Contributions to theoretical and numerical modeling of quantum tunneling in complex systems and application to chemical reactivity

In this thesis, we present methodological investigations aimed at simulating challenging reactive quantum systems. We consider 3 challenging properties: the system's size, important tunneling (particularly resonant deep tunneling), and non-adiabatic behavior. Our first project combines the ABC-DVR approach with Smolyak representation of the cumulative reaction probability operator to significantly extend the maximum number of degrees of freedom for which our new rigorous approach remains tractable. The efficient scaling with system size of our ABC-SR scheme was illustrated on several reaction path Hamiltonian models of chemical reactions. In our second project we developed two efficient methods based on the Time-Independent Quantum Trajectories (TIQT) formalism. The first allows rigorous computation of the reaction probability along any multidimensional ZPE-corrected reaction path with a single trajectory propagation. Its performance was illustrated in several dynamical regimes, including an application to the astrochemically relevant D + H⁺₃ → H + H₂D⁺ reaction. The second method is a hybrid quantum-classical approach propagating an ensemble of independent trajectories in the full-dimensional space of the reaction valley. Both approaches were found to be much more efficient, while keeping a very satisfying degree of accuracy, even in presence of resonant reactive scattering. In the perspective of treating chemical reactions proceeding by tunneling through an isolated reaction valley, theses approaches constitute promising tools notably relevant for gas-phase chemistry in the interstellar medium. Lastly, we devised the first stable numerical scheme based on the Time-Dependent Quantum Trajectories (TDQT) framework. Its great performance were studied on one-dimensional adiabatic system models, and we realised a proof-of-principle regarding its applicability to non-adiabatic processes formulated through exact factorization of electronic and nuclear wavefunctions. It outperformed classical nuclear dynamics regarding faithfulness to the true non-adiabatic dynamics of Tully models. Good performances of the 1D TDQT method make pursuing its extension to several degrees of freedom, and the development of a full-fledged non-adiabatic algorithm worthy of future investigations. (author)