Coordinates, Hamiltonian, and symmetry operations for the small-amplitude vibrational problem in methyl-top internal-rotor molecules like CH3CHO

Motivated by attempts to understand the mechanism(s) by which internal rotation of methyl tops strongly enhances intramolecular vibrational energy redistribution, a vibration-torsion-rotation Hamiltonian has been constructed for molecules containing one C-3 nu rotor. Internal rotation is taken to be slow compared to the other vibrations, so that the small-amplitude vibrational problem is solved for each value of the torsional angle, and the angular momentum operator associated with internal rotation motion is grouped with the three components of the total angular momentum operator. Even though the molecular symmetry group for two common basis-function sets is isomorphic with C-3 nu, small-amplitude vibrational eigenvectors resulting from diagonalization of the FG matrix may change sign when the methyl top is rotated by 2 pi, so that a double group of C-3 nu must be used to classify vibrational eigenvectors. This sign change seems to be related to the fact that the CH3CHO molecule passes through two chemically different C-s configurations during the internal rotation motion. Some changes in the G matrix are required because the torsional constraint is not orthogonal to traditional bond stretching and angle bending vibrations. Several remaining questions concerning application of the present formalism are pointed out. These will probably be answered only when the formalism is applied to vibrational data (particularly torsionally mediated perturbations) of example molecules like acetaldehyde and methanol. (C) 1997 Academic Press.