Preface |
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v | |
User's Guide |
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vii | |
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xxiii | |
Abbreviations |
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xxix | |
Notation |
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xxxiii | |
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1 | (16) |
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1 | (2) |
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One-to-One Correspondence |
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3 | (3) |
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Time-Dependent Kohn-Sham Equations |
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6 | (2) |
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8 | (2) |
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Adiabatic Connection Formula |
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10 | (1) |
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11 | (1) |
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Relation to Ground-State DFT |
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12 | (5) |
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Beyond the Runge-Gross Theorem |
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17 | (16) |
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17 | (1) |
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The Extended Runge-Gross Theorem: Different Interactions and Initial States |
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17 | (6) |
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Invertibility of the Linear Density Response Function |
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23 | (5) |
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Consequences of v-Representability for the Quantum Mechanical Action |
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28 | (5) |
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Introduction to the Keldysh Formalism |
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33 | (28) |
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33 | (1) |
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34 | (2) |
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Nonequilibrium Green Functions |
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36 | (2) |
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38 | (4) |
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The Kadanoff-Baym Equations |
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42 | (2) |
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Example: H2 in An Electric Field |
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44 | (2) |
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Conserving Approximations |
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46 | (3) |
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49 | (4) |
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Action Functional and TDDFT |
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53 | (4) |
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Example: Time-Dependent OEP |
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57 | (4) |
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Initial-State Dependence and Memory |
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61 | (14) |
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61 | (2) |
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History Dependence: An Example |
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63 | (1) |
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64 | (5) |
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Memory: An Exact Condition |
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69 | (2) |
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Role of Memory in Quantum Control Phenomena |
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71 | (3) |
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74 | (1) |
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Current Density Functional Theory |
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75 | (18) |
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75 | (1) |
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First Hints of Ultranonlocality: The Harmonic Potential Theorem |
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76 | (1) |
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77 | (3) |
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Current Density Functional Theory |
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80 | (1) |
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The xc Vector Potential for The Homogeneous Electron Liquid |
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81 | (4) |
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The xc Vector Potential for the Inhomogeneous Electron Liquid |
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85 | (1) |
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86 | (7) |
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Multicomponent Density-Functional Theory |
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93 | (14) |
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93 | (1) |
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93 | (4) |
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Definition of the Densities |
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96 | (1) |
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The Runge-Gross Theorem for Multicomponent Systems |
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97 | (1) |
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The Kohn-Sham Scheme for Multicomponent Systems |
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98 | (1) |
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The Multicomponent Action |
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99 | (3) |
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Linear Response and Multicomponent Systems |
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102 | (1) |
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103 | (3) |
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106 | (1) |
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Intermolecular Forces and Generalized Response Functions in Liouville Space |
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107 | (16) |
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107 | (1) |
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Quantum Dynamics in Liouville Space; Superoperators |
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108 | (3) |
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TDDFT Equations of Motion for the GRFs |
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111 | (1) |
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Collective Electronic Oscillator Representation of the GRF |
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112 | (4) |
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GRF Expressions for Intermolecular Interaction Energies |
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116 | (7) |
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Part II Approximate Functionals |
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Time-Dependent Deformation Approximation |
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123 | (14) |
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123 | (2) |
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DFT as Exact Quantum Continuum Mechanics |
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125 | (2) |
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Conservation Laws and the Hydrodynamic Formulation of DFT |
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125 | (1) |
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Definition of the xc Potentials |
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126 | (1) |
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Geometric Formulation of TDDFT |
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127 | (4) |
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Preliminaries: Static LDA vs. Time-Dependent LDA |
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127 | (2) |
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TDDFT in the Lagrangian Frame |
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129 | (2) |
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Time-Dependent Local Deformation Approximation |
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131 | (6) |
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General Formulation of the TDLDefA |
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131 | (1) |
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132 | (1) |
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Inclusion of Correlations: Elastic TDLDefA |
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133 | (4) |
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Exact-Exchange Methods and Perturbation Theory along the Adiabatic Connection |
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137 | (24) |
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137 | (3) |
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Exact Exchange Methods and Static Perturbation Theory |
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140 | (9) |
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Perturbation Theory along the Adiabatic Connection and the Static Exact Exchange Equation |
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140 | (3) |
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Implementations of Static Exact Exchange KS Methods |
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143 | (2) |
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Static Effective Exact Exchange KS Methods |
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145 | (4) |
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Time-Dependent Perturbation Theory and the Exact Exchange Kernel |
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149 | (12) |
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Time-Dependent Perturbation Theory along the Adiabatic Connection and the Time Dependent Exact Exchange Equation |
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149 | (4) |
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The Exact Exchange Kernel |
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153 | (8) |
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Approximate Functionals from Many-Body Perturbation Theory |
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161 | (20) |
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161 | (1) |
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Hedin's Equations and the Vertex Function |
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162 | (4) |
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The Bethe-Salpeter Equation |
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164 | (2) |
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The xc Kernel: Different Schemes Based on MBPT |
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166 | (7) |
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Static Long-Range Kernels |
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167 | (1) |
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168 | (3) |
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The fxc Perturbative Series: Convergence and Cancellations |
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171 | (2) |
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The Vertex Function Γ: a TDDFT-Based Approach |
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173 | (6) |
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Including Density-Functional Concepts into MBPT |
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178 | (1) |
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Conclusions and Perspectives |
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179 | (2) |
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181 | (16) |
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181 | (1) |
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Review of the Ground State |
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181 | (3) |
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181 | (1) |
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182 | (1) |
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Uniform and Nearly Uniform Gas |
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183 | (1) |
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Finite Versus Extended Systems |
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183 | (1) |
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183 | (1) |
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Conditions and Approximations |
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184 | (1) |
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184 | (1) |
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185 | (1) |
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185 | (3) |
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185 | (1) |
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186 | (1) |
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187 | (1) |
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187 | (1) |
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Coupling-Constant Dependence |
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188 | (1) |
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188 | (1) |
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188 | (3) |
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188 | (1) |
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189 | (1) |
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189 | (1) |
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189 | (1) |
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Coupling-Constant Dependence |
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189 | (1) |
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190 | (1) |
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190 | (1) |
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191 | (1) |
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Finite Versus Extended Systems, and Currents |
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191 | (1) |
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Gradient Expansion in the Current |
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192 | (1) |
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Response to Homogeneous Field |
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192 | (1) |
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192 | (1) |
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192 | (1) |
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Infinite Lifetimes of Eigenstates |
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192 | (1) |
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Single-Pole Approximation for Exchange |
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193 | (1) |
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Memory Correlation Approximations |
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193 | (1) |
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Double Excitations and Branch Cuts |
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193 | (1) |
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193 | (1) |
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194 | (3) |
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Part III Numerical Aspects |
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12 Propagators for the Time-Dependent Kohn-Sham Equations |
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197 | (14) |
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197 | (2) |
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Formulation of the Problem |
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199 | (2) |
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Approximations to the Exponential of an Operator |
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201 | (3) |
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202 | (1) |
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Krylov Subspace Projection |
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203 | (1) |
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204 | (1) |
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Analysis of Integrators for the TDSE |
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204 | (5) |
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``Classical'' Propagators |
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205 | (1) |
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Exponential Midpoint Rule |
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206 | (1) |
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Time-Reversal Symmetry Based Propagator |
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206 | (1) |
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206 | (1) |
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207 | (2) |
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209 | (2) |
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Solution of the Linear-Response Equations in a Basis Set |
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211 | (6) |
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211 | (1) |
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An Expansion in Orbital Products |
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211 | (1) |
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An Efficient Solution Scheme |
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212 | (5) |
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Excited-State Dynamics in Finite Systems and Biomolecules |
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217 | (10) |
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217 | (1) |
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Lagrangian of the Excited State Energy |
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218 | (2) |
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Lagrange Multipliers and Relaxed One-Particle Density Matrix |
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220 | (2) |
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222 | (2) |
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Coupling to Classical Force Fields |
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224 | (3) |
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Time Versus Frequency Space Techniques |
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227 | (16) |
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227 | (2) |
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228 | (1) |
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229 | (2) |
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231 | (2) |
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233 | (1) |
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Response Equation in Momentum/Frequency Space |
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234 | (2) |
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Space-Time Method for Response Calculations |
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236 | (2) |
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238 | (5) |
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Part IV Applications: Linear Response |
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Linear-Response Time-Dependent Density Functional Theory for Open-Shell Molecules |
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243 | (16) |
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243 | (2) |
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245 | (5) |
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Open-Shell Excitation Spectra from TDDFT |
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250 | (5) |
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Beyond the Adiabatic Approximation |
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255 | (2) |
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257 | (2) |
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259 | (12) |
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259 | (2) |
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261 | (2) |
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263 | (1) |
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264 | (7) |
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Semiconductor Nanostructures |
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271 | (16) |
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271 | (1) |
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Effective-Mass Approximation for Quantum Wells |
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272 | (3) |
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Intersubband Dynamics in Quantum Wells |
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275 | (6) |
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TDDFT Response Theory and Plasmon Dispersions |
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275 | (3) |
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278 | (3) |
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281 | (6) |
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Electronic Structure of Quantum Dots |
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282 | (1) |
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Collective Excitations: Kohn's Theorem and Beyond |
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283 | (4) |
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Solids from Time-Dependent Current DFT |
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287 | (14) |
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287 | (2) |
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Surface and Macroscopic Bulk Effects |
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289 | (3) |
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The Time-Dependent Current Density Functional Approach |
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292 | (4) |
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296 | (3) |
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299 | (2) |
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Optical Properties of Solids and Nanostructures from a Many-Body fxc Kernel |
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301 | (16) |
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301 | (1) |
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Applications to Solids and Surfaces |
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302 | (7) |
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Applications to One Dimensional Systems and Molecules |
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309 | (6) |
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315 | (2) |
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Linear Response Calculations for Polymers |
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317 | (6) |
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317 | (1) |
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The Counteracting Exchange Potential |
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318 | (2) |
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An Alternative to Orbital-Dependent Potentials |
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320 | (2) |
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322 | (1) |
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323 | (14) |
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323 | (1) |
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π → π* Transitions and Biochromophores |
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323 | (1) |
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Biochromophores in Proteins |
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324 | (4) |
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Proteins: Aminoacid Polymers |
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325 | (1) |
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326 | (1) |
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Proteins and Phrosthetic Groups |
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327 | (1) |
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328 | (2) |
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328 | (1) |
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329 | (1) |
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329 | (1) |
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330 | (6) |
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Green Fluorescent Protein and its Mutants: Structural Effects |
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331 | (4) |
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Astaxanthin and the Colour of the Lobster's Shell |
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335 | (1) |
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336 | (1) |
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Excited States and Photochemistry |
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337 | (20) |
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337 | (1) |
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Excited State Properties from TDDFT |
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337 | (5) |
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337 | (1) |
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338 | (2) |
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340 | (2) |
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342 | (1) |
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342 | (4) |
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Vertical Excitation and CD Spectra |
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342 | (2) |
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Excited State Structure and Dynamics |
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344 | (1) |
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Shortcomings of Present TDDFT |
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345 | (1) |
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346 | (7) |
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Aromatic Compounds and Fullerenes |
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346 | (1) |
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347 | (1) |
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Porphyrins and Related Compounds |
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348 | (2) |
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Transition Metal Compounds |
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350 | (1) |
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351 | (1) |
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Charge and Proton Transfer |
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352 | (1) |
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353 | (4) |
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Part V Applications: Beyond Linear Response |
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Atoms and Molecules in Strong Laser Fields |
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357 | (20) |
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357 | (2) |
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Atoms in Strong Laser Fields: An Overview |
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359 | (4) |
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359 | (2) |
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Above-Threshold Ionization |
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361 | (1) |
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361 | (1) |
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362 | (1) |
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TDDFT for Atoms in Strong Laser Fields |
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363 | (5) |
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Molecules in Strong Fields |
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368 | (6) |
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368 | (2) |
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A 1-D Example: H2 with Fixed Nuclei |
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370 | (3) |
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TDDFT for Molecules in Strong Fields |
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373 | (1) |
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Conclusion and Perspectives |
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374 | (3) |
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Highlights and Challenges in Strong-Field Atomic and Molecular Processes |
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377 | (14) |
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377 | (2) |
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Determination of the Spectra |
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379 | (1) |
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One-Photon Double Ionization of Helium |
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380 | (4) |
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Ionization of a Model Lithium Atom |
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384 | (2) |
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Dynamics of an H2 Molecule in a Strong Laser Field |
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386 | (3) |
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389 | (2) |
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Cluster Dynamics in Strong Laser Fields |
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391 | (16) |
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391 | (1) |
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392 | (4) |
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Coupled Ionic and Electronic Dynamics |
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392 | (2) |
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Self Interaction Correction |
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394 | (2) |
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Distributions of Emitted Electrons |
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396 | (7) |
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Computing Observables from Emission |
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396 | (1) |
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Multi-Plasmon Features in Photo-Electron Spectra |
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397 | (2) |
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Angular Distributions -- Low Intensity Domain |
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399 | (3) |
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Angular Distributions -- High Intensity Domain |
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402 | (1) |
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Pump-Probe Analysis of Ionic Dynamics |
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403 | (1) |
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404 | (3) |
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Excited-State Dynamics in Extended Systems |
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407 | (16) |
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407 | (3) |
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Real-Time Evolution of the Kohn-Sham Orbitals |
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410 | (2) |
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412 | (2) |
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Examples of TDDFT-MD Simulations |
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414 | (5) |
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Semiconductor Bulk and Surfaces |
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414 | (2) |
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416 | (3) |
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419 | (4) |
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Back to the Ground-State: Electron Gas |
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423 | (12) |
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423 | (1) |
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424 | (3) |
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427 | (1) |
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Approximations for the xc Kernel |
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428 | (6) |
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434 | (1) |
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The Exchange-Correlation Potential in the Adiabatic-Connection Fluctuation-Dissipation Framework |
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435 | (8) |
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435 | (1) |
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The RPA Exchange-Correlation Potential |
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436 | (3) |
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Asymptotic Behavior of the RPA Potential in Finite Systems |
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439 | (1) |
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The Bandgap Energy of Solids |
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440 | (2) |
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442 | (1) |
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Dispersion (Van Der Waals) Forces and TDDFT |
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443 | (20) |
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443 | (1) |
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Simple Models of the vdW Interaction between Small Systems |
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443 | (2) |
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Coupled-Fluctuation Model |
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443 | (1) |
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Model Based on the Static Correlation Hole: Failure of LDA/GGA at Large Separations |
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444 | (1) |
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Model Based on Small Distortions of the Ground State Density |
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444 | (1) |
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445 | (1) |
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The Simplest Models for vdW Energetics of Larger Systems |
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445 | (1) |
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Formal Perturbation Theory Approaches |
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446 | (2) |
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Second Order Perturbation Theory for Two Finite Nonoverlapping Systems |
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446 | (2) |
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vdW and Higher-Order Perturbation Theory |
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448 | (1) |
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Nonuniversality of vdW Asymptotics in Layered and Striated Systems |
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448 | (1) |
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Correlation Energies from Response Functions: The Fluctuation-Dissipation Theorem |
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449 | (4) |
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Basic Adiabatic Connection Fluctuation-Dissipation Theory |
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449 | (3) |
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Exact Exchange: A Strength of the ACFD Approach |
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452 | (1) |
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The xc Energy in the Random Phase Approximation |
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453 | (2) |
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Testing the RPA Correlation Energy For vdW in the Well-Separated Limit: The Second-Order Perturbation Regime |
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454 | (1) |
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Coupled Plasmons and the ACFD Approach |
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455 | (1) |
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Beyond the RPA: The ACFD with a Nonzero xc Kernel |
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455 | (4) |
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The Case of Two Small Distant Systems in the ACFD with a Nonzero xc Kernel |
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455 | (1) |
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Beyond the RPA in the ACFD: Energy-Optimized fxc Kernels |
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456 | (1) |
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Beyond the RPA in the ACFD: More Realistic Uniform-Gas Based fxc Kernels |
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457 | (1) |
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xc Kernels not Based on the Uniform Electron Gas |
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458 | (1) |
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Is the ACFD Energy Insensitive to fxc in Layered and Striated Systems having Zero Bandgap? |
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458 | (1) |
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Density-based Approximations for the Response Functions in ACFD vdW Theory |
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459 | (3) |
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Density-Based Approximations for the Non-Overlapping Regime |
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459 | (1) |
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``Seamless'' Density-Based vdW Approximations Valid into the Overlapped Regime |
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460 | (2) |
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462 | (1) |
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Kohn-Sham Master Equation Approach to Transport Through Single Molecules |
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463 | (16) |
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463 | (1) |
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Modeling a Molecular Junction |
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464 | (2) |
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Periodic Boundary Conditions |
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464 | (1) |
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465 | (1) |
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466 | (3) |
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467 | (1) |
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TDDFT and a KS Master Equation |
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468 | (1) |
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469 | (2) |
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469 | (1) |
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470 | (1) |
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471 | (5) |
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471 | (3) |
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474 | (2) |
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Comparison with Standard NEGF Treatment |
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476 | (1) |
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477 | (2) |
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Time-Dependent Transport Through Single Molecules: Nonequilibrium Green's Functions |
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479 | (14) |
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479 | (2) |
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An Exact Formulation Based on TDDFT |
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481 | (2) |
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Non-Equilibrium Green Functions |
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483 | (4) |
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487 | (1) |
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A Practical Implementation Scheme |
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488 | (3) |
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491 | (2) |
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493 | (14) |
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493 | (1) |
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Linear Response for the (N + 1)-Electron System |
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494 | (1) |
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495 | (7) |
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Transmission Amplitudes from the Susceptibility |
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495 | (3) |
|
TDDFT Equation for Transmission Amplitudes |
|
|
498 | (1) |
|
|
498 | (1) |
|
A Non-Trivial Example, N = 1 |
|
|
499 | (3) |
|
|
502 | (3) |
|
Single-Pole Approximation in the Continuum |
|
|
502 | (2) |
|
|
504 | (1) |
|
|
505 | (2) |
Acknowledgements |
|
507 | (2) |
References |
|
509 | (76) |
Index |
|
585 | |