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We develop nonequilibribrium Green's function based transport theory, whichincludes effects of nonadiabatic nuclear motion in the calculation of theelectric current in molecular junctions. Our approach is based on theseparation of slow and fast timescales in the equations of motion for theGreen's functions by means of the Wigner representation. Time derivatives withrespect to central time serves as a small parameter in the perturbativeexpansion enabling the computation of nonadiabatic corrections to molecularGreen's functions. Consequently, we produce series of analytic expressions fornon-adiabatic electronic Green's functions (up to the second order in thecentral time derivatives); which depend not solely on instantaneous moleculargeometry but likewise on nuclear velocities and accelerations. Extended formulafor electric current is derived which accounts for the non-adiabaticcorrections. This theory is concisely illustrated by the calculations on amodel molecular junction.

Nonequilibrium Green's function theory for nonadiabatic effects in quantum electron transport