A nine-dimensional high order perturbative study of the vibration of silane and its isotopomers

The vibrations of silane isotopomers with $T_d,$ $C_{\text{3v}},$ and $C_{\text{2v}}$ symmetry are studied by means of high order canonical Van Vleck perturbation theory (CVPT). Transforming the quartic ab initio force field of Martin, Baldridge, and Lee [Mol. Phys. 95, 254 (1999)] into curvilinear normal coordinates, CVPT is used to calculate energies that agree well with experimental data. Both low energy stretch–bend combination bands and high energy stretch local mode bands of silane up to 12 000 cm⁻¹ are well reproduced. The choice of polyad quantum number is discussed with respect to different molecules. Comparing sixth- to eighth-order level of theory, most of the levels agree to within 0.1 cm⁻¹. Spectroscopic constants are given for all the major isotopomers. The construction of the full cubic and quartic resonance operators for symmetric top species are summarized. The Si–H and Si–D stretch modes of $T_d$ and $C_{\text{3v}}$ symmetry species are studied with a 4D stretch variational model using both the fitted three-parameter potential and the quartic ab initio stretch potential. Large energy level differences between these two calculations indicate that the fitted potential constants of the stretch variational model are different from those derived directly from the ab initio surface. By comparing with the nine-dimensional CVPT calculation, it is shown that the direct and indirect Fermi resonances are responsible for the inability of the four-dimensional model to fit some stretch levels.