A quantum mechanical model of the upper bounds of the cascading contribution to the second hyperpolarizability

Microscopic cascading of second-order nonlinearities between two molecules has been proposed to yield an enhanced third-order molecular nonlinear-optical response. In this contribution, we investigate the two-molecule cascaded second hyperpolarizability and show that it will never exceed the fundamental limit of a single molecule with the same number of electrons as the two-molecule system. We show the apparent divergence behavior of the cascading contribution to the second hyperpolarizability vanishes when properly taking into account the intermolecular interactions. Although cascading can never lead to a larger nonlinear-optical response than a single molecule, it provides alternative molecular design configurations for creating materials with large third-order susceptibilities that may be difficult to design into a single molecule.