Ab initiopolarizability derivatives for methane: an application to Raman intensities of overtone and combination bands

The polarizability and its first and second derivatives have been calculated for methane at the following levels of approximation: ab initio SCF, singles and doubles CI and averaged coupled pair functional method; correlation and basis set effects have been investigated. The calculated polarizability surface predicts to experimental accuracy several observables related to the refractive index. The correlated first derivatives provide improved predictions of Raman scattering cross sections for the fundamentals. First and second derivatives are used to calculate scattering cross sections for selected overtone and combination bands including all totally symmetric bands in the pentad region. A comparison is made between cross sections based on perturbation expressions and on variational vibrational state functions. Deficiencies in the vibrational potential derived from rovibrational spectra are pointed out.