Cambridge University Press: Cambridge, 2000. xii + 314 pp. ISBN 0-521-66649-X. $32.95.

Orbitals in Chemistry is a deftly written book. In smooth-flowing easy-to-read prose, Gil provides a very brief introduction to quantum mechanics, an overview of the ideas underlying atomic and molecular orbitals, and discussions of the applications of orbitals to chemical bonding and reactivity, molecular geometry, spectroscopy, the fullerenes, transition metal complexes, and solids. The text, which extends for 289 pages and is divided into 12 chapters, is designed for undergraduate chemistry students and others who encounter atomic and molecular orbitals in their courses.

A major and unique strength of the book is reference to 85 papers on teaching, 73 of them from this Journal. These references and the associated discussions highlight subtle issues and common misinterpretations associated with quantum mechanics and the orbital concept. These references could easily be used to develop student projects to enhance understanding.

The book, however, does not include many derivations or details that would enable the reader to understand the origins of the ideas in terms of fundamental principles or to understand what actually must be done to apply the ideas quantitatively. Two examples of this omission are described in the following paragraphs.

Gil leads the reader through the mathematics of the particle in a box by starting with the Schrödinger equation and its solutions without explaining how one might find the solutions to this simple differential equation. While the connections between the boundary conditions, the form of the wave functions, and the quantization of energy are made, all the reader is asked to do with this information is to confirm that the wave functions for n = 1, 2, and 3, which are shown in a figure, are orthogonal. More is required to guide the student in real learning. Students do not appreciate what the particle-in-a-box model is telling them until they are asked to construct an energy-level diagram, graph the wave functions and probability densities, and reflect on what they have done. Even after those exercises, considerable additional understanding of quantum mechanics and appreciation for the physical relevance of this model are gained by having students apply the model in the analysis of cyanine dye spectra.

The use of the variational principle and method as ways of determining the atomic orbital coefficients in molecular orbitals are described. Yet explanations of why the approximate energy is always greater than the actual energy and why the desired result is obtained if the secular determinant is set equal to zero are lacking. Setting the secular determinant to zero is said to produce a polynomial, but it remains a mystery how this step is accomplished and how such polynomials are solved for the energies (p 161). A few pages later (p 163), in a discussion of the extended Hückel method, it is stated that the secular determinant is diagonalized to obtain the orbital energies and coefficients. Yet the term diagonalized is not defined, and nothing is said about why diagonalization produces the orbital energies and coefficients or why diagonalization is now used rather than solving a polynomial. At the end of this discussion, the reader is not asked to do anything with this information. Often students are frustrated when they are given much information that they do not understand or use. They may memorize this information for an exam, but little real learning occurs.

I once heard Richard Feynman tell a class, "If you want to learn about something, read a book. If you want to understand something, figure it out for yourself." Orbitals in Chemistry is the book to read if you want to learn something about atomic and molecular orbitals, but it does not provide the questions and problems that are necessary to guide the reader in developing a deep understanding of the material. In the preface (p ix), Gil says, "the reader is, thus, strongly, encouraged to solve the problems in the appropriate context (and compare his or her answers to those given at the end of the book), but it is not compulsory to do that in order to continue the reading and learning process."

The goal of the author therefore seems to be to present knowledge at the level of information, and this presentation is well done. To raise this knowledge to a higher level, as appropriate for courses in physical chemistry, the book would need to be supplemented heavily by questions, problems, and activities that more fully engage the reader in the learning process.