Analysis of the vibrational static and dynamic second hyperpolarizabilities of polyacetylene chains

The RHF/6-31G longitudinal vibrational second hyperpolarizabilities of increasingly longer polyacetylene chains have been computed within the double harmonic approximation. The [α²]^0,0 contribution converges rapidly with chain length to an asymptotic limit 30% larger than its electronic counterpart. The [μβ]^0,0 term converges much more slowly. It is only 4% of the electronic term for C₁₆H₁₈, the longest oligomer considered here, but the ratio is growing rapidly with chain length.