Relationship between static vibrational and electronic hyperpolarizabilities of π-conjugated push–pull molecules within the two-state valence-bond charge-transfer model

The two-state valence-bond charge-transfer (VB-CT) model for π-conjugated push–pull molecules is analyzed to yield several parameter-independent relations between vibrational and electronic hyperpolarizabilities. Ab initio computational tests show that these relations are not satisfied. As a byproduct of the ab initio calculations, we have found cases where the static vibrational first hyperpolarizability is much larger than the static electronic first hyperpolarizability. Our results also shed light on a controversy regarding normal coordinate polarizability derivatives.