A unified description of linear and nonlinear polarization in organic polymethine dyes

An internal or external electric field F can drive the chemical structure, bond order alternation, and electronic structure of linear polymethine dyes from a neutral, bond-alternated, polyene-like structure, through a cyanine-like structure, and ultimately to a zwitterionic (charge-separated) bond-alternated structure. As the structure evolves under the influence of F, the linear polarizability α, the first hyperpolarizability β, and the second hyperpolarizability γ are seen to be derivatives, with respect to F, of their next lower order polarization (for α) or polarizability (for β and γ). These derivative relations provide a unified picture of the dependence of the polarizability and hyperpolarizabilities on the structure in linear polymethine dyes. In addition, they allow for predictions of structure-property relations of higher order hyperpolarizabilities.