Physical limits on electronic nonlinear molecular susceptibilities

We apply sum rules to answer the question: What is the largest off-resonance electronic nonlinear susceptibility allowed by quantum mechanics? The sum-rule-restricted three-level model shows that the two-level limit yields the absolute maximum susceptibility, which is found to depend only on the first excited state transition energy and number of electrons-in agreement with a large set of second- and third-order susceptibility data from the literature. As such, the sum rules provide a target for the maximum possible off-resonant susceptibilities.