Torsional Splittings in Small-Amplitude Vibrational Fundamental States of Methanol-Type Molecules
Jon T. Hougen
Group-theoretical methods are used to show that inverted torsional splittings in fundamental levels of small-amplitude vibrations of methanol-like molecules can be understood (and parameterized) in terms of the splittings induced when a high-barrier torsional ground state pair of states of tA + tE symmetry in the molecular symmetry group G6 (isomorphic with C3v) is allowed to interact with small-amplitude vibrational modes of symmetry vE in G6. Such doubly degenerate vE vibrational modes arise rather naturally in G6 for those vibrations of the methyl top in methanol or acetaldehyde (point group C8) that are analogs of the degenerate stretch, bend, and rocking motions of the methyl group in CH3-C=C-H (point group C3v). The present treatment is somewhat different, but still fundamentally similar (as a comparison of model parameters shows), to the recent local mode explanation of inverted torsional splittings in the vE + vA1 set of three C-H stretching vibrations in methanol.