Theoretical study of the effect of structural modifications on the hyperpolarizabilities of indigo derivatives.

The static first and second hyperpolarizabilities of a number of indigo (In) derivatives, donor-In-donor, acceptor-In-acceptor, and donor-In-acceptor, have been calculated at the B3LYP/6-31+G* level. The various useful relations are obtained from the standard sum-overstate (SOS) expressions with the use of the Thomas-Kuhn (TK) sum rule. The variation of NLO properties, especially the second hyperpolarizability (gamma) of indigo compounds, can be satisfactorily explained in terms of ground-state electric moments, linear polarizability (alpha), and second-order polarizability (beta). The noncentrosymmetry arising from replacement of the ring NH of indigo with O and S atoms and also substitution with donor and acceptor at different ring positions of indigo lead to rather significant modulation of gamma. The appreciable decrease of third-order polarizability on pyramidalization of the NH2 group as explained in the present model is equivalent to the decrease of the dipole moment difference and increase of the transition energy in the two-state model.