Static and dynamic third-order susceptibilities in conjugated polymers: Hückel theory and VEH approach

We have calculated the static and dynamic third-order optical susceptibility in oligomers of polyacetylene, polyparaphenylene vinylene, and polythienylene vinylene in the framework of both the simple Hückel approach and the VEH methodology. All doubly excited states are explicitly included in a sum-over-states (SOS) formulation. For long chains, we apply the Hückel method to describe the electronic states. The damping factors associated with resonances with excited states are modulated as a function of excited-state energy; the full spectrum of χ⁽³⁾(-3ω; ω, ω, ω) is analysed. Both the length dependence and the dynamic behaviour of χ⁽³⁾(-3ω; ω, ω, ω) are found to be in excellent agreement with experiment. We have then been able to go beyond the Hückel-type parameterization by incorporating the formulation with the valence effective Hamiltonian (VEH) methodology. We study the static and dynamic second-order hyperpolarizabilities of polyenes, oligomers of polyparaphenylene vinylene and polythienylene vinylene. Our results show that a one-electron theory can provide an accurate description of the nonlinear optical response in conjugated polymers.