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Using the relationship between geometry and hyperpolarizability as a tool for developing new paradigms for molecular engineering

We consider how geometry and symmetry alone play a role in determining the magnitude of the hyperpolarizability. Using potential energy functions given by a superposition of force centers representing nuclei, we find that for certain specific geometries, such as asymmetric octupolar-like molecule with donors and acceptors of varying strengths at the branches, the hyperpolarizability is near the fundamental limit. The fact that the hyperpolarizability, when it is at the fundamental limit, is well approximated by a three-level model confirms the three-level ansatz. Our results suggest new design strategies for breaking beyond the apparent limit.