Connection formulas for thermal density functional theory

Pribram-Jones, A.; Burke, K.

doi:10.1103/PhysRevB.93.205140

Title: Connection formulas for thermal density functional theory

Abstract

We show that the adiabatic connection formula of ground-state density functional theory relates the correlation energy to a coupling-constant integral over a purely potential contribution, and is widely used to understand and improve approximations. The corresponding formula for thermal density functional theory is cast as an integral over temperatures instead, ranging upward from the system's physical temperature. We also show how to relate different correlation components to each other, either in terms of temperature or coupling-constant integrations. Lastly, we illustrate our results on the uniform electron gas.

Authors:

Pribram-Jones, A. ^[1]; Burke, K. ^[2]

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

Publication Date:: Mon May 23 00:00:00 EDT 2016

Research Org.:: Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1390013

Alternate Identifier(s):: OSTI ID: 1254215

Report Number(s):: LLNL-JRNL-689924
Journal ID: ISSN 2469-9950; PRBMDO

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

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review B

Additional Journal Information:: Journal Volume: 93; Journal Issue: 20; Journal ID: ISSN 2469-9950

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats


                    Pribram-Jones, A., and Burke, K. Connection formulas for thermal density functional theory.  United States: N. p., 2016. 
Web.  doi:10.1103/PhysRevB.93.205140.

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                    Pribram-Jones, A., & Burke, K. Connection formulas for thermal density functional theory.  United States.  https://doi.org/10.1103/PhysRevB.93.205140

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                    Pribram-Jones, A., and Burke, K. Mon .  
"Connection formulas for thermal density functional theory".  United States.  https://doi.org/10.1103/PhysRevB.93.205140.  https://www.osti.gov/servlets/purl/1390013.

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@article{osti_1390013,

  title        = {Connection formulas for thermal density functional theory},

  author       = {Pribram-Jones, A. and Burke, K.},

  abstractNote = {We show that the adiabatic connection formula of ground-state density functional theory relates the correlation energy to a coupling-constant integral over a purely potential contribution, and is widely used to understand and improve approximations. The corresponding formula for thermal density functional theory is cast as an integral over temperatures instead, ranging upward from the system's physical temperature. We also show how to relate different correlation components to each other, either in terms of temperature or coupling-constant integrations. Lastly, we illustrate our results on the uniform electron gas.},

  doi          = {10.1103/PhysRevB.93.205140},

  journal      = {Physical Review B},

  number       = 20,

  volume       = 93,

  place        = {United States},

  year         = {Mon May 23 00:00:00 EDT 2016},

  month        = {Mon May 23 00:00:00 EDT 2016}

}

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Works referenced in this record:

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journal, August 1974

Harris, J.; Jones, R. O.
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Spin-polarized electron liquid at arbitrary temperatures: Exchange-correlation energies, electron-distribution functions, and the static response functions
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Excitations and benchmark ensemble density functional theory for two electrons
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Pribram-Jones, Aurora; Yang, Zeng-hui; Trail, John R.
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Coupling-constant dependence of the density functional correlation energy
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Works referencing / citing this record:

Finite Temperatures by Means of Zero Kelvin Kohn-Sham Formalism of Density-Functional Theory
journal, July 2019

Querne, Mateus B. P.; Vieira, Daniel
Brazilian Journal of Physics, Vol. 49, Issue 5
DOI: 10.1007/s13538-019-00691-4

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Similar Records

Title: Connection formulas for thermal density functional theory

Abstract

Citation Formats

The surface energy of a bounded electron gas journal, August 1974

Exchange and correlation potentials for finite temperature quantum calculations at intermediate degeneracies journal, February 1981

Adiabatic connection from accurate wave-function calculations journal, March 2000

Statistical physics of dense plasmas: Thermodynamics, transport coefficients and dynamic correlations journal, May 1987

Forces in Molecules journal, August 1939

Spin-polarized electron liquid at arbitrary temperatures: Exchange-correlation energies, electron-distribution functions, and the static response functions journal, December 2000

Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism journal, May 1976

Excitations and benchmark ensemble density functional theory for two electrons journal, May 2014

Coupling-constant dependence of the density functional correlation energy journal, October 1998

Zur Rolle der kinetischen Elektronenenergie f�r die zwischenatomaren Kr�fte journal, March 1933

Inhomogeneous Electron Gas journal, November 1964

Strongly coupled plasmas: high-density classical plasmas and degenerate electron liquids journal, October 1982

The exchange-correlation energy of a metallic surface journal, December 1975

Adiabatic connection for strictly correlated electrons journal, September 2009

Statistical mechanics of simple coulomb systems journal, March 1980

Differential virial theorem for the fractional electron number: Derivative discontinuity of the Kohn-Sham exchange-correlation potential journal, June 1998

Strong Correlation in Kohn-Sham Density Functional Theory journal, December 2012

Density-Functional Theory for Strongly Interacting Electrons journal, October 2009

Correlation energies for some two- and four-electron systems along the adiabatic connection in density functional theory journal, February 1999

Self-Consistent Equations Including Exchange and Correlation Effects journal, November 1965

Finite Temperatures by Means of Zero Kelvin Kohn-Sham Formalism of Density-Functional Theory journal, July 2019

The surface energy of a bounded electron gas
journal, August 1974

Exchange and correlation potentials for finite temperature quantum calculations at intermediate degeneracies
journal, February 1981

Adiabatic connection from accurate wave-function calculations
journal, March 2000

Statistical physics of dense plasmas: Thermodynamics, transport coefficients and dynamic correlations
journal, May 1987

Forces in Molecules
journal, August 1939

Spin-polarized electron liquid at arbitrary temperatures: Exchange-correlation energies, electron-distribution functions, and the static response functions
journal, December 2000

Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism
journal, May 1976

Excitations and benchmark ensemble density functional theory for two electrons
journal, May 2014

Coupling-constant dependence of the density functional correlation energy
journal, October 1998

Zur Rolle der kinetischen Elektronenenergie f�r die zwischenatomaren Kr�fte
journal, March 1933

Inhomogeneous Electron Gas
journal, November 1964

Strongly coupled plasmas: high-density classical plasmas and degenerate electron liquids
journal, October 1982

The exchange-correlation energy of a metallic surface
journal, December 1975

Adiabatic connection for strictly correlated electrons
journal, September 2009

Statistical mechanics of simple coulomb systems
journal, March 1980

Differential virial theorem for the fractional electron number: Derivative discontinuity of the Kohn-Sham exchange-correlation potential
journal, June 1998

Strong Correlation in Kohn-Sham Density Functional Theory
journal, December 2012

Density-Functional Theory for Strongly Interacting Electrons
journal, October 2009

Correlation energies for some two- and four-electron systems along the adiabatic connection in density functional theory
journal, February 1999

Self-Consistent Equations Including Exchange and Correlation Effects
journal, November 1965

Finite Temperatures by Means of Zero Kelvin Kohn-Sham Formalism of Density-Functional Theory
journal, July 2019