Calculation, with the inclusion of vibrational corrections, of the dc-electric-field-induced second-harmonic-generation hyperpolarizability of methane

Calculations of γ̄(−2ω;ω,ω,0) for CH4 are reported for a number of frequencies (ω). This mean frequency-dependent second hyperpolarizability governs the nonlinear optical process: dc-electric-field-induced second-harmonic generation. Two levels of calculation have been carried out: one is based on the random phase approximation and the other on the multiconfigurational random phase approximation using a complete active space self-consistent-field wavefunction. This is the first calculation of γ̄(−2ω;ω,ω,0) that has been made for CH4 using electron-correlated wavefunctions. Included in the calculations are corrections for vibrational effects of which the zero-point vibrational-averaging correction is both dominant and significant (13–18% of the electronic values). Comparison with experiment shows that not all the electron correlation is captured by our treatment. The dispersion properties are also discussed.