Molecular Relaxation in Liquids

Chapter 1. Basic Concepts 1.1 Introduction 1.2 Response Functions and Fluctuations 1.3 Time Correlation Functions 1.4 Linear Response Theory 1.5 Fluctuation-Dissipation Theorem 1.6 Diffusion, Friction and Viscosity Chapter 2. Phenomenological Description of Relaxation in Liquids 2.1 Introduction 2.2 Langevin Equation 2.3 Fokker-Planck Equation 2.4 Smoluchowski Equation 2.5 Master Equations 2.6 The Special Case of Harmonic Potential Chapter 3. Density and Momentum Relaxation in Liquids 3.1 Introduction 3.2 Hydrodynamics at Large Length Scales 3.2.1 Rayleigh-Brillouin Spectrum 3.3 Hydrodynamic Relation Self-diffusion Coefficient and Viscosity 3.4 Slow Dynamics at Large Wavenumbers: de Gennes Narrowing 3.5 Extended Hydrodynamics: Dynamics at Intermediate Length Scale 3.6 Mode Coupling Theory Chapter 4. Relationship between Theory and Experiment 4.1 Introduction 4.2 Dynamic Light Scattering: Probe of Density Fluctuation at Long Length Scales 4.3 Magnetic Resonance Experiments: Probe of Single Particle Dynamics 4.4 Kerr Relaxation 4.5 Dielectric Relaxation 4.6 Fluorescence Depolarization 4.7 Solvation Dynamics (Time Dependent Fluorescence Stokes Shift) 4.8 Neutron Scattering: Coherent and Incoherent 4.9 Raman Lineshape Measurements 4.10 Coherent Anti-Stokes Raman Scattering (CARS) 4.11 Echo Techniques 4.12 Ultrafast Chemical Reactions 4.13 Fluorescence Quenching 4.14 Two-dimensional Infrared (2D IR) Spectroscopy 4.15 Single Molecule Spectroscopy Chapter 5. Orientational and Dielectric Relaxation 5.1 Introduction 5.2 Equilibrium and Time-Dependent Orientational Correlation Functions 5.3 Relationship with Experimental Observables 5.4 Molecular Hydrodynamic Description of Orientational Motion 5.4.1 The Equations of Motion 5.4.2 Limiting Situations 5.5 Markovian Theory of Collective Orientational Relaxation: Berne Treatment 5.5.1 Generalized Smoluchowski Equation Description 5.5.2 Solution by Spherical Harmonic Expansion 5.5.3 Relaxation of Longitudinal and Transverse Components 5.5.4 Molecular Theory of Dielectric Relaxation 5.5.5 Hidden Role of Translational Motion in Orientational Relaxation 5.5.6 Orientational de Gennes Narrowing at Intermediate Wave Numbers 5.5.7 Reduction to the Continuum Limit 5.6 Memory Effects in Orientational Relaxation 5.7 Relationship between Macroscopic and Microscopic Orientational Relaxations 5.8 The Special Case of Orientational Relaxation of Water Chapter 6. Solvation Dynamics in Dipolar Liquids 6.1 Introduction 6.2 Physical Concepts and Measurement 6.2.1 Measuring Ultrafast, Sub-100 fs Decay 6.3 Phenomenological Theories: Continuum Model Descriptions 6.3.1 Homogeneous Dielectric Models 6.3.2 Inhomogeneous Dielectric Models 6.3.3 Dynamic Exchange Model 6.4 Experimental Results: A Chronological Overview 6.4.1 Discovery of Multi-exponential Solvation Dynamics: Phase-I (1980-1990) 6.4.2 Discovery of Sub-ps Ultrafast Solvation Dynamics: Phase-II (1990-2000) 6.4.3 Solvation Dynamics in Complex Systems: Phase III (2000 - ) 6.5 Microscopic Theories 6.5.1 Molecular Hydrodynamics Description 6.5.2 Polarization and Dielectric Relaxation of Pure Liquid 6.5.2.1 Effects of Translational Diffusion in Solvation Dynamics 6.6 Simple Idealized Models 6.6.1 Overdamped Solvation: Brownian Dipolar Lattice 6.6.2 Underdamped Solvation: Stockmayer Liquid 6.7 Solvation Dynamics in Water, Acetonitrile and Methanol Revisited 6.7.1 The Sub 100 fs Ultrafast Component: Microscopic Origin 6.8 Effects of Solvation on Chemical Processes in the Solution Phase 6.8.1 Limiting Ionic Conductivity of Electrolyte Solutions: Control of a Slow Phenomenon by Ultrafast Dynamics 6.8.2 Effects of Ultrafast Solvation in Electron Transfer Reactions 6.8.3 Non-equilibrium Solvation Effects in Chemical Reaction 6.8.3.1 Strong Solvent Forces 6.8.3.2 Weak Solvent Forces 6.9 Solvation Dynamics in Several Related Systems 6.9.1 Solvation in Aqueous Electrolyte Solutions 6.9.2 Dynamics of Electron Solvation 6.9.3 Solvation Dynamics in Super-Critical Fluids 6.9.4 Nonpolar Solvation Dynamics 6.10 Computer Simulation Studies: Simple and Complex Systems Chapter 7. Activated Barrier Crossing Dynamics in Liquids 7.1 Introduction 7.2 Microscopic Aspects 7.2.1 Stochastic Models: Understanding from Eigenvalue Analysis 7.2.2 Validity of a Rate Law Description: Role of Macroscopic Fluctuations 7.2.3 Time Correlation Function Approach: Separation of Transient Behavior from Rate Law 7.3 Transition State Theory 7.4 Frictional Effects on Barrier Crossing Rate in Solution: Kramers' Theory 7.4.1 Low Friction Limit 7.4.2 Limitations of Kramers' Theory 7.4.3 Comparison of Kramers' Theory with Experiments 7.4.4 Comparison of Kramers' Theory with Computer Simulations 7.5 Memory Effects in Chemical Reactions: Grote-Hynes Generalization of Kramers' Theory 7.5.1 Frequency Dependence of Friction: General Aspects 7.5.1.1 Frequency Dependent Friction from Hydrodynamics 7.5.1.2 Frequency Dependent Friction from Mode Coupling Theory 7.5.2 Comparison of Grote-Hynes Theory with Experiments and Computer Simulations 7.6 Variational Transition State Theory 7.7 Multidimensional Reaction Surface 7.7.1 Multidimensional Kramers' Theory 7.8 Transition Path Sampling 7.9 Quantum Transition State Theory Appendix Chapter 8. Barrierless Reactions in Solutions 8.1 Introduction 8.2 Standard Models of Barrierless Reactions 8.2.1 Exactly Solvable Models for Photochemical Reactions 8.2.1.1 Oster-Nishijima Model 8.2.1.2 Staircase Model 8.2.1.3 Pinhole Sink Model 8.2.2 Approximate Solutions for Realistic Models 8.2.2.1 Delta Function Sink 8.2.2.2 Gaussian Sink 8.3 Inertial Effects in Barrierless Reactions: Viscosity Turnover of Rate 8.4 Memory Effects in Barrierless Reactions 8.5 Main Features of Barrierless Chemical Reactions 8.5.1 Excitation Wavelength Dependence 8.5.2 Negative Activation Energy 8.6 Multidimensional Potential Energy Surface 8.7 Analysis of Experimental Results 8.7.1 Photoisomerization and Ground State Potential Energy Surface 8.7.2 Decay Dynamics of Rhodopsin and Isorhodopsin 8.7.3 Conflicting Crystal Violet Isomerization Mechanism Chapter 9. Dynamical disorder, Geometric Bottlenecks and Diffusion Controlled Bimolecular Reactions 9.1 Introduction 9.2 Passage through Geometric Bottlenecks 9.2.1 Diffusion in a Two Dimensional Periodic Channel 9.2.2 Diffusion in a Random Lorentz Gas 9.3 Dynamical Disorder 9.4 Diffusion over a Rugged Energy Landscape 9.5 Diffusion Controlled Bimolecular Reactions Chapter 10. Electron Transfer Reactions 10.1 Introduction 10.2 Classification of Electron Transfer Reactions 10.2.1 Classification of Electron Transfer Reactions Based on Ligand Participation 10.2.2 Classification Based on Interactions between Reactant and Product Potential Energy Surfaces 10.3 Marcus Theory 10.3.1 Reaction Coordinate 10.3.2 Free Energy Surfaces: Force Constant of Polarization Fluctuation 10.3.3 Derivation of The Electron Transfer Reaction Rate 10.3.4 Experimental Verification Of Marcus Theory 10.4 Dynamical Solvent Effects on Electron Transfer Reactions (One Dimensional Descriptions) 10.5 Role of Vibrational Modes in Weakening Solvent Dependence 10.5.1 Role of Classical Intramolecular Vibrational Modes: Sumi-Marcus Theory 10.5.2 Role of High-Frequency Vibration Modes 10.5.3 Hybrid Model of Electron Transfer Reactions: Crossover from Solvent to Vibrational Control 10.6 Theoretical Formulation of Multi-Dimensional Electron Transfer 10.7 Effects of Ultrafast Solvation on Electron Transfer Reactions 10.7.1 Absence of Significant Dynamic Solvent Effects on ETR in Water, Acetonitrile & Methanol Appendix Chapter 11. Fõrster Resonance Energy Transfer 11.1 Introduction 11.2 A Brief Historical Perspective 11.3 Derivation of Förster Expression 11.3.1 Emission (or, Fluorescence) Spectrum 11.3.2 Absorption Spectrum 11.3.3 The Final Expression of Forster 11.4 Applications of Förster Theory in Chemistry, Biology and Material Science 11.4.1 FRET Based Glucose Sensor 11.4.2 FRET and Macromolecular Dynamics 11.4.3 FRET and Single Molecule Spectroscopy 11.4.4 FRET and Conjugated Polymers 11.5 Beyond Förster Formalism 11.5.1 Orientation Factor 11.5.2 Point Dipole Approximation 11.5.3 Optically Dark States Chapter 12. Vibrational Energy Relaxation 12.1 Introduction 12.2 Isolated Binary Collision (IBC) Model 12.3 Landau-Teller Expression: The Classical Limit 12.4 Weak Coupling Model: Time Correlation Function Representation of Transition Probability 12.5 Vibrational Relaxation at High Frequency: Quantum Effects 12.6 Experimental Studies of Vibrational Energy Relaxation 12.7 Computer Simulation Studies of Vibrational Energy Relaxation 12.7.1 Vibrational Energy Relaxation of Water 12.7.2 Vibrational Energy Relaxation in Liquid Oxygen and Nitrogen 12.8 Interference Effects on Vibrational Energy Relaxation on a Three Level Systems: Breakdown of the Rate Equation Description 12.9 Vibrational Life Time Dynamics in Supercritical Fluids Chapter 13. Vibrational Phase Relaxation 13.1 Introduction 13.2 Kubo-Oxtoby Theory of Vibrational Lineshapes 13.3 Homogeneous vs. Inhomogeneous Linewidths 13.4 Relative Role of Attractive and Repulsive Forces 13.5 Vibration-Rotation Coupling 13.6 Experimental Results of Vibrational Phase Relaxation 13.6.1 Semi-Quantitative Aspects of Dephasing Rates in Solution 13.6.2 Sub-Quadratic Quantum Number Dependence 13.7 Vibrational Dephasing Near Gas-Liquid Critical Point 13.8 Multidimensional IR Spectroscopy Chapter 14. Epilogue