Charge and Energy Transfer Dynamits in Molecular Systems

Transcription

1 Volkhard May, Oliver Kühn Charge and Energy Transfer Dynamits in Molecular Systems Second, Revised and Enlarged Edition WILEY- VCH WILEY-VCH Verlag GmbH & Co. KGaA

2 Contents 1 Introduction 19 2 Electronic and Vibrational Molecular States Introduction Molecular Schrödinger Equation Born Oppenheimer Separation Electronic Structure Methods Dielectric Continuum Model Medium Electrostatics Reaction Field Model Potential Energy Surfaces Harmonic Approximation and Normal Mode Analysis Operator Representation of the Normal Mode Hamiltonian Reaction Paths Diabatic versus Adiabatic Representation of the Molecular Hamiltonian Supplement The Hartree Fock Equations Franck Condon Factors The Two Level System The Linear Molecular Chain and the Molecular Ring 77 3 Dynamics of Isolated and Open Quantum Systems Introduction Time Dependent Schrödinger Equation The Time Evolution Operator The Interaction Representation The Golden Rule of Quantum Mechanics Transition from a Single State into a Continuum Transition Rate for a Thermal Ensemble The Nonequilibrium Statistical Operator and the Density Matrix The Density Operator The Density Matrix Equation of Motion for the Density Operator Wigner Representation of the Density Operator Dynamics of Coupled Multi Level Systems in a Heat Bath 108

3 14 Contents 3.5 The Reduced Density Operator and the Reduced Density Matrix The Reduced Density Operator Equation of Motion for the Reduced Density Operator Mean Field Approximation The Interaction Representation of the Reduced Density Operator The Projection Operator Second Order Equation of Motion for the Reduced Statistical Operator The Reservoir Correlation Function General Properties of Ca (t) Harmonic Oscillator Reservoir Nonlinear Coupling to a Harmonie Oscillator Reservoir The Spectral Density Linear Response Theory for the Reservoir Classical description of C., (t) Quantum Master Equation Markov Approximation Reduced Density Matrix in Energy Representation The Quantum Master Equation in Energy Representation Multi Level Redfield Equations The Secular Approximation State Expansion of the System Reservoir Coupling Model for Pure Dephasing Processes Some Estimates From Coherent to Dissipative Dynamics: A Simple Example Coordinate and Wigner Representation of the Reduced Density Matrix Generalized Rate Equations: The Liouville Space Approach Projection Operator Technique Rate Equations Perturbational Expansion of the Rate Expressions The Path Integral Representation of the Density Matrix Quantum Classical Hybrid Methods The Mean Field Approach The Surface Hopping Method Partial Wigner Representation as a Quantum Classical Hybrid Method Supplement Different Equations of Motion for the Reduced Density Operator Correlation Function for Nonlinear Couplings to the Reservoir Limit of Ultrashort Reservoir Correlation Time Markov Approximation and the Factorized Part of the Reservoir Correlation Function Numerical Propagation Methods The Monte Carlo Wave Function Method Vibrational Energy Redistribution and Relaxation Introduction 196

4 Contents Intramolecular Energy Redistribution Zeroth Order Basis Golden Rule and Beyond Intermolecular Vibrational Energy Relaxation Diatomic Molecule in Solid State Environment Diatomic Molecules in Polyatomic Solution Polyatomic Molecules in Solution System Bath Hamiltonian Higher Order Multi Quantum Relaxation Supplement Coherent Wave Packet Motion in a Harmonic Oscillator Intramolecular Electronic Transitions Introduction Optical Transitions Internal Conversion Processes The Optical Absorption Coefficient Basic Theoretical Concepts Golden Rule Formulation The Density of States Absorption Coefficient for Harmonic Potential Energy Surfaces Absorption Lineshape and Spectral Density Time Dependent Formulation of the Absorption Coefficient Dipole Dipole Correlation Function Absorption Coefficient and Wave Packet Propagation Cumulant Expansion of the Absorption Coefficient Absorption Coefficient and Reduced Density Operator Propagation Quasi Classical Computation of die Absorption Coefficient The Rate of Spontaneous Emission Optical Preparation of an Excited Electronic State Wave Function Formulation Density Matrix Formulation Nonlinear Optical Response Nonlinear Susceptibilities Internal Conversion Dynamics The Internal Conversion Rate Ultrafast Internal Conversion Supplement Absorption Coefficient for Displaced Harmonic Oscillators Cumulant Expansion for Harmonie Potential Energy Surfaces Electron Transfer Introduction Theoretical Models for Electron Transfer Systems The Electron Transfer Hamiltonian 296

5 16 Contents The Electron Vibrational Hamiltonian of a Donor Acceptor Complex Two Independent Sets of Vibrational Coordinates State Representation of the Hamiltonian Regimes of Electron Transfer Landau Zener Theory of Electron Transfer Nonadiabatic Electron Transfer in a Donor Acceptor Complex High Temperature Case High Temperature Case: Two Independent Sets of Vibrational Coordinates Low Temperature Case: Nuclear Tunneling The Mixed Quantum Classical Case Description of the Mixed Quantum Classical Case by a Spectral Density Nonadiabatic Electron Transfer in Polar Solvents The Solvent Polarization Field and the Dielectric Function The Free Energy of the Solvent The Rate of Nonadiabatic Electron Transfer in Polar Solvents Bridge Assisted Electron Transfer The Superexchange Mechanism Electron Transfer Through Long Bridges Nonequilibrium Quantum Statistical Description of Electron Transfer Unified Description of Electron Transfer in a Donor Bridge Acceptor System Transition to the Adiabatic Electron Transfer Photoinduced Ultrafast Electron Transfer Quantum Master Equation for Electron Transfer Reactions Rate Expressions Supplement Landau Zener Transition Amplitude The Multi Mode Marcus Formula The Free Energy Functional of the Solvent Polarization Second Order Electron Transfer Rate Fourth Order Donor Acceptor Transition Rate Proton Transfer Introduction Proton Transfer Hamiltonian Hydrogen Bonds Reaction Surface Hamiltonian for Intramolecular Proton Transfer Tunneling Splittings The Proton Transfer Hamiltonian in the Condensed Phase Adiabatic Proton Transfer Nonadiabatic Proton Transfer The Intermediate Regime: From Quantum to Quantum Classical Hybrid Methods Multidimensional Wave Packet Dynamics 399

6 Contents Surface Hopping Exciton Transfer Introduction The Exciton Hamiltonian The Two Level Model Single and Double Excitations of the Aggregate Delocalized Exciton States Exciton Vibrational Interaction Coupling to Intramolecular Vibrations Coupling to Aggregate Normal Mode Vibrations Exciton Vibrational Hamiltonian and Excitonic Potential Energy Surfaces Regimes of Exciton Transfer Förster Theory of Incoherent Exciton Transfer The Förster Transfer Rate Nonequilibrium Quantum Statistical Description of Förster Transfer Energy Transfer Between Delocalized States Transfer Dynamics in the Case of Weak Exciton Vibrational Coupling Site Representation Energy Representation The Aggregate Absorption Coefficient Absence of Exciton Vibrational Coupling Static Disorder Limit of Weak Exciton Vibrational Coupling Supplement Exciton Exciton Annihilation Laser Control of Charge and Energy Transfer Dynamics Introduction Optimal Control Theory The Control Functional and the Control Field Mixed State and Dissipative Dynamics Iterative Determination of the Optimal Pulse Laser Pulse Control of Particle Transfer Infrared Laser Pulse Control of Proton Transfer Controlling Photoinduced Electron Transfer Supplement Dissipative Backward Time Evolution Suggested Reading 481 Index 487