  We study the electrostatic potential of a molecular wire bridging two
metallic electrodes in the limit of weak contacts. With the use of a
tight-binding model including a fully three-dimensional treatment of the
electrostatics of the molecular junction, the potential is shown to be poorly
screened, dropping mostly along the entire molecule. In addition, we observe
pronounced Friedel oscillations that can be related to the breaking of
electron-hole symmetry. Our results are in semi-quantitative agreement with
recent state-of-the-art ab initio calculations and point to the need of a
three-dimensional treatment to properly capture the behavior of the
electrostatic potential. Based on these results, current-voltage curves are
calculated within the Landauer formalism. It is shown that Coulomb interaction
partially compensates the localization of the charges induced by the electric
field and consequently tends to suppress zones of negative differential
resistance.
