Continuous symmetry analysis of hyperpolarizabilities. Characterization of the second-order nonlinear optical response of distorted benzene

A direct relation between the first hyperpolarizability, β, of noncentrosymmetric molecular structures and the metric centrosymmetricity content, S(i), of such structures is shown for the first time. For a series of systematic, in-plane distortions (stretch, pull, shift, and squish deformations) of the model NLO chromophore benzene, we find a convincing monotonic relationship between calculated values of β and S(i). These results suggest that the dominant variation in β for these structures arises from the change in oscillator strength. More striking, these comparisons demonstrate the utility of the S(i) metric in correlating observable behavior with symmetry content.