Thermal Density Functional Theory: Time-Dependent Linear Response and Approximate Functionals from the Fluctuation-Dissipation Theorem.

The van Leeuwen proof of linear-response time-dependent density functional theory (TDDFT) is generalized to thermal ensembles. This allows generalization to finite temperatures of the Gross-Kohn relation, the exchange-correlation kernel of TDDFT, and fluctuation dissipation theorem for DFT. This produces a natural method for generating new thermal exchange-correlation approximations.

[1]  Jean-Pierre Antoine,et al.  Rigged Hilbert Spaces in Quantum Physics , 2009, Compendium of Quantum Physics.

[2]  D. Gericke,et al.  Comparison of electron–ion energy transfer in dense plasmas obtained from numerical simulations and quantum kinetic theory , 2013, 1307.6664.

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

[4]  W. Kohn,et al.  Quantum Theory of Electrical Transport Phenomena , 1957 .

[5]  Ansgar Liebsch,et al.  Electronic Excitations at Metal Surfaces , 2010 .

[6]  John M Prausnitz,et al.  Equation of State , 2020, Inverse Heat Conduction and Heat Exchangers.

[7]  J. Rehr,et al.  Theoretical approaches to x-ray absorption fine structure , 2000 .

[8]  S. Glenzer,et al.  X-ray Thomson scattering in high energy density plasmas , 2009 .

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

[10]  Gilbert W. Collins,et al.  Measurement of charged-particle stopping in warm dense plasma. , 2015, Physical review letters.

[11]  Sandrine A. Gaillard,et al.  Focusing of short-pulse high-intensity laser-accelerated proton beams , 2011, Nature Physics.

[12]  Kieron Burke,et al.  Excitations and benchmark ensemble density functional theory for two electrons. , 2014, The Journal of chemical physics.

[13]  J. Perdew,et al.  Hellmann-Feynman, virial, and scaling requisites for the exact universal density functionals. Shape of the correlation potential and diamagnetic susceptibility for atoms. , 1985, Physical review. A, General physics.

[14]  Burkhard Militzer,et al.  Rocky core solubility in Jupiter and giant exoplanets. , 2011, Physical review letters.

[15]  Car,et al.  Unified approach for molecular dynamics and density-functional theory. , 1985, Physical review letters.

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

[17]  Local and Semi-Local Density Functional Approximations for Exchange and Correlation: Why Do They Work, and Do They Work Best at Zero Temperature? , 2002 .

[18]  Carlsson,et al.  Electron liquid at any degeneracy. , 1986, Physical review. B, Condensed matter.

[19]  S. Ichimaru,et al.  Thermodynamics and Correlational Properties of Finite-Temperature Electron Liquids in the Singwi-Tosi-Land-Sjolander Approximation , 1986 .

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

[21]  David F Richards,et al.  Molecular dynamics simulations and generalized Lenard-Balescu calculations of electron-ion temperature equilibration in plasmas. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  K. Burke,et al.  Derivation of a generalized gradient approximation: The PW91 density functional , 1998 .

[23]  U. V. Barth,et al.  Linear density response function within the time-dependent exact-exchange approximation , 2008, 0807.0091.

[24]  B. Militzer,et al.  All-electron path integral Monte Carlo simulations of warm dense matter: application to water and carbon plasmas. , 2012, Physical review letters.

[25]  J. Kress,et al.  Viscosity and mutual diffusion of deuterium-tritium mixtures in the warm-dense-matter regime. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  J. Dufty,et al.  System-Size Dependence in Grand Canonical and Canonical Ensembles , 2015, 1502.00533.

[27]  F. Nogueira,et al.  A primer in density functional theory , 2003 .

[28]  Julian Yarkony,et al.  Fast computation of molecular random phase approximation correlation energies using resolution of the identity and imaginary frequency integration. , 2010, The Journal of chemical physics.

[29]  Kieron Burke,et al.  Thermal Density Functional Theory in Context , 2013, 1309.3043.

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

[31]  K. Giesbertz.  Invertibility of retarded response functions for Laplace transformable potentials: Application to one-body reduced density matrix functional theory. , 2015, The Journal of chemical physics.

[32]  P. Hohenberg,et al.  Inhomogeneous electron gas , 1964 .

[33]  Georg Kresse,et al.  Assessment of correlation energies based on the random-phase approximation , 2011, 1111.0173.

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

[35]  E K U Gross,et al.  Exact conditions in finite-temperature density-functional theory. , 2010, Physical review letters.

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

[37]  Ronald Redmer,et al.  Demixing of hydrogen and helium at megabar pressures. , 2009, Physical review letters.

[38]  B. Militzer,et al.  SOLUBILITY OF WATER ICE IN METALLIC HYDROGEN: CONSEQUENCES FOR CORE EROSION IN GAS GIANT PLANETS , 2012 .

[39]  Stuart A. Rice,et al.  Quantum Statistical Mechanics , 1963 .

[40]  John P. Perdew,et al.  Exchange-correlation energy of a metallic surface: Wave-vector analysis , 1977 .

[41]  J. Daligault,et al.  Gradient corrections to the exchange-correlation free energy , 2014, 1408.1380.

[42]  Gross,et al.  Excitation energies from time-dependent density-functional theory. , 1996, Physical review letters.

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

[44]  R. J. Mason,et al.  Laser-Driven Implosion of Spherical DT Targets to Thermonuclear Burn Conditions , 1973 .

[45]  B. Militzer,et al.  AB INITIO EQUATION OF STATE FOR HYDROGEN–HELIUM MIXTURES WITH RECALIBRATION OF THE GIANT-PLANET MASS–RADIUS RELATION , 2013, 1302.4691.

[46]  J. Nuckolls,et al.  Laser Compression of Matter to Super-High Densities: Thermonuclear (CTR) Applications , 1972, Nature.

[47]  Mark E. Casida,et al.  Time-Dependent Density Functional Response Theory of Molecular Systems: Theory, Computational Methods, and Functionals , 1996 .

[48]  Li.  Kohn-Sham equation for time-dependent ensembles. , 1985, Physical review. A, General physics.

[49]  Yang.  Dynamic linear response of many-electron systems: An integral formulation of density-functional theory. , 1988, Physical review. A, General physics.

[50]  J. Dobson.  Dispersion (van der Waals) forces and TDDFT , 2012 .

[51]  H. Eshuis,et al.  A parameter-free density functional that works for noncovalent interactions , 2011 .

[52]  B. Militzer,et al.  New phases of water ice predicted at megabar pressures. , 2010, Physical review letters.

[53]  Kieron Burke,et al.  DFT: A Theory Full of Holes? , 2014, Annual review of physical chemistry.

[54]  J. Kress,et al.  Electrical conductivity for warm, dense aluminum plasmas and liquids. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[55]  T. Tajima.  Laser acceleration in novel media , 2014 .

[56]  Travis Sjostrom,et al.  Accurate homogeneous electron gas exchange-correlation free energy for local spin-density calculations. , 2014, Physical review letters.

[57]  M. Basko,et al.  Energy loss and charge transfer of argon in a laser-generated carbon plasma. , 2013, Physical review letters.

[58]  Tong,et al.  Hohenberg-Kohn theorem for time-dependent ensembles. , 1985, Physical review. A, General physics.

[59]  K. Giesbertz.  Invertibility of the retarded response functions for initial mixed states: application to one-body reduced density matrix functional theory , 2016, 1601.00747.

[60]  R. Redmer,et al.  Ab Initio Equation of State Data for Hydrogen, Helium, and Water and the Internal Structure of Jupiter , 2007, 0712.1019.

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

[62]  A. Fisher,et al.  The transfer of energy between electrons and ions in solids , 2006, cond-mat/0603531.

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

[64]  B. Militzer,et al.  Sequestration of noble gases in giant planet interiors. , 2010, Physical review letters.

[65]  Ghosh,et al.  Density-functional theory for time-dependent systems. , 1987, Physical review. A, General physics.

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

[67]  M. Desjarlais,et al.  Probing the interiors of the ice giants: shock compression of water to 700 GPa and 3.8 g/cm³. , 2011, Physical review letters.

[68]  C. Blancard,et al.  Equation of state, transport coefficients, and stopping power of dense plasmas from the average-atom model self-consistent approach for astrophysical and laboratory plasmas , 2010 .

[69]  K. Burke,et al.  Exact Conditions and Their Relevance in TDDFT , 2012 .

[70]  M. Dharma-wardana,et al.  Exchange and correlation potentials for electron-ion systems at finite temperatures , 1984 .

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

[72]  K. Burke,et al.  Nonexistence of a Taylor expansion in time due to cusps , 2013, 1308.4445.

[73]  Kieron Burke,et al.  Connection formulas for thermal density functional theory , 2015, 1509.03060.

[74]  K. Burke,et al.  Several Theorems in Time-Dependent Density Functional Theory , 1999 .

[75]  Kieron Burke,et al.  Thermal Corrections to Density Functional Simulations of Warm Dense Matter , 2015 .