Prentice Hall: Upper Saddle River, NJ, 2000. x + 739 pp. Illustrations. ISBN 0-13-685512-1. $96.00.

Quantum mechanical phenomena form the basis of all chemical behavior, and some familiarity with elementary quantum mechanics is essential for any practicing chemist. Yet too often undergraduate students avoid the subject until their graduating semester, judging quantum mechanics to be "too mathematical" and hence both difficult and irrelevant. Graduate students outside the physical chemistry subdiscipline may even be able to complete their formal education without enrolling in a single graduate-level class in quantum mechanics.

At the same time, continuing technological advances have literally brought to our desktops sophisticated computational techniques, based on quantum mechanics, for predicting molecular properties and understanding chemical reactivity. These techniques are widely employed by theoreticians and experimentalists alike in academic and industrial laboratories. Without some appreciation for the underlying quantum mechanical principles, however, chemists risk treating these computational methods as black boxes whose internal workings are unimportant. We would find it unacceptable for well-educated chemists to use Raman or infrared spectrometers without some basic familiarity with the principles that govern these spectroscopic techniques. Quantum chemical calculations should be treated no differently in the chemistry curriculum.

The latest edition of Levine's Quantum Chemistry tries to remedy this situation. In his preface, Levine writes that it is "highly desirable for students in all areas of chemistry to understand modern methods of electronic structure calculation, and this book has been written with this goal in mind". To this end, he has incorporated into the latter part of the book a rather extensive discussion of "practical" quantum chemical calculations. Although this makes the text a nicely balanced treatment of quantum mechanics for graduate students in physical chemistry, with roughly equal emphasis on fundamentals and applications, the text does not (yet) achieve its laudable goal.

The book's 17 chapters are presented without any guideposts above the chapter level, and no overview of the book's organization is given in the preface. Nevertheless, the text can be divided conceptually into three parts of roughly equal length. The first part introduces those aspects of quantum theory that are commonly used by chemists, including the variational method and perturbation theory, and discusses the standard, exactly solvable model problems of quantum mechanics. The middle part of the book (Chapters 10 through 14) discusses the electronic structure of atomic and diatomic systems in considerable detail, presenting along the way a brief overview of group theory. The final three chapters focus on practical ab initio and semiempirical treatments of the electronic structure of polyatomic molecules.

The second and third parts of the text contain numerous citations to the literature through 1998; these will be invaluable to readers interested in current research applications of quantum chemical techniques. The text also includes several appealing practical tidbits. For example, Levine describes the Numerov-Cooley method for calculating the bound states of one-dimensional anharmonic oscillators and shows the reader how to implement the method using either an Excel spreadsheet or a Basic computer program. (Unfortunately, the text fails to refer the reader to Cooley's excellent 1961 Mathematics of Computation article for further details.) Levine also peppers the book with pointers to relevant resources that can be found on the World Wide Web.

The book would make a good text for a yearlong introduction to quantum mechanics and quantum chemistry for first-year graduate students in physical chemistry. Levine does not skimp on mathematical rigor, and it is rare to find a page with fewer than three equations. Each chapter ends with a large number of homework problems; answers to some of the problems are collected at the end of the book. The text probably contains too much material for a one-semester course, unless students have had an undergraduate-level introduction to quantum mechanics sufficiently thorough that Chapters 1 through 6 (which cover exactly solvable problems) can be reviewed in one or two weeks.

Unfortunately, it is precisely these chapters that present the greatest obstacle to achieving the text's stated goal: to introduce students outside of physical chemistry to modern electronic structure methods. These chapters develop the fundamental aspects of quantum mechanics without much reference to systems of chemical interest, either in the text or in the homework problems. In fact, the first multi-electron Hamiltonian to appear in the book is that for the helium atom, introduced in Chapter 9 in the context of perturbation theory.

Because the second and third parts of the book build on concepts and tools introduced in the first part, students who want to understand how and why quantum chemistry calculations work--and, just as importantly, why they sometimes fail--must be willing to invest a considerable amount of time mastering these concepts. Whether a school's institutional culture will encourage students outside of physical chemistry to make this investment is a question that only individual faculty members can answer. My fear is that time constraints will tempt students and instructors alike to focus on the book's first two parts, with occasional forays into the third part. The resulting course will provide a thorough introduction to quantum mechanics, but it will not be a quantum chemistry course.

Of course, there is no one- or two-week shortcut by which nonspecialists can master enough quantum mechanics to become informed users of quantum chemical techniques. Nevertheless, a text that integrated the fundamentals of quantum theory with a rigorous introduction to quantum chemistry could help instructors design a class that would benefit both these nonspecialists and graduate students in physical chemistry. Could such a class overcome the (undeserved) stigma associated with the physical chemistry curriculum? That remains to be seen.