  We study electronic transport in diatomic molecules connected to metallic
contacts in the regime where both electron-electron and electron-phonon
interactions are important. We find that the competition between these
interactions results in unique resonant conditions for interlevel transitions
and polaron formation: the Coulomb repulsion requires additional energy when
electrons attempt phonon-assisted interlevel jumps between fully or partially
occupied levels. We apply the equations of motion approach to calculate the
electronic Green's functions. The density of states and conductance through the
system are shown to exhibit interesting Rabi-like splitting of Coulomb blockade
peaks and strong temperature dependence under the it interacting resonant
conditions.
