  We develop a classical mapping approach suitable to describe vibrationally
coupled charge transport in molecular junctions based on the Cartesian mapping
for many-electron systems [J. Chem. Phys. 137, 154107 (2012)]. To properly
describe vibrational quantum effects in the transport characteristics, we
introduce a simple transformation rewriting the Hamiltonian in terms of
occupation numbers and use a binning function to facilitate quantization. The
approach provides accurate results for the nonequilibrium Holstein model for a
range of bias voltages, vibrational frequencies and temperatures. It also
captures the hallmarks of vibrational quantum effects apparent in step-like
structure in the current-voltage characteristics at low temperatures as well as
the phenomenon of Franck-Condon blockade.
