  We calculate the electronic transport through a molecular dimer, in which an
excess electron is delocalized over equivalent monomers, which can be locally
distorted. In this system the Born-Oppenheimer approximation breaks down
resulting in quantum entanglement of the mechanical and electronic motion. We
show that pseudo Jahn-Teller (pJT) dynamics of the molecule gives rise to
conductance peaks that indicate this violation. Their magnitude, sign and
position sharply depend on the electro-mechanical properties of the molecule,
which can be varied in recently developed three-terminal junctions with
mechanical control. The predicted effect depends crucially on the degree of
intramolecular delocalization of the excess electron, a parameter which is also
of fundamental importance in physical chemistry.
