The effects of torsion–vibration coupling on rotational spectra: Toluene reinterpreted and refitted

A re-examination of rotational line positions for toluene is reported, motivated by the recent observation that the methyl internal rotor states are perturbed by torsion-vibration coupling to vibrational mode M₂₀ (Gascooke et al., 2015). We demonstrate that the data can be fit equally well including or excluding torsion-vibration coupling. The torsion-vibration model required to account for the torsional band positions is thus shown to be consistent with the rotational line positions reported. It is found that including torsion-vibration coupling leads to changes in the values of the rotational and torsional constants, most significantly for A_F, AF′, F and V₆, as well as the higher order constants, with those involving powers of m, K and their cross-terms most affected. Expressions for these effects are provided based on a perturbation expansion, which shows the links between the two models. A primary indicator for the presence of torsion-vibration coupling is AF′ being significantly different to the rotational constant for the frame, A_F, and changing with m. Examination of published AF′/A_F ratios for several substituted toluenes suggests that torsion-vibration coupling is widespread in such molecules. Torsion-vibration coupling has been directly observed through local perturbations to torsional levels in substituted toluenes with both 3- and 6-fold torsion potentials, indicating that it will also affect rotational and torsional constants in molecules with a 3-fold barrier. This indicates that the assumption that the small amplitude vibrations can be ignored when considering the large amplitude methyl rotation requires reassessment.