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 be en constructed for molecules containing one C-3 nu rotor. Internal rot ation is taken to be slow compared to the other vibrations, so that th e small-amplitude vibrational problem is solved for each value of the torsional angle, and the angular momentum operator associated with int ernal rotation motion is grouped with the three components of the tota l angular momentum operator. Even though the molecular symmetry group for two common basis-function sets is isomorphic with C-3 nu, small-am plitude 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 eig envectors. This sign change seems to be related to the fact that the C H3CHO molecule passes through two chemically different C-s configurati ons during the internal rotation motion. Some changes in the G matrix are required because the torsional constraint is not orthogonal to tra ditional bond stretching and angle bending vibrations. Several remaini ng questions concerning application of the present formalism are point ed out. These will probably be answered only when the formalism is app lied to vibrational data (particularly torsionally mediated perturbati ons) of example molecules like acetaldehyde and methanol. (C) 1997 Aca demic Press.