Vibrational second hyperpolarizability of symmetrically substituted `quadrupolar' π-conjugated systems

Calculations of the electronic and vibrational second hyperpolarizabilities of various quadrupolar π-conjugated molecules performed at the ab initio Hartree-Fock level of approximation show that the vibrational contribution is large for most nonlinear optical phenomena. As for unsubstituted π-conjugated compounds, the Raman term which contributes to the dc-Kerr and degenerate four-wave mixing phenomena is of the same order of magnitude as the static electronic counterpart. The term related to the infrared and hyper-Raman intensities is substantial and, in the case of a squaraine dye, dictates the sign of the global response. This infrared-hyper-Raman term which is often negligible for unsubstituted compounds contributes substantially to the vibrational dc-Kerr and electric field-induced second harmonic generation responses.