Spherical top molecules and the molecular symmetry group

The energy levels and wavefunctions of spherical top molecules are classified using the appropriate molecular symmetry group, and the spatial three-dimensional rotation group K(spatial). We use these groups here for the molecules CH4, SF6 and C-60 as examples, and the appropriate molecular symmetry groups are T-d(M), O-h(M) and I-h(M) respectively. We consider rotational, vibrational and nuclear spin state symmetries. Nuclear spin statistical weights, perturbation restrictions, and optical selection rules obtained using these symmetries are also discussed. The concept of an equivalent rotation is generalized to apply to spherical top molecules and this unifies the symmetry treatment of spherical top molecules with that used for molecules of lower symmetry. It accords with the approach used by Hougen for the methane molecule [see, for example, HOUGEN, J. T., 1971, J. chem. Phys., 55, 1122]. We also try to make clear the distinction between +/- parity which is the symmetry under E*, and the g/u label which is determined from the effect of the molecular symmetry group operation (O) over cap(i) that is present for a centrosymmetric molecule like SF6 or C-60.