  Both experiments and theoretical studies have demonstrated that the
interaction between the current carrying electrons and the induced polarization
charge in single-molecule junctions leads to a strong renormalization of
molecular charging energies. However, the effect on electronic excitations and
molecular symmetries remain unclear. Using a theoretical framework developed
for semiconductor nanostructure based single-electron transistors (SETs), we
demonstrate that the image charge interaction breaks the molecular symmetries
in a benzene based single-molecule transistor operating in the Coulomb blockade
regime. This results in the appearance of a so-called blocking state, which
gives rise to negative differential resistance (NDR). We show that the
appearance of NDR and its magnitude in the symmetry-broken benzene SET depends
in a complicated way on the interplay between the many-body matrix elements,
the lead tunnel coupling asymmetry, and the bias polarity. In particular, the
current reducing property of the blocking state causing the NDR, is shown to
vanish under strongly asymmetric tunnel couplings, when the molecule is coupled
stronger to the drain electrode. The calculated IV characteristic may serve as
an indicator for image charge broken molecular symmetries in experimental
situations.
