Analysis of the gearing-antigearing torsional fundamental energy gap in dimethyl ether

Bimethyl rotor molecules, e.g., dimethyl ether (DME) exhibit two kinds of torsion: gearing (rotors turning out-of-phase) and antigearing (rotors turning in-phase). Although it is widely accepted that the fundamental frequencies of these two motions frequently differ by several tens of cm^-1, no systematic study of the physical origin of this splitting has been given. We report a series of dimethyl ether gearing/antigearing fundamental frequency splitting calculations where separate consideration of exchange repulsion, delocalization (hyperconjugation) interactions, and nonrotational phase space of the torsional coordinate indicate that the splitting is largely due to hyperconjugation between CH bonds of the two methyl groups. There is an inference that CH bond hyperconjugation is a major cause of the splitting in bimethyl rotor molecules, in general.