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

Pribram-Jones, Aurora; Grabowski, Paul E.; Burke, Kieron

doi:10.1103/PhysRevLett.116.233001

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

Journal Article · Wed Jun 08 00:00:00 EDT 2016 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.116.233001· OSTI ID:1389980

Pribram-Jones, Aurora ^[1]; Grabowski, Paul E. ^[2]; Burke, Kieron ^[3]

Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Univ. of California, Berkeley, CA (United States). Department of Chemistry
Univ. of California, Irvine, CA (United States). Dept. of Physics and Astronomy
Univ. of California, Irvine, CA (United States). Dept. of Chemistry and Dept. of Physics and Astronomy

We present that 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. Finally, this produces a natural method for generating new thermal exchange-correlation approximations.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC52-07NA27344; FG02-97ER25308

OSTI ID:: 1389980

Alternate ID(s):: OSTI ID: 1256152

Report Number(s):: LLNL-JRNL--689945

Journal Information:: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 23 Vol. 116; ISSN 0031-9007; ISSN PRLTAO

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (66)

DFT in a nutshell Burke, Kieron; Wagner, Lucas O. International Journal of Quantum Chemistry, Vol. 113, Issue 2 https://doi.org/10.1002/qua.24259	journal	July 2012
A Primer in Density Functional Theory Fiolhais, Carlos; Nogueira, Fernando; Marques, Miguel A. L. Lecture Notes in Physics https://doi.org/10.1007/3-540-37072-2	book	January 2003
Exact Conditions and Their Relevance in TDDFT Wagner, Lucas O.; Yang, Zeng-hui; Burke, Kieron Fundamentals of Time-Dependent Density Functional Theory https://doi.org/10.1007/978-3-642-23518-4_5	book	January 2012
Time-Dependent Density-Functional Theory Gross, E. K. U.; Kohn, W. Advances in Quantum Chemistry https://doi.org/10.1016/S0065-3276(08)60600-0	book	January 1990
Comparison of electron–ion energy transfer in dense plasmas obtained from numerical simulations and quantum kinetic theory Vorberger, J.; Gericke, D. O. High Energy Density Physics, Vol. 10 https://doi.org/10.1016/j.hedp.2013.10.006	journal	March 2014
Nonequilibrium Many-Body Theory of Quantum Systems Stefanucci, Gianluca; van Leeuwen, Robert https://doi.org/10.1017/CBO9781139023979	book	March 2013
A Parameter-Free Density Functional That Works for Noncovalent Interactions Eshuis, Henk; Furche, Filipp The Journal of Physical Chemistry Letters, Vol. 2, Issue 9 https://doi.org/10.1021/jz200238f	journal	April 2011
Laser Compression of Matter to Super-High Densities: Thermonuclear (CTR) Applications Nuckolls, John; Wood, Lowell; Thiessen, Albert Nature, Vol. 239, Issue 5368, p. 139-142 https://doi.org/10.1038/239139a0	journal	September 1972
Focusing of short-pulse high-intensity laser-accelerated proton beams Bartal, Teresa; Foord, Mark E.; Bellei, Claudio Nature Physics, Vol. 8, Issue 2 https://doi.org/10.1038/nphys2153	journal	December 2011
Time-dependent density functional theory: Past, present, and future Burke, Kieron; Werschnik, Jan; Gross, E. K. U. The Journal of Chemical Physics, Vol. 123, Issue 6 https://doi.org/10.1063/1.1904586	journal	August 2005
Equation of state, transport coefficients, and stopping power of dense plasmas from the average-atom model self-consistent approach for astrophysical and laboratory plasmas Faussurier, Gérald; Blancard, Christophe; Cossé, Philippe Physics of Plasmas, Vol. 17, Issue 5 https://doi.org/10.1063/1.3420276	journal	May 2010
Fast computation of molecular random phase approximation correlation energies using resolution of the identity and imaginary frequency integration Eshuis, Henk; Yarkony, Julian; Furche, Filipp The Journal of Chemical Physics, Vol. 132, Issue 23 https://doi.org/10.1063/1.3442749	journal	June 2010
Excitations and benchmark ensemble density functional theory for two electrons Pribram-Jones, Aurora; Yang, Zeng-hui; Trail, John R. The Journal of Chemical Physics, Vol. 140, Issue 18 https://doi.org/10.1063/1.4872255	journal	May 2014
Invertibility of retarded response functions for Laplace transformable potentials: Application to one-body reduced density matrix functional theory Giesbertz, K. J. H. The Journal of Chemical Physics, Vol. 143, Issue 5 https://doi.org/10.1063/1.4927075	journal	August 2015
Invertibility of the retarded response functions for initial mixed states: application to one-body reduced density matrix functional theory Giesbertz, K. J. H. Molecular Physics, Vol. 114, Issue 7-8 https://doi.org/10.1080/00268976.2016.1141253	journal	November 2015
Ab Initio Equation of State Data for Hydrogen, Helium, and Water and the Internal Structure of Jupiter Nettelmann, Nadine; Holst, Bastian; Kietzmann, André The Astrophysical Journal, Vol. 683, Issue 2 https://doi.org/10.1086/589806	journal	August 2008
Solubility of Water ice in Metallic Hydrogen: Consequences for core Erosion in gas Giant Planets Wilson, H. F.; Militzer, B. The Astrophysical Journal, Vol. 745, Issue 1 https://doi.org/10.1088/0004-637X/745/1/54	journal	December 2011
Ab Initio Equation of State for Hydrogen-Helium Mixtures with Recalibration of the Giant-Planet Mass-Radius Relation Militzer, B.; Hubbard, W. B. The Astrophysical Journal, Vol. 774, Issue 2 https://doi.org/10.1088/0004-637X/774/2/148	journal	August 2013
The transfer of energy between electrons and ions in solids Horsfield, A. P.; Bowler, D. R.; Ness, H. Reports on Progress in Physics, Vol. 69, Issue 4 https://doi.org/10.1088/0034-4885/69/4/R05	journal	March 2006
Assessment of correlation energies based on the random-phase approximation Paier, Joachim; Ren, Xinguo; Rinke, Patrick New Journal of Physics, Vol. 14, Issue 4 https://doi.org/10.1088/1367-2630/14/4/043002	journal	April 2012
Time-Dependent Density-Functional Theory Ullrich, Carsten A. https://doi.org/10.1093/acprof:oso/9780199563029.001.0001	book	December 2011
Quantum Theory of Electrical Transport Phenomena Kohn, W.; Luttinger, J. M. Physical Review, Vol. 108, Issue 3 https://doi.org/10.1103/PhysRev.108.590	journal	November 1957
Inhomogeneous Electron Gas Hohenberg, P.; Kohn, W. Physical Review, Vol. 136, Issue 3B, p. B864-B871 https://doi.org/10.1103/PhysRev.136.B864	journal	November 1964
Thermal Properties of the Inhomogeneous Electron Gas Mermin, N. David Physical Review, Vol. 137, Issue 5A https://doi.org/10.1103/PhysRev.137.A1441	journal	March 1965
Self-Consistent Equations Including Exchange and Correlation Effects Kohn, W.; Sham, L. J. Physical Review, Vol. 140, Issue 4A, p. A1133-A1138 https://doi.org/10.1103/PhysRev.140.A1133	journal	November 1965
Exchange and correlation potentials for electron-ion systems at finite temperatures Perrot, François; Dharma-wardana, M. W. C. Physical Review A, Vol. 30, Issue 5 https://doi.org/10.1103/PhysRevA.30.2619	journal	November 1984
Hohenberg-Kohn theorem for time-dependent ensembles Li, Tie-cheng; Tong, Pei-qing Physical Review A, Vol. 31, Issue 3 https://doi.org/10.1103/PhysRevA.31.1950	journal	March 1985
Kohn-Sham equation for time-dependent ensembles Li, Tiecheng; Li, Yanmin Physical Review A, Vol. 31, Issue 6 https://doi.org/10.1103/PhysRevA.31.3970	journal	June 1985
Hellmann-Feynman, virial, and scaling requisites for the exact universal density functionals. Shape of the correlation potential and diamagnetic susceptibility for atoms Levy, Mel; Perdew, John P. Physical Review A, Vol. 32, Issue 4 https://doi.org/10.1103/PhysRevA.32.2010	journal	October 1985
Frequency-dependent v -representability in density-functional theory Mearns, Daniel; Kohn, Walter Physical Review A, Vol. 35, Issue 11 https://doi.org/10.1103/PhysRevA.35.4796	journal	June 1987
Dynamic linear response of many-electron systems: An integral formulation of density-functional theory Yang, Weitao Physical Review A, Vol. 38, Issue 11 https://doi.org/10.1103/PhysRevA.38.5512	journal	December 1988
Nonexistence of a Taylor expansion in time due to cusps Yang, Zeng-hui; Burke, Kieron Physical Review A, Vol. 88, Issue 4 https://doi.org/10.1103/PhysRevA.88.042514	journal	October 2013
Exchange-correlation energy of a metallic surface: Wave-vector analysis Langreth, David C.; Perdew, John P. Physical Review B, Vol. 15, Issue 6 https://doi.org/10.1103/PhysRevB.15.2884	journal	March 1977
Electron liquid at any degeneracy Dandrea, R. G.; Ashcroft, N. W.; Carlsson, A. E. Physical Review B, Vol. 34, Issue 4 https://doi.org/10.1103/PhysRevB.34.2097	journal	August 1986
Current-density functional theory of the response of solids Maitra, Neepa T.; Souza, Ivo; Burke, Kieron Physical Review B, Vol. 68, Issue 4 https://doi.org/10.1103/PhysRevB.68.045109	journal	July 2003
Linear density response function within the time-dependent exact-exchange approximation Hellgren, Maria; von Barth, Ulf Physical Review B, Vol. 78, Issue 11 https://doi.org/10.1103/PhysRevB.78.115107	journal	September 2008
Gradient corrections to the exchange-correlation free energy Sjostrom, Travis; Daligault, Jérôme Physical Review B, Vol. 90, Issue 15 https://doi.org/10.1103/PhysRevB.90.155109	journal	October 2014
Electrical conductivity for warm, dense aluminum plasmas and liquids Desjarlais, M. P.; Kress, J. D.; Collins, L. A. Physical Review E, Vol. 66, Issue 2 https://doi.org/10.1103/PhysRevE.66.025401	journal	August 2002
Viscosity and mutual diffusion of deuterium-tritium mixtures in the warm-dense-matter regime Kress, J. D.; Cohen, James S.; Horner, D. A. Physical Review E, Vol. 82, Issue 3 https://doi.org/10.1103/PhysRevE.82.036404	journal	September 2010
Molecular dynamics simulations and generalized Lenard-Balescu calculations of electron-ion temperature equilibration in plasmas Benedict, Lorin X.; Surh, Michael P.; Castor, John I. Physical Review E, Vol. 86, Issue 4 https://doi.org/10.1103/PhysRevE.86.046406	journal	October 2012
Reduced coupled-mode approach to electron-ion energy relaxation Chapman, D. A.; Vorberger, J.; Gericke, D. O. Physical Review E, Vol. 88, Issue 1 https://doi.org/10.1103/PhysRevE.88.013102	journal	July 2013
Demixing of Hydrogen and Helium at Megabar Pressures Lorenzen, Winfried; Holst, Bastian; Redmer, Ronald Physical Review Letters, Vol. 102, Issue 11 https://doi.org/10.1103/PhysRevLett.102.115701	journal	March 2009
Sequestration of Noble Gases in Giant Planet Interiors Wilson, Hugh F.; Militzer, Burkhard Physical Review Letters, Vol. 104, Issue 12 https://doi.org/10.1103/PhysRevLett.104.121101	journal	March 2010
New Phases of Water Ice Predicted at Megabar Pressures Militzer, Burkhard; Wilson, Hugh F. Physical Review Letters, Vol. 105, Issue 19 https://doi.org/10.1103/PhysRevLett.105.195701	journal	November 2010
Exact Conditions in Finite-Temperature Density-Functional Theory Pittalis, S.; Proetto, C. R.; Floris, A. Physical Review Letters, Vol. 107, Issue 16 https://doi.org/10.1103/PhysRevLett.107.163001	journal	October 2011
Effect of Cusps in Time-Dependent Quantum Mechanics Yang, Zeng-hui; Maitra, Neepa T.; Burke, Kieron Physical Review Letters, Vol. 108, Issue 6 https://doi.org/10.1103/PhysRevLett.108.063003	journal	February 2012
Probing the Interiors of the Ice Giants: Shock Compression of Water to 700 GPa and 3.8 g / cm 3 Knudson, M. D.; Desjarlais, M. P.; Lemke, R. W. Physical Review Letters, Vol. 108, Issue 9 https://doi.org/10.1103/PhysRevLett.108.091102	journal	February 2012
Rocky Core Solubility in Jupiter and Giant Exoplanets Wilson, Hugh F.; Militzer, Burkhard Physical Review Letters, Vol. 108, Issue 11 https://doi.org/10.1103/PhysRevLett.108.111101	journal	March 2012
All-Electron Path Integral Monte Carlo Simulations of Warm Dense Matter: Application to Water and Carbon Plasmas Driver, K. P.; Militzer, B. Physical Review Letters, Vol. 108, Issue 11 https://doi.org/10.1103/PhysRevLett.108.115502	journal	March 2012
Energy Loss and Charge Transfer of Argon in a Laser-Generated Carbon Plasma Frank, A.; Blažević, A.; Bagnoud, V. Physical Review Letters, Vol. 110, Issue 11 https://doi.org/10.1103/PhysRevLett.110.115001	journal	March 2013
Accurate Homogeneous Electron Gas Exchange-Correlation Free Energy for Local Spin-Density Calculations Karasiev, Valentin V.; Sjostrom, Travis; Dufty, James Physical Review Letters, Vol. 112, Issue 7 https://doi.org/10.1103/PhysRevLett.112.076403	journal	February 2014
Measurement of Charged-Particle Stopping in Warm Dense Plasma Zylstra, A. B.; Frenje, J. A.; Grabowski, P. E. Physical Review Letters, Vol. 114, Issue 21 https://doi.org/10.1103/PhysRevLett.114.215002	journal	May 2015
Laser-Driven Implosion of Spherical DT Targets to Thermonuclear Burn Conditions Clarke, J. S.; Fisher, H. N.; Mason, R. J. Physical Review Letters, Vol. 30, Issue 3 https://doi.org/10.1103/PhysRevLett.30.89	journal	January 1973
Density-Functional Theory for Time-Dependent Systems Runge, Erich; Gross, E. K. U. Physical Review Letters, Vol. 52, Issue 12 https://doi.org/10.1103/PhysRevLett.52.997	journal	March 1984
Unified Approach for Molecular Dynamics and Density-Functional Theory Car, R.; Parrinello, M. Physical Review Letters, Vol. 55, Issue 22 https://doi.org/10.1103/PhysRevLett.55.2471	journal	November 1985
Local density-functional theory of frequency-dependent linear response Gross, E. K. U.; Kohn, Walter Physical Review Letters, Vol. 55, Issue 26 https://doi.org/10.1103/PhysRevLett.55.2850	journal	December 1985
Excitation Energies from Time-Dependent Density-Functional Theory Petersilka, M.; Gossmann, U. J.; Gross, E. K. U. Physical Review Letters, Vol. 76, Issue 8 https://doi.org/10.1103/PhysRevLett.76.1212	journal	February 1996
Several Theorems in Time-Dependent Density Functional Theory Hessler, Paul; Park, Jang; Burke, Kieron Physical Review Letters, Vol. 82, Issue 2 https://doi.org/10.1103/PhysRevLett.82.378	journal	January 1999
Theoretical approaches to x-ray absorption fine structure Rehr, J. J.; Albers, R. C. Reviews of Modern Physics, Vol. 72, Issue 3 https://doi.org/10.1103/RevModPhys.72.621	journal	July 2000
X-ray Thomson scattering in high energy density plasmas Glenzer, Siegfried H.; Redmer, Ronald Reviews of Modern Physics, Vol. 81, Issue 4 https://doi.org/10.1103/RevModPhys.81.1625	journal	December 2009
Europe Aims for a Cut-Rate Superlaser to Power Future Particle Accelerators Clery, Daniel Science, Vol. 341, Issue 6147 https://doi.org/10.1126/science.341.6147.704	journal	August 2013
Laser acceleration in novel media Tajima, T. The European Physical Journal Special Topics, Vol. 223, Issue 6 https://doi.org/10.1140/epjst/e2014-02154-6	journal	May 2014
Key Concepts in Time-Dependent Density-Functional Theory Van Leeuwen, Robert International Journal of Modern Physics B, Vol. 15, Issue 14 https://doi.org/10.1142/S021797920100499X	journal	June 2001
Thermodynamics and Correlational Properties of Finite-Temperature Electron Liquids in the Singwi-Tosi-Land-Sjölander Approximation Tanaka, Shigenori; Ichimaru, Setsuo Journal of the Physical Society of Japan, Vol. 55, Issue 7 https://doi.org/10.1143/JPSJ.55.2278	journal	July 1986
DFT: A Theory Full of Holes? Pribram-Jones, Aurora; Gross, David A.; Burke, Kieron Annual Review of Physical Chemistry, Vol. 66, Issue 1 https://doi.org/10.1146/annurev-physchem-040214-121420	journal	April 2015
Global fixed-point proof of time-dependent density-functional theory Ruggenthaler, M.; van Leeuwen, R. EPL (Europhysics Letters), Vol. 95, Issue 1 https://doi.org/10.1209/0295-5075/95/13001	journal	June 2011

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