Introduction to Quantum Mechanics in Chemistry

Introduction to Quantum Mechanics in Chemistry , Mark A. Ratner and George C. Schatz Prentice Hall, Upper Saddle River, N.J., 2001. $86.00 (305pp.). ISBN 0-13-895491-7

The 1998 Nobel Prize in Chemistry, awarded to Walter Kohn and John A. Pople, demonstrated the influence that computational quantum chemistry has had on the entire field of chemistry. This influence is likely to grow and spill into other active research areas in the near future. An introductory text bridging the gap between the basics of quantum mechanics and the application of ab initio and semi-empirical quantum chemistry theories to problems of chemical interest is thus highly desirable. The textbook, Introduction to Quantum Mechanics in Chemistry by Mark A. Ratner and George C. Schatz, which is aimed at nontheoretical chemists and undergraduate students, effectively provides this link. It is a concise, easily readable, and understandable introduction to quantum chemistry and the methods currently used in chemical applications.

After a brief review of the laws of classical mechanics and wave theory, the reader is introduced to the quantum mechanical treatment of the particle in a box, the rigid rotor, the harmonic oscillator, and the hydrogen atom. The variational method, electron spin, Slater determinants, and Hartree–Fock theory are presented along with the treatment of helium and other many-electron atoms. This review leads to the discussion of ab initio, density-functional, and semi-empirical quantum chemistry methods and their performance in typical applications. The suggested readings at the end of each chapter cite the classics in the field, to which interested students may go for more in-depth discussions of the topics.

Significant strengths of this book are the many exercises (and answers) that the authors disperse along the text and the wealth of problems given at the end of each chapter. These are extremely useful for working out derivations and deepening understanding of difficult parts. The “numerical” problems following the chapter “Applications of Electronic Structure Theory” involve the ab initio and density-functional computation of energies and structures of mostly small molecules and a comparison with the experimental and theoretical literature. Discussion of these problems allows the student to learn about the strengths and weaknesses of current computational methods. These problems are additionally well suited to an introductory, hands-on class in computational quantum chemistry. The last 30 pages of the book present solutions to the odd-numbered problems.

When writing a textbook that covers such a wide range of topics in only some 300 pages, the treatment of certain topics will surely require that compromises be made. Although one might argue that certain topics would deserve a more in-depth treatment, we feel that this textbook is well balanced overall. The book mentions, but does not discuss in detail, such advanced computational methods such as multi-configuration, self-consistent field, or coupled-cluster theory. Nevertheless, it provides a basic understanding of the principles underlying quantum chemistry. The reader, armed with this knowledge, can then more easily study advanced books in quantum chemistry. The chapter, “Applications of Group Theory,” however, might be difficult for undergraduates, because its coverage ranges from symmetry operations to constructing symmetry-adapted linear combinations—in a mere 20 pages. This chapter might well benefit from a more detailed discussion, or from a less ambitious coverage.

There is a conceptual similarity between Ratner and Schatz’s text and such other popular books in the subject as Quantum Chemistry, by Ira N. Levine (Prentice Hall, 1999). Levine’s book offers a more detailed discussion (some 600 pages) on several topics, but it mostly addresses a different audience: graduate students. The attempt of Ratner and Schatz to offer a concise and easily understandable text to undergraduate students is highly commendable.