Vibrational contributions to the molecular first and second hyperpolarizabilities of a push-pull polyene

The vibrational contributions to the first and second hyperpolarizabilities of a push-pull polyene are theoretically studied by using the valence-bond charge-transfer model. The formal relationships between the vibrational and electronic contributions to the hyperpolarizabilities are derived. It is found that there exist strong correlations between the vibrational contributions and bond length alternation of a push-pull polyene. By calculating these contributions numerically, it is proven that the vibrational contributions, estimated from the IR, Raman, and hyper-Raman measurements, to the hyperpolarizabilities can also provide a measure of the nonlinear optical property.