  It is demonstrated that non-equilibrium vibrational effects are enhanced in
molecular devices for which the effective potential for vibrations is sensitive
to the charge state of the device. We calculate the electron tunneling current
through a molecule accounting for the two simplest qualitative effects of the
charging on the nuclear potential for vibrational motion: a shift (change in
the equilibrium position) and a distortion (change in the vibrational
frequency). The distortion has two important effects: firstly, it breaks the
symmetry between the excitation spectra of the two charge states. This gives
rise to new transport effects which map out changes in the current-induced
non-equilibrium vibrational distribution with increasing bias voltage.
Secondly, the distortion modifies the Franck-Condon factors for electron
tunneling. Together with the spectral asymmetry this gives rise to pronounced
nuclear wave function interference effects on the electron transport. For
instance nuclear-parity forbidden transitions lead to differential conductance
anti-resonances, which are stronger than those due to allowed transitions. For
special distortion and shift combinations a coherent suppression of transport
beyond a bias voltage threshold is possible.
