Surface Hopping Molecular Dynamics

In this chapter we review the wide-spread trajectory surface hopping method for non-adiabatic dynamics simulations. The surface hopping method belongs to the class of mixed quantum-classical methods that propagate electrons quantum mechanically and nuclei classically. The main focus of the review is to present the most important concepts of the surface hopping method in an accessible and practically oriented way. The covered concepts include nuclear motion, wave function propagation, decoherence correction, the actual algorithm determining the surface hops, nuclear momentum adjustment, and inclusion of diverse coupling terms. Furthermore, the chapter discusses practical aspects of surface hopping simulations, like the choice of electronic structure method, initial condition generation, and ensemble analysis. A fully worked example completes the overview over the surface hopping method.