Nonlinear optical phenomena in conjugated organic chromophores. Theoretical investigations via a π-electron formalism

This contribution explores the use of perturbation theory and the chemically oriented, computationally efficient PPP π-electron model Hamiltonian to describe the first three molecular hyperpolarizabilities and their interrelationships. Relationships between various nonlinear phenomena are treated as degeneracy factors, and a more general definition emerges from this analysis. Derivations of formulas describing second- to fourth-order susceptibilities are given for the monoexcited CI (MECI) and doubly excited CI (DECI) perturbation approaches, and numerical results are in good to excellent agreement with experimental values where available for a variety of second- and third-order nonlinear phenomena (second harmonic generation, frequency mixing, linear electrooptic effect, optical rectification, third harmonic generation, dc-induced second harmonic generation, degenerate four-wave mixing, Kerr effect). Additional analysis of chromophore architecture-nonlinear optical relationships reveals that the observable second-order susceptibility, β_vec, is quite sensitive to intramolecular charge transfer and molecular distortions. This becomes even more pronounced in fourth-order phenomena since δ_iiiii is related to charge transfer in a cubic manner rather than linearly as in the case of β_iii. Third-order susceptibilities, γ_ijkl, function exactly as α_ij in a centrosymmetric system and are dominated by the size and shape of the electron cloud. However, in a noncentrosymmetric environment, γ_ijkl has a more complex behavior than either α_ij or β_ijk, and charge-transfer excitations can make an important contribution.