In the TSH method (summarized in section II A), the evolution of the system is represented by a swarm of independent classical nuclear trajectories, which can hop from one electronic state to another in a stochastic way. The forces acting on the nuclei are calculated on-the-fly along each trajectory and transitions between electronic levels are considered simultaneously. In this way, the TSH method is thus able to describe non-adiabatic phenomena such as photo-chemical and photo-physical processes.