Simuler les dynamiques ultra-rapides de transfert de proton intramoléculaire à l'état excité : de la dynamique moléculaire au formalisme tensoriel des produits de matrice

Excited-State Intramolecular Proton Transfer (ESIPT) is characterised by proton transfer between two molecular moieties upon photoexcitation, probed via an exceptionally large Stokes shift (> 100 nm) in fluorescence spectra. This ultrafast process, occurring at the limit of many experimental probe timescales, plays fundamental roles in diverse biological mechanisms and provides an excellent platform for developing tailored drug delivery systems and optical devices. Despite its apparent simplicity, ESIPT presents significant computational challenges due to the quantum nature of nuclear motion, which cannot be neglected because of out-of-equilibrium effects occurring in the ultrafast regime. This thesis investigates ultrafast ESIPT dynamics using two complementary theoretical approaches. First, the Matrix Product State (MPS) method is adapted to ESIPT models within an open quantum system framework. This exact numerical technique enables precise treatment of vibrational environments, facilitating an in-depth analysis of non-equilibrium dynamics. Building on this formalism, the kinetic isotope effect of two reference molecules undergoing sub-100-femtosecond ESIPT revealed an interplay between incoherent and coherent transfers alongside pulse-dependent time transfers. Second, ab initio molecular dynamics is employed to explore the ultrafast component of recently dis-covered dual-fluorescent ESIPT compounds based on a single benzene core. Although transfers are mostly longer than the picosecond timescale, normal mode analysis identified the presence of skeletal modes that could facilitate the transfer and potentially enable new reaction pathways. These results provide overall insights into vibrational effects that can impact ultrafast ESIPT mechanisms.