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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 (, \~{}) was viewed as a functional of the exact and fitted \~{} charge density. The energy expression was modified to be correct when \~{}= while at the same time allowing \~{} to be obtained variationally through (, { \~{}) } { \~{}}=0. Herein an expression for E (, \~{}V), where \~{}V is the fit to the Coulomb potential, is derived with similar properties. In particular, \~{}V can be determined variationally through (, { \~{}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.
Mintmire et al. (Fri,) studied this question.