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Because of the potentially large number of important applications ofnonlinear optics, researchers have expended a great deal of effort to optimizethe second-order molecular nonlinear-optical response, called thehyperpolarizability. The focus of our present studies is the {\em intrinsic}hyperpolarizability, which is a scale-invariant quantity that removes theeffects of simple scaling, thus being the relevant quantity for comparingmolecules of varying sizes. Past theoretical studies have focused on structuralproperties that optimize the intrinsic hyperpolarizability, which havecharacterized the structure of the quantum system based on the potential energyfunction, placement of nuclei, geometry, and the effects of external electricand magnetic fields. Those previous studies focused on single-electron modelsunder the influence of an average potential. In the present studies, wegeneralize our calculations to two-electron systems and include electroninteractions. As with the single-electron studies, universal properties arefound that are common to all systems -- be they molecules, nanoparticles, orquantum gases -- when the hyperpolarizability is near the fundamental limit.

The effect of electron interactions on the universal properties of systems with optimized intrinsic off-resonant hyperpolarizability