Hartree-Fock core local-density-approximation valence pseudopotentials

We derive the pseudopotential for an atom in which all the electrons are subject to a Hartree-Fock exchange potential arising from the core electrons, and a Kohn-Sham exchange-correlation potential arising from the valence electrons. When this ionic pseudopotential is transferred to a crystal, the self-consistent valence exchange-correlation potential has the simple form V_xc^val=V_xc(ρ_val). We show by explicit calculations of the lattice constants, cohesive energies, and bulk moduli of Na and GaAs that this pseudopotential is of similar quality, but has certain computational advantages over, a strictly local-density-approximation (LDA) pseudopotential with V_xc^val=V_xc(ρ_total)-V_xc(ρ_core). It is far superior to the LDA pseudopotential with V_xc^val=V_xc(ρ_val).