Hydrogen and lithium under high pressure.

192 p.In this thesis we present a first-principles analysis of the electronic, vibrational and superconducting properties of solid hydrogen and lithium under high pressure based on density functional theory (DFT). The main goal of this thesis is to provide an accurate theoretical description of lithium and hydrogen focusing on the regions of their respective phase diagrams where the superconducting properties, which are still potential in the case of hydrogen, emerge. With this in mind, we have presented electronic and vibrational spectra along with the coupling between the electronic and nuclear subsystems in order to obtain the superconducting properties of the analyzed materials. While our calculations rely on the DFT framework, we have accurately included the quantum behavior of the nuclei and anharmonic effects arising due to the lightness of the elements. For that purpose, we have used the stochastic self-consistent harmonic approximation, which accounts for quantum nuclear and anharmonic effects in a non- perturvative variational way