Internal rotation of a light symmetric top relative to a heavy planar framework: theoretical calculations of vibration/internal-rotation spectra including effects of rotational barriers and non-degeneracy of perpendicular symmetric top vibrations

Abstract

Model theoretical calculations have been made of the fine structure associated with the perpendicular vibrations of a ‘light’ symmetric top group (such as CH 3 , SiH 3 , etc.) resulting from its internal rotation with respect to an infinitely heavy planar framework. Investigations have been made of the effects on the internal rotational fine structure of the removal of the degeneracy of the perpendicular vibrations as required by the lower site symmetry. Separate calculations have been made for the cases where the removal of degeneracy is caused ( a ) by electronic effects which result in an angular variation of the appropriate force constant, or ( b ) by interaction with another vibration in the framework part of the molecule. It is found that no fine structure lines occur between the non-degenerate frequencies, but that the effect of internal rotation is to generate rotational wings outside this frequency range. The effects of a finite sixfold barrier to internal rotation on the vibrational/internal-rotational absorption band have been calculated for the degenerate and non-degenerate cases. It is shown that certain lines are split by amounts comparable to the barrier height, V 6 , which should therefore be experimentally obtainable from this type of spectrum in favourable cases. The effect of an increasing barrier is to cause more of the intensity within the overall band contour to occur in the vicinity of the vibrational frequency or frequencies, and less in the internal rotational wings, as expected on physical grounds.