In this section, the protonated formaldimine (CH 2 NH + 2 , denoted as system I) is used as a simple yet interesting example to investigate the capabilities of the new MTS-TSH method presented in section II B. In particular, we will investigate the possibility to use the MTS-TSH algorithm as a more efficient alternative to the standard FS-TSH algorithm. The physical process under investigation in this section is the photorelaxation of system I. This process is a typical example of photo-dynamics and is thus very handy to test new models for non-adiabatic molecular dynamics. All the calculations presented in this section have been performed with a local version of the CPMD plane-wave package. 11 For the reference TSH simulations, the nuclear forces and NACs are computed with the PBE0 hybrid functional. The same functional is thus used for the high level forces in the MTS calculations, while the low level forces are obtained from the PBE functional. For a fair comparison, all remaining parameters are kept the same in the reference and the MTS simulations.