The Coulomb operator in a Gaussian product basis

We discuss a scheme for Fock matrix evaluation in Hartree-Fock calculations that significantly reduces the work required to evaluate the Coulomb contributions. The method is based upon a representation of densities in terms of products of Gaussian basis functions, which are expanded in a new set of auxiliary Gaussians without further approximations by virtue of the Gaussian product theorem. The matrix elements of the Coulomb operator are then evaluated in the same auxiliary basis set, and all transformations to the final LCAO representation is done outside the innermost loops.