On the dilemma of the potential energy calculations with geometry optimization for spectroscopic purposes: application to a two-dimensional problem

Theoretical techniques for determining the potential energy functions for the double methyl rotation with full optimization of geometry are considered. It is emphasized that, although the methyl groups apparently lose their C3 symmetry because of environmental effects, the dynamical three-fold symmetry properties must be conserved. The problem is examined in the case of biacetyl as an example of a two-C3 rotor problem and applied to the ab initio determination of the lowest levels of the torsional far-infrared spectrum of this molecule. After recording the dynamically symmetric approach, which makes the variational and symmetry principles compatible, it is shown that the methods which average the energy of the energetically `equivalentʹ conformations furnish the closest solutions to those of the correct approach.