  We present a novel mixed quantum-classical approach to the coupled
electron-nuclear dynamics based on the exact factorization of the
electron-nuclear wave function, recently proposed in [A. Abedi, N. T. Maitra,
and E. K. U. Gross, Phys. Rev. Lett. 105, 123002 (2010)]. In this framework,
classical nuclear dynamics is derived as the lowest order approximation of the
time dependent Schr\"odinger equation that describes the evolution of the
nuclei. The effect of the time dependent scalar and vector potentials,
representing the exact electronic back-reaction on the nuclear subsystem, is
consistently derived within the classical approximation. We examine with an
example the performance of the proposed mixed quantum-classical scheme in
comparison with exact calculations.

Chemical Physics