In this thesis, density functional theory (DFT) calculations and DFT based ab initio molecular dynamics simulations have been employed in order to gain insights into materials properties like diffusion, adsorption, catalysis, and structure. In transition metals, absorbed hydrogen atoms self-trap due to localization of metal d-electrons. The self-trapping state is shown to highly influence hydrogen diffusion in the classical over-barrier jump temperature region. Li diffusion in Li-N-H systems is investigated. The diffusion in Li3N is shown to be controlled by the concentration of vacancies. Exchanging one Li for H (Li2NH), gives a system where the diffusion no longer is dependent on the concentrations of vacancies, but instead on N-H rotations. Furthermore, exchanging another Li for H (LiNH2), results in a blockade of Li diffusion. For high-surface area hydrogen storage materials, metal organic frameworks and covalent organic frameworks, the hydrogen adsorption is studied. In metal organic frameworks, a Li-decoration is also suggested as a way to increase the hydrogen adsorption energy. In NaAlH4 doped with transition metals (TM), the hypothesis of TM-Al intermetallic alloys as the main catalytic species is supported. The source of the catalytic effect of carbon nanostructures on hydrogen desorption from NaAlH4 is shown to be the high electronegativity of the carbon nanostructures. A space-group optimized ab initio random structure search method is used to find a new ground state structure for BeC2 and MgC2. The fast change between the amorphous and the crystalline phase of GeSbTe phase-change materials is suggested to be due to the close resemblance between the local amorphous structure and the crystalline structure. Finally, we show that more than 80% of the voltage in the lead acid battery is due to relativistic effects. / Felaktigt tryckt som Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 702