Density functional theory (DFT) increasingly is being used to investigate systems at finite temperatures that are high (i.e., a significant fraction of the Fermi temperature). Common procedure is to use a standard Kohn-Sham (KS) DFT code with thermal occupation
of the KS states through the Fermi-Dirac distribution. Familiar approximate zero-temperature exchange and correlation (XC) functionals typically are used. However, a few finite-temperature XC approximations have been proposed. Without truly ab initio calibration results (e.g. QMC), finite-temperature electron gas data are mostly based on finite-temperature extensions of approximate methods such as RPA, or the Singwi-Tosi-Land-Sjolander dielectric formulation, and interpolation methods, for example, classical mapping approaches. As a result, nearly all of the literature for finite-temperature XC functionals is for LDA with the exception being the gradient expansion for exchange at finite temperature. In this setting, the finite-temperature Hartree-Fock approximation by definition includes the correct temperature dependence of the exchange-only energy and as such may be used as a benchmark for finite-temperature exchange functionals. I present and discuss equation of state calculations with both finite temperature Hartree-Fock and DFT with various functionals.
For confined hydrogen systems these are all-electron calculations while for periodically bounded hydrogen and lithium they are pseudopotential calculations. Conditions range from ambient density and temperature through the warm dense matter regime. The results illustrate both merits and deficiencies of current finite-temperature XC functionals and point the way to improvements. Supported by US DoE Grant DE-SC0002139.