Fitting the Coulomb potential variationally in linear-combination-of-atomic-orbitals density-functional calculations

A previously developed method for self-consistent-field density-functional calculations involving a variational fit to the charge density is generalized to the case in which the total (electronic plus nuclear) Coulomb potential is fit. Previously the total energy E(ρ, ̃ \~ρ) was viewed as a functional of the exact ρ and fitted ̃ \~ρ charge density. The energy expression was modified to be correct when ̃ \~ρ=ρ while at the same time allowing ̃ \~ρ to be obtained variationally through ∂E(ρ, ̃ \~ρ)∂ ̃ \~ρ=0. Herein an expression for E(ρ, ̃ \~V), where ̃ \~V is the fit to the Coulomb potential, is derived with similar properties. In particular, ̃ \~V can be determined variationally through ∂E(ρ, ̃ \~V)∂ ̃ \~V=0. In various linear-combination-of-atomic-orbitals calculations on atomic neon, the superiority of variational over conventional least-squares-fitting methods is demonstrated.