The nucleonic evolution near electron energy level crossings plays an outstanding role in laser-controlled femtosecond chemistry. The notoriously high number of degrees of freedom (three times the number of nuclei) enforces computational schemes, which are based on the adiabatic decoupling provided by the time-dependent Born-Oppenheimer approximation. Such approaches, however, break down in the presence of electron energy level crossings. We present a novel algorithm, which implements a Markov process combining classical transport and non-adiabatic transitions. Opposed to the well-established trajectory surface hopping algorithms of chemical physics, our rigorously derived approach is based on precise criteria for hopping-time and position as well as an explicit Landau-Zener type transition rate for the non-adiabatic transfer.

(The work is joint with S. Teufel, University of Warwick. For the algorithm's analytic derivation see preprint 114 of the DFG priority program 1095 on Multiscale Problems.)