Effect of Various Choices of Localizing Potentials in the Adams—Gilbert Local-Orbitals Equations

Approximations to the Adams---Gilbert local-orbitals formulation of Hartree---Fock theory have been useful in studying the electronic properties of insulating solids. The approximations used depend upon the smallness of the interatomic overlaps. Since the choice of localizing potential is arbitrary, we study various simple choices of localizing potential, to see which choice produces localized orbitals with the least overlap. The test system is LiF, and fully self-consistent solid-state calculations are performed for 16 choices of localizing potential. We conclude that the smallness of overlap is only weakly dependent upon the choice of localizing potential and find that all valid choices of localizing potential produced orbitals which overlap less than the equivalent free-ion orbitals.