Calculation of Energy Levels for Internal Torsion and Over-All Rotation. III

Abstract

A general treatment of hindered internal rotation is given for molecules that can be regarded as a rigid symmetric top attached to a rigid frame which may be completely asymmetric. The perturbation approach developed in previous papers is simplified and extended by use of a method which relates the perturbation coefficients to the exact energy levels obtainable for the limiting case of two coaxial symmetric tops. Tables are given which provide the torsional energy levels and the perturbation coefficients through fourth order in the coupling between internal and over-all rotation. The tables apply to the lowest three groups of torsional states for a potential barrier of the form V(α)=12VN(1−cosNα)+12V2N(1−cos2Nα), where the periodicity N is arbitrary and O<̄V2N/VN<5%. The range of validity of the approximations is examined, and it is concluded that in most applications the previous second order treatment yields reliable values of the barrier height. Situations in which higher order corrections affect microwave spectra are illustrated by a reanalysis of the data for methyl silane and acetaldehyde.