Introduction to Group Theory with Applications

¿PrefaceAcknowledgmentsChapter 1 Symmetry Operations 1-1 Introduction 1-2 Point Symmetry Operations 1-3 The Stereographic Projection 1-4 The 32 Crystallographic Point Groups 1-5 Related Considerations 1-6 Space Group Example Notes ProblemsChapter 2 Group Concepts 2-1 Introduction 2-2 Definition of a Group 2-3 Symmetry Operations Form a Group 2-4 Related Group Concepts 2-5 Isomorphism and Homomorphism 2-6 Special Kinds of Groups 2-7 More Involved Group Concepts (including a Factor Group of a Space Group) Appendix to Chapter 2 Notes ProblemsChapter 3 Matrix Representations of Finite Groups 3-1 Introduction 3-2 Representations 3-3 Irreducible Representations 3-4 Representations of a Factor Group Appendix to Chapter 3 Notes ProblemsChapter 4 Characters of Matrix Representations of Finite Groups 4-1 Properties of Characters of Irreducible Representations 4-2 Character Tables 4-3 Reduction of a Reducible Representation 4-4 Basis Functions 4-5 Examples-Neumann Principle 4-6 Atomic Positions 4-7 The Hamiltonian Appendix to Chapter 4 Notes ProblemsChapter 5 Vibrations of Molecules and Crystals 5-1 3N Degrees of Freedom 5-2 General Considerations 5-3 Number and Type of Normal Modes for Molecules 5-4 Internal Coordinates 5-5 Crystals 5-6 Eigenvectors and Symmetry Adapted Vectors 5-7 Projection Operators 5-8 Projection Operators Applied to Normal Coordinates Notes ProblemsChapter 6 Normal Modes (Direct Product and Selection Rules) 6-1 Direct Product of Irreducible Representations 6-2 Vibrational Wave Function 6-3 Selection Rules-Infrared and Raman 6-4 Molecular Approximations (Site Symmetry and Davydov Splitting) Notes ProblemsChapter 7 Quantum Mechanics 7-1 Atomic Wave Functions 7-2 Transformation of Functions 7-3 Eigenfunctions as Basis Functions 7-4 Proper Rotations and Angular Momentum 7-5 Perturbations 7-6 Matrix Elements (Selection Rules) 7-7 General Secular Equation Problem Appendix to Chapter 7 Notes ProblemsChapter 8 Crystal Field Theory (and Atomic Physics) 8-1 Rotations in Terms of Euler Angles 8-2 Representations of the Full Rotation Group 8-3 Reduction of Symmetry 8-4 Energy Level Diagrams (Correlation Diagrams) 8-5 Crystal Double Groups 8-6 Correlation Diagrams including Double Groups 8-7 Other Crystal Field Effects Appendix to Chapter 8 Notes ProblemsChapter 9 Hybrid Functions 9-1 Introduction 9-2 Simple Hybrid Functions and Bonding 9-3 Tetrahedral Hybridization 9-4 Other Hybrid Functions 9-5 p-Hybrid Functions 9-6 Comment on Hybrid Orbitals (Slater Determinant) Notes ProblemsChapter 10 Molecular Orbital Theory 10-1 Hydrogen Molecular Ion 10-2 Simple MO Theory 10-3 Transition Metal Complexes 10-4 LCAO-MO of p-Electrons in Conjugated Hydrocarbons 10-5 Woodward-Hoffman Rules Notes ProblemsChapter 11 Symmetry of Crystal Lattices 11-1 The Real Affine Group 11-2 Space Group 11-3 Translational Lattice 11-4 International Tables for X-Ray Crystallography, International Notation, etc.