Two-state model for the first hyperpolarizability of donor-acceptor substituted systems

A simple two-state model is developed describing the first hyperpolarizability β. The model is applicable to molecules consisting of an electron donor separated from an electron acceptor by a π-conjugated link. This approach has the advantage of yielding simple algebraic expressions for the hyperpolarizability. The relationship between β0 (the hyperpolarizability extrapolated to zero frequency) and the wavelength of the absorption maximum λmax is shown explicitly. This relationship is consistent with experimental results for p-substituted benzenes. One also obtains an expression relating β0 and the length of the conjugated system connecting donor and acceptor ends of the molecule.