Graphical representations are presented for variation along the steepest-descent internal-rotation path in methanol of the normal mode frequencies and their associated expansion coefficients in several sets of internal coordinates and in Cartesian atomic displacement vectors di(), as determined for the three CH stretching motions (3, 2, and 9) by projected frequency calculations from the Gaussian suite of programs. The methyl-group CH stretching modes are interesting because the symmetry environment of each C-H bond changes significantly during the internal rotation, i.e., each of the methyl bonds takes turns passing (twice for a complete torsional revolution) through the plane of symmetry of the COH frame of the molecule. No accumulation of geometric phase is observed in any of these plots, and all quantities return to their original values after the internal rotation angel increases by 2. A simple two-vibrational-state, three-parameter model, closely based on earlier models from the literature, can be used to understand nearly quantitatively much of the -variation observed in the Gaussian plots, including a number of cusp-like features. In particular, when the three parameters in the model are determined from a fit to the Gaussian projected frequencies for 2 and 9 along the internal rotation path, it is found that the Renner-Teller-like torsion-vibration interaction term is slightly larger in magnitude than the Jahn-Teller-like term, which is consistent with no accumulation of geometric phase in the various plots. Finally, a highly simplified example calculation is given to illustrate the changes that will be necessary to move from the usual diabatic torsion-vibration treatments in the literature to an adiabatic treatment that uses Gaussian projected frequency output directly in the calculation.
Citation: Journal of Molecular Spectroscopy
Pub Type: Journals
ab initio, CH stretching vibrations, methanol, normal modes, torsional dependence, vibrational displacement vectors