  Within a phonon-assisted resonance level model we develop a self-consistent
procedure for calculating electron transport currents in molecular junctions
with intermediate to strong electron-phonon interaction. The scheme takes into
account the mutual influence of the electron and phonon subsystems. It is based
on the 2nd order cumulant expansion, used to express the correlation function
of the phonon shift generator in terms of the phonon momentum Green function.
Equation of motion (EOM) method is used to obtain an approximate analog of the
Dyson equation for the electron and phonon Green functions in the case of
many-particle operators present in the Hamiltonian. To zero-order it is similar
in particular cases (empty or filled bridge level) to approaches proposed
earlier. The importance of self-consistency in resonance tunneling situations
(partially filled bridge level) is stressed. We confirm, even for strong
vibronic coupling, a previous suggestion concerning the absence of phonon
sidebands in the current vs. gate voltage plot when the source-drain voltage is
small.
