  Conical intersections between molecular electronic potential surfaces greatly
affect various properties of the molecule. Molecular gauge theory is capable of
explaining many of these often unexpected phenomena deriving from the physics
of the conical intersection. Here we give an example of anomalous dynamics in
the paradigm of the Exe Jahn-Teller model, which does not allow a simple
explenation in terms of standard molecular gauge theory. By introducing a dual
gauge theory, we unwind this surprising behavior by identifying it with an
intrinsic spin Hall effect. Thus, this work link knowledge of condensed matter
theories with molecular vibrations. Furthermore, via ab initio calculations the
findings are as well demonstrated to appear in realistic systems such as the
Li3 molecule.
