Amending the LCAO Basis Set in the Hartree-Fock-Roothaan Approximation to First-Order Perturbation Theory

We have formulated the first-order Hartree-Fock equations for multielectron systems exposed to an external perturbation in the LCAO (Linear Combination of Atomic Orbital) approximation. The perturbation theory corrections to these equations have been found in the form of expansions in unperturbed equations and terms which depend explicitly on this perturbation. The ideas leading to this amendment are implicit in previous studies, but the significance of its existence has not yet been sufficiently emphasized and its simple explicit form has not been presented. With the proposed approach, one may obtain the first-order correction perturbation energy in the presence of any perturbation, knowing merely the overlap. This may further facilitate linear scaling computation of the energy correction.