A Brief Compendium of Time-Dependent Density Functional Theory

Time-dependent density functional theory (TDDFT) is a formally exact approach to the time-dependent electronic many-body problem which is widely used for calculating excitation energies. We present a survey of the fundamental framework, practical aspects, and applications of TDDFT. This paper is mainly intended for nonexperts (students or researchers in other areas) who would like to learn about the present state of TDDFT without going too deeply into formal details.

[1]  Thomas Strobel,et al.  Role of the Charge Transfer State in Organic Donor–Acceptor Solar Cells , 2010, Advanced materials.

[2]  Kohl,et al.  Time-dependent density-functional theory: Conceptual and practical aspects. , 1986, Physical review letters.

[3]  E. Gross,et al.  Multicomponent density-functional theory for electrons and nuclei. , 2001, Physical review letters.

[4]  D. Bowler,et al.  Linear Scaling Constrained Density Functional Theory in CONQUEST. , 2011, Journal of chemical theory and computation.

[5]  G. Vignale,et al.  Solving the ultranonlocality problem in time-dependent spin-density-functional theory. , 2003, Physical review letters.

[6]  M. Dion,et al.  Erratum: Van der Waals Density Functional for General Geometries [Phys. Rev. Lett. 92, 246401 (2004)] , 2005 .

[7]  Daniel Karlsson,et al.  Time-dependent density-functional theory meets dynamical mean-field theory: real-time dynamics for the 3D Hubbard model. , 2010, Physical review letters.

[8]  Angel Rubio,et al.  Propagators for the time-dependent Kohn-Sham equations. , 2004, The Journal of chemical physics.

[9]  Multidomain decomposition approach to time-dependent density functional calculations , 2011 .

[10]  Paul-Gerhard Reinhard,et al.  NONLINEAR ELECTRON DYNAMICS IN METAL CLUSTERS , 2000 .

[11]  Momentum distributions in time-dependent density-functional theory : Product-phase approximation for nonsequential double ionization in strong laser fields , 2007, 0704.1423.

[12]  Á. Rubio,et al.  Nonlinear phenomena in time-dependent density-functional theory: What Rabi oscillations can teach us , 2011, 1101.2880.

[13]  Basile F. E. Curchod,et al.  Erratum: Local control theory in trajectory-based nonadiabatic dynamics (Physical Review A - Atomic, Molecular, and Optical Physics) , 2012 .

[14]  M. Gatti Design of effective kernels for spectroscopy and molecular transport: time-dependent current-density-functional theory. , 2010, The Journal of chemical physics.

[15]  G. Scuseria,et al.  Restoring the density-gradient expansion for exchange in solids and surfaces. , 2007, Physical review letters.

[16]  Kieron Burke,et al.  Density-potential mapping in time-dependent density-functional theory , 2010 .

[17]  E K U Gross,et al.  Bootstrap approximation for the exchange-correlation kernel of time-dependent density-functional theory. , 2011, Physical review letters.

[18]  Martin J. Packer,et al.  A new implementation of the second‐order polarization propagator approximation (SOPPA): The excitation spectra of benzene and naphthalene , 1996 .

[19]  Kieron Burke,et al.  Time-dependent density functional theory: past, present, and future. , 2005, The Journal of chemical physics.

[20]  Ghosh,et al.  Density-functional theory of many-electron systems subjected to time-dependent electric and magnetic fields. , 1988, Physical review. A, General physics.

[21]  M. Ventra,et al.  Stochastic time-dependent current-density functional theory: a functional theory of open quantum systems , 2008, 0805.3734.

[22]  D. Truhlar,et al.  A new local density functional for main-group thermochemistry, transition metal bonding, thermochemical kinetics, and noncovalent interactions. , 2006, The Journal of chemical physics.

[23]  Serdar Ogut,et al.  Ab Initio Excitation Spectra and Collective Electronic Response in Atoms and Clusters , 1999 .

[24]  Gianluca Stefanucci,et al.  Nonequilibrium Many-Body Theory of Quantum Systems: A Modern Introduction , 2013 .

[25]  Filipp Furche,et al.  On the density matrix based approach to time-dependent density functional response theory , 2001 .

[26]  P. Hohenberg,et al.  Inhomogeneous Electron Gas , 1964 .

[27]  M. Petersilka,et al.  Excitation energies from time-dependent density-functional theory. , 1996 .

[28]  Takashi Nakatsukasa,et al.  Real‐time, real‐space implementation of the linear response time‐dependent density‐functional theory , 2006 .

[29]  Shen Li,et al.  A density functional for sparse matter , 2009, Journal of physics. Condensed matter : an Institute of Physics journal.

[30]  X. Andrade,et al.  Efficient formalism for large-scale ab initio molecular dynamics based on time-dependent density functional theory. , 2007, Physical review letters.

[31]  Shampa Raghunathan,et al.  The Lack of Resonance Problem in Coherent Control with Real-Time Time-Dependent Density Functional Theory. , 2012, Journal of chemical theory and computation.

[32]  D. Bauer,et al.  Time-dependent Kohn-Sham approach to quantum electrodynamics , 2010, 1011.4162.

[33]  D R Bowler,et al.  Calculations for millions of atoms with density functional theory: linear scaling shows its potential , 2009, Journal of physics. Condensed matter : an Institute of Physics journal.

[34]  Jie Liu,et al.  Molecular-orbital-free algorithm for the excited-state force in time-dependent density functional theory. , 2011, The Journal of chemical physics.

[35]  Shampa Raghunathan,et al.  Critical Examination of Explicitly Time-Dependent Density Functional Theory for Coherent Control of Dipole Switching. , 2011, Journal of chemical theory and computation.

[36]  Adrienn Ruzsinszky,et al.  Some Fundamental Issues in Ground-State Density Functional Theory: A Guide for the Perplexed. , 2009, Journal of chemical theory and computation.

[37]  M. Head‐Gordon,et al.  Excitation Energies from Time-Dependent Density Functional Theory for Linear Polyene Oligomers: Butadiene to Decapentaene , 2001 .

[38]  R. Baer,et al.  A well-tempered density functional theory of electrons in molecules. , 2007, Physical chemistry chemical physics : PCCP.

[39]  G. Kresse,et al.  Optical response of the sodium alanate system: GW0-BSE calculations and thin film measurements , 2011 .

[40]  G. Vignale,et al.  Spin gaps and spin-flip energies in density-functional theory , 2009, 0911.1712.

[41]  E. Engel,et al.  Density Functional Theory , 2011 .

[42]  Angel Rubio,et al.  Time-dependent density-functional approach for biological chromophores: the case of the green fluorescent protein. , 2003, Physical review letters.

[43]  C. Ullrich,et al.  Asymmetry of above-threshold ionization of metal clusters in two-color laser fields: A time-dependent density-functional study , 2004 .

[44]  L. Reining,et al.  Double excitations in finite systems. , 2009, The Journal of chemical physics.

[45]  Nicholas C. Handy,et al.  On the determination of excitation energies using density functional theory , 2000 .

[46]  C. Ambrosch-Draxl,et al.  Optical absorption spectra of semiconductors and insulators including electron-hole correlations: An ab initio study within the LAPW method , 2002 .

[47]  C. Ullrich,et al.  Metallic clusters in strong femtosecond laser pulses , 1997 .

[48]  David S. Sholl,et al.  Density Functional Theory , 2009 .

[49]  C. Almbladh,et al.  Some open questions in TDDFT: Clues from lattice models and Kadanoff-Baym dynamics , 2011, 1103.2291.

[50]  Alfred Maquet,et al.  Photoionization of atoms using time-dependent density functional theory , 2003 .

[51]  J. Werschnik,et al.  Quantum optimal control theory , 2007, 0707.1883.

[52]  Godby,et al.  Accurate exchange-correlation potential for silicon and its discontinuity on addition of an electron. , 1986, Physical review letters.

[53]  M. Stener,et al.  Photoionization of mercury: A relativistic time-dependent density-functional-theory approach , 2002 .

[54]  J. Perdew,et al.  Density-Functional Theory for Fractional Particle Number: Derivative Discontinuities of the Energy , 1982 .

[55]  M. E. Casida,et al.  Troubleshooting time-dependent density-functional theory for photochemical applications: oxirane. , 2007, The Journal of chemical physics.

[56]  L. Reining,et al.  Dynamical response function in sodium studied by inelastic x-ray scattering spectroscopy , 2011 .

[57]  V. U. Nazarov,et al.  Optics of semiconductors from meta-generalized-gradient-approximation-based time-dependent density-functional theory. , 2011, Physical review letters.

[58]  Kieron Burke,et al.  DFT in a nutshell , 2013 .

[59]  Godby,et al.  Density-Polarization Functional Theory of the Response of a Periodic Insulating Solid to an Electric Field. , 1995, Physical review letters.

[60]  Carlo Adamo,et al.  Extensive TD-DFT Benchmark: Singlet-Excited States of Organic Molecules. , 2009, Journal of chemical theory and computation.

[61]  D. Salahub,et al.  Excited-state potential energy curves from time-dependent density-functional theory: A cross section of formaldehyde's 1A1 manifold , 1998 .

[62]  L. Reining,et al.  Transforming nonlocality into a frequency dependence: a shortcut to spectroscopy. , 2007, Physical review letters.

[63]  N A Lima,et al.  Density functionals not based on the electron gas: local-density approximation for a Luttinger liquid. , 2003, Physical review letters.

[64]  P. Norman,et al.  Quadratic response functions in the relativistic four-component Kohn-Sham approximation. , 2008, The Journal of chemical physics.

[65]  S. H. Vosko,et al.  Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis , 1980 .

[66]  R. W. Godby,et al.  Long-wavelength behavior of the exchange-correlation kernel in the Kohn-Sham theory of periodic systems , 1997 .

[67]  J. Venter,et al.  The Century of Biology , 2004 .

[68]  M. Broyer,et al.  Optical Properties of Au Nanoclusters from TD-DFT Calculations , 2011 .

[69]  C. Mottet,et al.  Optical properties of pure and core-shell noble-metal nanoclusters from TDDFT: The influence of the atomic structure , 2011 .

[70]  M. Ventra,et al.  Foundations of stochastic time-dependent current-density functional theory for open quantum systems: Potential pitfalls and rigorous results , 2012, 1209.5529.

[71]  Angel Rubio,et al.  Excited states dynamics in time-dependent density functional theory , 2002, cond-mat/0206307.

[72]  K. Burke Perspective on density functional theory. , 2012, The Journal of chemical physics.

[73]  Xavier Andrade,et al.  Optical and magnetic properties of boron fullerenes. , 2009, Physical chemistry chemical physics : PCCP.

[74]  C. A. Ullrich,et al.  Time-dependent V-representability on lattice systems. , 2008, The Journal of chemical physics.

[75]  C. Ullrich,et al.  Real-time electron dynamics with exact-exchange time-dependent density-functional theory. , 2007, Physical review letters.

[76]  R. Leeuwen,et al.  LETTER TO THE EDITOR: Electron correlation effects in the double ionization of He , 1998 .

[77]  L. Reining,et al.  Time-dependent density-functional theory for extended systems , 2007 .

[78]  Enhanced excitonic effects in the energy loss spectra of LiF and Ar at large momentum transfer , 2012, 1204.2724.

[79]  A. Aspuru‐Guzik,et al.  Time-dependent density functional theory of open quantum systems in the linear-response regime. , 2010, The Journal of chemical physics.

[80]  Exchange and correlation kernels at the resonance frequency: Implications for excitation energies in density-functional theory , 1999, cond-mat/9905119.

[81]  K. Pernal Excitation energies from range-separated time-dependent density and density matrix functional theory. , 2012, The Journal of chemical physics.

[82]  I. Tavernelli,et al.  Trajectory surface hopping within linear response time-dependent density-functional theory. , 2007, Physical review letters.

[83]  T. Van Voorhis,et al.  Implementation and assessment of a simple nonlocal van der Waals density functional. , 2010, The Journal of chemical physics.

[84]  Wang,et al.  Accurate and simple analytic representation of the electron-gas correlation energy. , 1992, Physical review. B, Condensed matter.

[85]  G. Vignale,et al.  Erratum: Time-dependent current-density-functional theory for the linear response of weakly disordered systems Phys. Rev. B 65, 245102 (2002) , 2004 .

[86]  F. Fuchs,et al.  Efficient O(N 2 ) approach to solve the Bethe-Salpeter equation for excitonic bound states , 2008, 0805.0659.

[87]  M. Ventra Electrical Transport in Nanoscale Systems , 2008 .

[88]  Elliott H. Lieb,et al.  Density Functionals for Coulomb Systems , 1983 .

[89]  Wolfram Koch,et al.  A Chemist's Guide to Density Functional Theory , 2000 .

[90]  Efthimios Kaxiras,et al.  Mechanisms for ultrafast nonradiative relaxation in electronically excited eumelanin constituents. , 2008, Biophysical journal.

[91]  Baldassare Di Bartolo,et al.  Spectroscopy and dynamics of collective excitations in solids , 1997 .

[92]  K. Hirao,et al.  A long-range-corrected time-dependent density functional theory. , 2004, The Journal of chemical physics.

[93]  F. Gadéa,et al.  Charge-transfer correction for improved time-dependent local density approximation excited-state potential energy curves: Analysis within the two-level model with illustration for H2 and LiH , 2000 .

[94]  E. Gross,et al.  Multicomponent density-functional theory for time-dependent systems , 2007 .

[95]  E K U Gross,et al.  Dynamical Coulomb blockade and the derivative discontinuity of time-dependent density functional theory. , 2009, Physical review letters.

[96]  D. Bowler,et al.  O(N) methods in electronic structure calculations. , 2011, Reports on progress in physics. Physical Society.

[97]  R. D’Agosta,et al.  A stochastic approach to open quantum systems , 2011, Journal of physics. Condensed matter : an Institute of Physics journal.

[98]  E. Gross,et al.  Density-Functional Theory for Time-Dependent Systems , 1984 .

[99]  G. Bertsch,et al.  Nonadiabatic generation of coherent phonons. , 2012, The Journal of chemical physics.

[100]  E J Baerends,et al.  Charge transfer, double and bond-breaking excitations with time-dependent density matrix functional theory. , 2008, Physical review letters.

[101]  Efthimios Kaxiras,et al.  Real-time, local basis-set implementation of time-dependent density functional theory for excited state dynamics simulations. , 2008, The Journal of chemical physics.

[102]  Jochen Autschbach,et al.  Charge-transfer excitations and time-dependent density functional theory: problems and some proposed solutions. , 2009, Chemphyschem : a European journal of chemical physics and physical chemistry.

[103]  J. Ángyán,et al.  Hybrid functional with separated range , 2005 .

[104]  Shih-I Chu,et al.  Time-dependent density-functional theory for strong-field multiphoton processes: Application to the study of the role of dynamical electron correlation in multiple high-order harmonic generation , 1998 .

[105]  Chengbu Liu,et al.  Time-dependent four-component relativistic density functional theory for excitation energies. , 2004, The Journal of chemical physics.

[106]  C. Ullrich,et al.  Time-dependent transition density matrix , 2011 .

[107]  G. Scuseria,et al.  Assessment of a long-range corrected hybrid functional. , 2006, The Journal of chemical physics.

[108]  Gustavo E. Scuseria,et al.  A novel form for the exchange-correlation energy functional , 1998 .

[109]  Carsten A. Ullrich,et al.  Time-Dependent Density-Functional Theory: Concepts and Applications , 2012 .

[110]  J. Tully Perspective: Nonadiabatic dynamics theory. , 2012, The Journal of chemical physics.

[111]  S. Conti,et al.  TIME-DEPENDENT DENSITY FUNCTIONAL THEORY BEYOND THE ADIABATIC LOCAL DENSITY APPROXIMATION , 1997 .

[112]  N. Maitra On correlated electron-nuclear dynamics using time-dependent density functional theory. , 2006, The Journal of chemical physics.

[113]  I. Tokatly,et al.  Time-dependent current density functional theory on a lattice , 2010, 1011.2715.

[114]  Shampa Raghunathan,et al.  Coherent control and time-dependent density functional theory: towards creation of wave packets by ultrashort laser pulses. , 2012, The Journal of chemical physics.

[115]  Lucia Reining,et al.  Many-body perturbation theory using the density-functional concept: beyond the GW approximation. , 2005, Physical review letters.

[116]  Angel Rubio,et al.  Bound excitons in time-dependent density-functional theory: optical and energy-loss spectra. , 2003, Physical review letters.

[117]  Kari Laasonen,et al.  Ab Initio Molecular Dynamics , 1994, Methods in molecular biology.

[118]  Andrew P. Horsfield,et al.  Modelling non-adiabatic processes using correlated electron-ion dynamics , 2010 .

[119]  Á. Rubio,et al.  Excited states of the green fluorescent protein chromophore: Performance of ab initio and semi‐empirical methods , 2012 .

[120]  Quong,et al.  First-principles evaluation of dynamical response and plasmon dispersion in metals. , 1993, Physical review letters.

[121]  P. Y. Yu,et al.  Fundamentals of Semiconductors , 1995 .

[122]  Stochastic time-dependent current-density-functional theory. , 2007, Physical review letters.

[123]  G. F. Bertsch,et al.  Time-dependent density functional theory for strong electromagnetic fields in crystalline solids , 2011, 1112.2291.

[124]  R. Gibbard,et al.  Comments on , 2016, Journal of pharmacy practice.

[125]  Basile F. E. Curchod,et al.  Mixed quantum-classical dynamics with time-dependent external fields: A time-dependent density-functional-theory approach , 2010 .

[126]  A. Dreuw,et al.  Dependence of Excited State Potential Energy Surfaces on the Spatial Overlap of the Kohn-Sham Orbitals and the Amount of Nonlocal Hartree-Fock Exchange in Time-Dependent Density Functional Theory. , 2010, Journal of chemical theory and computation.

[127]  H. G. Tsai,et al.  TD-DFT study of the excited-state potential energy surfaces of 2-(2'-hydroxyphenyl)benzimidazole and its amino derivatives. , 2010, The journal of physical chemistry. A.

[128]  Troy Van Voorhis,et al.  Nonlocal van der Waals density functional made simple. , 2009, Physical review letters.

[129]  Excitonic effects in time-dependent density-functional theory: An analytically solvable model , 2004, cond-mat/0406344.

[130]  Burke,et al.  Generalized Gradient Approximation Made Simple. , 1996, Physical review letters.

[131]  Beyond time-dependent exact exchange: the need for long-range correlation. , 2006, The Journal of chemical physics.

[132]  I. Tavernelli,et al.  Trajectory-based solution of the nonadiabatic quantum dynamics equations: an on-the-fly approach for molecular dynamics simulations. , 2011, Physical chemistry chemical physics : PCCP.

[133]  A. Marini,et al.  Double excitations in correlated systems: a many-body approach. , 2011, The Journal of chemical physics.

[134]  F. Angelis,et al.  Spectroscopic properties of cyclometallated iridium complexes by TDDFT , 2009 .

[135]  Daniele Varsano,et al.  Optical properties of triplex DNA from time-dependent density functional theory. , 2012, The journal of physical chemistry. B.

[136]  W. Cai,et al.  Plasmonics for extreme light concentration and manipulation. , 2010, Nature materials.

[137]  Giovanni Vignale,et al.  Quantum Theory of the Electron Liquid , 2005 .

[138]  G. Schatz,et al.  From Discrete Electronic States to Plasmons: TDDFT Optical Absorption Properties of Agn(n= 10, 20, 35, 56, 84, 120) Tetrahedral Clusters , 2008 .

[139]  Basile F. E. Curchod,et al.  Trajectory-based nonadiabatic dynamics with time-dependent density functional theory. , 2013, Chemphyschem : a European journal of chemical physics and physical chemistry.

[140]  L. Reining,et al.  Dynamical response function in sodium and aluminum from time-dependent density-functional theory , 2011 .

[141]  R. Baer,et al.  Reliable prediction of charge transfer excitations in molecular complexes using time-dependent density functional theory. , 2009, Journal of the American Chemical Society.

[142]  E K U Gross,et al.  Correlated electron-nuclear dynamics: exact factorization of the molecular wavefunction. , 2012, The Journal of chemical physics.

[143]  Takashi Nakatsukasa,et al.  First-principles electron dynamics simulation for optical breakdown of dielectrics under an intense laser field , 2008 .

[144]  F. Bechstedt,et al.  Optical spectra of Si nanocrystallites: Bethe-Salpeter approach versus time-dependent density-functional theory , 2008 .

[145]  V. Turkowski,et al.  Time-dependent density-functional approach for exciton binding energies , 2009, 0903.0027.

[146]  Kieron Burke,et al.  Double excitations within time-dependent density functional theory linear response. , 2004, The Journal of chemical physics.

[147]  Lasse Jensen,et al.  Theoretical studies of plasmonics using electronic structure methods. , 2011, Chemical reviews.

[148]  E K U Gross,et al.  Exact factorization of the time-dependent electron-nuclear wave function. , 2010, Physical review letters.

[149]  Kohn,et al.  Local density-functional theory of frequency-dependent linear response. , 1985, Physical review letters.

[150]  Xavier Andrade,et al.  Time-dependent density-functional theory in massively parallel computer architectures: the octopus project , 2012, Journal of physics. Condensed matter : an Institute of Physics journal.

[151]  Alán Aspuru-Guzik,et al.  Time-dependent current-density functional theory for generalized open quantum systems. , 2009, Physical chemistry chemical physics : PCCP.

[152]  Claudio Verdozzi,et al.  Time-dependent density-functional theory and strongly correlated systems: insight from numerical studies. , 2007, Physical review letters.

[153]  Fan Zhang,et al.  A dressed TDDFT treatment of the 21Ag states of butadiene and hexatriene , 2004 .

[154]  Time-dependent Kohn–Sham approach to multiple ionization , 2000 .

[155]  Collective intersubband transitions in quantum wells: A comparative density-functional study , 1998, cond-mat/9806252.

[156]  Robert van Leeuwen,et al.  KEY CONCEPTS IN TIME-DEPENDENT DENSITY-FUNCTIONAL THEORY , 2001 .

[157]  Tobias Burnus,et al.  Time-dependent electron localization function , 2005 .

[158]  J. Dobson,et al.  Calculation of dispersion energies , 2012, Journal of physics. Condensed matter : an Institute of Physics journal.

[159]  M. Levy Universal variational functionals of electron densities, first-order density matrices, and natural spin-orbitals and solution of the v-representability problem. , 1979, Proceedings of the National Academy of Sciences of the United States of America.

[160]  R. Baer,et al.  Density functional theory with correct long-range asymptotic behavior. , 2004, Physical review letters.

[161]  Roi Baer,et al.  Tuned range-separated hybrids in density functional theory. , 2010, Annual review of physical chemistry.

[162]  G. Stefanucci,et al.  Towards a description of the Kondo effect using time-dependent density-functional theory. , 2011, Physical review letters.

[163]  M. Hubin-franskin,et al.  Electronic excitation of carbon dioxide in the 10.5-18 eV range studied by inelastic electron scattering spectroscopy , 1988 .

[164]  Kohn,et al.  Current-Dependent Exchange-Correlation Potential for Dynamical Linear Response Theory. , 1996, Physical review letters.

[165]  J. Tully Molecular dynamics with electronic transitions , 1990 .

[166]  H. Tachikawa,et al.  TD-DFT calculations of the potential energy curves for the trans-cis photo-isomerization of protonated Schiff base of retinal. , 2004, Journal of photochemistry and photobiology. B, Biology.

[167]  S. Grimme Calculation of the Electronic Spectra of Large Molecules , 2004 .

[168]  L. Reining,et al.  Electronic excitations: density-functional versus many-body Green's-function approaches , 2002 .

[169]  Lucia Reining,et al.  Efficient ab initio calculations of bound and continuum excitons in the absorption spectra of semico , 2007, 0705.3140.

[170]  K. Burke,et al.  Density functional theory of the electrical conductivity of molecular devices. , 2005, Physical review letters.

[171]  Angel Rubio,et al.  The challenge of predicting optical properties of biomolecules: What can we learn from time-dependent density-functional theory? , 2009 .

[172]  G. Guo,et al.  Significant role of the DNA backbone in mediating the transition origin of electronic excitations of B-DNA--implication from long range corrected TDDFT and quantified NTO analysis. , 2011, Physical chemistry chemical physics : PCCP.

[173]  George F. Bertsch,et al.  Time-dependent local-density approximation in real time , 1996 .

[174]  E. Gross,et al.  Fundamentals of time-dependent density functional theory , 2012 .

[175]  Leeor Kronik,et al.  Excitation Gaps of Finite-Sized Systems from Optimally Tuned Range-Separated Hybrid Functionals. , 2012, Journal of chemical theory and computation.

[176]  G. Vignale Real-time resolution of the causality paradox of time-dependent density-functional theory , 2008, 0803.2727.

[177]  L. Hedin NEW METHOD FOR CALCULATING THE ONE-PARTICLE GREEN'S FUNCTION WITH APPLICATION TO THE ELECTRON-GAS PROBLEM , 1965 .

[178]  Á. Rubio,et al.  Time-dependent density-functional theory. , 2009, Physical chemistry chemical physics : PCCP.

[179]  A TDDFT study of the excited states of DNA bases and their assemblies. , 2006, The journal of physical chemistry. B.

[180]  Andreas Görling,et al.  Failure of time-dependent density functional methods for excitations in spatially separated systems , 2006 .

[181]  M. E. Casida,et al.  Progress in time-dependent density-functional theory. , 2011, Annual review of physical chemistry.

[182]  Andreas Savin,et al.  Combining long-range configuration interaction with short-range density functionals , 1997 .

[183]  N. Handy,et al.  A new hybrid exchange–correlation functional using the Coulomb-attenuating method (CAM-B3LYP) , 2004 .

[184]  J. Chayes,et al.  Density functional approach to quantum lattice systems , 1985 .

[185]  R. Ahlrichs,et al.  Absolute configuration of D(2)-symmetric fullerene C(84). , 2002, Journal of the American Chemical Society.

[186]  W. Kohn,et al.  Self-Consistent Equations Including Exchange and Correlation Effects , 1965 .

[187]  F. Aryasetiawan,et al.  The GW method , 1997, cond-mat/9712013.

[188]  Effect of cusps in time-dependent quantum mechanics. , 2011, Physical review letters.

[189]  T. Helgaker,et al.  Linear response at the 4-component relativistic density-functional level: application to the frequency-dependent dipole polarizability of Hg, AuH and PtH2 , 2005 .

[190]  E K U Gross,et al.  Adiabatic approximation in nonperturbative time-dependent density-functional theory. , 2008, Physical review letters.

[191]  R. Leeuwen,et al.  Causality and symmetry in time-dependent density-functional theory , 1998 .

[192]  Allan,et al.  Linear optical response in silicon and germanium including self-energy effects. , 1989, Physical review letters.

[193]  R. Dreizler,et al.  Density Functional Theory: An Advanced Course , 2011 .

[194]  Walter Kohn,et al.  Nobel Lecture: Electronic structure of matter-wave functions and density functionals , 1999 .

[195]  C. Ullrich,et al.  A minimal model for excitons within time-dependent density-functional theory. , 2012, The Journal of chemical physics.

[196]  M. Ruggenthaler,et al.  Global fixed-point proof of time-dependent density-functional theory , 2010, 1011.3375.

[197]  N. Maitra,et al.  Perspectives on double-excitations in TDDFT , 2011, 1101.3379.

[198]  G. Vignale,et al.  Theory of the linewidth of intersubband plasmons in quantum wells. , 2001, Physical review letters.

[199]  Jana Fuhrmann,et al.  Reviews In Computational Chemistry , 2016 .

[200]  A. Rubio,et al.  Ab-initio angle and energy resolved photoelectron spectroscopy with time-dependent density-functional theory , 2012 .

[201]  E. Gross,et al.  Time-dependent density functional theory. , 2004, Annual review of physical chemistry.

[202]  L. Kronik,et al.  Orbital-dependent density functionals: Theory and applications , 2008 .

[203]  A. Zunger,et al.  Self-interaction correction to density-functional approximations for many-electron systems , 1981 .

[204]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[205]  W. Domcke,et al.  Ab initio potential-energy functions for excited state intramolecular proton transfer: a comparative study of o-hydroxybenzaldehyde, salicylic acid and 7-hydroxy-1-indanone , 1999 .

[206]  J J Rehr,et al.  Real-time time-dependent density functional theory approach for frequency-dependent nonlinear optical response in photonic molecules. , 2007, The Journal of chemical physics.

[207]  Vogl,et al.  Generalized Kohn-Sham schemes and the band-gap problem. , 1996, Physical review. B, Condensed matter.

[208]  Garry Rumbles,et al.  Excitons in nanoscale systems , 2006, Nature materials.

[209]  N. Vast,et al.  Long-range contribution to the exchange-correlation kernel of time-dependent density functional theory , 2004 .

[211]  Bertsch,et al.  Time-dependent local-density approximation in real time. , 1996, Physical review. B, Condensed matter.

[212]  Wenli Zou,et al.  Time-dependent four-component relativistic density-functional theory for excitation energies. II. The exchange-correlation kernel. , 2005, The Journal of chemical physics.

[213]  A. Marini,et al.  Ab initiocalculation of the exchange-correlation kernel in extended systems , 2003 .

[214]  Todd J. Martínez,et al.  Conical intersections and double excitations in time-dependent density functional theory , 2006 .

[215]  Mark Earl Casida,et al.  In Recent Advances in Density-Functional Methods , 1995 .

[216]  G. Scuseria,et al.  Comparative assessment of a new nonempirical density functional: Molecules and hydrogen-bonded complexes , 2003 .

[217]  M. E. Casida,et al.  Mixed time-dependent density-functional theory/classical trajectory surface hopping study of oxirane photochemistry. , 2008, The Journal of chemical physics.

[218]  M. Frisch,et al.  Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields , 1994 .

[219]  Georg Kresse,et al.  Why does the B3LYP hybrid functional fail for metals? , 2007, The Journal of chemical physics.

[220]  E K U Gross,et al.  Excitations in time-dependent density-functional theory. , 2003, Physical review letters.

[221]  M. Head‐Gordon,et al.  Failure of time-dependent density functional theory for long-range charge-transfer excited states: the zincbacteriochlorin-bacteriochlorin and bacteriochlorophyll-spheroidene complexes. , 2004, Journal of the American Chemical Society.

[222]  Joel Yuen-Zhou,et al.  Time-dependent density functional theory for open quantum systems with unitary propagation. , 2009, Physical review letters.

[223]  D. Sholl,et al.  Density Functional Theory: A Practical Introduction , 2009 .

[224]  Donald G Truhlar,et al.  Density functional for spectroscopy: no long-range self-interaction error, good performance for Rydberg and charge-transfer states, and better performance on average than B3LYP for ground states. , 2006, The journal of physical chemistry. A.

[225]  John P. Perdew,et al.  Physical Content of the Exact Kohn-Sham Orbital Energies: Band Gaps and Derivative Discontinuities , 1983 .

[226]  J. Perdew,et al.  Assessing the performance of recent density functionals for bulk solids , 2009, 0903.4037.

[227]  M Elstner,et al.  A global investigation of excited state surfaces within time-dependent density-functional response theory. , 2004, The Journal of chemical physics.

[228]  M. Dion,et al.  van der Waals density functional for general geometries. , 2004, Physical review letters.

[229]  G. Scuseria,et al.  Climbing the density functional ladder: nonempirical meta-generalized gradient approximation designed for molecules and solids. , 2003, Physical review letters.

[230]  A. Becke,et al.  Density-functional exchange-energy approximation with correct asymptotic behavior. , 1988, Physical review. A, General physics.

[231]  Mark S Gordon,et al.  Benchmarking the performance of time-dependent density functional methods. , 2012, The Journal of chemical physics.

[232]  Exchange-correlation kernels for excited states in solids , 2001, cond-mat/0103357.

[233]  H. Appel,et al.  octopus: a tool for the application of time‐dependent density functional theory , 2006 .

[234]  N. Mermin Thermal Properties of the Inhomogeneous Electron Gas , 1965 .

[235]  N. Maitra,et al.  Semiclassical electron correlation in density-matrix time propagation. , 2010, Physical review letters.

[236]  E. Baerends,et al.  Double excitation effect in non-adiabatic time-dependent density functional theory with an analytic construction of the exchange-correlation kernel in the common energy denominator approximation. , 2009, Physical chemistry chemical physics : PCCP.

[237]  K. Hirao,et al.  A long-range correction scheme for generalized-gradient-approximation exchange functionals , 2001 .

[238]  A. Tkatchenko,et al.  Accurate and efficient method for many-body van der Waals interactions. , 2012, Physical review letters.

[239]  J. Tao,et al.  Performance of a nonempirical meta-generalized gradient approximation density functional for excitation energies. , 2007, The Journal of chemical physics.

[240]  Parr,et al.  Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. , 1988, Physical review. B, Condensed matter.

[241]  M. Ruggenthaler,et al.  Rabi oscillations and few-level approximations in time-dependent density functional theory. , 2009, Physical review letters.

[242]  K. Capelle,et al.  A bird's-eye view of density-functional theory , 2002 .

[243]  Andreas Dreuw,et al.  Single-reference ab initio methods for the calculation of excited states of large molecules. , 2005, Chemical reviews.

[244]  E K U Gross,et al.  Controlling the dynamics of many-electron systems from first principles: a combination of optimal control and time-dependent density-functional theory. , 2010, Physical review letters.

[245]  Kieron Burke,et al.  Current-density functional theory of the response of solids , 2003 .

[246]  J. Cirac,et al.  Improvement of frequency standards with quantum entanglement , 1997, quant-ph/9707014.

[247]  Werner Hanke,et al.  Many-particle effects in the optical spectrum of a semiconductor , 1980 .

[248]  A. Fetter,et al.  Quantum Theory of Many-Particle Systems , 1971 .

[249]  M. Manninen,et al.  The Kadanoff–Baym approach to double excitations in finite systems , 2011, 1108.4106.

[250]  T. Van Voorhis,et al.  Communication: Conical intersections using constrained density functional theory-configuration interaction. , 2010, The Journal of chemical physics.

[251]  L. Reining,et al.  Macroscopic and microscopic components of exchange-correlation interactions , 2003 .

[252]  C. Ullrich,et al.  Direct calculation of exciton binding energies with time-dependent density-functional theory , 2013, 1302.6972.

[253]  I. Tokatly,et al.  Time-dependent density functional theory on a lattice , 2012, 1206.6267.

[254]  G. Bertsch,et al.  First-principles description for coherent phonon generation in diamond , 2010, Journal of physics. Condensed matter : an Institute of Physics journal.

[255]  R. Leeuwen,et al.  Density-potential mappings in quantum dynamics , 2012, 1203.5894.

[256]  André D. Bandrauk,et al.  Nonlinear time-dependent density-functional-theory study of ionization and harmonic generation in CO{sub 2} by ultrashort intense laser pulses: Orientational effects , 2010 .

[257]  Roi Baer,et al.  Quantum memory effects in the dynamics of electrons in gold clusters , 2006 .

[258]  Paul A. Wiggins,et al.  Excited state surfaces in density functional theory: a new twist on an old problem. , 2009, The Journal of chemical physics.

[259]  I. Tokatly Time-dependent density functional theory for many-electron systems interacting with cavity photons. , 2013, Physical review letters.

[260]  R. Leeuwen,et al.  MAPPING FROM DENSITIES TO POTENTIALS IN TIME-DEPENDENT DENSITY-FUNCTIONAL THEORY , 1999 .

[261]  K. Burke,et al.  Accuracy of density functionals for molecular electronics: The Anderson junction , 2012, 1201.1310.

[262]  S. Kümmel,et al.  Hydrodynamic perspective on memory in time-dependent density-functional theory , 2009 .

[263]  David Beljonne,et al.  The Role of Driving Energy and Delocalized States for Charge Separation in Organic Semiconductors , 2012, Science.

[264]  A. Tkatchenko,et al.  Accurate molecular van der Waals interactions from ground-state electron density and free-atom reference data. , 2009, Physical review letters.

[265]  Angel Rubio,et al.  Quantum coherence controls the charge separation in a prototypical artificial light-harvesting system , 2012, Nature Communications.

[266]  Angel Rubio,et al.  Excitonic effects in solids described by time-dependent density-functional theory. , 2002, Physical review letters.

[267]  K. Varga Multidomain decomposition approach to large scale electronic structure calculations , 2010 .

[268]  I. D’Amico,et al.  Dissipation through spin Coulomb drag in electronic spin transport and optical excitations , 2006 .

[269]  D. Chong Recent Advances in Density Functional Methods Part III , 2002 .