Comparison of independently calculated ab initio normal-mode displacements for the three C–H stretching vibrations of methanol along the internal rotation path

Abstract

Graphical displays of normal-mode coefficients from recent quantum chemical projected-frequency calculations are compared with analogous displays constructed after reexamination of results from more extensive higher-level calculations described earlier in the literature. Such comparisons confirm the facts that: (i) no geometrical phase is accumulated in these coefficients when the methyl top undergoes one complete internal-rotation revolution with respect to the frame, and (ii) some of the coefficients, when plotted against the internal rotation angle, exhibit near-cusp-like behavior at one or two angles. The connection between these graphical displays and the magnitude of “Jahn–Teller-like” and “Renner–Teller-like” torsion–vibration interaction terms in a previously reported model Hamiltonian, as well as the connection between the lack of geometric-phase accumulation in these graphs and the number of conical intersections enclosed by one full internal-rotation motion, are briefly discussed.