Foundations of Physics, Vol. 20, No. 10, 1990
Book Review Basic Principles and Techniques of Molecular Quantum Mechanics. By Ralph E. Christoffersen. Springer-Verlag, 677 pp., $79.00 (hardeover).
New York, New York, 1989,
The decade between 1980 and 1990 has witnessed the evolution of quantum chemistry from a discipline concerned primarily with interpreting the results of experiment to one with considerable a priori predictive power. This evolution is the result of a symbiosis between computer technology and theoretical insights, hard won over many decades of research by a multitude of scientists. It is now possible for a nonspecialist in theoretical chemistry to use large sophisticated computer programs as black-boxes to approximate the solution to the Schr6dinger equation with sufficient accuracy so as to be useful in interpreting and predicting chemistry. This is a remarkable development that has the potential for changing the way chemists go about their business. To use these powerful codes intelligently one must remember that they are an implementation of concepts, techniques, and approximations developed by many researchers over the last 50 years, and the numerical predictions cannot be better than the theory on which the algorithms are based. Christoffersen's text is concerned with providing, this background by developing a fundamental understanding of the theoretical underpinnings of modern electronic structure theory. The text consists of 677 pages, including the index, and is divided into 12chapters. The first chapter touches on the experimental basis of quantum theory while the second and third are devoted to a thorough presentation of vector spaces, linear transformations, and matrix theory. This mathematical section will be tough going for many chemistry students but those who stay the course will be amply rewarded by the insights this algebraic approach brings to the subsequent discussion. The fourth chapter is an axiomatic discussion of quantum mechanics and draws heavily on the mathematics developed in the earlier chapter. The next three chapters discuss one-dimensional problems, angular momentum (orbital and spin 1269 0015-9018/90/10(10-1269506~00/0 © 1990 Plenum Publishing Corporation
Book Review
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for a single particle), the H atom, and the H + molecule. These first seven chapters contain material normally found in elementary quantum mechanics texts. The application of this introductory material to molecules begins in Chapter 8 with a discussion of the molecular Hamiltonian, the Born-Oppenheimer approximation, and relativistic effects. The variation principle and perturbation theory are introduced in Chapter 9. The last three chapters deal with the machinery required to construct and interpret a many-electron wave-function. Chapter 10 introduces the Pauli principle, Slater determinants, and group (representation) theory. Chapter 11 is devoted to the Hartree-Fock theory and its matrix implementation by Hall and Roothaan. The text finishes with a chapter titled, "Beyond HartreeFock Theory." This is a 77-page summary of configuration interaction methods with some discussion of many-body perturbation theory and multiconfiguration SCF theories. Each chapter ends with a set of exercises, many of which permit one to continue the exploration of arguments presented in the text. The text has a decidedly formal algebraic tone, reflecting the influence of Per-Olov L6wdin. Especially attractive are the many references to the original literature, classic textbooks and useful compendia. Several topics which one might have expected to find have been omitted. There is no discussion of gradient techniques for determining geometries and vibrational frequencies. Density functional theory as well as application of the unitary group to electronic structure theory are not discussed. The title of the text, however, is consistent with the choice of topics. They are basic to a fundamental understanding of molecular quantum mechanics in general and quantum chemistry in particular, and the student who masters the material in this text will have a solid foundation for further study. James F. Harrison
Department of Chemistry Michigan State University East Lansing, Michigan 48824-1322
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