Charge and Energy Transfer Dynamics in Molecular Systems - May, Volkhard

. .

Résumé :

Preface to the Fourth Edition xiii

Preface to the Third Edition xv

Preface to the Second Edition xvii

Preface to the First Edition xix

1 Introduction 1

2 Electronic and Vibrational Molecular States 7

2.1 Introduction 7

2.2 Molecular Schr?dinger Equation 9

2.3 Born-Oppenheimer Separation 11

2.3.1 Born-Oppenheimer Approximation 13

2.4 Electronic Structure Methods 15

2.4.1 The Hartree-Fock Equations 17

2.4.2 Density Functional Theory 19

2.5 Potential Energy Surfaces 21

2.5.1 Harmonic Approximation and Normal Mode Analysis 24

2.5.2 Operator Representation of the Normal Mode Hamiltonian 27

2.5.3 Construction of System-Bath Models 31

2.6 Adiabatic versus Diabatic Representation of the Molecular Hamiltonian 36

2.6.1 Adiabatic Picture 36

2.6.2 Diabatic Picture 37

2.6.3 Two-State Case 40

2.7 Condensed-phase Approaches 42

2.7.1 Dielectric Continuum Model 43

2.7.1.1 Medium Electrostatics 43

2.7.1.2 Reaction Field Model 47

2.7.2 Explicit Quantum-classical Solvent Model 49

2.8 Supplement 51

2.8.1 Franck-Condon Factors 51

2.8.2 The Two-level System 52

2.8.3 The Linear Molecular Chain and the Molecular Ring 55

References 57

Further Reading 57

3 Dynamics of Isolated and Open Quantum Systems 59

3.1 Introduction 60

3.2 Time-dependent Schr?dinger Equation 66

3.2.1 Wave Packets 66

3.2.2 The Interaction Representation 69

3.2.3 Multidimensional Wave Packet Dynamics 71

3.3 The Golden Rule of Quantum Mechanics 75

3.3.1 Transition from a Single State into a Continuum 75

3.3.2 Transition Rate for a Thermal Ensemble 78

3.3.3 Green's Function Approach 81

3.4 The Nonequilibrium Statistical Operator and the Density Matrix 84

3.4.1 The Density Operator 84

3.4.2 The Density Matrix 86

3.4.3 Equation of Motion for the Density Operator 88

3.4.4 Wigner Representation of the Density Operator 90

3.4.5 Dynamics of Coupled Multilevel Systems in a Heat Bath 93

3.5 The Reduced Density Operator and the Reduced Density Matrix 96

3.5.1 The Reduced Density Operator 96

3.5.2 Equation of Motion for the Reduced Density Operator 97

3.5.3 Mean-field Approximation 98

3.5.4 The Interaction Representation of the Reduced Density Operator 99

3.5.5 The Nakajima-Zwanzig Equation 101

3.5.6 Second-order Equation of Motion for the Reduced Density Operator 105

3.6 Quantum Master Equation 107

3.6.1 Markov Approximation 109

3.7 The Reservoir Correlation Function 112

3.7.1 General Properties of C uv (t) 112

3.7.2 Harmonic Oscillator Reservoir 114

3.7.3 The Spectral Density 116

3.7.4 Linear Response Theory for the Reservoir 120

3.7.5 Classical Description of C uv (t) 122

3.8 Reduced Density Matrix in Energy Representation 123

3.8.1 The Quantum Master Equation in Energy Representation 123

3.8.2 Multilevel Redfield Equations 126

3.8.2.1 Population Transfer: a = b, c = d 127

3.8.2.2 Coherence Dephasing: a ? b, a = c, b = d 129

3.8.2.3 Remaining Elements of R ab,cd 129

3.8.3 The Secular Approximation 130

3.8.4 State Expansion of the System-Reservoir Coupling 131

3.8.4.1 Some Estimates 132

3.9 Coordinate and Wigner Representation of the Reduced Density Matrix 133

3.10 The Path Integral Representation of the Density Matrix 135

3.11 Hierarchy Equations of Motion Approach 140

3.12 Coherent to Dissipative Dynamics of a Two-level System 143

3.12.1 Coherent Dyn...

Biographie:

Volkhard May studied physics at Humboldt University, Berlin, and received his Ph.D. in Theoretical Physics in 1981, and his Habilitation at the College of Education, G?strow, in 1987. His research activities focused on the theory of transfer phenomena in molecular nanostructures. He is retired since 2019.

Oliver K?hn received his PhD from Humboldt University, Berlin. Since 2008 he is a Professor of Theoretical Physics at the University of Rostock. His current research focusses on dynamics of condensed phase systems such as molecular aggregates and novel materials....

Sommaire:
Charge and Energy Transfer Dynamics in Molecular Systems

Comprehensive resource offering knowledge on charge and energy transfer dynamics in molecular systems and nanostructures

Charge and Energy Transfer Dynamics in Molecular Systems provides a unified description of different charge and energy transfer phenomena in molecular systems with emphasis on the theory, bridging the regimes of coherent and dissipative dynamics and thus presenting classic rate theories as well as modern treatments of ultrafast phenomena. Starting from microscopic models, the common features of the different transfer processes are highlighted, along with applications ranging from vibrational energy flow in large polyatomic molecules, the motion of protons in solution, up to the concerted dynamics of electronic and nuclear degrees of freedom in molecules and molecular aggregates.

The newly revised and updated Fourth Edition contains a more detailed coverage of recent developments in density matrix theory, mixed quantum-classical methods for dynamics simulations, and a substantially expanded treatment of time-resolved spectroscopy.

The book is written in an easy-to-follow style, including detailed mathematical derivations, thus making even complex concepts understandable and applicable.

Charge and Energy Transfer Dynamics in Molecular Systems includes information on:

• Electronic and vibrational molecular states, covering molecular Schr?dinger equation, Born-Oppenheimer separation and approximation, Hartree-Fock equations and other electronic structure methods
• Dynamics of isolated and open quantum systems, covering multidimensional wave packet dynamics, and different variants of density operator equations
• Interaction of molecular systems with radiation fields, covering linear and nonlinear optical response using the correlation function approach
• Intramolecular electronic transitions, covering optical transition and internal conversion processes
• Transfer processes of electrons, protons, and electronic excitation energy

Providing in-depth coverage of the subject, Charge and Energy Transfer Dynamics in Molecular Systems is an essential resource for anyone working on timely problems of energy and charge transfer in physics, chemistry and biophysics as well as for all engaged in nanoscience and organic electronics....