Wh. Adams, ON THE LIMITS OF VALIDITY OF THE SYMMETRIZED RAYLEIGH-SCHRODINGER PERTURBATION-THEORY, International journal of quantum chemistry, 60(1), 1996, pp. 273-285
We explain that the symmetrized Rayleigh-Schrodinger (SRS) perturbatio
n theory formula for intermolecular interaction energies cannot be der
ived 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 uni
que value for this limit when the perturbation expansion is divergent,
which is generally the case. The exact ground-state interaction energ
y 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 b
elieving that the SRS theory can, however, give results of useful accu
racy when truncated to second order in the energy. Because this study
completes our demonstration that the simplest intermolecular perturbat
ion theories are generally invalid when carried to infinite order, we
review the alternative theories that promise to be valid. (C) 1996 Joh
n Wiley & Sons, Inc.