Exact Phillips-Kleinman-like pseudopotential for transition metals

The old Phillips-Kleinman pseudopotential is based on a projection operator P=1-${\mathit{tsum}}_{\mathit{c}}$ ‖${\mathrm{\psi }}_{\mathit{c}}$〉〈${\mathrm{\psi }}_{\mathit{c}}$‖ such that ψ=Pcphi where cphi is a smooth pseudoeigenfunction and the ${\mathrm{\psi }}_{\mathit{c}}$ are core eigenfunctions. We introduce a new projection operator and the pseudo-Hamiltonian it engenders, which is applicable to cases such as 3d and 2p valence functions that have no core functions of the same symmetry, and apply it to atomic Cu to demonstrate its rapid convergence. Its ease of applicability and convergence are similar to that of Vanderbilt’s recent pseudopotential but, unlike his, ours yields exact self-consistent Kohn-Sham eigenvalues, eigenfunctions, and total energies.