Cooperative interactions in supramolecular aggregates: linear and nonlinear responses in calix[4]arenes.

The linear and nonlinear optical polarizabilities of donor-acceptor (D-pi-A) chromophores in confined geometries of calix4]arenes are investigated through a model for interacting polar-polarizable molecules. Both the linear polarizability (alpha) and the first hyperpolarizability (beta) decrease with increasing the interdipolar angle, as expected in the oriented-gas picture. However, within the polar-polarizable model we predict deviations from the additive result, irrespective of the interdipolar angle. Depending on the nature of the chromophore, electrostatic intermolecular interactions between polar and polarizable chromophores lead to cooperative damping or enhancement of the optical responses. Specifically, for chromophores whose ground state is dominated by the neutral D-pi-A structure both alpha and beta are suppressed with respect to the prediction of the oriented-gas model, whereas the opposite holds true for chromophores whose ground state is dominated by the zwitterionic D(+)-pi-A(-). These results explain recent experimental data on a calix4]arene functionalized with a donor-acceptor dye for nonlinear optical applications. Density functional theory calculations on the relevant crystal structure further support our interpretation.