Mémoire, Partim A, COLLÉGIALITÉ

Abstract

The field of attosecond chemistry is now at the crossroads. The experimental techniques allowing us to study and describe coherent ultrafast dynamics are becoming increasingly detailed and accessible. This novel understanding of the fastest processes at play in chemistry comes, however, with difficulties: the experimental data is most of the time difficult to interpret and rarely allows for an unambiguous description of the effect at play. This is why simulations and models are crucial for this discipline: they allow for the interpretation of the results and give a glimpse of the phenomena at play. This thesis is devoted to using a linear algebra decomposition, the singular value decomposition, to provide an understanding of the complex coupled electronic and nuclear quantum dynamics resulting from an excitation from a short (atto- to femtosecond) optical pulse. The first use describes the few-rank approximation of the initial density matrix of an ensemble of randomly oriented molecular systems to decrease the computational cost of averaging grid-based simulations, while retaining a good accuracy. This allows us to gain insight into the ultrafast Jahn-Teller rearrangement of the methane cation upon tunnel ionization and to understand the inherent isotope effect. The results obtained are in good agreement with experimental data. The second use investigates the value of the Schmidt decomposition of the wavefunction in order to characterize entanglement between electronic and nuclear degrees of freedom in the quantum dynamics of a photoexcited molecular system. The Schmidt decomposition is isomorphic to the singular value decomposition and provides a description of the entanglement in a bipartite system. We therefore use this description in the case of the quantum dynamics of the LiH molecule. This allows us to characterize the entanglement produced by an exciting short optical pulse and non-adiabatic couplings. This also proves to be a valuable insight into both the transfer of amplitudes from one electronic state to the other and the coherent motion of the wave packets on the potential energy surfaces.