  Non-equilibrium Green's function theory for non-adiabatic effects in quantum
transport [Kershaw and Kosov, J.Chem. Phys. 2017, 147, 224109 and J. Chem.
Phys. 2018, 149, 044121] is extended to the case of interacting electrons. We
consider a general problem of quantum transport of interacting electrons
through a central region with dynamically changing geometry. The approach is
based on the separation of time scales in the non-equilibrium Green's functions
and the use of Wigner transformation to solve the Kadanoff-Baym equations. The
Green's functions and correlation self-energy are non-adiabatically expanded up
to the second order central time derivatives. We produced expressions for
Green's functions with non-adiabatic corrections and modified formula for
electric current; both depend not only on instantaneous molecular junction
geometry but also on nuclear velocities and accelerations. The theory is
illustrated by the study of electron transport through a model single-resonant
level molecular junction with local electron-electron repulsion and a
dynamically changing geometry.
