Computational simulations of quantum molecular dynamics are indispensable for understanding and predicting phenomena in physical chemistry. This thesis explores molecular processes where multiple electronic states play a role. A significant part of this work is dedicated to studying charge migration, which is initiated by ionizing a molecule into a superposition of electronic states. The decoherence induced by the nuclei is often neglected, leading to predictions that could be challenging to observe experimentally. Here, we use semiclassical dynamics to include nuclear motion and propose an algorithm to efficiently identify molecules with long-lasting charge migration triggered by valence ionization. We highlight several previously unexplored molecules that exhibit long-lasting charge migration, suggesting them as promising candidates for future experimental studies.

Applications in attochemistry are based on molecules in which electronic motion can be controlled long enough to direct chemical reactivity. Advancing our understanding of the fundamental principles behind electronic decoherence due to electron-nuclear correlations is essential for designing such compounds. To address this, we compare charge migration in a series of structurally similar organic molecules of increasing size and flexibility. Surprisingly, extending the carbon skeleton in propynal prolongs the duration of charge migration. Semiclassical dynamics provides valuable insight into the mechanisms of decoherence. In particular, the overall decoherence can be decomposed into contributions from individual nuclear vibrations without additional calculations, enabling the identification of the normal modes responsible for the observed prolonged coherence.

The use of semiclassical methods neglecting nonadiabatic effects to describe dynamics involving multiple electronic states is limited to exceptional cases where the coupling between these states is negligible. In general, more advanced propagation methods are required to account for nonadiabatic effects. We develop and apply two different new mixed quantum-classical methods, based on Ehrenfest dynamics, that partially capture nuclear quantum effects without requiring the propagation of independent trajectories.

First, we present applications of the thawed Gaussian Ehrenfest dynamics, a method that combines single-trajectory Ehrenfest dynamics with the thawed Gaussian wavepacket dynamics. We highlight a significant limitation shared by other single-trajectory mean-field methods preventing electronic population transfer induced by conical intersections between electronic states belonging to different irreducible representations. In contrast, the thawed Gaussian Ehrenfest dynamics provide a good qualitative picture of the dynamics in the vicinity of conical intersections between electronic states of the same symmetry.

Second, we introduce SPEED, a variation of multitrajectory Ehrenfest dynamics, where all trajectories are propagated using a common time-dependent quadratic effective potential in the diabatic representation. This approach is equivalent to multitrajectory Ehrenfest dynamics when the diabatic potential energy surfaces and couplings are at most quadratic. We applied SPEED to study nonadiabatic dynamics involving conical intersections, atomic chemisorption on solid surfaces, and charge transfer between molecules, demonstrating its capability to efficiently and accurately describe various types of systems.