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

Abstract

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 AF, 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, AF, and changing with m. Examination of published AF′/AF 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.