Symmetry and Spectroscopy: An Introduction to Vibrational and Electronic Spectroscopy

Description

Title Page Contents Preface Note on units and conventions 0. Opening remarks 1. A chemist’s view of group theory 1-1. Introduction 1-2. Symmetry Operations and Molecules 1-3. Groups 1-4. Point Groups 1-5. Classification of Molecules into Point Groups 1-6. Matrix Representation of Symmetry Operations 1-7. Characters and Character Tables 1-8. Decomposition of Reducible Representations and the Direct Product Additional Problems Related Reading 2. A skirmish with quantum mechanics 2-1. Introduction 2-2. Light A. Some Properties of Light B. Equations of Waves C. Absorption of Light 2-3. The Postulates of Quantum Mechanics A. Wave-Like Properties of Matter B. The Schrödinger Equation C. The Meaning of Ψ 2-4. Some Simple Illustrations from Quantum Mechanics A. The Particle in a One-Dimensional Box B. The Particle in a Three-Dimensional Box: Degeneracy of States C. The Uncertainty Principle D. Potential Barriers Related Reading 3. Vibrational spectroscopy 3-1. Introduction 3-2. Infrared and Raman Spectra A. The Phenomena B. A Molecular Explanation 3-3. Diatomic Molecules A. Rotation B. The Harmonic Oscillator C. The Anharmonic Oscillator D. The Quantum Mechanics of Vibration and Rotation E. The Population of Energy Levels F. Analysis of the Carbon Monoxide Spectrum G. The Effect of Temperature 3-4. Transitions between Stationary States 3-5. The Normal Modes of Vibration of Polyatomic Molecules 3-6. Selection Rules and Polarization A. What are Selection Rules? B. The Physical Basis of Selection Rules for Fundamental Transitions C. The Selection Rules in Action D. Polarization E. Overtones, Combination Bands, and Hot Bands F. Inversion Doubling 3-7. Symmetry Coordinates and Normal Modes 3-8. Stretching Mode Analysis 3-9. Assignment of Real Spectra 3-10. The Resonance Raman Effect 3-11. Functional Group Analysis Additional Problems Related Reading 4. Molecular orbital theory 4-1. Introduction 4-2. Atoms A. Atomic Orbitals B. Atomic Configurations 4-3. Photoelectron Spectroscopy 4-4. The LCAO Molecular Orbital Method 4-5. Diatomic Molecules 4-6. Polyatomic Molecules A. Carbon Dioxide B. Hydrogen Cyanide C. Ethylene D. Formaldehyde E. Methyl Cation, CH₃⁺ F. Electron Deficient Bonding 4-7. The Huckel Method 4-8. Transition Metal Complexes Additional Problems Related Reading 5. Electronic spectroscopy 5-1. Introduction 5-2. Another Look at Molecular Vibrations 5-3. Basic Notions A. Origin of Spectra B. Electronic Configurations C. Wave Functions, the Pauli Principle and Spin Degeneracy D. Stationary States 5-4. Selection Rules A. Transition Moments, Band Intensities, and the Franck-Condon Principle B. Spin-Selection Rules C. Orbital Selection Rules D. Vibronic Selection Rules 5-5. The Electronic Spectra of Some Diatomic Molecules A. Hydrogen B. Nitrogen C. Oxygen D. Spin-Orbit Splitting in the Photoelectron Spectra of the Dihalogens 5-6. The Fate of Absorbed Energy 5-7. Single Bonds, Double Bonds, and Lone Pairs A. Saturated Compounds B. Double Bonds C. Lone Pairs and Double Bonds D. Aromatic Compounds 5-8. Vibronic Analysis A. p-Difluorobenzene B. The 260 nm Absorption Band of Benzene C. The Phosphorescence of Benzene 5-9. Transition Metal Complexes A. Energy Levels and States B. d-d Spectra C. Charge Transfer 5-10. Concluding Remarks Additional Problems Related Reading Appendices Appendix A. Character tables Nonaxial Groups Cn Groups Cnv Groups Cnh Groups Dn Groups Dnd Groups Dnh Groups S2n Groups Cubic Groups Icosahedral Group Linear Groups Spherical Group Appendix B. Direct products Notes to Character Tables Direct products of imaginary characters Direct products of trigonometric functions Direct products in infinite point groups Appendix C. Overtones of degenerate vibrations Appendix D. The shapes of atomic orbitals Appendix E. Physical constants Appendix F. Energy conversions Appendix G. Answers to problems Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Index