With the idea of proposing solid state systems that have a high storage capacity of molecular hydrogen, a density functional theory study of magnesium oxide (MgO)n clusters (n = 1-10) was carried out. Hydrogen-magnesium oxide systems presented adsorption energy values in accordance with the previously reported studies of physisorption processes; additionally negative values of ΔGads were found describing adsorption as a favorable process. Here, the (MgO)7 cluster presented the highest adsorption energy. The storage capacity by weight of the magnesium oxide clusters was greater than the recommended percentage (7.5%) by the U.S. Department of Energy. QTAIM analysis and non-covalent index plots highlighted the weak nature of the interaction between the MgO clusters and hydrogen molecules, and the fundamental role of the Mg-O bonds' polarity in the systems' storage capacity.