Fundamentals of Quantum Chemistry: Molecular Spectroscopy and Modern Electronic Structure Computations , Michael R. Mueller Kluwer Academic/Plenum, New York, 2001. $69.50 (265 pp.). ISBN 0-306-46596-5
Michael R. Mueller’s Fundamentals of Quantum Chemistry is designed as a practical introductory textbook for undergraduate and graduate students. Physical chemists and chemical physicists have a need for quantum mechanics texts that cover normal modes of vibration, molecular orbitals, and chemical reaction dynamics. Physics-oriented texts often omit these topics.
Quantum mechanics texts more specifically designed for chemists have been available for more than 50 years, with three current high-quality examples being Molecular Quantum Mechanics by P. W. Atkins and R. S. Friedman (Oxford U. Press, 1996), Quantum Chemistry, 4th ed., by Ira N. Levine (Prentice Hall, 1991), and Quantum Mechanics in Chemistry by George C. Schatz and Mark A. Ratner (Prentice Hall, 1953; Dover, 2002). Mueller’s book is not designed to compete with these excellent texts, but rather to present the basics of the subject to even second-year undergraduates. The author, however, recognizes that for some students this is a terminal course in quantum chemistry.
The book includes applications of quantum mechanics to the vibration, rotation, and electronic structure of molecules. Solid-state chemistry and polymers are excluded, as are most aspects of dynamics, although there are 16 pages on one-dimensional scattering.
We might ask, If one has the attention of young chemistry-oriented students for one semester, is this a good introduction to the subject? Quantum mechanical calculations are now firmly established as an everyday tool in the chemistry laboratory, especially for molecular geometries (conformational analysis), energy levels (spectroscopy), properties (dipole moments, polarizabilities), heats of reaction and equilibria (thermochemistry), and reaction mechanics (reactive barrier heights and thermochemical kinetics). Furthermore, chemists need to understand the conceptual framework of quantum mechanics, especially discreteness, uncertainty, coherence, interference, orbital symmetry, and tunneling. How well does the present text succeed in preparing students to appreciate the quantum mechanical concepts underlying modern calculations and interpretations of chemical phenomena?
In my opinion the book is well done in a limited number of these areas but is deficient in that it does not provide a broad enough view. For example, a point in favor of the book is that the critical Born–Oppenheimer separation of electronic and nuclear motion is explained, but a weak point is that the author does not address some important questions: How good is the Born–Oppenheimer approximation as a quantitative method for normal molecules? (Very good indeed.) Or when do we need to go beyond this approximation? (For photochemistry, for example.)
Consider another example: harmonic vibrations and normal coordinates. Normal coordinates are explained in words, without derivation, which is a reasonable compromise for beginning students. Furthermore, the example of internal rotation (torsion) is provided, and the students can see a case in which the harmonic approximation breaks down. But the internal rotation problem is presented only in the context of rotations, and its relation to the harmonic approximation is not presented.
The author presents the self-consistent field (SCF) method for atoms but does not tie it in to the early chapters, in which the variational principle is presented; the student might not realize that the SCF method is an example of the variational method. The comparison between the configuration interaction method and perturbation theory for treating electronic correlation is too oversimplified to be helpful.
The treatment of electronic structure is the strongest part of the book, especially in that the author introduces molecular mechanics, semiempirical molecular orbital theory, solvation effects, and density functional theory (DFT), although all at a very introductory level. The discussion of DFT gives the impression that one can systematically optimize the exchange-correlation density functionals until they converge “closer and closer” to the correct result, but this is not true. The author also errs in stating that including solvation is formidable; this is not true either. Only one paragraph is devoted to transition states, and it is drastically inadequate.
In my opinion the text is too simplified and restricted in scope to be a good choice for introducing students to quantum chemistry. It does not provide the student with an adequate understanding of the fundamentals and concepts.
