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Time-Dependent Density-Functional Theory: Concepts and Applications [Minkštas viršelis]

(Department of Physics and Astronomy, University of Missouri - Columbia)
  • Formatas: Paperback / softback, 536 pages, aukštis x plotis x storis: 244x164x28 mm, weight: 908 g
  • Serija: Oxford Graduate Texts
  • Išleidimo metai: 14-May-2019
  • Leidėjas: Oxford University Press
  • ISBN-10: 0198841930
  • ISBN-13: 9780198841937
Kitos knygos pagal šią temą:
  • Formatas: Paperback / softback, 536 pages, aukštis x plotis x storis: 244x164x28 mm, weight: 908 g
  • Serija: Oxford Graduate Texts
  • Išleidimo metai: 14-May-2019
  • Leidėjas: Oxford University Press
  • ISBN-10: 0198841930
  • ISBN-13: 9780198841937
Kitos knygos pagal šią temą:
Time-dependent density-functional theory (TDDFT) describes the quantum dynamics of interacting electronic many-body systems formally exactly and in a practical and efficient manner. TDDFT has become the leading method for calculating excitation energies and optical properties of large molecules, with accuracies that rival traditional wave-function based methods, but at a fraction of the computational cost.

This book is the first graduate-level text on the concepts and applications of TDDFT, including many examples and exercises, and extensive coverage of the literature.

The book begins with a self-contained review of ground-state DFT, followed by a detailed and pedagogical treatment of the formal framework of TDDFT. It is explained how excitation energies can be calculated from linear-response TDDFT. Among the more advanced topics are time-dependent current-density-functional theory, orbital functionals, and many-body theory. Many applications are discussed, including molecular excitations, ultrafast and strong-field phenomena, excitons in solids, van der Waals interactions, nanoscale transport, and molecular dynamics.

Recenzijos

This is a very pedagogical introduction to the central ideas of time-dependent density-functional theory. The theory is described in depth and illustrated with many insightful examples and applications in atomic, molecular and condensed matter physics. This is a valuable book for both students and researchers. * Robert van Leeuwen, University of Jyvaskyla *

List of abbreviations
xiii
1 Introduction
1(9)
1.1 A survey of time-dependent phenomena
1(6)
1.2 Preview of and guide to this book
7(3)
2 Review of ground-state density-functional theory
10(35)
2.1 The formal framework of DFT
11(10)
2.2 Exact properties
21(9)
2.3 Approximate functionals
30(15)
PART I THE BASIC FORMALISM OF TDDFT
3 Fundamental existence theorems
45(14)
3.1 Time-dependent many-body systems
45(5)
3.2 The Runge--Gross theorem
50(4)
3.3 The van Leeuwen theorem
54(5)
4 The time-dependent Kohn--Sham scheme
59(14)
4.1 The time-dependent Kohn--Sham equation
59(2)
4.2 Spin-dependent systems
61(1)
4.3 The adiabatic approximation
62(3)
4.4 The meaning of self-consistency in DFT and TDDFT
65(2)
4.5 Numerical time propagation
67(6)
5 Time-dependent observables
73(18)
5.1 Explicit density functionals
73(8)
5.2 Implicit density functionals
81(7)
5.3 The time-dependent energy
88(3)
6 Properties of the time-dependent xc potential
91(32)
6.1 What is the universal xc functional?
91(2)
6.2 Some exact conditions
93(5)
6.3 Galilean invariance and the harmonic potential theorem
98(5)
6.4 Memory and causality
103(4)
6.5 Initial-state dependence
107(4)
6.6 Time-dependent variational principles
111(4)
6.7 Discontinuity upon change of particle number
115(8)
PART II LINEAR RESPONSE AND EXCITATION ENERGIES
7 The formal framework of linear-response TDDFT
123(34)
7.1 General linear-response theory
124(8)
7.2 Spectroscopic observables
132(5)
7.3 Linear density response in TDDFT
137(6)
7.4 Warm-up exercise: TDDFT for two-level systems
143(2)
7.5 Calculation of excitation energies: the Casida equation
145(6)
7.6 The Tamm--Dancoff approximation and other simplifications
151(2)
7.7 Excitation energies with time-dependent Hartree--Fock theory
153(4)
8 The frequency-dependent xc kernel
157(19)
8.1 Exact properties
157(6)
8.2 Approximations
163(1)
8.3 The xc kernels of the homogeneous electron liquid
164(12)
9 Applications to atomic and molecular systems
176(37)
9.1 Excitation energies of small systems: basic trends and features
177(5)
9.2 Molecular excited-state properties with TDDFT: an overview
182(7)
9.3 Double excitations
189(6)
9.4 Charge-transfer excitations
195(7)
9.5 The Sternheimer equation
202(2)
9.6 Optical spectra via time propagation schemes
204(9)
PART III FURTHER DEVELOPMENTS
10 Time-dependent current-DFT
213(39)
10.1 The adiabatic approximation and beyond
213(2)
10.2 The failure of nonadiabatic local approximations in TDDFT
215(3)
10.3 The formal framework of TDCDFT
218(7)
10.4 The VK functional
225(6)
10.5 Applications of TDCDFT in the linear-response regime
231(10)
10.6 Memory effects: elasticity and dissipation
241(11)
11 The time-dependent optimized effective potential
252(27)
11.1 The static OEP approach for orbital functionals
253(10)
11.2 The TDOEP scheme
263(13)
11.3 TDOEP in the linear regime
276(3)
12 Extended systems
279(25)
12.1 Electronic structure and excitations of periodic solids
279(6)
12.2 Spectroscopy of density fluctuations: plasmons
285(4)
12.3 Optical absorption and excitons
289(10)
12.4 TDCDFT in periodic systems
299(5)
13 TDDFT and many-body theory
304(29)
13.1 Perturbation theory along the adiabatic connection
304(4)
13.2 Nonequilibrium Green's functions and the Keldysh action
308(10)
13.3 Xc kernels from many-body theory
318(15)
PART IV SPECIAL TOPICS
14 Long-range correlations and dispersion interactions
333(18)
14.1 The adiabatic-connection fluctuation-dissipation approach
333(7)
14.2 Van der Waals interactions
340(11)
15 Nanoscale transport and molecular junctions
351(23)
15.1 Basic concepts
352(3)
15.2 Transport in the linear-response limit
355(5)
15.3 Finite-bias and non-steady-state transport
360(14)
16 Strong-field phenomena and optimal control
374(20)
16.1 Multiphoton ionization
376(10)
16.2 High-order harmonic generation
386(2)
16.3 Optimal control
388(6)
17 Nuclear motion
394(22)
17.1 Potential-energy surfaces
394(7)
17.2 Ab initio molecular dynamics
401(12)
17.3 Multicomponent TDDFT
413(3)
Appendix A Atomic units
416(3)
A.1 Atomic units in vacuum
416(1)
A.2 Atomic units in the effective-mass approximation
417(2)
Appendix B Functionals and functional derivatives
419(3)
Appendix C Densities and density matrices
422(3)
Appendix D Hartree-Fock and other wave-function approaches
425(4)
Appendix E Constructing the xc potential from a given density
429(5)
E.1 Ground-state densities
429(2)
E.2 Time-dependent densities
431(3)
Appendix F DFT for excited states
434(5)
F.1 Generalized Kohn--Sham schemes for excited states
434(2)
F.2 Ensemble formalism
436(3)
Appendix G Systems with noncollinear spins
439(6)
G.1 DFT for noncollinear spins
439(1)
G.2 Linear response and excitation energies
440(5)
Appendix H The dipole approximation
445(5)
H.1 Interaction with electromagnetic waves
445(2)
H.2 Dipole matrix elements and dipole moments
447(3)
Appendix I A brief review of classical fluid dynamics
450(5)
I.1 Basics and ideal fluids
450(2)
I.2 Viscous fluids and dissipation
452(3)
Appendix J Constructing the scalar xc kernel from the tensor xc kernel
455(3)
Appendix K Semiconductor quantum wells
458(7)
K.1 Effective-mass approximation and subband levels
459(3)
K.2 Intersubband dynamics
462(3)
Appendix L TDDFT in a Lagrangian frame
465(12)
L.1 Fluid motion in the Lagrangian and laboratory frames
466(3)
L.2 TDDFT in the Lagrangian frame
469(2)
L.3 The small-deformation approximation
471(2)
L.4 The nonlinear elastic approximation
473(1)
L.5 Validity of the VK potential and breakdown of the adiabatic approximation
474(3)
Appendix M Inversion of the dielectric matrix
477(2)
Appendix N Review literature on DFT and many-body theory
479(3)
Appendix O TDDFT computer codes
482(2)
References 484(27)
Index 511
Carsten A. Ullrich, Department of Physics and Astronomy, University of Missouri - Columbia.