  We present quantum electron transport theory that incorporates dynamical
effects of motion of atoms on electrode-molecule interfaces in the calculations
of the electric current. The theory is based on non-equilibrium Green's
functions. We separate time scales in the Green's functions on fast relative
time and slow central time. The derivative with respect to the central time
serves as a small parameter in the theory. We solve the real-time Kadanoff-Baym
equations for molecular Green's functions using Wigner representation and keep
terms up to the second order with respect to the central time derivatives.
Molecular Green's functions and consequently the electric current are expressed
as functions of molecular junction coordinates as well as velocities and
accelerations of molecule-electrode interface nuclei. We apply the theory to
model a molecular system and study the effects of non-adiabatic nuclear motion
on molecular junction conductivity.
