Perturbation theory applied to potential energy surfaces. I. The choice of a suitable reference function ψ(0)

Abstract

The effect of the choice of zero order wave function on the accuracy of third-order perturbation theory is examined. The restricted Hartree–Fock, unrestricted Hartree–Fock, and generalized valence bond wave functions are considered as zero order wave functions for both Epstein–Nesbet and Mo/ller–Plesset perturbation theory. In each case the third-order perturbation results are reported for the H2 X1Σ+g potential energy curve. The behavior of Epstein–Nesbet perturbation theory relative to Mo/ller–Plesset perturbation theory is found to be independent of ψ(0). However, the nature of the perturbation and hence the absolute accuracy of both perturbation theories is determined by the choice of ψ(0). A comparison with CI calculations demonstrates that of the three examples, only the GVB perturbation theory is consistently accurate over the entire potential surface. The RHF expansion as expected becomes slowly convergent at large internuclear separations as a direct result of improper dissociation. On the other hand, the third-order UHF perturbation calculations have large errors (∼0.0225 hartree) at intermediate internuclear separations (3–4 bohr) where there is a strong contribution from single excitations. In contrast, the third-order EN–GVB perturbation theory has a maximum error of only 0.0001 hartree for any H2 geometry. The errors in the MP–GVB expansion for H2 are about an order of magnitude larger but can be considerably reduced (to ∼0.0002 hartree) by using the geometric approximation.