15min:

DAVID S. PERRY AND XIAOLIANG WANG, Department of Chemistry, University of Akron, Akron, OH 44325-3601..

Torsional tunnelling about the C-O bond splits the vibrational ground state of methanol into A and E states. For K=0, the A state is 9.11 cm^-1 below the E state; for K>0, the torsional energies follow the expected cosine pattern. For the ₂ asymmetric C-H stretch, the splitting is inverted, i.e., E below A at K=0, and smaller in magnitude (-3.26 cm^-1), but the torsional energies still follow an approximately regular cosine pattern. The limited information available on the ₉ asymmetric C-H stretch indicates that it is also inverted (about -5 cm^-1). However, the ₃ symmetric C-H stretch is normal with A below E (+9.07 cm^-1).

In order to treat the inverted torsional tunnelling behavior, a local mode Hamiltonian with G₆ symmetry has been developed. Three parameters are sufficient to fit the frequencies of the three C-H stretch band origins. These are the harmonic local C-H stretch frequency \omega=2935.8 cm^-1, the local-local coupling \lambda=-43.9 cm^-1, and the lowest order torsion-vibration interaction constant µ=10.5 cm^-1. Qualitatively, the torsion-vibration interaction µ results from the fact that the force constant for the C-H bond trans to the O-H is higher than for the gauche C-H bonds. When combined with the known ground state torsional potential, the same three parameters are sufficient to account for the sign and magnitude of the torsional tunnelling splitting of all three C-H stretch fundamentals. The inversion of the torsional tunnelling for the ₂ and ₉ vibrations is a systematic property of the Hamiltonian and not the result of an accidental stretch-torsion resonance. Therefore, the inverted torsional tunnelling is a general result attributable to the molecular symmetry.