Four center integrals for Coulomb interactions in small molecules

Abstract

In this work we make some progress on studying four center integrals for the Coulomb energy for both Hartree Fock (HF) and Density Functional Theory (DFT) calculations for small molecules. We consider basis wave functions of the form of an arbitrary radial wave function multiplied by a spherical harmonic and study four center Coulomb integrals for them. We reformulated these Coulomb four center integrals in terms of some derivatives of integrals of nearly factorable functions which then depend on the Bessel transform of the radial wave functions considered.