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

Abstract

It is shown that the torsional splitting patterns in methanol-like molecules, with the excitation of small amplitude vibrational modes in the methyl group, are determined by mechanisms that can be formulated in an almost identical fashion to that for ethane-like molecules. This is achieved by treating ethane-like molecules by the internal axis method (IAM) and methanol-like molecules by the principal axis method (PAM) or rho-axis method (RAM). Using the extended molecular groups G₆(EM) or C_6v(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 G_s 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 E_1d, E_2d pairs for ethane) or ‘inverted’ (pure B₁, B₂ pairs for methanol and pure E_1s, E_2s pairs for ethane) can be formed as limit cases. Actual splitting patterns occur between the above limits, and are basically determined 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, observed in perpendicular vibrational modes of the methyl group of methanol, can be predicted by these theoretical considerations. Similar considerations apply to molecules of G₁₂ symmetry.