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Title: Status of free-energy representations for the homogeneous electron gas

Abstract

Renewed interest in the homogeneous electron gas (HEG) has been stimulated by recent accurate simulations of it over a wide range of densities and temperatures. Those data, combined with known theoretical limits, have led to analytical representations of the free energy. Such a representation is, at least in principle, the complete HEG equation of state. The initial objective here is to establish that the two best representations of the simulation data and constraints are effectively the same in both functional form and accuracy of representation. The second objective is to disclose and delineate a significant difficulty. Despite their expected accuracy for the free energy, the underlying functional form is not adequate for derived thermodynamic properties. As an example, the specific heats obtained from the representations exhibit anomalies suggesting the need first for additional simulation data in critical regimes, then for refined fitting functions. Here, the existing representations are, however, almost certainly adequate for applications based on the free energy alone (e.g., density functional theory for warm dense matter). The third objective is to show that, despite their inability to provide a complete thermodynamic description of the HEG, the best analytical representations do provide a fully adequate exchange-correlation local density approximationmore » for free energy density functional calculations.« less

Authors:
 [1];  [2];  [2]
  1. Univ. of Rochester, Rochester, NY (United States). Lab for Laser Energetics
  2. Univ. of Florida, Gainesville, FL (United States)
Publication Date:
Research Org.:
Univ. of Rochester, Rochester, NY (United States). Lab for Laser Energetics
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
Contributing Org.:
Laboratory for Laser Energetics, University of Rochester
OSTI Identifier:
1526438
Alternate Identifier(s):
OSTI ID: 1514735
Report Number(s):
2019-24, 1502
Journal ID: ISSN 2469-9950; PRBMDO; 2019-24, 1502, 2461
Grant/Contract Number:  
NA0003856; SC0002139
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 99; 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

Karasiev, Valentin V., Trickey, S. B., and Dufty, James W. Status of free-energy representations for the homogeneous electron gas. United States: N. p., 2019. Web. doi:10.1103/PhysRevB.99.195134.
Karasiev, Valentin V., Trickey, S. B., & Dufty, James W. Status of free-energy representations for the homogeneous electron gas. United States. doi:10.1103/PhysRevB.99.195134.
Karasiev, Valentin V., Trickey, S. B., and Dufty, James W. Wed . "Status of free-energy representations for the homogeneous electron gas". United States. doi:10.1103/PhysRevB.99.195134. https://www.osti.gov/servlets/purl/1526438.
@article{osti_1526438,
title = {Status of free-energy representations for the homogeneous electron gas},
author = {Karasiev, Valentin V. and Trickey, S. B. and Dufty, James W.},
abstractNote = {Renewed interest in the homogeneous electron gas (HEG) has been stimulated by recent accurate simulations of it over a wide range of densities and temperatures. Those data, combined with known theoretical limits, have led to analytical representations of the free energy. Such a representation is, at least in principle, the complete HEG equation of state. The initial objective here is to establish that the two best representations of the simulation data and constraints are effectively the same in both functional form and accuracy of representation. The second objective is to disclose and delineate a significant difficulty. Despite their expected accuracy for the free energy, the underlying functional form is not adequate for derived thermodynamic properties. As an example, the specific heats obtained from the representations exhibit anomalies suggesting the need first for additional simulation data in critical regimes, then for refined fitting functions. Here, the existing representations are, however, almost certainly adequate for applications based on the free energy alone (e.g., density functional theory for warm dense matter). The third objective is to show that, despite their inability to provide a complete thermodynamic description of the HEG, the best analytical representations do provide a fully adequate exchange-correlation local density approximation for free energy density functional calculations.},
doi = {10.1103/PhysRevB.99.195134},
journal = {Physical Review B},
number = 19,
volume = 99,
place = {United States},
year = {2019},
month = {5}
}

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Works referenced in this record:

Exact conditions on the temperature dependence of density functionals
journal, May 2016


Nuclear fusion in dense plasmas
journal, April 1993


Thermodynamics and Correlational Properties of Finite-Temperature Electron Liquids in the Singwi-Tosi-Land-Sjölander Approximation
journal, July 1986

  • Tanaka, Shigenori; Ichimaru, Setsuo
  • Journal of the Physical Society of Japan, Vol. 55, Issue 7
  • DOI: 10.1143/JPSJ.55.2278

Quantum Monte Carlo study of the three-dimensional spin-polarized homogeneous electron gas
journal, August 2013


Improved analytical representation of combinations of Fermi–Dirac integrals for finite-temperature density functional calculations
journal, July 2015

  • Karasiev, Valentin V.; Chakraborty, Debajit; Trickey, S. B.
  • Computer Physics Communications, Vol. 192
  • DOI: 10.1016/j.cpc.2015.03.002

Importance of finite-temperature exchange correlation for warm dense matter calculations
journal, June 2016


Ab Initio Quantum Monte Carlo Simulation of the Warm Dense Electron Gas in the Thermodynamic Limit
journal, October 2016


Path-Integral Monte Carlo Simulation of the Warm Dense Homogeneous Electron Gas
journal, April 2013


Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis
journal, August 1980

  • Vosko, S. H.; Wilk, L.; Nusair, M.
  • Canadian Journal of Physics, Vol. 58, Issue 8
  • DOI: 10.1139/p80-159

Equation of state for weakly coupled quantum plasmas
journal, April 2004


Ab initio Exchange-Correlation Free Energy of the Uniform Electron Gas at Warm Dense Matter Conditions
journal, September 2017


Accurate and simple analytic representation of the electron-gas correlation energy
journal, June 1992


The uniform electron gas at warm dense matter conditions
journal, May 2018


Effective mass of quasiparticles from thermodynamics
journal, July 2017


Free energy of the uniform electron gas: Testing analytical models against first-principles results
journal, March 2017

  • Groth, Simon; Dornheim, Tobias; Bonitz, Michael
  • Contributions to Plasma Physics, Vol. 57, Issue 3
  • DOI: 10.1002/ctpp.201600082

Path integrals in the theory of condensed helium
journal, April 1995


Ground State of the Electron Gas by a Stochastic Method
journal, August 1980


Ab Initio Thermodynamic Results for the Degenerate Electron Gas at Finite Temperature
journal, September 2015


Ab initio quantum Monte Carlo simulation of the warm dense electron gas
journal, May 2017

  • Dornheim, Tobias; Groth, Simon; Malone, Fionn D.
  • Physics of Plasmas, Vol. 24, Issue 5
  • DOI: 10.1063/1.4977920

On the Kubo-Greenwood model for electron conductivity
journal, January 2018

  • Dufty, James; Wrighton, Jeffrey; Luo, Kai
  • Contributions to Plasma Physics, Vol. 58, Issue 2-3
  • DOI: 10.1002/ctpp.201700102

Accurate Homogeneous Electron Gas Exchange-Correlation Free Energy for Local Spin-Density Calculations
journal, February 2014


Nonempirical Semilocal Free-Energy Density Functional for Matter under Extreme Conditions
journal, February 2018


Exchange and correlation potentials for electron-ion systems at finite temperatures
journal, November 1984


Interaction picture density matrix quantum Monte Carlo
journal, July 2015

  • Malone, Fionn D.; Blunt, N. S.; Shepherd, James J.
  • The Journal of Chemical Physics, Vol. 143, Issue 4
  • DOI: 10.1063/1.4927434

    Works referencing / citing this record:

    Exchange-correlation contributions to thermodynamic properties of the homogeneous electron gas from a cumulant Green's function approach
    journal, November 2019


    Strongly coupled electron liquid: Ab initio path integral Monte Carlo simulations and dielectric theories
    journal, January 2020


    Exchange-correlation thermal effects in shocked deuterium: Softening the principal Hugoniot and thermophysical properties
    journal, June 2019