  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 $Z^2$ (compared to the static IC
approximation) where $Z$ is the quasiparticle renormalization factor. We show
that $Z$ can be expressed either in terms of the plasma frequency of the
electrode or as the overlap between the ground states of the electrode with and
without an electron on the molecule. 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.
