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

We fit finite-temperature path integral Monte Carlo calculations of the exchange-correlation energy of the 3D finite-temperature homogeneous electron gas in the warm-dense regime [rₛ≡(3/4πn)1/3aB^-1<40 and Θ≡T/TF>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.