A GROUP-THEORETICAL TREATMENT OF ELECTRONIC, VIBRATIONAL, TORSIONAL, AND ROTATIONAL MOTIONS IN THE DIMETHYLACETYLENE MOLECULE

The Hamiltonian for the dimethylacetylene molecule is expressed in terms of a set of coordinates which allow a separation of the molecular wave function into an electronic part, a vibrational part, a torsional part, and a rotational part. Symmetry species are introduced which can be used to classify separately any one of the parts of the molecular wave function as well as the total wave function itself. These symmetry species correspond not only to the single-valued representations of the group proposed by Longuet-Higgins for the dimethylacetylene molecule, but also to double-valued representations of that group. The use of these symmetry species and of the corresponding selection rules is illustrated by the example of an optical transition which would correspond to a [Formula: see text] transition in the linear portion of the dimethylacetylene molecule.