  We have developed a simple algorithm for defining a single proxy state which
accounts for state truncation in the sum-over-states calculations of the
dispersion of the molecular hyperpolarizabilities. The transition strengths
between the proxy state and the truncated set of states are determined using
the Thomas-Reiche-Kuhn sum rules. In addition to the sum rules, this method
requires as an input the off-resonant polarizability. This proxy state method
can augment experimentally determined parameters or finite-state theories to
allow for a more accurate prediction of the nonlinear optical properties of
molecular systems. We benchmark this approach by comparison with exact
perturbation calculations of one-dimensional power law potentials.
