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 [r_s≡⁽3 ^/4πn⁾1^/3aB-1<40 and Θ≡T/ T_F>0.0625]. In doing so, we construct a Padé approximant which collapses to Debye-Hückel 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.