scholarly journals Exchange-correlation energy for the three-dimensional homogeneous electron gas at arbitrary temperature

2013 ◽  
Vol 88 (8) ◽  
Author(s):  
Ethan W. Brown ◽  
Jonathan L. DuBois ◽  
Markus Holzmann ◽  
David M. Ceperley
Keyword(s):  
Correlation Energy ◽  
Electron Gas ◽  
Three Dimensional ◽  
Exchange Correlation ◽  
Arbitrary Temperature

scholarly journals Approximate bounds and temperature dependence of adiabatic connection integrands for the uniform electron gas

2021 ◽  
Author(s):  
Brittany P. Harding ◽  
Zachary Mauri ◽  
Aurora Pribram-Jones
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Correlation Energy ◽  
Electron Gas ◽  
High Energy ◽  
Zero Temperature ◽  
Temperature Dependent ◽  
Functional Theory ◽  
Exchange Correlation ◽  
Uniform Electron Gas

Thermal density functional theory is commonly used in simulations of warm dense matter, a highly energetic phase characterized by substantial thermal effects and by correlated electrons demanding quantum mechanical treatment. The numerous approximations for the exchange-correlation energy component in zero-temperature density functional theory, though often used in these high-energy-density simulations with Fermi-weighted electronic densities, are known to miss temperature-dependent effects in the electronic structure of these systems. In this work, the temperature-dependent adiabatic connection is demonstrated and analyzed using a well-known parameterization of the uniform electron gas free energy. Useful tools based on this formalism for analyzing and constraining approximations of the exchange-correlation at zero temperature are leveraged for the finite-temperature case. Inspired by the Lieb-Oxford inequality, which provides a lower bound for the ground-state exchange-correlation energy, bounds for the exchange-correlation at finite-temperatures are approximated for various degrees of electronic correlation.

scholarly journals Approximate bounds and temperature dependence of adiabatic connection integrands for the uniform electron gas

2021 ◽  
Author(s):  
Brittany P. Harding ◽  
Zachary Mauri ◽  
Aurora Pribram-Jones
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Correlation Energy ◽  
Electron Gas ◽  
High Energy ◽  
Zero Temperature ◽  
Temperature Dependent ◽  
Functional Theory ◽  
Exchange Correlation ◽  
Uniform Electron Gas

Thermal density functional theory is commonly used in simulations of warm dense matter, a highly energetic phase characterized by substantial thermal effects and by correlated electrons demanding quantum mechanical treatment. The numerous approximations for the exchange-correlation energy component in zero-temperature density functional theory, though often used in these high-energy-density simulations with Fermi-weighted electronic densities, are known to miss temperature-dependent effects in the electronic structure of these systems. In this work, the temperature-dependent adiabatic connection is demonstrated and analyzed using a well-known parameterization of the uniform electron gas free energy. Useful tools based on this formalism for analyzing and constraining approximations of the exchange-correlation at zero temperature are leveraged for the finite-temperature case. Inspired by the Lieb-Oxford inequality, which provides a lower bound for the ground-state exchange-correlation energy, bounds for the exchange-correlation at finite temperatures are approximated for various degrees of electronic correlation.

Finite-T correlations and free exchange-correlation energy of quasi-one-dimensional electron gas

2018 ◽  
Vol 32 (05) ◽  
pp. 1850060 ◽  
Author(s):  
Vinayak Garg ◽  
Akariti Sharma ◽  
R. K. Moudgil
Keyword(s):  
Correlation Function ◽  
Pair Correlation Function ◽  
Correlation Energy ◽  
Pair Correlation ◽  
Electron Gas ◽  
Dimensional Electron ◽  
One Dimensional ◽  
Exchange Correlation ◽  
Dimensional Electron Gas ◽  
Plasmon Dispersion

We have studied the effect of temperature on static density–density correlations and plasmon excitation spectrum of quasi-one-dimensional electron gas (Q1DEG) using the random phase approximation (RPA). Numerical results for static structure factor, pair-correlation function, static density susceptibility, free exchange-correlation energy and plasmon dispersion are presented over a wide range of temperature and electron density. As an interesting result, we find that the short-range correlations exhibit a non-monotonic dependence on temperature T, initially growing stronger (i.e. the pair-correlation function at small inter-electron spacing assuming relatively smaller values) with increasing T and then weakening above a critical T. The cross-over temperature is found to increase with increasing coupling among electrons. Also, the [Formula: see text] peak in the static density susceptibility [Formula: see text] at T = 0 K smears out with rising T. The free exchange-correlation energy and plasmon dispersion show a significant variation with T, and the trend is qualitatively the same as in higher dimensions.

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