Symmetry in Chemistry by Hans H. Jaffe, Milton Orchin, Jaffe
Because symmetry arguments are a powerful tool in teaching such concepts as hybridization, group and molecular orbitals, selection rules in absorption spectroscopy, crystal structure, and other topics, a book devoted exclusively to symmetry in chemistry, developed in an essentially nonmathematical way, is a must for students and research workers interested in these subjects. This is such a book. After an introduction to symmetry, the authors offer lucid discussions of symmetry elements and operations, multiple symmetry operations, multiplication tables and point groups, group theory, applications, and crystal symmetry. Three appendices provide complete character tables, tables of the number of normal vibrations in various symmetry species, and tables showing the direct sums of excited states and combination states of degenerate vibrations. Intended as a supplementary text for both undergraduate and graduate students who seek a broad background for understanding structural problems, this concise treatment will also appeal to the large group of practicing chemists who wish to review the applications of symmetry and group theory.
1. Introduction 1.1 Symmetry as a Universal theme 1.2 Symmetry in Chemistry 1.3 Coordinate systems 2. Symmetry Elements and Symmetry Operations 2.1 Rotation about a Symmetry Axis 2.2 Inversion (or Reflection) at a Center of Symmetry 2.3 Reflection at a Plane of Symmetry (Mirror Plane) 2.4 Rotation about an Axis, Followed by Reflection at a Plane Normal to This Axis 2.5 Rotation-Inversion Axes 2.6 The Identity 2.7 Symmetry Properties of Orbitals 2.8 The Relation Between Symmetry and Optical Activity 3. Multiple Symmetry Operations. Multiplication Tables and Point Groups 3.1 Groups 3.2 Multiplication of Operations 3.3 Stereographic Projections 3.4 Multiplication Tables 3.5 Point Groups 3.6 Rules for Classification into Point Groups 3.7 Equivalent Atoms 4. Group Theory 4.1 Nondegenerate Point Groups 4.2 Degenerate Point Groups 4.3 Classes of Operations 5. Applications 5.1 Group Orbitals 5.2 Number of Normal Vibrations 5.3 Selection Rules and Polarization. The Direct Product 6. Crystal Symmetry 6.1 The Solid State 6.2 Plane Lattices and Plane Groups 6.3 Space Lattices and Space Groups 6.4 Close Packing Appendix 1. Character Tables Appendix 2. The Number of Normal Vibrations in Various Symmetry Species Appendix 3. The Direct Sums of Excited States and Combination States of Degenerate Vibrations Index