On the physical interpretation of ab initio normal-mode coordinates for the three C–H stretching vibrations of methanol along the internal-rotation path

Abstract

Graphical representations are presented for variation along the steepest-descent internal-rotation path in methanol of the normal mode frequencies and their associated eigenvectors in several sets of internal coordinates and in Cartesian atomic displacement vectors di(γ), as determined for the three CH stretching vibrations (ν3, ν2, and ν9) 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 angle γ increases by 2π. 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 γ-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 ν2 and ν9 at the top and bottom of 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 computation is presented to illustrate the changes that will be necessary in order to move from the usual diabatic torsion–vibration treatments in the literature to adiabatic treatments, in which the normal-mode Cartesian displacement vectors given at each point along the internal rotation path by the Gaussian projected frequency calculation are used directly in the torsion–vibration energy level calculation.