Exact conditions on the temperature dependence of density functionals
Abstract
Universal exact conditions guided the construction of most ground-state density functional approximations in use today. Here, we derive the relation between the entropy and Mermin free energy density functionals for thermal density functional theory. Both the entropy and sum of kinetic and electron-electron repulsion functionals are shown to be monotonically increasing with temperature, while the Mermin functional is concave downwards. Analogous relations are found for both exchange and correlation. The importance of these conditions is illustrated in two extremes: the Hubbard dimer and the uniform gas.
- Authors:
-
- Univ. of California, Irvine, CA (United States)
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Univ. of California, Berkeley, CA (United States)
- Publication Date:
- Research Org.:
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1389943
- Alternate Identifier(s):
- OSTI ID: 1253430
- Report Number(s):
- LLNL-JRNL-693119
Journal ID: ISSN 2469-9950; PRBMDO
- Grant/Contract Number:
- AC52-07NA27344; DE14-017426
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review B
- Additional Journal Information:
- Journal Volume: 93; Journal Issue: 19; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
Citation Formats
Burke, K., Smith, J. C., Grabowski, P. E., and Pribram-Jones, A. Exact conditions on the temperature dependence of density functionals. United States: N. p., 2016.
Web. doi:10.1103/PhysRevB.93.195132.
Burke, K., Smith, J. C., Grabowski, P. E., & Pribram-Jones, A. Exact conditions on the temperature dependence of density functionals. United States. https://doi.org/10.1103/PhysRevB.93.195132
Burke, K., Smith, J. C., Grabowski, P. E., and Pribram-Jones, A. Sun .
"Exact conditions on the temperature dependence of density functionals". United States. https://doi.org/10.1103/PhysRevB.93.195132. https://www.osti.gov/servlets/purl/1389943.
@article{osti_1389943,
title = {Exact conditions on the temperature dependence of density functionals},
author = {Burke, K. and Smith, J. C. and Grabowski, P. E. and Pribram-Jones, A.},
abstractNote = {Universal exact conditions guided the construction of most ground-state density functional approximations in use today. Here, we derive the relation between the entropy and Mermin free energy density functionals for thermal density functional theory. Both the entropy and sum of kinetic and electron-electron repulsion functionals are shown to be monotonically increasing with temperature, while the Mermin functional is concave downwards. Analogous relations are found for both exchange and correlation. The importance of these conditions is illustrated in two extremes: the Hubbard dimer and the uniform gas.},
doi = {10.1103/PhysRevB.93.195132},
journal = {Physical Review B},
number = 19,
volume = 93,
place = {United States},
year = {Sun May 15 00:00:00 EDT 2016},
month = {Sun May 15 00:00:00 EDT 2016}
}
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Works referenced in this record:
Generalized Gradient Approximation Made Simple
journal, October 1996
- Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
- Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868
Generalized Gradient Approximation Made Simple [Phys. Rev. Lett. 77, 3865 (1996)]
journal, February 1997
- Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
- Physical Review Letters, Vol. 78, Issue 7
Ramp compression of diamond to five terapascals
journal, July 2014
- Smith, R. F.; Eggert, J. H.; Jeanloz, R.
- Nature, Vol. 511, Issue 7509
Shock-Wave Exploration of the High-Pressure Phases of Carbon
journal, December 2008
- Knudson, M. D.; Desjarlais, M. P.; Dolan, D. H.
- Science, Vol. 322, Issue 5909
Exact Conditions in Finite-Temperature Density-Functional Theory
journal, October 2011
- Pittalis, S.; Proetto, C. R.; Floris, A.
- Physical Review Letters, Vol. 107, Issue 16
Free-Electron X-Ray Laser Measurements of Collisional-Damped Plasmons in Isochorically Heated Warm Dense Matter
journal, September 2015
- Sperling, P.; Gamboa, E. J.; Lee, H. J.
- Physical Review Letters, Vol. 115, Issue 11
Local density-functional theory of frequency-dependent linear response
journal, December 1985
- Gross, E. K. U.; Kohn, Walter
- Physical Review Letters, Vol. 55, Issue 26
Orbital-dependent density functionals: Theory and applications
journal, January 2008
- Kümmel, Stephan; Kronik, Leeor
- Reviews of Modern Physics, Vol. 80, Issue 1
Density-functional-theory approach to the thermodynamics of the harmonically confined one-dimensional Hubbard model
journal, July 2015
- Campo, V. L.
- Physical Review A, Vol. 92, Issue 1
Path-Integral Monte Carlo Simulation of the Warm Dense Homogeneous Electron Gas
journal, April 2013
- Brown, Ethan W.; Clark, Bryan K.; DuBois, Jonathan L.
- Physical Review Letters, Vol. 110, Issue 14
Spin-polarized electron liquid at arbitrary temperatures: Exchange-correlation energies, electron-distribution functions, and the static response functions
journal, December 2000
- Perrot, François; Dharma-wardana, M. W. C.
- Physical Review B, Vol. 62, Issue 24
Universal variational functionals of electron densities, first-order density matrices, and natural spin-orbitals and solution of the v-representability problem
journal, December 1979
- Levy, M.
- Proceedings of the National Academy of Sciences, Vol. 76, Issue 12
Harmonic-Potential Theorem: Implications for Approximate Many-Body Theories
journal, October 1994
- Dobson, John F.
- Physical Review Letters, Vol. 73, Issue 16
Electronic Structure of Warm Dense Copper Studied by Ultrafast X-Ray Absorption Spectroscopy
journal, April 2011
- Cho, B. I.; Engelhorn, K.; Correa, A. A.
- Physical Review Letters, Vol. 106, Issue 16
Inhomogeneous Electron Gas
journal, November 1964
- Hohenberg, P.; Kohn, W.
- Physical Review, Vol. 136, Issue 3B, p. B864-B871
Direct observation of an abrupt insulator-to-metal transition in dense liquid deuterium
journal, June 2015
- Knudson, M. D.; Desjarlais, M. P.; Becker, A.
- Science, Vol. 348, Issue 6242
Strongly coupled plasmas: high-density classical plasmas and degenerate electron liquids
journal, October 1982
- Ichimaru, Setsuo
- Reviews of Modern Physics, Vol. 54, Issue 4
Nonlocal orbital-free noninteracting free-energy functional for warm dense matter
journal, November 2013
- Sjostrom, Travis; Daligault, Jérôme
- Physical Review B, Vol. 88, Issue 19
Hellmann-Feynman, virial, and scaling requisites for the exact universal density functionals. Shape of the correlation potential and diamagnetic susceptibility for atoms
journal, October 1985
- Levy, Mel; Perdew, John P.
- Physical Review A, Vol. 32, Issue 4
Ab Initio Thermodynamic Results for the Degenerate Electron Gas at Finite Temperature
journal, September 2015
- Schoof, T.; Groth, S.; Vorberger, J.
- Physical Review Letters, Vol. 115, Issue 13
The Hubbard dimer: a density functional case study of a many-body problem
journal, September 2015
- Carrascal, D. J.; Ferrer, J.; Smith, J. C.
- Journal of Physics: Condensed Matter, Vol. 27, Issue 39
Scaling, bounds, and inequalities for the noninteracting density functionals at finite temperature
journal, September 2011
- Dufty, James W.; Trickey, S. B.
- Physical Review B, Vol. 84, Issue 12
Shock Compression of Quartz to 1.6 TPa: Redefining a Pressure Standard
journal, November 2009
- Knudson, M. D.; Desjarlais, M. P.
- Physical Review Letters, Vol. 103, Issue 22
Ab Initio Equation of State for Hydrogen-Helium Mixtures with Recalibration of the Giant-Planet Mass-Radius Relation
journal, August 2013
- Militzer, B.; Hubbard, W. B.
- The Astrophysical Journal, Vol. 774, Issue 2
Thermal Properties of the Inhomogeneous Electron Gas
journal, March 1965
- Mermin, N. David
- Physical Review, Vol. 137, Issue 5A
Nonempirical generalized gradient approximation free-energy functional for orbital-free simulations
journal, October 2013
- Karasiev, Valentin V.; Chakraborty, Debajit; Shukruto, Olga A.
- Physical Review B, Vol. 88, Issue 16
First-principles calculation of entropy for liquid metals
journal, December 2013
- Desjarlais, Michael P.
- Physical Review E, Vol. 88, Issue 6
Electron liquid at any degeneracy
journal, August 1986
- Dandrea, R. G.; Ashcroft, N. W.; Carlsson, A. E.
- Physical Review B, Vol. 34, Issue 4
Accurate Homogeneous Electron Gas Exchange-Correlation Free Energy for Local Spin-Density Calculations
journal, February 2014
- Karasiev, Valentin V.; Sjostrom, Travis; Dufty, James
- Physical Review Letters, Vol. 112, Issue 7
Generalized-gradient-approximation noninteracting free-energy functionals for orbital-free density functional calculations
journal, September 2012
- Karasiev, Valentin V.; Sjostrom, Travis; Trickey, S. B.
- Physical Review B, Vol. 86, Issue 11
Gradient corrections to the exchange-correlation free energy
journal, October 2014
- Sjostrom, Travis; Daligault, Jérôme
- Physical Review B, Vol. 90, Issue 15
Exchange and correlation potentials for electron-ion systems at finite temperatures
journal, November 1984
- Perrot, François; Dharma-wardana, M. W. C.
- Physical Review A, Vol. 30, Issue 5
Self-Consistent Equations Including Exchange and Correlation Effects
journal, November 1965
- Kohn, W.; Sham, L. J.
- Physical Review, Vol. 140, Issue 4A, p. A1133-A1138
Fermionic path-integral Monte Carlo results for the uniform electron gas at finite temperature
journal, March 2015
- Filinov, V. S.; Fortov, V. E.; Bonitz, M.
- Physical Review E, Vol. 91, Issue 3
Ab Initio Simulations for the Ion-Ion Structure Factor of Warm Dense Aluminum
journal, April 2014
- Rüter, Hannes R.; Redmer, Ronald
- Physical Review Letters, Vol. 112, Issue 14
Works referencing / citing this record:
Warming Up Density Functional Theory
book, November 2017
- Smith, Justin C.; Sagredo, Francisca; Burke, Kieron
- Frontiers of Quantum Chemistry
Hohenberg–Kohn Theorems for Interactions, Spin and Temperature
journal, September 2019
- Garrigue, Louis
- Journal of Statistical Physics, Vol. 177, Issue 3
Importance of finite-temperature exchange correlation for warm dense matter calculations
journal, June 2016
- Karasiev, Valentin V.; Calderín, Lázaro; Trickey, S. B.
- Physical Review E, Vol. 93, Issue 6
The importance of finite-temperature exchange-correlation for warm dense matter calculations
text, January 2016
- Karasiev, Valentin V.; Calderín, Lázaro; Trickey, S. B.
- arXiv
Nonempirical Semi-local Free-Energy Density Functional for Matter Under Extreme Conditions
text, January 2016
- Karasiev, Valentin V.; Dufty, James W.; Trickey, S. B.
- arXiv
Ab initio Exchange-Correlation Free Energy of the Uniform Electron Gas at Warm Dense Matter Conditions
text, January 2017
- Groth, Simon; Dornheim, Tobias; Sjostrom, Travis
- arXiv
Hohenberg-Kohn theorems for interactions, spin and temperature
text, January 2019
- Garrigue, Louis
- arXiv