Symmetry in Chemistry

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