Knowledge Bank

The concept of a ``normal mode'' in dimethylacetylene for the limiting case of almost free internal rotation can be given a precise meaning. The method is based essentially on a determination of the normal modes in the usual way, but a separate determination is made for each value of the torsional angle $\gamma$. Various quantities appearing in the vibrational problem, which normally are constants, must be considered in this procedure as functions of the angle $\gamma$. The normal modes so defined can be shown to transform according to the irreducible representations of a molecular symmetry group constructed especially for dimethylacetylene. A rigorous derivation of the nuclear kinetic energy operator, similar to the treatment of Wilson and Howard, can be carried out within the framework of the procedure under discussion.