Extensive studies in the past have focused on precise calculations of the nonlinear-optical susceptibility of thousands of molecules.In this work,we use the broader approach of considering how geometry and symmetry alone play a role,irrespective of molecular constraints.We investigate the nonlinear optical response of potential energy functions that are given by a superposition of force centers (representing the nuclear charges) that lie in various planar geometrical arrangements.We find that for certain specific geometries,such as an octupolarlike molecule with donors and acceptors of varying strengths at the branches,the hyperpolarizability is near the fundamental limit.In these cases,the molecule is observed to be well approximated by a three-level model,consistent with the three-level ansatz previously used to calculate the fundamental limits.However,when the hyperpolarizability is below the apparent limit (about a factor of 30 below the fundamental limit),the system is no longer representable by a three-level model,where both two-level and many-state models are found to be appropriate,depending on the symmetry.
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