This thesis deals with first-principles calculations based on density functional theory to investigate hydrogen storage related properties in various high-surface area materials and the ground state crystal structures in alkaline earth dicarbide systems. High-surface area materials have been shown to be very promising for hydrogen storage applications owing to them containing numerous hydrogen adsorption sites and good kinetics for adsorption/desorption. However, one disadvantage of these materials is their very weak interaction with adsorbed hydrogen molecules. Hence, for any feasible applications, the hydrogen interaction energy of these materials must be enhanced.  In metal organic frameworks, approaches for improving the hydrogen interaction energy are opening the metal oxide cluster and decorating hydrogen attracting metals, e.g. Li, at the adsorption sites of the host.  In covalent organic framework-1, the effects of the H2-H2 interaction are also found to play a significant role for enhancing the hydrogen adsorption energy. Moreover, ab initio molecular dynamics simulations reveal that hydrogen molecules can be trapped in the host material due to the blockage from adjacent adsorbed hydrogen molecules. In light metal hydride systems, hydrogen ions play two different roles, namely they can behave as "promoter" and "inhibitor" of Li diffusion in lithium imide and lithium amide, respectively.  By studying thermodynamics of Li+ and proton diffusions in the mixture between lithium amide and lithium hydride, it was found that Li+ and proton diffusions inside lithium amide are more favorable than those between lithium amide and lithium hydride. Finally, our results show that the ground state configuration of BeC2 and MgC2 consists of five-membered carbon rings connected through a carbon atom forming an infinitely repeated chain surrounded by Be/Mg ions, whereas the stable crystal structure of the CaC2, SrC2 and BaC2 is the chain type structure, commonly found in the alkaline earth dicarbide systems. / Felaktigt tryckt som Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 712