  Using non-equilibrium Green's functions, we derive a formula for the electron
current through a lead-molecule-lead nanojunction where the interactions are
not restricted to the central region, but are spread throughout the system,
including the leads and the lead-molecule interfaces. The current expression
consists of two sets of terms. The first set corresponds to a generalised Meir
and Wingreen expression where the leads' self-energies are renormalised by the
interactions crossing at the molecule-lead contacts. The second set corresponds
to inelastic scattering events in the leads arising from any arbitrary
interaction, including electron-electron and electron-phonon coupling, treated
beyond mean-field approximations. Using different levels of approximation, we
are able to recover well-known expressions for the current. We also analyse how
practical calculations can be performed with our formalism by using the new
concept of generalised embedding potentials.
