Symmetry and Spectroscopy

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