Frequency dependent hyperpolarizabilities of polyynes

Ab initio calculations have been performed for the static and dynamic polarizability and hyperpolarizability for a series of polyynes C _2nH₂ using self-consistent field (SCF) (n=1-6) and multiconfiguration self-consistent field (MCSCF) (n=1-4) wave functions. We have considered the longitudinal component of the static hyperpolarizability and the same component of the dynamic hyperpolarizability measured in electric-field induced second harmonic generation γ^ESHG=γ(- 2ω;ω,ω,0). The frequency dependence of the polarizability and hyperpolarizability has been rationalized in terms of the coefficients in expansions in ω². The static hyperpolarizabilities vary smoothly with the chain length and satisfy γ(C_2nH ₂)=γ (C₂H₂) ×n^X, where X≈3.0. The dynamic hyperpolarizability satisfies a similar relation where X increases slowly with ω.