The main goal of this thesis was to develop a general framework to numerically simulate a range of time-dependent phenomena in molecules starting from charge migration to describing non-linear spectroscopy. During this work, the program module RhoDyn, intended to study ultrafast electron dynamics within the density-matrix-based time-dependent restricted active space configuration interaction framework, has been implemented as a part of the open-source OpenMOLCAS project. The formalism employed in this study provides a comprehensive treatment of electron correlation and spin-orbit coupling effects. It also naturally incorporates energy and phase relaxation effects due to nuclei, photoionization, Auger decay processes, and other dissipative terms, enabling a thorough exploration of the electron dynamics in small molecules. Another point of this thesis is to present the results of work concerning photon-induced ultrafast spin dynamics being theoretically modeled within the implemented framework of ab-initio calculations. The effect of chemical structure on the ultrafast spin-flip dynamics in core-excited states of transition metal complexes has been studied. It was shown that slight variations in the coordination sphere do not lead to qualitative differences in dynamics, whereas the nature of the central atom is more critical. Detailed analysis of spin-orbit coupling-driven dynamics in core-excited states, based on the preselection of states and utilizing the Wigner-Eckart theorem, is conducted to outline and facilitate future experimental investigations.