Using a proxy state to improve the accuracy of truncated hyperpolarizability calculations

We present a simple algorithm for defining a single proxy state that 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 further constrained by the zero-frequency linear 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 to exact perturbation calculations of one-dimensional power law potentials.