  We study the effect of electron-vibron interactions on the inelastic
transport properties of single-molecule nanojunctions. We use the
non-equilibrium Green's functions technique and a model Hamiltonian to
calculate the effects of second-order diagrams (double-exchange DX and
dressed-phonon DPH diagrams) on the electron-vibration interaction and consider
their effects across the full range of parameter space. The DX diagram,
corresponding to a vertex correction, introduces an effective dynamical
renormalization of the electron-vibron coupling in both the purely inelastic
and the inelastic-resonant features of the IETS. The purely inelastic features
correspond to an applied bias around the energy of a vibron, while the
inelastic-resonant features correspond to peaks (resonance) in the conductance.
The DPH diagram affects only the inelastic resonant features. We also discuss
the circumstances in which the second-order diagrams may be approximated in the
study of more complex model systems.
