Internal rotation with a low threefold barrier ; comparison between different basis functions

Abstract

For the treatment of the effects of a C3v internal rotor on the rotational spectrum of a molecule we have compared two different sets of basis functions, i.e. Mathieu functions and free rotor functions. In both cases the internal axes system was used. The behaviour of two model substances, based on the geometries of 1-chloro-2-butyne and meta-fluorotoluene, was studied for values of V3 up to 100 cm−1. It was found that for this range of barriers the use of basis functions from more than one torsional state is often necessary for a good description of the energy levels. The size of the matrix to be diagonalized depends on the barrier height and the molecular geometry, but is often larger for free rotor functions than for Mathieu functions. Thus for low barrier problems the use of the latter type of functions, which have not often been used in that region, should be more seriously considered.