This thesis is devoted to the theoretical study of the dynamical processes induced by light-matter interactions in molecules and molecular systems. To this end, the multidimensional nuclear dynamics probed in resonant inelastic X-ray scattering (RIXS) of small molecules, exemplified by H₂O (g) and H₂S (g), as well as more complex molecular systems, exemplified by NH₃ (aq) and kaolinite clay, are modelled. The computational methodology consists of a combination of ab initio quantum chemistry calculations, quantum nuclear wave packet dynamics and in certain cases molecular dynamics modelling. This approach is used to simulate K-edge RIXS spectra and the theoretical results are evaluated against experimental measurements.

Specifically, the vibrational profile for decay back to the electronic ground state of the H₂O molecule displays a vibrational selectivity introduced by the dynamics in the core-excited state. Simulation of the inelastic decay channel to the electronic |1b₁^-1,4a₁¹> valence-excited state shows that the splitting of the spectral profile arises from the contribution of decay in the OH fragment. The character of the S1s^-1 and S2p^-1 core-excited states of the H₂S molecule has been investigated and distinct similarities and differences with the H₂O molecule have been identified. RIXS has also been used as a probe of the hydrogen bonding environment in aqueous ammonia and by detailed analysis of the valence orbitals of NH₃ and water, the spectral profiles are explained. Finally, it is shown that vibrations of weakly hydrogen bonding OH are excited in RIXS decay to the electronic ground state in kaolinite.