The project aims to use first principles calculations, both time dependent and time independent, to study the excited state dynamics and lifetime in systems relevant for both solar cell and solar fuel applications. Here, new experiments with pump-probe TRPES (Time-Resolved X-ray Photoelectron Spectroscopy) and free electron lasers are approaching low femtosecond dynamics of electronic states are available as well as highly resolved vibration spectra. Using core-hole clocks, PES can also reach low attosecond time scales. Here, first principles based methods will be developed and utilized in order to better understand the de-excitation process occurring in solar cells and photocatalyst, with the ultimate goal to understand the dynamics of the excitation and the following relaxation processes. Here at the first stage of the project, the electronic structure will be treated within the Time Dependent DFT formalism (TD-DFT), to estimate the lifetimes of the core-hole excitations that occur when solar cell materials and photocatalysts are exposed to irradiation. These calculations will initially be used to study the instantaneous relaxation approximation, where the thermalization from excited state will be studied. In the second phase of the project , the time dependence of both the nuclear degrees of freedom and the electronic degrees of freedom will be taken into account by merging time dependent density functional theory with first principles molecular dynamics as well as more standar linear response DFT to obtain the vibrational signatures. This will enable us to access both the normal vibrational spectrum as well as routes to go beyond the adiabatic approximation and study how the excited states are affected from the perspective of the life-times of the excitations by the electron-phonon interaction.