In the group theoretical language developed in Chapter 12, a spherical rotor is a molecule that belongs to a cubic or icosahedral point group, a symmetric rotor is a molecule with at least a threefold axis of symmetry, and an asymmetric rotor is a molecule without a threefold (or higher) axis. Linear molecules are linear rotors. Classify each of the following molecules as a spherical, symmetric, linear, or asymmetric rotor and justify your answers with group theoretical arguments:
(a) CH4,
(b) CH3CN,
(c) CO2
(d) CH3OH,
(e) Benzene,
(f') Pyridine