Symmetry and degeneracy manifolds in Jahn-Teller molecules

We consider problems in dealing with molecular systems of n identical nuclei. One problem is that of finding suitable internal coordinates. For n <= 4, these can be simply the internuclear distances. For n > 4, it is shown that, with perhaps one exception, there is no internal coordinate system that treats all nuclei equivalently. We also consder the properties of conical intersections between two Born-Oppenheimer electronic energy surfaces, in particular the problem of identifying the two coordinates that remove the degeneracy to first order in the near neighborhoods of symmetry manifolds.