Dynamical image-charge effect in molecular tunnel junctions: Beyond energy level alignment

When an electron tunnels between two metal contacts it temporarily induces an image charge (IC) in the electrodes which acts back on the tunneling electron. It is usually assumed that the IC forms instantaneously such that a static model for the image potential applies. Here we investigate how the finite IC formation time affects charge transport through a molecule suspended between two electrodes. For a single-level model, an analytical treatment shows that the conductance is suppressed by a factor Z(2), where Z is the quasiparticle renormalization factor, compared to the static IC approximation. We show that Z can be expressed either in terms of the plasma frequency of the electrode or as the overlap between electrode wave functions corresponding to an empty and filled level, respectively. First-principles GW calculations for benzene-diamine connected to gold electrodes show that the dynamical corrections can reduce the conductance by more than a factor of two when compared to static GW or density functional theory where the molecular energy levels have been shifted to match the exact quasiparticle levels.