On the limits of validity of the symmetrized Rayleigh-Schr�dinger perturbation theory

We explain that the symmetrized Rayleigh-Schrödinger (SRS) perturbation theory formula for intermolecular interaction energies cannot be derived under assumptions which are generally true, and that the formula must generally become indeterminate when the perturbation expansion is carried to infinite order. Although one can use a limiting procedure to calculate the interaction energy to infinite order, there is no unique value for this limit when the perturbation expansion is divergent, which is generally the case. The exact ground-state interaction energy is among the possible limits, but there is no known prescription for reaching that limit. For LiH we present numerical results for one of the possible limits, showing that the SRS energy formula can give very inaccurate results over a range of nuclear separations, its accuracy decreasing rapidly with increasing separation. We review reasons for believing that the SRS theory can, however, give results of useful accuracy when truncated to second order in the energy. Because this study completes our demonstration that the simplest intermolecular perturbation theories are generally invalid when carried to infinite order, we review the alternative theories that promise to be valid.