A Pictorial Approach to Molecular Bonding and Vibrations by John G. Verkade

Reviewed by Gabriela C. Weaver University of Colorado at Denver Chemistry Department, Campus Box 194, P. O. Box 173364, Denver, CO 80217-3364 gweaver@carbon.cudenver.edu

A Pictorial Approach to Molecular Bonding and Vibrations by John G. Verkade. 367 pages including index. ISBN 0-387-94811-2. 2nd Ed. 1997, Springer-Verlag, New York.

This textbook presents a method that does not require a detailed knowledge of group theory for predicting molecular orbital shapes and vibrational modes. This alternative method uses the symmetries of the canonical orbitals to generate linear combinations of atomic orbitals for molecules. The author introduces the concept of a "generator orbital," which is one of the s, p, or d orbitals used in an imaginary central position in the molecule, to predict the symmetries for the generated atomic orbital combinations. The method is quite intriguing, and successfully predicts both molecular orbitals and molecular vibrational modes quite well. Since the method is based on the idea of matching symmetries to those of the generator orbitals, it lends itself extremely well to visualization of the orbitals and motions being predicted. This visualization can be a valuable addition to the teaching of MO and normal-mode concepts.

The first three chapters are introductory, providing some review of the concepts needed to understand molecular orbitals. Chapter 1 covers the basic concepts of waves, electron orbitals, normalization, and orthogonality. Chapter 2 reviews the shapes of the canonical atomic orbitals and the concepts of orbital hybridization. It uses a very intuitive approach to predict the shapes of atomic orbitals from the number and orientation of the nodes. Chapter 3 is the first place where the generator orbitals are mentioned, and their use for generating molecular orbitals of simple diatomic molecules is illustrated. The remainder of the book applies the use of generator orbitals to systems of increasing complexity, with each chapter devoted to a particular molecular geometry or type of structure. The sequence begins with linear triatomic molecules and progresses through octahedral, tetrahedral, and other symmetries, culminating with polymers, cages, and solid-state materials.

The book includes a problem set with each chapter. The selection of problems provides a well-balanced combination of conceptual and calculation-based problems. In addition, many of the problems involve the use of pictorial methods for their solutions. One of the changes made with this edition of the text was the creation of a piece of software called Node Game, which can be freely downloaded from a provided WWW URL. Many of the problems in the chapter problem sets can be solved using Node Game and numerous references are made in the text to concepts that can be clarified by looking at them using the software. However, I did not find the use of the software very clear; overall it could benefit from more extensive instructions.

The author suggests that this textbook can be used across the undergraduate curriculum, beginning with general chemistry and including organic, inorganic, and physical chemistry. He proposes that the first six chapters can be used in general chemistry and then reviewed in physical chemistry. Portions of the other chapters are suggested as appropriate for the organic and inorganic courses. I believe, however, that the level and writing style of the book do not lend themselves well to providing the primary or initial instruction on those concepts covered in the text. For example, in Section 1.3 the author talks about conjugated p-bond systems in his introduction to waves, but most students will not have learned about these systems before their general chemistry class. In that section he also uses method of separation of variables when showing the solution for a time-independent wavefunction for a bound electron. Later he discusses probability amplitudes, uses the concept of normalization without any detailed explanation, and introduces the concept of building separate sets of orthonormal orbitals as possible solutions. These are ideas that I believe are too advanced for most first-year chemistry students to fully grasp and be able to use in the later chapters.

Much of the material in the book is dependent on an understanding of symmetry operations and elements. However, the author does not devote any space to discussing these. The construction of molecular orbitals from generator orbitals requires that one think about, or visualize, the effects of symmetry on the atomic orbitals being combined. It would be difficult for students to carry out the generator orbital method without having mastered these concepts first. Symmetry operations are taught by some instructors in the general chemistry curriculum, but certainly not by all of them. Thus, this particular omission is one of the issues that makes the book more appropriate for students who have already been exposed to many of the basic ideas of molecular orbital shapes, molecular orbital energies, bonding versus antibonding orbitals, hybridization, symmetry, and wavefunctions. I think this book is most appropriate for use with advanced students such as those in physical chemistry, senior inorganic chemistry, or at the graduate level. Even in those cases, this material would work best if it served as an accompaniment to the concepts normally taught in those courses. In that capacity, I believe this text provides some important intuitive approaches to molecular bonding and motion that could truly benefit students by increasing their understanding. It is an excellent way to ensure that students with varied learning styles can be served.

Overall, this is a good contribution to the educational literature that presents some novel and very useful approaches to teaching molecular bonding. It would serve as an excellent accompaniment to instruction in advanced undergraduate courses.