Knowledge Bank

We have developed a model to explain the relative intensities of low energy, pure torsional bands observed in $S1-S0$ spectra of toluene-like molecules having six-fold internal $symmetry.1$ Within the Born Oppenheimer approximation, the transitions $m21,m30$, and $m41$ are Franck-Condon forbidden. Nevertheless, these bands always appear in $S1-S0$ absorption spectra with similar relative intensities. We report relative intensity ratios for five molecules: toluene, $d3-toluene,\backslash emphp$-fluorotoluene, Phenylsilane, and 2,6-difluorotoluen, We also show how expanding the $S1-S0$ transition dipole moment as a Fourier series in the torsional coordinate $\alpha$ predicts relative intensities in quantitative agreement with experiment. The model fixes the symmetry of the upper state of the stronger $m30$ transition as $a1$''. Securing this assignment means the preferred $S1$ conformation is staggered for all molecules studied thus far. This $(m^\{3+\}\}\_\{0\}$ assignment also plays a crucial role when interpreting conformational preferences in $S0$ and $D0.$