Classification of Rotational Energy Levels for Symmetric-Top Molecules

It is shown that the rotational energy levels of a symmetric-top molecule can be classified according to symmetry species of the full symmetry group of the molecule. Useful selection rules for electric-dipole transitions between rotational energy levels thus classified are presented. It is shown that the rotational energy levels can be labeled in addition by a convenient quantum number G, which is essentially a generalization of the +l, —l labels. Selection rules for this quantum number are presented, which, together with those for the symmetry species, allow one to determine easily the allowed branches for a transition between any two vibronic states in a symmetric-top molecule.