  In this work we investigate the effects of the electron-electron interaction
between a molecular junction and the metallic leads in time-dependent quantum
transport. We employ the recently developed embedded Kadanoff-Baym method
[Phys. Rev. B 80, 115107 (2009)] and show that the molecule-lead interaction
changes substantially the transient and steady-state transport properties. We
first show that the mean-field Hartree-Fock (HF) approximation does not capture
the polarization effects responsible for the renormalization of the molecular
levels neither in nor out of equilibrium. Furthermore, due to the time-local
nature of the HF self-energy there exists a region in parameter space for which
the system does not relax after the switch-on of a bias voltage. These and
other artifacts of the HF approximation disappear when including correlations
at the second-Born or GW levels. Both these approximations contain polarization
diagrams which correctly account for the screening of the charged molecule. We
find that by changing the molecule-lead interaction the ratio between the
screening and relaxation time changes, an effect which must be properly taken
into account in any realistic time-dependent simulation. Another important
finding is that while in equilibrium the molecule-lead interaction is
responsible for a reduction of the HOMO-LUMO gap and for a substantial
redistribution of the spectral weight between the main spectral peaks and the
induced satellite spectrum, in the biased system it can have the opposite
effect, i.e., it sharpens the spectral peaks and opens the HOMO-LUMO gap.
