Hybridization effect upon the vibrational second hyperpolarizability: An ab initio study of acetylene, ethylene, and ethane

The vibrational second hyperpolarizability of acetylene, ethylene, and ethane has been computed ab initio at the restricted Hartree–Fock (RHF) and second-order Møller–Plesset (MP2) levels with inclusion of the first-order anharmonicity contributions. It turns out that by going from sp3 to sp carbons, [μβ]0,0, [μ2α]1,0, and [μ2α]0,1 increase substantially whereas [α2]0,0 decreases slightly. For the intensity-dependent refractive index (IDRI), this vibrational contribution amounts to 10–20% of the static electronic counterpart, whereas for the anisotropic Kerr constant it attains 50% in the case of C2H2.