Molecular hydrogen is known to form stable, "nonclassical" sigma complexes with transition metal centers that are stabilized by donor-acceptor interactions and electrostatics. In this computational study, we establish that strong H-2 sorption sites can be obtained in metal-organic frameworks by incorporating open transition metal sites on the organic linkers. Using density functional theory and energy decomposition analysis, we investigate the nature and characteristics of the. H-2 interaction with models of exposed open metal binding sites {half-sandwich piano-stool shaped complexes of the form (Arene)ML3-n(H-2)(n) [M = Cr, Mo, V-, Mn+; Arene = C6H5X (X = H, F, Cl, OCH3, NH2, CH3, CF3) or C6H3Y2X (Y = COOH, X = CF3, CI; L = CO; n = 1-3]}. The metal-H-2 bond dissociation energy of the studied complexes is calculated to be between 48 and 84 kJ/mol, based on the introduction of arene substituents, changes to the metal core, and of charge-balancing ligands. Thus, design of the binding site controls the H-2 binding affinity and could be potentially used to control the magnitude of the H-2 interaction energy to achieve reversible sorption characteristics at ambient conditions. Energy decomposition analysis illuminates both the possibilities and present challenges associated with rational materials design.