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

This paper concerns itself primarily with three questions: (i) What is the range of commonly used definitions for the internal rotation angle, and how do variations within this range affect intercomparisons among results from various laboratories? (ii) Do the force-constant and projected-frequency variations with internal rotation angle delivered by present commercial ab initio packages have sufficient precision to allow meaningful extraction of higher-order vibration–torsion–rotation interaction terms? (iii) What fraction of the extensive dynamics literature on vibrational frequencies along the chemical reaction path can be easily adapted for use in high-resolution spectroscopic studies of small-amplitude vibrations in methyl top internal rotor molecules? Aspects of these questions are discussed both from an algebraic and from a numerical computation point of view.