Vibrational symmetry classification and torsional tunneling splitting patterns in G6(EM), G12 and G36(EM)molecules

It is shown that the torsional splitting patterns in methanol-like mols., with the excitation of small amplitude vibrational modes in the Me group, are detd. by mechanisms that can be formulated in an almost identical fashion to that for ethanelike mols. This is achieved by treating ethane-like mols. by the internal axis method (IAM) and methanol-like mols. by the principal axis method (PAM) or rho-axis method (RAM). Using the extended mol. groups G6(EM) or C6v(M) for methanol and G36(EM) for ethane, vibrations perpendicular to the internal rotation axis are conveniently described by modes of higher degeneracy (E for methanol and Gs for ethane) in the absence of coupling of top and frame. Head-tail coupling operators, except the cos-type barrier terms, lower the degeneracy, causing vibrational splittings. Coupled vibrational pairs with torsional splitting patterns that we call 'regular' (pure A1, A2 pairs for methanol and pure E1d, E2d pairs for ethane) or 'inverted' (pure B1, B2 pairs for methanol and pure E1s, E2s pairs for ethane) can be formed as limit cases. Actual splitting patterns occur between the above limits, and are basically detd. by torsional Coriolis coupling, which can tune more or less to resonance pairs of uncoupled basis levels linked by specific head-tail coupling operators. The inversion of torsional splitting patterns, obsd. in perpendicular vibrational modes of the Me group of methanol, can be predicted by these theor. considerations. Similar considerations apply to mols. of G12 symmetry.