Molecular Spectroscopy

Table of Contents
Introduction and Review
Historical Perspective
Definitions, Derivations and Discovery
Review of Quantum Mechanics
Approximate Solutions to the Schrödinger Equation: Variation and Perturbation Theory
Statistical Mechanics
Summary
Problems
Bibliography

The Nature of Electromagnetic Radiation
Introduction
The Classical Description of Electromagnetic Radiation
Propagation of Light in Matter
Quantum Mechanical Aspects of Light
Summary
Problems
Bibliography

Electric and Magnetic Properties of Molecules and Bulk Matter
Introduction
Electric Properties of Molecules
Electric Properties of Bulk Matter
Magnetic Properties of Matter
Summary
Problems
Bibliography

Time-dependent Perturbation Theory of Spectroscopy
Introduction: Time Dependence in Quantum Mechanics
Time-Dependent Perturbation Theory
Rate Expression for Emission
Perturbation Theory Calculation of Polarizability
Quantum Mechanical Expression for Emission Rate
Time Dependence of the Density Matrix
Summary
Problems
Bibliography

The Time-Dependent Approach to Spectroscopy
Introduction
Time-Correlation Functions and Spectra as Fourier-Transform Pairs
The Properties of Time-Correlation Functions and Spectral Lineshapes
The Fluctuation Dissipation Theorem
Rotational Correlation Functions and Pure Rotational Spectra
Reorientational Spectroscopy of Liquids: Single-Molecule and Collective Dynamics
Vibration-Rotation Spectra
Spectral Moments
Summary
Problems
Bibliography

Experimental Consideration: Absorption: Emission, and Scattering
Introduction
Einstein A and B Coefficients for Absorption and Emission
Absorption and Stimulated Emission
Electronic Absorption and Emission Spectroscopy
Measurement of Light Scattering: The Raman and Rayleigh Effects
Spectral Lineshapes
Summary
Problems
Bibliography

Atomic Spectroscopy
Introduction
Good Quantum Numbers and Not So Good Quantum Numbers
Selection Rules for Atomic Absorption and Emission
The Effect of External Fields
Atomic Lasers and The Principles of Laser Emission
Summary
Problems
Bibliography

Rotational Spectroscopy
Introduction
Energy Levels for Free Rigid Rotors
Angular Momentum Coupling in Non-1Σ Electronic States
Nuclear Statistics and the J states of Homonuclear Diatomics
Rotational Absorption and Emission Spectroscopy
Rotational Raman Spectroscopy
Corrections to the Rigid-Rotor Approximation
Internal Rotation
Summary
Problems
Bibliography

Vibrational Spectroscopy of Diatomic Molecules
Introduction
The Born-Oppenheimer Approximation and Its Consequences
The Harmonic Oscillator Model
Selection Rules for Vibrational Transitions
Beyond the Rigid-Rotor Harmonic Oscillator Approximation
Summary
Problems
Bibliography

Vibrational Spectroscopy of Polyatomics
Introduction
Normal Modes of Vibration
Quantum Mechanics of Polyatomic Vibrations
Group Theoretical Treatment of Vibrations
Selection Rules for Infrared Absorption and Raman Scattering: Group Theoretical Prediction of Activity
Rotational Structure
Anharmonicity
Selection Rules at Work: Benzene
Solvent Effects on Infrared Spectra
Summary
Problems
Bibliography

Electronic Spectroscopy
Introduction
Diatomic Molecules: Electronic State and Selection Rules
Vibrational Structure in Electronic Spectra and Diatomics
Born-Oppenheimer Breakdown in Diatomic Molecules
Polyatomic Molecules: Electronic States and Selection Rules
Transition Metal Complexes: Forbidden Transitions and the Jahn-Teller Effect
Emission Spectra of Polyatomic Molecules
Nonradiative Relaxation of Polyatomic Molecules
Chromophores
Solvent Effects in Electronic Spectroscopy
Summary
Problems
Bibliography

Raman and Resonance Raman Spectroscopy
Introduction
Selection Rules in Raman Scattering
Polarization in Raman Scattering
Rotational and Vibrational Dynamics in Raman Scattering
Analysis of Raman Excitation Profiles
Surface-Enhanced Raman ScatteringSummary
Problems
Bibliography

Nonlinear Optical Spectroscopy
Introduction
Classical Approaches to Nonlinear Optical Processes
Quantum Mechanical Approach to Nonlinear Optical Processes
Feynman Diagrams and Calculation of Time-Dependent Response Functions
Experimental Applications of Nonlinear Processes
Summary
Problems
Bibliography

Time-Resolved Spectroscopy
Introduction
Time-Resolved Fluorescence Spectroscopy
Time-Resolved Four Wave Mixing Experiments
Transient Grating and Photon Echo Experiments
Two-Dimensional Spectroscopy
Summary
Problems
Bibliography

Appendix A Math Review
Vectors and Tensors in Three Dimensions
Matrices
Operations with Cartesian and Spherical Tensors
Spherical Harmonics
Wigner Rotation Functions and Spherical Tensors
The Clebsch-Gordan Series and 3j Symbols

Appendix B Principles of Electrostatics
Units
Some Applications of Gauss’ Law
Some Mathematical Details

Appendix C Group Theory
Point Groups and Symmetry Operations
Information Conveyed by The Character Tables
Direct Products and Reducible Representations
Character Tables