Knowledge Bank

The effect of internal rotation on the redundancies in the torsion-rotation Hamiltonian $HTR$ and on the dipole moment operator for methyl silane like molecules ($G18$ symmetry) is examined. It is shown that $HTR$ contains a new term with selection rules $\Delta K=\pm 3,\Delta \sigma =0$, and $\Delta vT\prime \prime$ arbitrary, where $vT$ and $\sigma$ label the torsional levels and sub-levels, respectively. As a result, the distortion dipole moment $\mu 0$ which arises from mixing of $\Delta K=\pm 3$ level in molecules with $C3v$ symmetry cannot, in systems like methyl silane, be ascribed entirely to centrifugal distortion but can contain a significant contribution from torsional effects. Furthermore, new transitions can appear in the pure torsional bands which may be strong enough to observe in low barrier molecules. Finally, the physical origin of the leading torsional terms in the dipole moment expression which give rise to pure torsional band is described.