As we have seen in section II A, non-adiabatic dynamics performed with a TSH algorithm are stochastic by nature due to the randomness used in the hopping procedure. This stochastic behaviour makes it difficult to compare individual trajectories obtained with a TSH algorithm. To properly compare different non-adiabatic models, one needs to look at a statistical ensemble of trajectories. Before we present such results in section III C, we first consider in this section a deterministic version of TSH in which the random number r used in eqs. ( ) and ( ) has been fixed arbitrarily to r = 0.3. We note that, the only MTS algorithm tested here and in the next section is the one presented in section II B, i.e., low level (PBE) LZ transition probabilities are used during the inner steps to trigger a high level (PBE0) calculation which confirms or not the electronic transition.