  We consider exciton effects on current in molecular nanojunctions, using a
model comprising a two two-level sites bridge connecting free electron
reservoirs. Expanding the density operator in the many-electron eigenstates of
the uncoupled sites, we obtain a 16X16 density matrix in the bridge subspace
whose dynamics is governed by Liuoville equation that takes into account
interactions on the bridge as well as electron injection and damping to and
from the leads. Our consideration can be considerably simplified by using the
pseudospin description based on the symmetry properties of Lie group SU(2). We
study the influence of the bias voltage, the Coulomb repulsion and the
energy-transfer interactions on the steady-state current and in particular
focus on the effect of the excitonic interaction between bridge sites. Our
calculations show that in case of non-interacting electrons this interaction
leads to reduction in the current at high voltage for a homodimer bridge. In
other words, we predict the effect of \textquotedblleft
exciton\textquotedblright blocking. The effect of \textquotedblleft
exciton\textquotedblright blocking is modified for a heterodimer bridge, and
disappears for strong Coulomb repulsion at sites. In the latter case the
exciton type interactions can open new channels for electronic conduction. In
particular, in the case of strong Coulomb repulsion, conduction exists even
when the electronic connectivity does not exist.
