The intensity of forbidden torsional transitions in electronic spectra of molecules with a 6-fold barrier: Application to toluenes

Franck-Condon forbidden transitions involving methyl rotor modes are seen in the S₁ ← S₀ spectrum of toluene and toluene-like molecules. The strongest of these rotor transitions (m^″ = 1 → m^′ = 2, m^″ = 0 → m^′ = 3a₁^″, and m^″ = 1 → m^′ = 4) have been shown by Walker et al. [J. Chem. Phys. 102, 8718 (1995)] to gain intensity through the rotor equivalent of the Herzberg-Teller mechanism. Despite the m^″ = 0 → m^′ = 3a₂^″ transition being forbidden in this formalism, it is sporadically observed. We show that this transition derives oscillator strength from incomplete mixing of the −3 and +3 free rotor basis states due to torsion-rotation coupling. Calculations demonstrate that this mechanism quantitatively explains the intensities observed for toluene, including their temperature dependence. Because the −3/+3 mixing is weakest when the torsional barrier height, V₆, is small, the m^″ = 0 → m^′ = 3a₂^″ transition increases in intensity as |V₆| decreases. The temperature and |V₆| dependencies explain why reports of the 0 → 3a₂^″ transition have been intermittent. The torsion-rotation coupling mechanism is predicted to also give significant intensity to m = 0 → m = 6a₂^′ transitions relative to m = 0 → m = 6a₁^′ transitions and to provide intensity to 0 → 3a₂ transitions in molecules with a 3-fold (V₃) barrier. Comparison between the observed and calculated rotor band contours shows, unexpectedly, that the 3a₁^″ constants fail to predict the 3a₂^″ contour despite these two states being derived from the same free rotor basis states. Comparison with the observed spectrum also reveals differences in the separation of the S₁ 3a₂^″ and 3a₁^″ levels. The V₆ value determined from analysis of the high resolution, rotationally resolved m^″ = 0 → m^′ = 3a₁^″ spectrum overestimates the 3a₂^″-3a₁^″ separation by 0.6 cm⁻¹. We postulate that this may be due to torsion-vibration coupling. The observed toluene torsion-rotation contours have been modeled to provide estimates of the rotational constants for several of the torsional states.