Modern Optical Spectroscopy: From Fundamentals to Applications in Chemistry, Biochemistry and Biophysics

Contents
List of Boxes
1: Introduction
	1.1 Overview
	1.2 The Beer-Lambert Law
	1.3 Regions of the Electromagnetic Spectrum
	1.4 Absorption Spectra of Proteins and Nucleic Acids
	1.5 Absorption Spectra of Mixtures
	1.6 The Photoelectric Effect
	1.7 Techniques for Measuring Absorbance
	1.8 Pump-Probe and Photon-Echo Experiments
	1.9 Linear and Circular Dichroism
	1.10 Distortions of Absorption Spectra by Light Scattering or Nonuniform Distributions of the Absorbing Molecules
	1.11 Fluorescence
	1.12 IR and Raman Spectroscopy
	1.13 Lasers
	1.14 Nomenclature
	1.15 Questions
	References
2: Basic Concepts of Quantum Mechanics
	2.1 Wavefunctions, Operators and Expectation Values
		2.1.1 Wavefunctions
		2.1.2 Operators and Expectation Values
			Box 2.1 Operators for Observable Properties Must Be Hermitian
			Box 2.2 Commutators and Formulations of the Position, Momentum and Hamiltonian Operators
	2.2 The Time-Dependent and Time-Independent Schrödinger Equations
		Box 2.3 The Origin of the Time-Dependent Schrödinger Equation
		2.2.1 Superposition States
	2.3 Spatial Wavefunctions
		2.3.1 A Free Particle
		2.3.2 A Particle in a Box
			Box 2.4 Linear Momentum
		2.3.3 The Harmonic Oscillator
			Box 2.5 Hermite Polynomials
		2.3.4 Atomic Orbitals
		2.3.5 Molecular Orbitals
		2.3.6 Wavefunctions for Large Systems
	2.4 Spin Wavefunctions and Singlet and Triplet States
		Box 2.6 Boltzmann, Fermi-Dirac and Bose-Einstein Statistics
	2.5 Transitions Between States: Time-Dependent Perturbation Theory
	2.6 Lifetimes of States and the Uncertainty Principle
	2.7 Questions
	References
3: Light
	3.1 Electromagnetic Fields
		3.1.1 Electrostatic Forces and Fields
		3.1.2 Electrostatic Potentials
		3.1.3 Electromagnetic Radiation
			Box 3.1 Maxwell´s Equations and the Vector Potential
		3.1.4 Energy Density and Irradiance
		3.1.5 Electromagnetic Momentum
	3.2 The Black-Body Radiation Law
	3.3 Linear and Circular Polarization
	3.4 Quantum Theory of Electromagnetic Radiation
	3.5 Superposition States and Interference Effects in Quantum Optics
	3.6 Refraction, Evanescent Radiation, and Surface Plasmons
	3.7 The Classical Theory of Dielectric Dispersion
	3.8 Nonlinear Optics
	3.9 Birefringence and Electro-Optic Effects
	3.10 Optical Wavepackets and Mode-Locked Lasers
	3.11 Local-Field Correction Factors
	3.12 Questions
	References
4: Electronic Absorption
	4.1 Interactions of Electrons with Oscillating Electric Fields
		Box 4.1 Energy of a Dipole in an External Electric Field
		Box 4.2 Multipole Expansion of the Energy of a Set of Charges in a Variable External Field
	4.2 The Rates of Absorption and Stimulated Emission
		Box 4.3 The Behavior of the Function [exp(iy)-1]/y as y goes to 0
		Box 4.4 The Function sin2x/x2 and Its Integral
	4.3 Transition Dipoles and Dipole Strengths
		Box 4.5 The Oscillating Electric Dipole of a Superposition State
		Box 4.6 The Mean-Squared Energy of Interaction of an External Field with Dipoles in an Isotropic System
		Box 4.7 Physical Constants and Conversion Factors for Absorption of Light
	4.4 Calculating Transition Dipoles for π Molecular Orbitals
	4.5 The Role of Molecular Symmetry in Electronic Transitions
	4.6 Using Group Theory to Determine Whether a Transition Is Allowed by Symmetry
	4.7 Linear Dichroism
	4.8 Configuration Interactions
		Box 4.8 Evaluating Configuration-Interaction Coefficients
	4.9 Calculating Electric Transition Dipoles with the Gradient Operator
		Box 4.9 The Relationship between Matrix Elements of the Electric Dipole and Gradient Operators
		Box 4.10 Matrix Elements of the Gradient Operator for Atomic 2p Orbitals
		Box 4.11 Selection Rules for Electric-Dipole Excitations of Linear Polyenes
	4.10 Transition Dipoles for Excitations to Singlet and Triplet States
	4.11 The Born-Oppenheimer Approximation, Franck-Condon Factors, and the Shapes of Electronic Absorption Bands
		Box 4.12 Recursion Formulas for Vibrational Overlap Integrals
		Box 4.13 Thermally Weighted Franck-Condon Factors
	4.12 Spectroscopic Hole Burning
	4.13 Effects of the Surroundings on Molecular Transition Energies
	4.14 The Electronic Stark Effect
		Box 4.14 Electronic Stark Spectroscopy of Immobilized Molecules
	4.15 Spectroscopy of Transition-Metal Complexes
	4.16 Thermodynamics of Photoexcitation
	4.17 Questions
	References
5: Fluorescence
	5.1 The Einstein Coefficients for Absorption and Emission
	5.2 The Stokes Shift
	5.3 The Mirror-image Law
	5.4 The Strickler-Berg Equation and Other Relationships Between Absorption and Fluorescence
		Box 5.1 The ν3 Factor in the Strickler-Berg Equation
	5.5 Quantum Theory of Absorption and Emission
		Box 5.2 Creation and Annihilation Operators
	5.6 Fluorescence Yields and Lifetimes
	5.7 Fluorescent Probes and Tags
	5.8 Quantum Dot Fluorescence
	5.9 Photobleaching
	5.10 Fluorescence Anisotropy
	5.11 Single-molecule Fluorescence and High-resolution Fluorescence Microscopy
	5.12 Fluorescence Correlation Spectroscopy
		Box 5.3 Binomial, Poisson and Gaussian Distributions
	5.13 Intersystem Crossing, Phosphorescence, and Delayed Fluorescence
	5.14 Electron Transfer from Excited Molecules
	5.15 Solar Cells and Light-emitting Diodes
	5.16 Aggregation-induced Emission
	5.17 Questions
	References
6: Vibrational Absorption
	6.1 Vibrational Normal Modes and Wavefunctions
		Box 6.1 Normal Coordinates and Molecular-dynamics Simulations
	6.2 Vibrational Excitation
	6.3 Selection Rules and Effects of Anharmonicity
	6.4 Comparisons of IR and Raman Spectroscopy
	6.5 Effects of Molecular Symmetry in IR and Raman Spectroscopy
	6.6 Rotational Absorption and Fine Structure
	6.7 Infrared Spectroscopy of Proteins and Nucleic Acids
	6.8 Vibrational Stark Effects
	6.9 IR Lasers
	6.10 Questions
	References
7: Resonance Energy Transfer
	7.1 Introduction
	7.2 The Förster Theory
		Box 7.1 Dipole-dipole Interactions
	7.3 Using Energy Transfer to Study Fast Processes in Single Protein Molecules
	7.4 Exchange Coupling
	7.5 Energy Transfer in Photosynthetic Antennas
	7.6 Questions
	References
8: Exciton Interactions
	8.1 Stationary States of Systems with Interacting Molecules
		Box 8.1 Why Must the Secular Determinant Be Zero?
		Box 8.2 Avoided Crossings and Conical Intersections of Energy Surfaces
		Box 8.3 Exciton States Are Stationary in the Absence of Further Perturbations
	8.2 Effects of Exciton Interactions on the Absorption Spectra of Oligomers
		Box 8.4 The Sum Rule for Exciton Dipole Strengths
	8.3 Transition-Monopole Treatments of Interaction Matrix Elements and Mixing with Charge-Transfer Transitions
	8.4 Exciton Absorption Band Shapes and Dynamic Localization of Excitations
	8.5 Exciton States in Photosynthetic Antenna Complexes
	8.6 Excimers and Exciplexes
	8.7 Questions
	References
9: Circular Dichroism
	9.1 Magnetic Transition Dipoles and n - π Transitions
		Box 9.1 Quantum Theory of Magnetic-Dipole and Electric-Quadrupole Transitions
	9.2 The Origin of Circular Dichroism
		Box 9.2 Ellipticity and Optical Rotation
	9.3 Circular Dichroism of Dimers and Higher Oligomers
	9.4 UV Circular Dichroism of Proteins and Nucleic Acids
	9.5 Vibrational Circular Dichroism
	9.6 Magnetic Circular Dichroism
	9.7 Questions
	References
10: Coherence and Dephasing
	10.1 Oscillations Between Quantum States of an Isolated System
	10.2 The Density Matrix
		Box 10.1 Time Dependence of the Density Matrix for an Isolated Three-State System
	10.3 The Stochastic Liouville Equation
	10.4 Effects of Stochastic Relaxations on the Dynamics of Quantum Transitions
		Box 10.2 The ``Watched-Pot´´ or ``Quantum Zeno´´ Paradox
	10.5 A Density-Matrix Treatment of Absorption of Weak, Continuous Light
	10.6 The Relaxation Matrix
		Box 10.3 The Relaxation Matrix for a Two-State System
		Box 10.4 Dephasing by Static Inhomogeneity
	10.7 More General Relaxation Functions and Spectral Lineshapes
	10.8 Anomalous Fluorescence Anisotropy
		Box 10.5 Orientational Averages of Vector Dot Products
	10.9 Questions
	References
11: Pump-Probe Spectroscopy, Photon Echoes, Two-Dimensional Spectroscopy and Vibrational Wavepackets
	11.1 First-Order Optical Polarization
	11.2 Third-Order Optical Polarization and Non-linear Response Functions
	11.3 Pump-Probe Spectroscopy
	11.4 Photon Echoes
	11.5 Two-Dimensional Electronic and Vibrational Spectroscopy
	11.6 Transient Gratings
	11.7 Vibrational Wavepackets
	11.8 Wavepacket Pictures of Spectroscopic Transitions
	11.9 Questions
	References
12: Raman Scattering and Other Multi-photon Processes
	12.1 Types of Light Scattering
	12.2 The Kramers-Heisenberg-Dirac Theory
		Box 12.1 Quantum Theory of Electronic Polarizability
	12.3 The Wavepacket Picture of resonance Raman Scattering
	12.4 Selection Rules for Raman Scattering
	12.5 Surface-enhanced Raman Scattering
	12.6 Applications of Raman Spectroscopy
	12.7 Coherent (Stimulated) Raman Scattering
	12.8 Multi-photon Absorption
	12.9 Quasielastic (Dynamic) Light Scattering (Photon Correlation Spectroscopy)
	12.10 Mie scattering by Larger Particles
	12.11 Questions
	References
Appendix A
	Vectors
	Matrices
	Fourier Transforms
	Phase Shift and Modulation Amplitude in Frequency-Domain Spectroscopy
	CGS and SI Units and Abbreviations
	Harmonic-Oscillator Wavefunction Integrals
References
Index