Vibrational first hyperpolarizability of methane and its fluorinated analogs

The vibrational first hyperpolarizability of methane and its fluorinated analogs has been computed ab initio at the Hartree-Fock and Möller-Plesset second-order levels of approximation by adopting the perturbation approach due to Bishop and Kirtman. Both the pure vibrational and the zero-point vibrational averaging contributions have been determined. In the static limit, it turns out that the pure vibrational term is at least of the same order of magnitude as its electronic counterpart and the ratio $|{\Vib{\beta}}/{\Elec{\beta}}|$ increases with the fluorine content. The first-order anharmonicity correction to this pure vibrational term increases also with the fluorine content whereas the zero-point vibrational averaging is one/two order of magnitude smaller and decreases with the fluorine content. The suitability of the bond additivity scheme and of the infinite optical frequency approximation is assessed as well as the consistency between experimentally-derived dc-Pockels and second harmonic generation first hyperpolarizability values.