Symmetry forcing and convergence properties of perturbation expansions for molecular interaction energies

Abstract

AbstractThe convergence properties of perturbation theories for molecular interaction energies are tested by performing high‐accuracy high‐order numerical calculations for a ground‐state hydrogen atom interacting with a proton. It is shown that a strong symmetry forcing used in the Eisenschitz‐London‐Hirschfelder‐van der Avoird (EL‐HAV) theory leads to rapidly convergent perturbation expansion whereas a weak symmetry forcing, peculiar to the Murrell‐Shaw‐Musher‐Amos (MSMA) theory, is not able to guarantee the convergence of the resulting perturbation series. The perturbation expansion introduced recently by Jeziorski and Kolos and corresponding to an intermediate symmetry forcing is shown to converge rapidly ensuring the correct asymptotic behavior of the interaction energy calculated through second order. Despite the divergence of the resulting perturbation series the MSMA theory is shown to give very useful results at the distances corresponding to the van der Waals minimum. In this region, however, virtually the same results can be obtained by using a simpler theory employing a properly symmetrized wave function of the usual Rayleigh‐Schrödinger (RS) polarization theory.