Double harmonic vibrational second hyperpolarizabilities of polyyne chains

The RHF/6-31G longitudinal vibrational second hyperpolarizabilities of increasingly longer polyyne chains have been computed within the double harmonic oscillator approximation. Similarly to polyacetylene, the largest contribution comes from the [α²]^0,0 term. About 95% of the latter arises from what we call the quasi-ECC mode. It converges rapidly with chain length to an asymptotic limit slightly (7%) smaller than its static electronic counterpart. The [μβ]^0,0 term is negligible. The inclusion of electron correlation within the MP2/6-31G scheme leads to a decrease of the γ^v/γ^e ratio by a factor going from roughly 3 for the dimer to 2 for the tetramer.