Knowledge Bank

The selection rules for torsion vibrations of molecules having two or three symmetrically arranged ($CH3$) tops have been analyzed by using group theoretical methods. The selection rules were established by using a symmetry group that contains the $C2$ symmetry elements of the $CH3$ tops as well as the point group elements of the whole molecule. This analysis predicted infrared allowed transitions which should be forbidden according to the common treatment of the torsion vibration problem. In particular, for two tops molecules having $C2v$ and three tops molecules having $Cav$ point group symmetry, the transition between the ground and the first exited torsional state consist of two instead of one infrared active transition.