Structure-function relationships for .beta., the first molecular hyperpolarizability

A four-orbital model is used to map the overall dependence of β, the first electronic hyperpolarizability, on chemical parameters such as donor/acceptor strength and coupling between bridge and donor/acceptor orbitals. These calculations are used to develop general structure-property relationships for β and to demonstrate the physical origin of maxima, minima, and zeros in β. Comparison with multiorbital calculations on specific molecules show that the general relationships apply to more complex structures as well. A number of strategies for manipulating β by varying molecular structure emerge from the analysis. We show that the absolute maxima in the β surfaces fall outside of the range that has been probed using conventional organic donors and acceptors