Metal-organic frameworks (MOFs) show considerable promise as materials for gas storage and separation. Many MOF structures have open metal sites, which allow for coordination of gas molecules to the metal centers. In this work, we use coupled-cluster and symmetry-adapted perturbation theory to probe the interaction between hydrogen gas and unsaturated metal sites in mimic structures based on the MOF HKUST-1. The interactions are of a mixed electrostatic/dispersive nature, with the relative magnitudes of these components dependent on the metal center. The strongest binding was found for magnesium- and zinc-containing MOFs, with an overall interaction energy of -4.5 kcal mol(-1).