Quantum and quantum-classical studies of photo-induced ultrafast processes

The interpretation of photo-induced processes relies nowadays strongly on numerical simulations. An important aspect to be taken into account is the quantum character of the dynamics, consequence of the interaction between the nuclear and the electronic dynamics, involving several electronic states. Many theories and algorithms of excited state molecular dynamics have been developed over the years, but are still in continuous development. The most used methods are the mixed quantum-classical algorithms, which introduce a description of nuclear dynamics based on classical trajectories coupled to a quantum description of electronic dynamics. As a consequence of such a classical approximation, some effects can be lost (as the quantum decoherence effect). In this respect, the quantum-classical numerical approach based on exact factorization seems to show an improvement in the description of quantum decoherence, compared to trajectory surface hopping method. The main obstacle to the wide application of exact factorization is its numerical cost, because the quantum-classical algorithm requires to propagate a large number of trajectories in parallel, contrary to trajectory surface hopping, for which the trajectories can be propagated independently. This numerical cost also prevents the use of exact factorization with ab initio techniques of high-level electronic structure. The ultimate goal of this thesis is to interface the exact factorization methods, with the FOMO-CI semi-empirical electronic structure method. The high computational efficiency of using a semiempirical method will make it possible to easily compute many trajectories for long timescales for medium to large molecular systems.