The importance of finite-temperature exchange-correlation for warm dense matter calculations

Abstract: Effects of explicit temperature dependence in the exchange-correlation (XC) free-energy functional upon calculated properties of matter in the warm dense regime are investigated. The comparison is between the KSDT finite-temperature local density approximation (TLDA) XC functional [Phys.\ Rev.\ Lett.\ \textbf{112}, 076403 (2014)] parametrized from restricted path integral Monte Carlo data on the homogeneous electron gas (HEG) and the conventional Monte Carlo parametrization ground-state LDA XC functional (Perdew-Zunger, "PZ") evaluated with $T$-dependent densities. Both Kohn-Sham (KS) and orbital-free density functional theory (OFDFT) are used, depending upon computational resource demands. Compared to the PZ functional, the KSDT functional generally lowers the direct-current (DC) electrical conductivity of low density Al, yielding improved agreement with experiment. The greatest lowering is about 15\% for T= 15 kK. Correspondingly, the KS band structure of low-density fcc Al from KSDT exhibits a clear increase in inter-band separation above the Fermi level compared to the PZ bands. In some density-temperature regimes, the Deuterium equations of state obtained from the two XC functionals exhibit pressure differences as large as 4\% and a 6\% range of differences. However, the Hydrogen principal Hugoniot is insensitive to explicit XC $T$-dependence because of cancellation between the energy and pressure-volume work difference terms in the Rankine-Hugoniot equation. Finally, the temperature at which the HEG becomes unstable is $T\geq$ 7200 K for $T$-dependent XC, a result that the ground-state XC underestimates by about 1000 K.