High concentrations of molecular hydrogen adsorption on MOF-5 were evaluated at the semiempirical PM6 (periodic and cluster) and ab initio MP2 (cluster) theoretical levels. From the semiempirical calculations, an uptake of 3.9% weight on the inorganic building unit of MOF-5 was estimated, in good agreement with a recent accurate estimation of 4.5–5.2%. Although PM6 allows a correct estimation of the maximum uptake, the adsorption energy was overestimated and hence ab initio calculations, including a correlation treatment at the MP2 level as well as corrections for basis set superposition error, were performed with full optimisation, including the 6-31G basis set, which rendered an adsorption energy (per hydrogen molecule) of −0.14 kcal mol⁻¹. The crucial role of the quality of the basis set, as well as the importance of simulating high hydrogen loading (resembling experimental measurements), are remarked. Single point calculations (using the 6-31G geometry) with improved basis sets 6-31G(d,p) and 6-31++G(d,p) yielded adsorption energies of −0.33 and −0.57 kcal mol⁻¹, the latter in reasonable agreement with a recent experimental estimation of −1.0 kcal mol⁻¹. The role of the intermolecular hydrogen interactions is highlighted in this study, since many previous computational studies were performed at low hydrogen loadings, far from the experimental uptake conditions.