Is there a fundamental limit on nonlinear molecular susceptibilities?

Nonlinear optical materials have been the focus of studies to maximize their nonlinear optical susceptibility because of their possible applications. Complex quantum expressions are often simplified with two and three state models that consider the competition between excited states,[1, 2, 3, 4] symmetry,[5] and bond length alternation.[6] We ask the question: Is there a fundamental upper limit of the nonlinear susceptibility, and, can this limit be achieved? We use the Thomas-Kuhn quantum sum rules, which are general and apply to any system and find that the off-resonant diagonal components of the second and third-order susceptibilities are bounded by a function that depends on the number of electrons and the transition energy to the first excited state. A large set of measurements from the literature[7] are all found to be bounded by this horizon function as predicted. Further improvements in susceptibilities will therefore require more creative approaches that are presently used.