragement and assistance with funding for much of this work came from Leon Esterowitz of the Naval Research Laboratory and Rudolph Buser and Albert Pinto of the center for Night Vision and Electro-Optics.

This concise, class-tested book was refined over the authors’ 30 years as instructors at MIT and the University Federal of Minas Gerais (UFMG) in Brazil. The approach centers on the conviction that teaching group theory along with applications helps students to learn, understand and use it for their own needs. Thus, the theoretical background is confined to introductory chapters. Subsequent chapters develop new theory alongside applications so that students can retain new concepts, build on concepts already learned, and see interrelations between topics. Essential problem sets between chapters aid retention of new material and consolidate material learned in previous chapters.

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.

This book presents a computational scheme for calculating the electronic properties of crystalline systems at an ab-ini tio Hartree-Fock level of approximation. The first chapter is devoted to discussing in general terms the limits and capabilities of this approximation in solid state studies, and to examining the various options that are open for its implementation. The second chapter illustrates in detail the algorithms adopted in one specific computer program, CRYSTAL, to be submitted to QCPE. Special care is given to illustrating the role and in:fluence of computational parameters, because a delicate compromise must always be reached between accuracy and costs. The third chapter describes a number of applications, in order to clarify the possible use of this kind of programs in solid state physics and chemistry. Appendices A, B, and C contain various standard expressions, formulae, and definitions that may be useful for reference purposes; appendix D is intended to facilitate the interpretations of symbols, conventions, and acronyms that occur in the book. Thanks are due to all those who have contributed to the implementation and test of the CRYSTAL program, especially to V.R. Saunders and M. Causal, and to F. Ricca, E. Ferrero, R. Or lando, E. Ermondi, G. Angonoa, P. Dellarole, G. Baracco.

These notes on the use of one particular form of the time-dependent rate constant to describe the reaction patterns in condensed media have been put together primarily to encourage chemists to try and accept this new way of experimental data treatment. A number of applications is shown and interpretative aspects are discussed. Emphasized are the problems that need to be currently solved. Some of them are also of current interest in condensed phase physics from which the chemical kinetics benefits a great deal. It was inevitable that the choice of subject matter from both rapidly expanding fields and its form of pre sentation reflect to some extent the author's own interests and some important topics are treated briefly or even omitted. Fully recognizing this, I would like to acknowledge with gratitude the contributions to the subject of all my coworkers in the Laboratories of Lodz, Detroit Mi, MUlheim/Ruhr, and Houston Tx, and of those who helped me in preparing this text. Dr. Wlodzi~ierz Lefik and my son WojciecQ recalculated most of the experimental results, Mrs. Aleksandra Karczewska redrew all the figures. Special thanks go to my wife Ewa for her invaluable assistance in all works and for the final form of the text. AP Lodz, February 1986 CONTENTS 1. Introduction 1 2. Reaction kinetics of species trapped in glassy matrices 6 Excess electrons (6): Post-irradiated decay (6). Spectral relaxation (11). Photostimulated decay (15). Photostimu lated conversion into trapped hydrogen atoms (17). Radio luminescence kinetics (21).