Accurate Homogeneous Electron Gas Exchange-Correlation Free Energy for Local Spin-Density Calculations

An accurate analytical parametrization for the exchange-correlation free energy of the homogeneous electron gas, including interpolation for partial spin polarization, is derived via thermodynamic analysis of recent restricted path integral Monte Carlo (RPIMC) data. This parametrization constitutes the local spin density approximation (LSDA) for the exchange-correlation functional in density functional theory. The new finite-temperature LSDA reproduces the RPIMC data well, satisfies the correct high-density and low- and high-$T$ asymptotic limits, and is well behaved beyond the range of the RPIMC data, suggestive of broad utility.

Figure 1

${ϵ}_{\mathrm{xc}}$ and $f_{\mathrm{xc}}$ from fit $A$ for the unpolarized $\zeta =0$ (top) and the fully polarized $\zeta =1$ (bottom) HEG at $r_{\mathrm{s}}=1$, 2, and 40 along with RPIMC data and BDHC fit for ${ϵ}_{\mathrm{xc}}$.