Charge and Energy Transfer Dynamics in Molecular Systems, 4e

Cover
Title Page
Copyright
Contents
Preface to the Fourth Edition
Preface to the Third Edition
Preface to the Second Edition
Preface to the First Edition
Chapter 1 Introduction
Chapter 2 Electronic and Vibrational Molecular States
2.1 Introduction
2.2 Molecular Schrödinger Equation
2.3 Born–Oppenheimer Separation
2.3.1 Born–Oppenheimer Approximation
2.4 Electronic Structure Methods
2.4.1 The Hartree–Fock Equations
2.4.2 Density Functional Theory
2.5 Potential Energy Surfaces
2.5.1 Harmonic Approximation and Normal Mode Analysis
2.5.2 Operator Representation of the Normal Mode Hamiltonian
2.5.3 Construction of System–Bath Models
2.6 Adiabatic versus Diabatic Representation of the Molecular Hamiltonian
2.6.1 Adiabatic Picture
2.6.2 Diabatic Picture
2.6.3 Two‐State Case
2.7 Condensed‐phase Approaches
2.7.1 Dielectric Continuum Model
2.7.1.1 Medium Electrostatics
2.7.1.2 Reaction Field Model
2.7.2 Explicit Quantum‐classical Solvent Model
2.8 Supplement
2.8.1 Franck–Condon Factors
2.8.2 The Two‐level System
2.8.3 The Linear Molecular Chain and the Molecular Ring
References
Further Reading
Chapter 3 Dynamics of Isolated and Open Quantum Systems
3.1 Introduction
3.2 Time‐dependent Schrödinger Equation
3.2.1 Wave Packets
3.2.2 The Interaction Representation
3.2.3 Multidimensional Wave Packet Dynamics
3.3 The Golden Rule of Quantum Mechanics
3.3.1 Transition from a Single State into a Continuum
3.3.2 Transition Rate for a Thermal Ensemble
3.3.3 Green's Function Approach
3.4 The Nonequilibrium Statistical Operator and the Density Matrix
3.4.1 The Density Operator
3.4.2 The Density Matrix
3.4.3 Equation of Motion for the Density Operator
3.4.4 Wigner Representation of the Density Operator
3.4.5 Dynamics of Coupled Multilevel Systems in a Heat Bath
3.5 The Reduced Density Operator and the Reduced Density Matrix
3.5.1 The Reduced Density Operator
3.5.2 Equation of Motion for the Reduced Density Operator
3.5.3 Mean‐field Approximation
3.5.4 The Interaction Representation of the Reduced Density Operator
3.5.5 The Nakajima–Zwanzig Equation
3.5.6 Second‐order Equation of Motion for the Reduced Density Operator
3.6 Quantum Master Equation
3.6.1 Markov Approximation
3.7 The Reservoir Correlation Function
3.7.1 General Properties of Cuv(t)
3.7.2 Harmonic Oscillator Reservoir
3.7.3 The Spectral Density
3.7.4 Linear Response Theory for the Reservoir
3.7.5 Classical Description of Cuv(t)
3.8 Reduced Density Matrix in Energy Representation
3.8.1 The Quantum Master Equation in Energy Representation
3.8.2 Multilevel Redfield Equations
3.8.2.1 Population Transfer: a=b, c=d
3.8.2.2 Coherence Dephasing: a≠b, a=c, b=d
3.8.2.3 Remaining Elements of Rab,cd
3.8.3 The Secular Approximation
3.8.4 State Expansion of the System–Reservoir Coupling
3.8.4.1 Some Estimates
3.9 Coordinate and Wigner Representation of the Reduced Density Matrix
3.10 The Path Integral Representation of the Density Matrix
3.11 Hierarchy Equations of Motion Approach
3.12 Coherent to Dissipative Dynamics of a Two‐level System
3.12.1 Coherent Dynamics
3.12.2 Dissipative Dynamics Using Eigenstates
3.12.3 Dissipative Dynamics Using Zeroth‐order States
3.13 Trajectory‐based Methods
3.13.1 The Mean‐field Approach
3.13.2 The Surface Hopping Method
3.14 Generalized Rate Equations: The Liouville Space Approach
3.14.1 Projection Operator Technique
3.14.2 Generalized Rate Equations
3.14.3 Rate Equations
3.14.4 The Memory Kernels
3.14.5 Second‐order Rate Expressions
3.14.6 Fourth‐order Rate Expressions
3.14.6.1 Three‐level System with Sequential Coupling
3.15 Supplement
3.15.1 Thermofield Dynamics
3.15.2 Stochastic Schrödinger Equation
References
Further Reading
Chapter 4 Interaction of Molecular Systems with Radiation Fields
4.1 Introduction
4.2 Absorption of Light
4.2.1 Linear Absorption Coefficient
4.2.2 Dipole–Dipole Correlation Function
4.3 Nonlinear Optical Response
4.3.1 Nonlinear Polarization
4.3.2 Nonlinear Response Functions
4.3.3 Eigenstate Expansion of the Response Functions
4.3.4 Cumulant Expansion of the Response Functions
4.3.5 Rotating Wave Approximation
4.3.6 Pump–Probe Spectroscopy
4.3.7 Two‐dimensional Spectroscopy
4.4 Field Quantization and Spontaneous Emission of Light
References
Further Reading
Chapter 5 Vibrational Dynamics: Energy Redistribution, Relaxation, and Dephasing
5.1 Introduction
5.2 Intramolecular Vibrational Energy Redistribution
5.2.1 Zeroth‐order Basis and State Mixing
5.2.2 Golden Rule and Beyond
5.3 Intermolecular Vibrational Energy Relaxation
5.3.1 The System–Reservoir Hamiltonian
5.3.2 Instantaneous Normal Modes
5.3.3 Generalized Langevin Equation
5.3.4 Classical Force–Force Correlation Functions
5.3.5 Dissipative Dynamics of a Harmonic Oscillator
5.4 Polyatomic Molecules in Solution
5.4.1 System–Reservoir Hamiltonian
5.4.2 Higher Order Multiquantum Relaxation
5.5 Quantum–Classical Approaches to Relaxation and Dephasing
References
Further Reading
Chapter 6 Intramolecular Electronic Transitions
6.1 Introduction
6.1.1 Optical Transitions
6.1.2 Internal Conversion Processes
6.2 The Optical Absorption Coefficient
6.2.1 Golden Rule Formulation
6.2.2 The Density of States
6.2.3 Absorption Coefficient for Harmonic Potential Energy Surfaces
6.2.4 Absorption Lineshape and Spectral Density
6.2.5 Cumulant Expansion of the Absorption Coefficient
6.2.6 Absorption Coefficient for Model Spectral Densities
6.3 Absorption Coefficient and Dipole–Dipole Correlation Function
6.3.1 Absorption Coefficient and Wave Packet Propagation
6.3.2 Absorption Coefficient and Reduced Density Operator Propagation
6.3.3 Mixed Quantum–Classical Computation of the Absorption Coefficient
6.4 The Emission Spectrum
6.5 Optical Preparation of an Excited Electronic State
6.5.1 Wave Function Formulation
6.5.1.1 Case of Short Pulse Duration
6.5.1.2 Case of Long Pulse Duration
6.5.2 Density Matrix Formulation
6.6 Internal Conversion Dynamics
6.6.1 The Internal Conversion Rate
6.6.2 Ultrafast Internal Conversion
6.7 Supplement
6.7.1 Absorption Coefficient for Displaced Harmonic Oscillators
References
Further Reading
Chapter 7 Electron Transfer
7.1 Classification of Electron Transfer Reactions
7.2 Theoretical Models for Electron Transfer Systems
7.2.1 The Electron Transfer Hamiltonian
7.2.2 The Electron–Vibrational Hamiltonian of a Donor–Acceptor Complex
7.2.2.1 The Spin‐Boson Model
7.2.2.2 Two Independent Sets of Vibrational Coordinates
7.2.3 Electron–Vibrational State Representation of the Hamiltonian
7.3 Regimes of Electron Transfer
7.3.1 Landau–Zener Theory of Electron Transfer
7.4 Nonadiabatic Electron Transfer in a Donor–Acceptor Complex
7.4.1 High‐temperature Case
7.4.2 High‐temperature Case: Two Independent Sets of Vibrational Coordinates
7.4.3 Low‐temperature Case: Nuclear Tunneling
7.4.4 The Mixed Quantum–Classical Case
7.4.5 Description of the Mixed Quantum–Classical Case by a Spectral Density
7.5 Bridge‐Mediated Electron Transfer
7.5.1 The Superexchange Mechanism
7.5.2 Electron Transfer Through Arbitrary Large Bridges
7.5.2.1 Case of Small Intrabridge Transfer Integrals
7.5.2.2 Case of Large Intrabridge Transfer Integrals
7.6 Nonequilibrium Quantum Statistical Description of Electron Transfer
7.6.1 Unified Description of Electron Transfer in a Donor–Bridge–Acceptor System
7.6.2 Transition to the Adiabatic Electron Transfer
7.7 Heterogeneous Electron Transfer
7.7.1 Nonadiabatic Charge Injection into the Solid State Described in a Single‐Electron Model
7.7.1.1 Low‐temperature Case
7.7.1.2 High‐temperature Case
7.7.1.3 HET‐induced Lifetime
7.7.2 Ultrafast Photoinduced HET from a Molecule into a Semiconductor. A Case Study
7.7.3 Nonadiabatic Electron Transfer from the Solid State into the Molecule
7.8 Charge Transmission Through Single Molecules
7.8.1 Inelastic Charge Transmission
7.8.1.1 An Example
7.8.2 Elastic Charge Transmission
7.8.2.1 An Example
7.8.2.2 Inclusion of Vibrational Levels
7.9 Photoinduced Ultrafast Electron Transfer
7.9.1 Quantum Master Equation for Electron Transfer Reactions
7.9.2 Rate Expressions
7.10 Supplement
7.10.1 Landau–Zener Transition Amplitude
7.10.2 The Multimode Marcus Formula
7.10.3 Second‐order Electron Transfer Rate
7.10.4 Fourth‐order Donor–Acceptor Transition Rate
7.10.5 Rate of Elastic Charge Transmission Through a Single Molecule
References
Further Reading
Chapter 8 Proton Transfer
8.1 Introduction
8.2 Proton Transfer Hamiltonian
8.2.1 Hydrogen Bonds
8.2.2 Reaction Surface Hamiltonian for Intramolecular Proton Transfer
8.2.3 Tunneling Splittings
8.2.4 The Proton Transfer Hamiltonian in the Condensed Phase
8.2.4.1 Adiabatic Representation
8.2.4.2 Diabatic Representation
8.3 Adiabatic Proton Transfer
8.4 Nonadiabatic Proton Transfer
8.5 The Intermediate Regime: From Quantum to Quantum–Classical Hybrid Methods
8.5.1 Multidimensional Wave Packet Dynamics
8.5.2 Surface Hopping
8.6 Proton‐coupled Electron Transfer
References
Further Reading
Chapter 9 Excitation Energy Transfer
9.1 Introduction
9.2 The Aggregate Hamiltonian
9.2.1 The Intermolecular Coulomb Interaction
9.2.1.1 Dipole–Dipole Coupling
9.2.2 The Two‐level Model
9.2.2.1 Classification of the Coulomb Interactions
9.2.3 Single and Double Excitations of the Aggregate
9.2.3.1 The Ground State Matrix Element
9.2.3.2 The Single Excited State Matrix Elements
9.2.3.3 The Double Excited State Matrix Elements
9.2.3.4 Off‐Diagonal Matrix Elements and Coupling to the Radiation Field
9.2.3.5 Neglect of Intermolecular Electrostatic Coupling
9.2.4 Introduction of Delocalized Exciton States
9.2.4.1 The Molecular Heterodimer
9.2.4.2 The Finite Molecular Chain and the Molecular Ring
9.3 Exciton–Vibrational Interaction
9.3.1 Exclusive Coupling to Intramolecular Vibrations
9.3.2 Coupling to Aggregate Normal Mode Vibrations
9.3.3 Differentiating Between Intramolecular and Reservoir Normal Mode Vibrations
9.3.4 Exciton–Vibrational Hamiltonian and Excitonic Potential Energy Surfaces
9.4 Regimes of Excitation Energy Transfer
9.4.1 Quantum Statistical Approaches to Excitation Energy Transfer
9.5 Transfer Dynamics in the Case of Weak Excitonic Coupling: Förster Theory
9.5.1 The Transfer Rate
9.5.2 The Förster Rate
9.5.3 Nonequilibrium Quantum Statistical Description of Förster Transfer
9.5.3.1 Case of Common Vibrational Coordinates
9.5.3.2 Case of Vibrational Modulation of the Excitonic Coupling
9.6 Transfer Dynamics in the Case of Strong Excitonic Coupling
9.6.1 Rate Equations for Exciton Dynamics
9.6.2 Density Matrix Equations for Exciton Dynamics
9.6.3 Site Representation
9.6.4 Excitation Energy Transfer Among Different Aggregates
9.6.5 Exciton Transfer in the Case of Strong Exciton–Vibrational Coupling
9.6.6 Nonperturbative and Non‐Markovian Exciton Dynamics
9.7 Optical Properties of Aggregates
9.7.1 Case of No Exciton–Vibrational Coupling
9.7.1.1 Static Disorder
9.7.2 Inclusion of Exciton–Vibrational Coupling
9.7.2.1 The n‐Particle Expansion
9.7.2.2 Weak Exciton–Vibrational Coupling
9.7.2.3 Strong Exciton–Vibrational Coupling
9.8 Excitation Energy Transfer Including Charge‐transfer States
9.8.1 Excitation Energy Transfer Via Two‐electron Exchange
9.8.2 Charge‐transfer Excitons and Charge Separation
9.9 Exciton–Exciton Annihilation
9.9.1 Three‐level Description of the Molecules in the Aggregate
9.9.2 The Rate of Exciton–Exciton Annihilation
9.10 Supplement
9.10.1 Second Quantization Notation of the Aggregate Hamiltonian
9.10.2 Photon‐mediated Long‐range Excitation Energy Transfer
9.10.2.1 Preparatory Considerations for the Rate Computation
9.10.2.2 Photon Correlation Functions
9.10.2.3 The Rate of Photon‐mediated Excitation Energy Transfer
9.10.2.4 Some Estimates
9.10.3 Fourth‐order Rate of Two‐electron‐transfer‐assisted EET
References
Further Reading
Index
EULA