Torsion-rotation-vibration effects in the degenerate vibrational fundamental (v12 = 1 ← 0) of CH3SiH3

Abstract

Abstract The lowest-lying degenerate fundamental of a polar symmetric rotor undergoing hindered internal rotation has been studied. The spectrum arising from the excitation ( v 12 = 1 ← 0) of the silyl rock in CH 3 SiH 3 has been measured between 485 and 565 cm −1 with Fourier transform spectroscopy at an effective resolution of 0.0045 cm −1 . Almost 1500 lines originating in the ground torsional state have been identified. Two interesting torsional effects are observed in the spectra. First, resonant or near-resonant perturbations are seen between ( v 12 = 1, v 6 = 0) and ( v 12 = 0, v 6 = 3) for many different ( K , σ) series, where v 6 is the principal torsional quantum number and σ labels the torsional sublevels. The perturbation is shown to result from the xy -Coriolis interaction and a higher-order Coriolis-like term that arises from the off-diagonal part of the operator responsible for the l -doubling. Second, for given lower state J and K , the unperturbed σ-splittings in ( v 12 = 1, l = −1) and in ( v 12 = 1, l = +1) are almost identical and, except for a scale factor, approximate the σ-splittings for the lower state. This effect is shown to result from a z -Coriolis operator linear in the torsional and vibrational angular momenta. The form of the effective Hamiltonian is severely constrained by the large number of precision data obtained earlier on different torsional levels in the ground vibrational state. The global data set of 2011 frequencies is fitted to within experimental error by a model which includes 12 molecular parameters in addition to the 21 constants introduced earlier for ( v 12 = 0). The effective Hamiltonian for a doubly degenerate vibrational fundamental of E 1 symmetry and the leading interactions between this state and the ground vibrational state are discussed in detail.