Torsional Angle Definitions and Linear and Quadratic Force Field Variations along the Torsional Coordinate for CH3OH and CH3CHO

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

“…In spite of this excellent force-field behavior, however, the projected vibrational frequencies we obtained along the large-amplitude internal-rotation coordinate did not always extrapolate well to the vibrational frequencies obtained at the saddle and minimum of the potential surface (see Fig. 4 of [6]). …”

“…Just as observed for the C-H stretch modes, the two higher-frequency asymmetric methyl CH-bending modes were predicted to have inverted tunneling splittings with reduced amplitudes, while the splitting pattern for the lower frequency symmetric-bend mode was predicted to be normal. The third paper [6] showed that G98 delivered very smooth linear and quadratic force-constant plots as a function of angle along the internal rotation coordinate c and that when coordinates symmetrized in the permutation inversion group G 6 were used, each plot exhibited the sin 3c or cos 3c behavior expected from the symmetry species of the vibrational coordinate(s) that are multiplied by the given force constant. In spite of this excellent force-field behavior, however, the projected vibrational frequencies we obtained along the large-amplitude internal-rotation coordinate did not always extrapolate well to the vibrational frequencies obtained at the saddle and minimum of the potential surface (see Fig.…”

Torsion–rotation global analysis and database for the CH318OH isotopomer of methanol

“…Out of the 79 reported fit parameters in Table 7, 15 have been used for the first time in our methanol isotopic global fits. In the early stages of the fitting, we had fixed k 6 and k 7 to ab initio values (k 6 = 0.09539 cm À1 and k 7 = 0.17912 cm À1 ) [33] because these two parameters are involved in an indeterminacy relation together with F and V 6 [34]. However, through careful trial and error tests we found that it was not necessary or helpful to fix these terms and, indeed, we were able to improve our standard deviation after the k 6 and k 7 terms were removed in the final stages of fitting.…”

Ab initio determination of spectroscopic parameters for ethane-like molecules in the ground vibrational state

“…This affords us a number of simplifications relating to choice of coordinates. In particular, subtleties in the choice of torsional coordinate, discussed extensively elsewhere (see, for instance, [26] and for a more general discussion [28]), are not relevant here.…”

“…While previous ab initio studies have been largely successful, they have been restricted to structural parameters and/or a small number of spectroscopic parameters [18,[25][26][27]. In this paper, we present a more complete calculation of the ground state model parameters for ethane-like molecules from the results of ab initio calculations.…”