Time-dependent density-functional theory : concepts and applications
Time-dependent density-functional theory (TDDFT) is a quantum mechanical framework which describes the dynamics of interacting electronic many-body systems formally exactly and in a computationally efficient manner. This book presents the concepts of TDDFT at the graduate level. An overview is given...
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| Hlavný autor: | |
|---|---|
| Médium: | E-kniha Kniha |
| Jazyk: | English |
| Vydavateľské údaje: |
Oxford
Oxford University Press
2012
Oxford University Press, Incorporated |
| Vydanie: | 1 |
| Edícia: | Oxford Graduate Texts |
| Predmet: | |
| ISBN: | 9780199563029, 0199563020 |
| On-line prístup: | Získať plný text |
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- Cover -- Time-Dependent Density-Functional Theory: Concepts and Applications -- Copyright -- Preface -- Contents -- List of abbreviations -- 1: Introduction -- 1.1 A survey of time-dependent phenomena -- 1.1.1 A journey through 20 orders of magnitude -- 1.1.2 What do we want to describe? -- 1.2 Preview of and guide to this book -- 1.2.1 Prerequisites and other remarks -- 2: Review of ground-state density-functional theory -- 2.1 The formal framework of DFT -- 2.1.1 The electronic many-body problem -- 2.1.2 The Hohenberg-Kohn theorem -- 2.1.3 Constrained search -- 2.1.4 The Kohn-Sham equations -- 2.2 Exact properties -- 2.2.1 Orbitals, eigenvalues, and asymptotics -- 2.2.2 Self-interaction -- 2.2.3 The band gap in solids and derivative discontinuities -- 2.2.4 Uniform limit -- 2.3 Approximate functionals -- 2.3.1 The local-density approximation -- 2.3.2 Generalized gradient approximations -- 2.3.3 Climbing the ladder of approximations -- 2.3.4 Other approximations -- 2.3.5 Lower-dimensional systems -- Part I: The basic formalism of TDDFT -- 3: Fundamental existence theorems -- 3.1 Time-dependent many-body systems -- 3.1.1 Time-dependent Schr¨odinger equation -- 3.1.2 Time evolution operators -- 3.1.3 Continuity equation and local conservation laws -- 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 -- 4.5.1 The Crank-Nicolson algorithm -- 4.5.2 The predictor-corrector scheme -- 4.5.3 Absorbing boundary conditions -- 5: Time-dependent observables -- 5.1 Explicit density functionals -- 5.1.1 The density and other visualization tools -- 5.1.2 The particle number -- 5.1.3 Moments of the density
- 15.3 Finite-bias and non-steady-state transport
- 7.4 Warm-up exercise: TDDFT for two-level systems -- 7.5 Calculation of excitation energies: the Casida equation -- 7.5.1 Derivation -- 7.5.2 Discussion -- 7.5.3 The Casida formalism for spin-unpolarized systems -- 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 -- 8.1.1 Basic symmetries, analyticity, and high-frequency and static limits -- 8.1.2 The zero-force theorem and the long-range property -- 8.1.3 Variational principle and causality -- 8.2 Approximations -- 8.3 The xc kernels of the homogeneous electron liquid -- 8.3.1 Definitions -- 8.3.2 Exact properties -- 8.3.3 Parametrizations -- 8.3.4 Analytic continuation -- 9: Applications to atomic and molecular systems -- 9.1 Excitation energies of small systems: basic trends and features -- 9.1.1 The exact Kohn-Sham spectrum -- 9.1.2 Results for closed-shell atoms and N2 -- 9.1.3 Discussion -- 9.2 Molecular excited-state properties with TDDFT: an overview -- 9.2.1 Quantum chemical methods and their computational cost -- 9.2.2 Vertical excitation energies -- 9.2.3 Excited-state forces and geometries -- 9.3 Double excitations -- 9.3.1 What do we mean by single and multiple excitations? -- 9.3.2 Performance of TDDFT for double excitations -- 9.3.3 Dressed TDDFT approach -- 9.4 Charge-transfer excitations -- 9.4.1 Limit of large separation -- 9.4.2 Long-range (mostly hybrid) xc functionals -- 9.4.3 Constructing the exact xc kernel -- 9.5 The Sternheimer equation -- 9.6 Optical spectra via time propagation schemes -- 9.6.1 Formal aspects and initial excitation mechanism -- 9.6.2 Applications -- 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 -- 10.2.1 The Gross-Kohn approximation -- 10.2.2 The ultranonlocality problem -- 10.3 The formal framework of TDCDFT -- 10.3.1 Upgrading from densities to currents -- 10.3.2 Existence theorems of TDCDFT -- 10.3.3 The zero-force and zero-torque theorems -- 10.3.4 TDCDFT in linear response -- 10.3.5 Relation to static CDFT -- 10.4 The VK functional -- 10.4.1 The xc vector potential in a weakly perturbed uniform system -- 10.4.2 Discussion: viscoelastic stresses in the electron liquid -- 10.4.3 Local approximation -- 10.4.4 Spin-dependent generalization -- 10.5 Applications of TDCDFT in the linear-response regime -- 10.5.1 Applications in the quasi-static limit -- 10.5.2 Applications at finite frequency: excitations and linewidths -- 10.5.3 Intrinsic and extrinsic dissipation -- 10.6 Memory effects: elasticity and dissipation -- 10.6.1 A simple exercise: the classical damped harmonic oscillator -- 10.6.2 The VK functional in the time domain -- 10.6.3 Dissipation, multiple excitations, and thermodynamic limit -- 11: The time-dependent optimized effective potential -- 11.1 The static OEP approach for orbital functionals -- 11.1.1 Explicit versus implicit density functionals -- 11.1.2 The OEP integral equation -- 11.1.3 Properties of the OEP -- 11.1.4 The KLI approximation and related schemes -- 11.1.5 Exact-exchange DFT versus HF theory -- 11.1.6 Applications -- 11.2 The TDOEP scheme -- 11.2.1 Variational principle -- 11.2.2 The TDOEP equation: derivation and properties -- 11.2.3 Approximations -- 11.2.4 First case study: full versus approximate TDOEP -- 11.2.5 Second case study: discontinuity in the xc potential -- 11.3 TDOEP in the linear regime -- 12: Extended systems -- 12.1 Electronic structure and excitations of periodic solids -- 12.1.1 Band structure: metals versus insulators
- 5.2 Implicit density functionals -- 5.2.1 Ion probabilities -- 5.2.2 Kinetic-energy spectra -- 5.2.3 Other 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 -- 6.2.1 The adiabatic limit -- 6.2.2 The zero-force theorem -- 6.2.3 Self-interaction -- 6.2.4 Sum rules involving the time-dependent energy -- 6.2.5 Scaling -- 6.3 Galilean invariance and the harmonic potential theorem -- 6.3.1 Accelerated reference frames and generalized translational invariance -- 6.3.2 The harmonic potential theorem -- 6.4 Memory and causality -- 6.4.1 Causality of the xc potential, and history dependence -- 6.4.2 A simple example and a paradox -- 6.5 Initial-state dependence -- 6.5.1 An example -- 6.5.2 Connection between history and initial-state dependence -- 6.6 Time-dependent variational principles -- 6.6.1 The Dirac-Frenkel stationary-action principle -- 6.6.2 The variational principle of TDDFT -- 6.6.3 The adiabatic approximation -- 6.7 Discontinuity upon change of particle number -- 6.7.1 Time-dependent ensembles and derivative discontinuity -- 6.7.2 Time-varying particle numbers -- Part II: Linear response and excitation energies -- 7: The formal framework of linear-response TDDFT -- 7.1 General linear-response theory -- 7.1.1 Definitions and time-dependent response -- 7.1.2 Frequency-dependent response and Lehmann representation -- 7.1.3 Basic symmetries and analytic behavior of the response functions -- 7.1.4 The fluctuation-dissipation theorem -- 7.1.5 High-frequency behavior -- 7.2 Spectroscopic observables -- 7.3 Linear density response in TDDFT -- 7.3.1 The Runge-Gross theorem in linear response and the question of invertibility -- 7.3.2 Linear response of the Kohn-Sham system -- 7.3.3 Spin-dependent formalism
- 12.1.2 Linear response in periodic systems -- 12.1.3 The dielectric tensor -- 12.1.4 The macroscopic dielectric function -- 12.2 Spectroscopy of density fluctuations: plasmons -- 12.2.1 The excitation spectrum of a homogeneous system -- 12.2.2 Plasmon excitations in real metals -- 12.3 Optical absorption and excitons -- 12.3.1 Excitons: basic models -- 12.3.2 TDDFT and the optical absorption of insulators -- 12.3.3 Excitonic effects with TDDFT: a two-band model -- 12.4 TDCDFT in periodic systems -- 12.4.1 Existence theorems -- 12.4.2 Performance of the VK functional for bulk metals and insulators -- 13: TDDFT and many-body theory -- 13.1 Perturbation theory along the adiabatic connection -- 13.1.1 The adiabatic connection -- 13.1.2 Perturbative expansion of the xc potential -- 13.2 Nonequilibrium Green's functions and the Keldysh action -- 13.2.1 The Keldysh contour -- 13.2.2 The Keldysh action principle -- 13.2.3 Nonequilibrium Green's functions -- 13.3 xc kernels from many-body theory -- 13.3.1 Diagrammatic expansion of the xc kernel -- 13.3.2 xc kernels from the Bethe-Salpeter equation -- Part IV: Special topics -- 14: Long-range correlations and dispersion interactions -- 14.1 The adiabatic-connection fluctuation-dissipation approach -- 14.1.1 Adiabatic-connection expression for the correlation energy -- 14.1.2 The RPA and beyond -- 14.2 Van der Waals interactions -- 14.2.1 Introduction -- 14.2.2 Long-range interaction between separated systems -- 14.2.3 Van der Waals density functionals -- 15: Nanoscale transport and molecular junctions -- 15.1 Basic concepts -- 15.1.1 Potential barriers, transmission coefficients, and conductance -- 15.1.2 The Landauer approach -- 15.2 Transport in the linear-response limit -- 15.2.1 Conductance from the conductivity tensor -- 15.2.2 xc contributions to the resistivity