Calculation of the tau dependence of the vibration-internal rotation-overall rotation interactions in CH3OH from molecular structure and molecular dynamics

The Guan and Quade theory for vibration-large-amplitude internal-motion-rotation interactions has been applied to the internal rotation problem in CH(3)OH. Through the molecular dynamics, the cos 3tau and sin 3tau dependence of the torsional-rotational coefficients in the effective Hamiltonian have been calculated from molecular structure. The internal rotation coordinate tau(') for the vibrationally distorted molecule is shown to have the necessary threefold symmetry for all values of tau('). For the methyl deformation modes, the vibrational dependence of the internal rotation potential energy is shown to have a threefold symmetry. The S(t) and S(t)S(t) dependence of the inertia tensor and Coriolis coupling coefficients has been developed in terms of curvilinear internal coordinates. The T transformation separating rotation from vibrations in zeroth order is then applied, the kinetic-energy tensor inverted to momentum space, and finally the effective torsion-rotation coefficients are calculated by Van Vleck perturbation theory. When compared to the empirical results, the kinetic-energy contributions to the cos 3tau and sin 3tau dependence of the coefficients are as follows: 54% of P(a)(2) is accounted for, 28% of P(a)P(b), 16% of P(a)P(c), and 91% of the asymmetry. The calculation is inadequate to account for the P(b)(2),P(c)(2), and P(b)P(c) coefficients, ranging from factors of 20-70, even with the incorrect sign for some of the terms. Anharmonic force contributions from the vibrations have not been used in the calculation since these forces are not known at this time.