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