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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| Language: | English |
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Oxford
Oxford University Press
2012
Oxford University Press, Incorporated |
| Edition: | 1 |
| Series: | Oxford Graduate Texts |
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| ISBN: | 9780199563029, 0199563020 |
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| Abstract | 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 of the current state of the art of the field, with many applications in physics, (bio)chemistry, and materials science. The book begins with a self-contained review of ground-state density-functional theory, followed by four main parts. The first part presents the formal framework of TDDFT, beginning with the basic existence theorems of Runge, Gross, and van Leeuwen. The time-dependent Kohn-Sham scheme and the properties of the time-dependent exchange-correlation potential are then discussed in detail. The second part deals with the TDDFT formulation of linear-response theory, which can be used to calculate electronic excitation energies in principle exactly using the Casida equation. An overview is given of the performance of TDDFT for atomic and molecular excitation energies, with many examples. Special attention is paid to challenging cases such as double or charge-transfer excitations. The third part of the book focuses on further developments, including time-dependent current-density-functional theory, the optimized effective potential, and the connection to many-body theory. This part also deals with excitations in extended systems, such as plasmons and excitons. Several special TDDFT topics are discussed in part four: van der Waals interactions, nanoscale transport, strong-field phenomena, and coupled electron-nuclear motion and molecular dynamics. Additional resources are provided in several appendices. |
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| AbstractList | 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 of the current state of the art of the field, with many applications in physics, (bio)chemistry, and materials science. The book begins with a self-contained review of ground-state density-functional theory, followed by four main parts. The first part presents the formal framework of TDDFT, beginning with the basic existence theorems of Runge, Gross, and van Leeuwen. The time-dependent Kohn-Sham scheme and the properties of the time-dependent exchange-correlation potential are then discussed in detail. The second part deals with the TDDFT formulation of linear-response theory, which can be used to calculate electronic excitation energies in principle exactly using the Casida equation. An overview is given of the performance of TDDFT for atomic and molecular excitation energies, with many examples. Special attention is paid to challenging cases such as double or charge-transfer excitations. The third part of the book focuses on further developments, including time-dependent current-density-functional theory, the optimized effective potential, and the connection to many-body theory. This part also deals with excitations in extended systems, such as plasmons and excitons. Several special TDDFT topics are discussed in part four: van der Waals interactions, nanoscale transport, strong-field phenomena, and coupled electron-nuclear motion and molecular dynamics. Additional resources are provided in several appendices. Time-dependent density-functional theory (TDDFT) is a quantum mechanical approach for the dynamical properties of electrons in matter. It's widely used in (bio)chemistry and physics to calculate molecular excitation energies and optical properties of materials. This is the first graduate-level text on the formal framework and applications of TDDFT. |
| Author | Ullrich, Carsten A |
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| Keywords | many-body theory plasmons density-functional theory excitons molecular dynamics van der Waals interactions Kohn-Sham equations nanoscale transport excitations |
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| Snippet | Time-dependent density-functional theory (TDDFT) is a quantum mechanical framework which describes the dynamics of interacting electronic many-body systems... Time-dependent density-functional theory (TDDFT) is a quantum mechanical approach for the dynamical properties of electrons in matter. It's widely used in... |
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| SubjectTerms | Condensed Matter Physics Density functionals Mathematical physics |
| TableOfContents | 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 |
| Title | Time-dependent density-functional theory : concepts and applications |
| URI | https://cir.nii.ac.jp/crid/1130000795195422592 https://doi.org/10.1093/acprof:oso/9780199563029.001.0001 https://ebookcentral.proquest.com/lib/[SITE_ID]/detail.action?docID=829457 https://www.vlebooks.com/vleweb/product/openreader?id=none&isbn=9780191626913&uid=none https://www.vlebooks.com/vleweb/product/openreader?id=none&isbn=9780191627446 |
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