List of abbreviations ........................................ xiii
1 Introduction ................................................. 1
1.1 A survey of time-dependent phenomena .................... 1
1.2 Preview of and guide to this book ....................... 7
2 Review of ground-state density-functional theory ............ 10
2.1 The formal framework of DFT ............................ 11
2.2 Exact properties ....................................... 21
2.3 Approximate functionals ................................ 30
PART I THE BASIC FORMALISM OF TDDFT
3 Fundamental existence theorems .............................. 45
3.1 Time-dependent many-body systems ....................... 45
3.2 The Runge-Gross theorem ................................ 50
3.3 The van Leeuwen theorem ................................ 54
4 The time-dependent Kohn-Sham scheme ......................... 59
4.1 The time-dependent Kohn-Sham equation .................. 59
4.2 Spin-dependent systems ................................. 61
4.3 The adiabatic approximation ............................ 62
4.4 The meaning of self-consistency in DFT and TDDFT ....... 65
4.5 Numerical time propagation ............................. 67
5 Time-dependent observables .................................. 73
5.1 Explicit density functionals ........................... 73
5.2 Implicit density functionals ........................... 81
5.3 The time-dependent energy .............................. 88
6 Properties of the time-dependent xc potential ............... 91
6.1 What is the universal xc functional? ................... 91
6.2 Some exact conditions .................................. 93
6.3 Galilean invariance and the harmonic potential
theorem ................................................ 98
6.4 Memory and causality .................................. 103
6.5 Initial-state dependence .............................. 107
6.6 Time-dependent variational principles ................. 111
6.7 Discontinuity upon change of particle number .......... 115
PART II LINEAR RESPONSE AND EXCITATION ENERGIES
7 The formal framework of linear-response TDDFT .............. 123
7.1 General linear-response theory ........................ 124
7.2 Spectroscopic observables ............................. 132
7.3 Linear density response in TDDFT ...................... 137
7.4 Warm-up exercise: TDDFT for two-level systems ......... 143
7.5 Calculation of excitation energies: the Casida
equation .............................................. 145
7.6 The Tamm-Dancoff approximation and other
simplifications ....................................... 151
7.7 Excitation energies with time-dependent Hartree-Fock
theory ................................................ 153
8 The frequency-dependent xc kernel .......................... 157
8.1 Exact properties ...................................... 157
8.2 Approximations ........................................ 163
8.3 The xc kernels of the homogeneous electron liquid ..... 164
9 Applications to atomic and molecular systems ............... 176
9.1 Excitation energies of small systems: basic trends
and features .......................................... 177
9.2 Molecular excited-state properties with TDDFT: an
overview .............................................. 182
9.3 Double excitations .................................... 189
9.4 Charge-transfer excitations ........................... 195
9.5 The Sternheimer equation .............................. 202
9.6 Optical spectra via time propagation schemes ......... 204
PART III FURTHER DEVELOPMENTS
10 Time-dependent current-DFT ................................. 213
10.1 The adiabatic approximation and beyond ................ 213
10.2 The failure of nonadiabatic local approximations in
TDDFT ................................................. 215
10.3 The formal framework of TDCDFT ........................ 218
10.4 The VK functional ..................................... 225
10.5 Applications of TDCDFT in the linear-response
regime ................................................ 231
10.6 Memory effects: elasticity and dissipation ............ 241
11 The time-dependent optimized effective potential ........... 252
11.1 The static OEP approach for orbital functionals ....... 253
11.2 The TDOEP scheme ...................................... 263
11.3 TDOEP in the linear regime ............................ 276
12 Extended systems ........................................... 279
12.1 Electronic structure and excitations of periodic
solids ................................................ 279
12.2 Spectroscopy of density fluctuations: plasmons ........ 285
12.3 Optical absorption and excitons ....................... 289
12.4 TDCDFT in periodic systems ............................ 299
13 TDDFT and many-body theory ................................. 304
13.1 Perturbation theory along the adiabatic connection .... 304
13.2 Nonequilibrium Green's functions and the Keldysh
action ................................................ 308
13.3 xc kernels from many-body theory ...................... 318
PART IV SPECIAL TOPICS
14 Long-range correlations and dispersion interactions ........ 333
14.1 The adiabatic-connection fluctuation-dissipation
approach .............................................. 333
14.2 Van der Waals interactions ............................ 340
15 Nanoscale transport and molecular junctions ................ 351
15.1 Basic concepts ........................................ 352
15.2 Transport in the linear-response limit ................ 355
15.3 Finite-bias and non-steady-state transport ............ 360
16 Strong-field phenomena and optimal control ................. 374
16.1 Multiphoton ionization ................................ 376
16.2 High-order harmonic generation ........................ 386
16.3 Optimal control ....................................... 388
17 Nuclear motion ............................................. 394
17.1 Potential-energy surfaces ............................. 394
17.2 Ab initio molecular dynamics .......................... 401
17.3 Multicomponent TDDFT .................................. 413
Appendix A Atomic units ...................................... 416
A.l Atomic units in vacuum ................................. 416
A.2 Atomic units in the effective-mass approximation ....... 417
Appendix В Functionals and functional derivatives ............. 419
Appendix С Densities and density matrices ..................... 422
Appendix D Hartree—Fock and other wave-function approaches .... 425
Appendix E Constructing the xc potential from a given
density .................................................... 429
E.l Ground-state densities ................................ 429
E.2 Time-dependent densities .............................. 431
Appendix F DFT for excited states ......................... 434
F.1 Generalized Kohn-Sham schemes for excited states ...... 434
F.2 Ensemble formalism .................................... 436
Appendix G Systems with noncollinear spins ................... 439
G.l DFT for noncollinear spins ............................ 439
G.2 Linear response and excitation energies ............... 440
Appendix H The dipole approximation .......................... 445
H.l Interaction with electromagnetic waves ................ 445
H.2 Dipole matrix elements and dipole moments ............. 447
Appendix I A brief review of classical fluid dynamics ........ 450
I.1 Basics and ideal fluids ............................... 450
1.2 Viscous fluids and dissipation ........................ 452
Appendix J Constructing the scalar xc kernel from the
tensor xc kernel ........................................... 455
Appendix К Semiconductor quantum wells ....................... 458
K.l Effective-mass approximation and subband levels ........ 459
K.2 Intersubband dynamics .................................. 462
Appendix L TDDFT in a Lagrangian frame ....................... 465
L.l Fluid motion in the Lagrangian and laboratory frames .. 466
L.2 TDDFT in the Lagrangian frame ......................... 469
L.3 The small-deformation approximation ................... 471
L.4 The nonlinear elastic approximation ................... 473
L.5 Validity of the VK potential and breakdown of the
adiabatic approximation ............................... 474
Appendix M Inversion of the dielectric matrix ................ 477
Appendix N Review literature on DFT and many-body theory ..... 479
Appendix О TDDFT computer codes .............................. 482
References .................................................... 484
Index ......................................................... 511
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