On the convergence of the symmetrized Rayleigh–Schrödinger perturbation theory for molecular interaction energies

Abstract

The generalized Heitler–London perturbation theory for molecular interaction energies proposed recently by Tang and Toennies [J. Chem. Phys. 95, 5981 (1991)] is proved to be equivalent to the symmetrized Rayleigh–Schrödinger perturbation expansion. This theory is applied to the interaction of two hydrogen atoms and is shown to reproduce the interaction energy in the region of the van der Waals minimum to within about 1% already in the third-order treatment. It is shown that the convergence radius of this theory is the same as that of the polarization perturbation theory, i.e., is marginally greater than unity at large interatomic distances R. This proximity to unity results in a prohibitively slow high-order convergence of the expansion in the region of the van der Waals minimum. Consequently, for the singlet state at large R a small part of the exchange energy cannot be recovered in practice by a direct term-by-term summation of the series. The perturbation series resulting from the application of the theory to the antisymmetric triplet state of H2 converges to an unphysical energy lying above the energy of the triplet state. At large R the difference between the physical energy and the unphysical limit of the series is very small and can be neglected in practical applications of the theory.