Fast First-Principles Predictions for Warm Dense Matter with Orbital-free Free Energy Density Functional Theory*

Warm dense matter encompasses the phase-space region between ordinary condensed matter and
plasmas. That poses inconvenient challenges for theory. Conventional Kohn-Sham density functional theory (KS-DFT) is
computationally demanding due to a large number of thermally occupied bands involved at high temperature. Meanwhile, path-integral Monte
Carlo (PIMC) has intrinsic difficulties for the low-temperature scenario. In contrast, orbital-free free energy density functional theory (OF-FEDFT) is a consistent approach spanning the whole T range. The key to OF-FEDFT usage is good approximate
functionals. Here we extend the recent LKT ground-state generalized gradient approximation (GGA) non-interacting kinetic energy density functional (KEDF) (Phys. Rev. B 98, 041111(R) (2018)) to a semi-local free energy functional. In tests on hydrogen at elevated
T, it outperforms the previously best single-point free energy functional, VT84F (Phys. Rev. B 88, 161108(R) (2013))
for the equation of state (EOS). For deuterium, it is roughly comparable to KS-DFT and PIMC in accuracy.