shows that the additional deviations due to the energy-only algorithm (dotted) are much smaller than the deviations between reference (solid) and fitted calculations (dashed). So energy-only seems to be a reasonable simplification, when accurate PE surfaces are available. The results are compared with the populations obtained from full quantum calculations and previous trajectory based semi-classical surface-hopping simulations of the same model. The population transfer from the S 2 to the S 1 state is slightly slower compared to the previous surface-hopping simulations with the Landau-Zener algorithm. This can be explained by the fact that in the calculations here, all trajectories start from the adiabatic S 2 state. In the previous simulations trajectories are excited to the bright diabatic B 2u state. Subsequently, the system is transformed to the adiabatic representation, leading to slightly different initial conditions, i.e. not all trajectories start from the adiabatic S 2 state. Comparing the population transfer obtained from surface hopping simulations, following the scheme proposed here, with full quantum dynamics simulations using the MCTDH method, it is apparent that the population transfer is accurately reproduced. To sum up, the different preparation scheme of the initial conditions has more influence on the results than the semi-classical approximations during the simulations.