  We study inelastic electron tunneling through a molecular junction using the
non-equilibrium Green function (NEGF) formalism. The effect of the mutual
influence between the phonon and the electron subsystems on the electron
tunneling process is considered within a general self-consistent scheme.
Results of this calculation are compared to those obtained from the simpler
Born approximation and the simplest perturbation theory approaches, and some
shortcomings of the latter are pointed out. The self-consistent calculation
allows also for evaluating other related quantities such as the power loss
during electron conduction. Regarding the inelastic spectrum, two types of
inelastic contributions are discussed. Features associated with real and
virtual energy transfer to phonons are usually observed in the second
derivative of the current I with respect to the voltage when plotted against
the latter. Signatures of resonant tunneling driven by an intermediate
molecular ion appear as peaks in the first derivative d(current)/d(voltage) and
may show phonon sidebands. The dependence of the observed vibrationally induced
lineshapes on the junction characteristics, and the linewidth associated with
these features are also discussed.
