QuantitiesTs[n] andTc[n] in density-functional theory

Abstract

Levy’s constrained-search procedure [Proc. Natl. Acad. Sci. U.S, North 76, 6062 (1979)] is employed to show how to determine Kohn-Sham and Hartree-Fock-Kohn-Sham orbitals and kinetic energies ${\mathit{T}}_{\mathit{s}}$ and ${\mathit{T}}_{\mathit{c}}$, for the two-electron, four-electron, and the general case starting from the electron density. Numerical results are presented for the species ${\mathrm{H}}^{\mathrm{-}}$ through ${\mathit{F}}^{7+}$ and the atom Be. The Pauli potential is also determined for Be. The small differences among Kohn-Sham, Hartree-Fock, and Hartree-Fock-Kohn-Sham orbitals suggest that determination of Kohn-Sham orbitals from the density in this way is an attractive procedure for getting an orbital description from an electron density.