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

Abstract

We fit finite-temperature path integral Monte Carlo calculations of the exchange-correlation energy of the $3\text{D}$ finite-temperature homogeneous electron gas in the warm-dense regime [${r}_{s}\ensuremath{\equiv}{(3/4\ensuremath{\pi}n)}^{1/3}{a}_{B}^{\ensuremath{-}1}<40$ and $\ensuremath{\Theta}\ensuremath{\equiv}T/{T}_{F}>0.0625$]. In doing so, we construct a Pad\'e approximant which collapses to Debye-H\"uckel theory in the high-temperature, low-density limit. Likewise, the zero-temperature limit matches the numerical results of ground-state quantum Monte Carlo, as well as analytical results in the high-density limit.