The sum of hyperpolarizabilities approach to third-order non-linear optical susceptibilities of π-conjugated polymer crystals

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Abstract
Non-resonant third-order non-linear optical susceptibilities χ(3) zzzz are estimated for infinite conjugation lengths of polymers, such as polyacetylene, polydiacetylene and poly-yne in their crystal states, by using the calculated static second hyperpolarizability γ and the sum of hyperpolarizabilities approach. The static second hyperpolarizability of the oligomers is calculated by using an ab initio coupled perturbed Hartree–Fock (CPHF) method. The CPHF calculation for the polyacetylene oligomer reproduces the experimental values of the longitudinal component γzzzz of γ observed at non-resonant wavelengths. The static second hyperpolarizability γ of the infinite polymers is extrapolated from those of their oligomers considering the saturation behaviour of γ in a longer chain region. This combination of the CPHF calculation and the sum of hyperpolarizability approach is successfully applied to the evaluation of χ(3) zzzz of bulk polyacetylene. However, the above method cannot correctly reproduce χ(3) zzzz of polydiacetylene crystal. The results are discussed considering the difference between polyacetylene and polydiacetylene; i.e., excitonic or non-excitonic nature of their excited states.