INTERMOLECULAR PERTURBATION-THEORY - RENORMALIZED INTERACTION ENERGIES

For intermolecular perturbation theories in which it is assumed that t he unperturbed wave function of the composite system is a product of t he unperturbed wave functions of its components, and which satisfy one general constraint, we derive two renormalized interaction energy exp ressions which are more accurate than the perturbation expansions, whe n all are evaluated to comparable order. This is accomplished by focus ing on the parameter lambda in terms of which the perturbation expansi ons are derived rather than on the potential of interaction between co mponents. In the derivation of each renormalized energy formula, we di scard zeroth- through infinite-order terms which do not contribute to the interaction energy when the interaction is turned on fully, i.e., when lambda = 1. The first renormalized interaction energy when lambda = 1 is identical in form to the interaction energy in the symmetrized Rayleigh-Schrodinger (SRS) theory, but not in interpretation. The wav e function appearing in the renormalized energy cannot generally be th at assumed in the SRS theory, and the renormalized energy to zeroth or der in lambda is not zero. The latter is not surprising because we dis carded a zeroth-order term in the derivation. The second renormalized interaction energy formula is derived from the first by using the same set of assumptions and arguments that were used in deriving the first . We expect it to be more accurate than the first, which is expected t o be more accurate than the sum of the perturbation energies, all eval uated to comparable order. These expectations are supported by the res ults of calculations on LiH using two perturbation theories, the polar ization approximation and the Amos-Musher theory. The first-order wave functions for both were calculated in the configuration interaction ( CI) approximation; then the interaction energies were calculated by su mming the perturbation energies through third order and by evaluating the renormalized energy expressions. The perturbation results are comp ared to interaction energies calculated by full CI with the same basis set. As important as the formulas is the light our analysis throws on the meaning of order in intermolecular perturbation theory. (C) 1996 John Wiley & Sons, Inc.