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 Vxcᵛᵃˡ=Vxc(ρᵥₐₗ). 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 Vxcᵛᵃˡ=Vxc(ρₜₒₜₐₗ)-Vxc(ρcore). It is far superior to the LDA pseudopotential with Vxcᵛᵃˡ=Vxc(ρᵥₐₗ).