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Symmetry and Fourier analysis of the ab-initio-determined torsional variation of structural and Hessian-related quantities for application to vibration-torsion-rotation interactions in CH3OH

Published

Author(s)

Li-Hong Xu, Jon T. Hougen, Jonathan M. Fisher, Ronald M. Lees

Abstract

The aim of the present paper is to investigate the use of quantum chemistry calculations to obtain the torsional dependence of various structural and vibrational-force-field-related quantities that could help in estimating the vibration-torsion-rotation interaction terms needed to treat perturbations observed in the spectra of methanol-like molecules. We begin by using the Gaussian suite of programs to determine the steepest-descent path from a stationary point at the top of the internal rotation potential barrier in methanol to a stationary point at the bottom of the barrier, i.e., at the equilibrium structures. This procedure requires determining the gradient ÑV of the potential (as calculated in mass-weighted Cartesian coordinates) along the internal rotation path. In addition, we use the Gaussian suite to calculate the Hessian ÑÑV along this path and to generate from these second derivatives the 3N-7 small-amplitude vibrational frequencies and the 3N Cartesian vibrational displacements for each of these vibrations. We then symmetrize the internal coordinates used in the gradient, Hessian and vibrational displacements to take into account the periodic variation of the behavior of the three methyl hydrogen atoms Hi as they pass in turn through the Cs plane of the HOC frame. The symmetrized linear combinations of the CHi stretches, of the OCHi bends, and of the HOCHi dihedral angles of the methyl group depend on the internal rotation angle g and are determined by considering coordinate transformations from the G6 permutation-inversion group appropriate for internally rotating methanol. This symmetrization procedure permits us to explore the feasibility of expressing the structures, gradients, Hessians, and vibrational displacement vectors along the internal rotation path as short Fourier series in g, which is one of the main goals of this paper.
Citation
Journal of Molecular Spectroscopy
Volume
260

Keywords

Ab Initio, Fourier Expansions, Group Theory, Internal Rotation, Projected Vibrational Frequencies, Steepest Descent Path, Vibration-Torsion-Rotation Interactions

Citation

Xu, L. , Hougen, J. , Fisher, J. and Lees, R. (2010), Symmetry and Fourier analysis of the ab-initio-determined torsional variation of structural and Hessian-related quantities for application to vibration-torsion-rotation interactions in CH3OH, Journal of Molecular Spectroscopy, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=903523 (Accessed July 31, 2021)
Created January 11, 2010, Updated February 19, 2017