Hans H. Jaffé - Symmetry in Chemistry

The idea for the present book first took form when we were reviewing and rewriting the material discussed in Chapter 4 of our Theory and Applications of Ultraviolet Spectroscopy (John Wiley and Sons, New York, 1962). Although the classical topics involving symmetry considerations, such as optical activity, dipole moments, and conformational analysis, are usually adequately treated in chemistry texts used by students before they begin their first or second year of graduate work, we were struck by the paucity of comprehensive but essentially nonmathematical treatments of symmetry and group theory in such texts. We were convinced that, because symmetry arguments are such a powerful tool in the teaching of such concepts as hybridization, group and molecular orbitals, selection rules in absorption spectroscopy, and crystal structure, a small book devoted exclusively to symmetry in chemistry, developed in an essentially nonmathematical way, could be a great aid to students and research workers interested in these subjects. The growing importance of absorption spectroscopy, the enhanced status of structural inorganic chemistry, and the increasing popularity of molecular-orbital theory all indicate that an understanding of symmetry and elementary group theory will be an essential ingredient of the background of an educated chemist. We are convinced that most chemists will soon use point group and symmetry species notation with the same ease and understanding that practicing chemists now use conformational notation.

With these thoughts in mind, we started to organize the material for this book in November, 1962. Shortly after we began our work, the superb little book by F. A. Cotton appeared. Because his book covered many of the topics we had intended to cover, especially the application of group theory to electronic spectra, we shifted our emphasis a bit to make our book more complementary. Nevertheless, we did not depart from our basic objective, which was to provide a comprehensive but nonmathematical treatment of symmetry and its manifestations and applications.

After completing our first three chapters, which are completely nonmathematical, the reader will be able to classify readily almost any molecule under discussion into its appropriate point group. The technique of stereographic projections for symmetry elements in the various point groups is used extensively, because in our experience this technique facilitates the verification of multiple symmetry operations and is also useful for determining the classes of symmetry operations and order of the point group. In Chapter 4 we discuss translations and rotations of molecules under the symmetry operations appropriate to them. This discussion leads into the topics of symmetry species and character tables and the classification of normal vibrations and molecular orbitals. An elementary treatment of vectors and matrix algebra is included for readers who wish this refresher or for those who have not been exposed to these subjects. This discussion is kept to the bare minimum that will provide the background required for a qualitative understanding of group theory. In Chapter 5 we discuss some applications of symmetry and simple group theory to the generation of group orbitals, to the determination of the number of normal vibrations, and to the problem of selection rules in absorption spectroscopy. Chapter 6 is devoted to crystal symmetry, a subject seldom treated in chemical texts. In all chapters, digressions from the main arguments or discussion of the elementary mathematical concepts are set in small print so that readers familiar with such material can skip these sections without interrupting the main train of thought. The appendices provide complete character tables, tables giving the number of normal vibrations in various symmetry species, and tables showing the direct sums of excited states and combinations states of degenerate vibrations.

The book is intended as a supplementary text for both under-graduate and graduate students who seek a broad background for understanding structural problems. Thus use of the book can be synchronized with the growth of their interest and understanding. We hope the book will be particularly appealing to the large group of practicing chemists who completed their formal education before the applications of symmetry and group theory became so popular and so necessary for an understanding of the modern literature.