Approximations are applied to the three-level perturbation theory expressions for the third order optical polarizability. We conclude there will be three competing dominant terms, γ ≈ γc + γn + γtp each of which can be optimized at different molecular electronic structures. The two-photon term, γtp, has been commonly ascribed as the most dominant one for γ. However, the other two terms, which optimize at different structures, potentially offer equivalent or larger overall γ. The term, γn, will be optimized at structures with large second order polarizability β, while the term, γC, optimizes at certain centrosymmetric free electron structures with large first order polarization, α Optimization by γc is the preferred route, since this leads to elimination of the canceling terms which limit optimization by γtp or γn. Recent EFISH results have confirmed our earlier speculations that the free electron squarylium dye structures are particularly good for optimization by way of γc. Strategies are presented to selectively optimize to either of the three structure types and to obtain molecules with even larger γ.
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