Cover -- Contents -- List of abbreviations -- 1 Introduction -- 1.1 A survey of time-dependent phenomena -- 1.2 Preview of and guide to this book -- 2 Review of ground-state density-functional theory -- 2.1 The formal framework of DFT -- 2.2 Exact properties -- 2.3 Approximate functionals -- PART I: THE BASIC FORMALISM OF TDDFT -- 3 Fundamental existence theorems -- 3.1 Time-dependent many-body systems -- 3.2 The Runge-Gross theorem -- 3.3 The van Leeuwen theorem -- 4 The time-dependent Kohn-Sham scheme -- 4.1 The time-dependent Kohn-Sham equation -- 4.2 Spin-dependent systems -- 4.3 The adiabatic approximation -- 4.4 The meaning of self-consistency in DFT and TDDFT -- 4.5 Numerical time propagation -- 5 Time-dependent observables -- 5.1 Explicit density functionals -- 5.2 Implicit density functionals -- 5.3 The time-dependent energy -- 6 Properties of the time-dependent xc potential -- 6.1 What is the universal xc functional? -- 6.2 Some exact conditions -- 6.3 Galilean invariance and the harmonic potential theorem -- 6.4 Memory and causality -- 6.5 Initial-state dependence -- 6.6 Time-dependent variational principles -- 6.7 Discontinuity upon change of particle number -- PART II: LINEAR RESPONSE AND EXCITATION ENERGIES -- 7 The formal framework of linear-response TDDFT -- 7.1 General linear-response theory -- 7.2 Spectroscopic observables -- 7.3 Linear density response in TDDFT -- 7.4 Warm-up exercise: TDDFT for two-level systems -- 7.5 Calculation of excitation energies: the Casida equation -- 7.6 The Tamm-Dancoff approximation and other simplifications -- 7.7 Excitation energies with time-dependent Hartree-Fock theory -- 8 The frequency-dependent xc kernel -- 8.1 Exact properties -- 8.2 Approximations -- 8.3 The xc kernels of the homogeneous electron liquid -- 9 Applications to atomic and molecular systems.

9.1 Excitation energies of small systems: basic trends and features -- 9.2 Molecular excited-state properties with TDDFT: an overview -- 9.3 Double excitations -- 9.4 Charge-transfer excitations -- 9.5 The Sternheimer equation -- 9.6 Optical spectra via time propagation schemes -- PART III: FURTHER DEVELOPMENTS -- 10 Time-dependent current-DFT -- 10.1 The adiabatic approximation and beyond -- 10.2 The failure of nonadiabatic local approximations in TDDFT -- 10.3 The formal framework of TDCDFT -- 10.4 The VK functional -- 10.5 Applications of TDCDFT in the linear-response regime -- 10.6 Memory effects: elasticity and dissipation -- 11 The time-dependent optimized effective potential -- 11.1 The static OEP approach for orbital functionals -- 11.2 The TDOEP scheme -- 11.3 TDOEP in the linear regime -- 12 Extended systems -- 12.1 Electronic structure and excitations of periodic solids -- 12.2 Spectroscopy of density fluctuations: plasmons -- 12.3 Optical absorption and excitons -- 12.4 TDCDFT in periodic systems -- 13 TDDFT and many-body theory -- 13.1 Perturbation theory along the adiabatic connection -- 13.2 Nonequilibrium Green's functions and the Keldysh action -- 13.3 xc kernels from many-body theory -- PART IV: SPECIAL TOPICS -- 14 Long-range correlations and dispersion interactions -- 14.1 The adiabatic-connection .uctuation-dissipation approach -- 14.2 Van der Waals interactions -- 15 Nanoscale transport and molecular junctions -- 15.1 Basic concepts -- 15.2 Transport in the linear-response limit -- 15.3 Finite-bias and non-steady-state transport -- 16 Strong-field phenomena and optimal control -- 16.1 Multiphoton ionization -- 16.2 High-order harmonic generation -- 16.3 Optimal control -- 17 Nuclear motion -- 17.1 Potential-energy surfaces -- 17.2 Ab initio molecular dynamics -- 17.3 Multicomponent TDDFT -- Appendix A: Atomic units.

A.1 Atomic units in vacuum -- A.2 Atomic units in the effective-mass approximation -- Appendix B: Functionals and functional derivatives -- Appendix C: Densities and density matrices -- Appendix D: Hartree-Fock and other wave-function approaches -- Appendix E: Constructing the xc potential from a given density -- E.1 Ground-state densities -- E.2 Time-dependent densities -- Appendix F: DFT for excited states -- F.1 Generalized Kohn-Sham schemes for excited states -- F.2 Ensemble formalism -- Appendix G: Systems with noncollinear spins -- G.1 DFT for noncollinear spins -- G.2 Linear response and excitation energies -- Appendix H: The dipole approximation -- H.1 Interaction with electromagnetic waves -- H.2 Dipole matrix elements and dipole moments -- Appendix I: A brief review of classical fluid dynamics -- I.1 Basics and ideal fluids -- I.2 Viscous fluids and dissipation -- Appendix J: Constructing the scalar xc kernel from the tensor xc kernel -- Appendix K: Semiconductor quantum wells -- K.1 Effective-mass approximation and subband levels -- K.2 Intersubband dynamics -- Appendix L: TDDFT in a Lagrangian frame -- L.1 Fluid motion in the Lagrangian and laboratory frames -- L.2 TDDFT in the Lagrangian frame -- L.3 The small-deformation approximation -- L.4 The nonlinear elastic approximation -- L.5 Validity of the VK potential and breakdown of the adiabatic approximation -- Appendix M: Inversion of the dielectric matrix -- Appendix N: Review literature on DFT and many-body theory -- Appendix O: TDDFT computer codes -- References -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- X.