Symmetric Nonlocal Weighted Density Approximations from the Exchange-Correlation Hole of the Uniform Electron Gas

2012 ◽  
Vol 8 (11) ◽  
pp. 4081-4093 ◽  
Author(s):  
Rogelio Cuevas-Saavedra ◽  
Debajit Chakraborty ◽  
Sandra Rabi ◽  
Carlos Cárdenas ◽  
Paul W. Ayers
Keyword(s):  
Electron Gas ◽  
Weighted Density ◽  
Exchange Correlation ◽  
Correlation Hole ◽  
Uniform Electron Gas

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.

scholarly journals Ab initio Exchange-Correlation Free Energy of the Uniform Electron Gas at Warm Dense Matter Conditions

2017 ◽  
Vol 119 (13) ◽  
Author(s):  
Simon Groth ◽  
Tobias Dornheim ◽  
Travis Sjostrom ◽  
Fionn D. Malone ◽  
W. M. C. Foulkes ◽  
...  
Keyword(s):  
Free Energy ◽  
Ab Initio ◽  
Electron Gas ◽  
Dense Matter ◽  
Warm Dense Matter ◽  
Exchange Correlation ◽  
Uniform Electron Gas
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