The possibility to follow the electronic and structural transformations that a molecular system undergoes after light absorption is a long-standing dream. The realization of this dream is possible only through a joint theoretical and experimental effort. New spectroscopic techniques based on interaction with high frequency radiation permit the investigation of molecular structural dynamics at an unprecedented level of detail. In particular, time-resolved photoelectron spectroscopy (TRPES) has emerged as the leading technique in this field. However, the interpretation of TRPES experiments requires advanced theory. Theoretical methods for calculating TRPES observables need to be accurate, so that a direct link between the structure of a molecule and the experimental observable can be established. They also need to be efficient because the simulation of time-resolved experiments requires calculations to be performed for hundreds or even thousands of molecular geometries. In order to meet these conditions, which are at the very heart of this project, advances on several fronts will be made: (i) we will improve the numerical efficiency of the computation of photoionization observables. Our goal is to make the numerical effort required for the computation of very accurate cross sections and asymmetry parameters comparable to the one for the computation of the excited state dynamics; (ii) better-quality methods for nonadiabatic molecular dynamics will be developed by the inclusion of nuclear quantum effects in simulations; (iii) we will improve the numerical efficiency of nonadiabatic molecular dynamics simulations by porting part of the calculation to graphical processor units (GPU). This will allow us to explore the dynamics of complex structures such as hydrated nucleobases, stacked and paired DNA bases.We feel that with advanced algorithmic techniques the dream is not so far away.