Application of Symmetry Principles to the Rotation-Internal Torsion Levels of Molecules with Two Equivalent Methyl Groups

Abstract

The set of coordinate transformations, corresponding to symmetry operations, which leave invariant the Hamiltonian operator for a molecule with two equivalent methyl groups, is obtained. These constitute a group which is a direct product of two simple groups, i.e., C_3v×C_3v. The possible species for the energy levels, their degeneracies, their statistical weights, and the selection rules are worked out by group theory techniques which use only the properties of the smaller groups. The higher symmetry and higher degeneracies given by approximate Hamiltonians are briefly discussed.