  We present an application of a new formalism to treat the quantum transport
properties of fully interacting nanoscale junctions. We consider a model
single-molecule nanojunction in the presence of two kinds of electron-vibron
interactions. In terms of the electron density matrix, one interaction is
diagonal in the central region and the second off-diagonal between the central
region and the left electrode. We use a non-equilibrium Green's function
technique to calculate the system's properties in a self-consistent manner. The
interaction self-energies are calculated at the Hartree-Fock level in the
central region and within a dynamical mean-field-like approach for the crossing
interaction. Our calculations are performed for different transport regimes
ranging from the far off-resonance to the quasi-resonant regime, and for a wide
range of parameters. They show that a non-equilibrium (i.e. bias dependent)
dynamical (i.e. energy dependent) renormalisation is obtained for the contact
between the left electrode and the central region in the form of a
non-equilibrium renormalisation of the lead embedding potential. The
conductance is affected by the renormalisation of the contact: the amplitude of
the main resonance peak is modified as well as `the lineshape of the first
vibron side-band.
