Critical appraisal of the Mapping Approach to Surface Hopping

In this thesis work, the non-adiabatic dynamics method known as the Mapping Approach to Surface Hopping (MASH) is analyzed. The original algorithm for two-state systems is presented, along with the proposed implementations for multi-state systems (MMASH and UNSMASH) and a new multistate MASH proposal. A form of decoherence is introduced, which, together with partial sampling, constitutes the main features of the new SMASH scheme. In order to demonstrare the accuracy the new method, it was applied to various one-dimensional models. Finally, on-the-fly dynamics were performed on different molecular systems, and the results obtained were compared with those from the fewest switches algorithm.