  We develop nonequilibribrium Green's function based transport theory, which
includes effects of nonadiabatic nuclear motion in the calculation of the
electric current in molecular junctions. Our approach is based on the
separation of slow and fast timescales in the equations of motion for the
Green's functions by means of the Wigner representation. Time derivatives with
respect to central time serves as a small parameter in the perturbative
expansion enabling the computation of nonadiabatic corrections to molecular
Green's functions. Consequently, we produce series of analytic expressions for
non-adiabatic electronic Green's functions (up to the second order in the
central time derivatives); which depend not solely on instantaneous molecular
geometry but likewise on nuclear velocities and accelerations. Extended formula
for electric current is derived which accounts for the non-adiabatic
corrections. This theory is concisely illustrated by the calculations on a
model molecular junction.
