Charge-consistent redefinition of Fock integrals

The Fock integrals in the Hartree-Fock (HF) theory have been redefined such that every orbital pair density of an electron appearing in the conventional definition is replaced by a net neutral density that is the sum of the orbital pair density and an appropriate portion of the nuclear charge density. These charge-consistent Fock integrals in the canonical HF orbitals are shown to differ from the conventional ones only in the diagonal elements and by merely a constant, thus not altering the HF energy, orbitals, correlation energies, etc. They are shown numerically to converge much more rapidly with respect to the number of unit cells included in the lattice sums for one-dimensional solids because they contain no charge-multipole interactions in their definition unlike the conventional Fock integrals. The multipole expansion of the long-range lattice sums in the charge-consistent Fock integrals is also formulated and implemented for one-dimensional solids.