  The role of exchange-correlation effects in non-equilibrium quantum transport
through molecular junctions is assessed by analyzing the IV curve of a generic
two-level model using self-consistent many-body perturbation theory (second
Born and GW approximations) on the Keldysh contour. For weak molecule-lead
coupling we identify a mechanism which can lead to anomalously strong peaks in
the dI/dV due to a bias-induced interplay between the position of the HOMO and
LUMO levels. The effect is suppressed by self-interaction errors and is
therefore unlikely to be observed in standard transport calculations based on
density functional theory. Inclusion of dynamic correlations lead to
substantial renormalization of the energy levels. In particular, we find a
strong enhancement of quasi-particle (QP) scattering at finite bias which
reduces the QP lifetimes significantly with a large impact on the IV curve.
