Hartree-Fock soft Coulomb hole to estimate correlation energies in atoms, molecules and polymers

We have shown that the empirical correction introduced into the Hartree-Fock method to calculate correlation energies for atoms and therefore to remove the error caused by the so-called Coulomb hole can be extended from atoms to molecules and polymers. A reformulation was required of the necessary parameter representation. The reparametrization has been performed staying as close as possible to the original expressions for atoms reported by Chakravorty and Clementi (S.J. Chakravorty and E. Clementi, Phys. Rev. A, 39 (1989) 2290). In addition to their work, where the correlation energy has been calculated with the self-consistent Hartree-Fock wavefunction and the correction integrals, we have performed investigations, including the perturbation operator in the Fock operator, so that the total energy also contains the correlation energy. The applications of this approach to atoms and molecules show that the total electron correlation energies and ionization potentials calculated as differences of total energies can be obtained very satisfactorily. On the basis of the reported calculations it turns out that one obtains better agreement with reference values of more sophisticated calculations when the correction integrals are used to build up the Fock matrix. Furthermore we have found that the magnitude of the correlation energy depends only weakly on the size of the basis sets, which makes this empirical method very attractive for its application to large molecular and polymeric systems.