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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.
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.
The aim of this book is to give a comprehensive treatment of the different methods for the construction of spin eigenfunctions and to show their interrelations. The ultimate goal is the construction of an antisymmetric many-electron wave function that has both spatial and spin parts and the calculation of the matrix elements of the Hamiltonian over the total wave function. The representations of the symmetric group playa central role both in the construction of spin functions and in the calculation of the matrix elements of the Hamiltonian, so this subject will be treated in detail. We shall restrict the treatment to spin-independent Hamiltonians; in this case the spin does not have a direct role in the energy expression, but the choice of spin functions influences the form of spatial functions through the antisymmetry principle; the spatial functions determine the energy of the system. We shall also present the "spin-free quantum chemistry" approach of Matsen and co-workers, in which one starts immediately with the construction of spatial functions that have the correct permutational symmetries. By presenting both the conventional and the spin-free approach, one gains a better understanding of certain aspects of the elec tronic correlation problem. The latest advance in the calculation of the matrix elements of the Hamiltonian is the use of the representations of the unitary group, so this will be the last subject. It is a pleasant task to thank all those who helped in writing this book.
THIS VOLUME, WHICH IS DESIGNED FOR STAND-ALONE USE IN TEACHING AND RESEARCH, FOCUSES ON QUANTUM CHEMISTRY, AN AREA OF SCIENCE THAT MANY CONSIDER TO BE THE CENTRAL CORE OF COMPUTATIONAL CHEMISTRY. TUTORIALS AND REVIEWS COVER * HOW TO OBTAIN SIMPLE CHEMICAL INSIGHT AND CONCEPTS FROM DENSITY FUNCTIONAL THEORY CALCULATIONS, * HOW TO MODEL PHOTOCHEMICAL REACTIONS AND EXCITED STATES, AND * HOW TO COMPUTE ENTHALPIES OF FORMATION OF MOLECULES. * A FOURTH CHAPTER TRACES CANADIAN RESEARCH IN THE EVOLUTION OF COMPUTATIONAL CHEMISTRY. * ALSO INCLUDED WITH THIS VOLUME IS A SPECIAL TRIBUTE TO QCPE. FROM REVIEWS OF THE SERIES "Reviews in Computational Chemistry proves itself an invaluable resource to the computational chemist. This series has a place in every computational chemist's library."-JOURNAL OF THE AMERICAN CHEMICAL SOCIETY
The rivers run into the sea, yet the sea is not full Ecclesiastes What is quantum chemistry? The straightforward answer is that it is what quan tum chemists do. But it must be admitted, that in contrast to physicists and chemists, "quantum chemists" seem to be a rather ill-defined category of scientists. Quantum chemists are more or less physicists (basically theoreticians), more or less chemists, and by large, computationists. But first and foremost, we, quantum chemists; are conscious beings. We may safely guess that quantum chemistry was one of the first areas in the natural sciences to lie on the boundaries of many disciplines. We may certainly claim that quantum chemists were the first to use computers for really large scale calculations. The scope of the problems which quantum chemistry wishes to answer and which, by its unique nature, only quantum chemistry can answer is growing daily. Retrospectively we may guess that many of those problems meet a daily need, or are say, technical in some sense. The rest are fundamental or conceptual. The daily life of most quantum chemists is usually filled with grasping the more or less technical problems. But it is at least as important to devote some time to the other kind of problems whose solution will open up new perspectives for both quantum chemistry itself and for the natural sciences in general.
As the structure and behavior of molecules and crystals depend on their different symmetries, group theory becomes an essential tool in many important areas of chemistry. It is a quite powerful theoretical tool to predict many basic as well as some characteristic properties of molecules. Whereas quantum mechanics provide solutions of some chemical problems on the basis of complicated mathematics, group theory puts forward these solutions in a very simplified and fascinating manner. Group theory has been successfully applied to many chemical problems. Students and teachers of chemical sciences have an invisible fear from this subject due to the difficulty with the mathematical jugglery. An active sixth dimension is required to understand the concept as well as to apply it to solve the problems of chemistry. This book avoids mathematical complications and presents group theory so that it is accessible to students as well as faculty and researchers. Chemical Applications of Symmetry and Group Theory discusses different applications to chemical problems with suitable examples. The book develops the concept of symmetry and group theory, representation of group, its applications to I.R. and Raman spectroscopy, U.V spectroscopy, bonding theories like molecular orbital theory, ligand field theory, hybridization, and more. Figures are included so that reader can visualize the symmetry, symmetry elements, and operations.
"Quantum Chemistry" is the course material of a European Summer School in Quantum Chemistry, organized by Bj|rn O. Roos. It consists of lectures by outstanding scientists who participate in the education of students and young scientists. The book has a wider appeal as additional reading for University courses. Contents: P.-A. Malmquist: Mathematical Tools in Quantum Chemistry J. Olsen: The Method of Second Quantization P.R. Taylor: Molecular Symmetry and Quantum Chemistry B.O. Roos: The Multiconfigurational (MC) Self-Consistent Field (SCF) Theory P.E.M. Siegbahn: The Configuration Interaction Method T. Helgaker: Optimization of Minima and Saddle Points P.R. Taylor: Accurate Calculations and Calibration U. Wahlgren: Effective Core Potential Method
Principles and Applications of Quantum Chemistry offers clear and simple coverage based on the author's extensive teaching at advanced universities around the globe. Where needed, derivations are detailed in an easy-to-follow manner so that you will understand the physical and mathematical aspects of quantum chemistry and molecular electronic structure. Building on this foundation, this book then explores applications, using illustrative examples to demonstrate the use of quantum chemical tools in research problems. Each chapter also uses innovative problems and bibliographic references to guide you, and throughout the book chapters cover important advances in the field including: Density functional theory (DFT) and time-dependent DFT (TD-DFT), characterization of chemical reactions, prediction of molecular geometry, molecular electrostatic potential, and quantum theory of atoms in molecules. - Simplified mathematical content and derivations for reader understanding - Useful overview of advances in the field such as Density Functional Theory (DFT) and Time-Dependent DFT (TD-DFT) - Accessible level for students and researchers interested in the use of quantum chemistry tools
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.
Informal, effective undergraduate-level text introduces vibrational and electronic spectroscopy, presenting applications of group theory to the interpretation of UV, visible, and infrared spectra without assuming a high level of background knowledge. 200 problems with solutions. Numerous illustrations. "A uniform and consistent treatment of the subject matter." — Journal of Chemical Education.