  Molecules in molecular junctions are subject to current-induced forces that
can break chemical bonds, induce reactions, destabilize molecular geometry, and
halt the operation of the junction. Theories behind current-driven molecular
dynamics simulations rely on a perturbative time-scale separation within the
system with subsequent use of nonequilibrium Green's functions (NEGF) to
compute conservative, non-conservative, and stochastic forces exerted by
electrons on nuclear degrees of freedom. We analyze the effectiveness of this
approximation, paying particular attention to the phenomenon of negative
viscosities. The perturbative approximation is directly compared to the
nonequilibrium Ehrenfest approach. We introduce a novel time-stepping approach
to calculate the forces present in the Ehrenfest method via exact integration
of the equations of motion for the nonequilibrium Green's functions, which does
not necessitate a time-scale separation within the system and provides an exact
description for the corresponding classical dynamics. We observe that negative
viscosities are not artifacts of a perturbative treatment but also emerge in
Ehrenfest dynamics. However, the effects of negative viscosity have the
possibility of being overwhelmed by the predominantly positive dissipation due
to the higher-order forces unaccounted for by the perturbative approach.
Additionally, we assess the validity of the white-noise approximation for the
stochastic forces, finding that it is justifiable in the presence of a clear
time-scale separation and is more applicable when the current-carrying
molecular orbital is moved outside of the voltage window. Finally, we
demonstrate the method for molecular junction models consisting of one and two
classical degrees of freedom.
