Jellium work function for all electron densities

The work function and surface energy of jellium have been calculated for low (${r}_{s}$=12), metallic (2\ensuremath{\le}${r}_{s}$\ensuremath{\le}6), and high (0.5\ensuremath{\le}${r}_{s}$\ensuremath{\le}2) bulk electron densities. As the density increases, the work function peaks at 3.8 eV (${r}_{s}$=1.7), minimizes at 3.6 eV (${r}_{s}$=0.9, a density higher than that of metastable metallic hydrogen), peaks again at 3.7 eV (${r}_{s}$=0.6), and finally drops toward a high-density limit around 2.0 eV (${r}_{s}$\ensuremath{\rightarrow}0). The self-consistent calculations, which employ an accurate electron-gas exchange-correlation energy within the local-density approximation, are numerically challenging at high densities. Exchange-only calculations, which display the same double-peaked density dependence, are also reported. The high-density limits for the work function with and without correlation (2.0 and 1.0 eV, respectively) have been estimated in two ways: (1) from an extension of Peuckert's argument, and (2) from the Thomas-Fermi-Dirac-Gombas approximation.