Molecular Relaxation in Liquids

Biman Bagchi is Professor at the Indian Institute of Science in Bangalore, India.

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. Forster Resonance Energy Transfer ; 11.1 Introduction ; 11.2 A Brief Historical Perspective ; 11.3 Derivation of Forster 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 Forster 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 Forster 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