In Fig. , the collective evolution of the state populations along the dynamics are represented. The main characteristics of the photorelaxation process are well reproduced by all three MTS-TSH runs. In particular, the population is transferred from S 2 to S 1 in the first 10 to 20 fs and then slowly decays into the ground state. We note that the tail of the population of S 2 seem to become larger with the MTS factor, which shows the limit of the MTS scheme. This is reflected in the average lifetime of S 2 , for which we get 8.7 fs in the reference runs, while the MTS simulations lead to lifetimes of 10.1, 11.3, and 13.8 Regarding the computational efficiency, the real speed-ups obtained over all the trajectories are 2.08, 2.56 and 2.86 for the MTS factors 4, 6, and 8, respectively. These speed-ups are in good agreement with the ideal speed-ups reporter in Fig. , which are 2.24, 2.76, and ) and ( ), respectively, are also reported. The ideal speed-ups are identical to the ones in Fig. .