In order for hydrogen gas to be used as a fuel, it must be stored in sufficient quantity on board the vehicle. Efforts are being made to increase the hydrogen storage capabilities of metal-organic frameworks (MOFs) by introducing unsaturated metal sites into their linking element(s), as hydrogen adsorption centers. In order to devise successful hydrogen storage strategies there is a need for a fundamental understanding of the weak and elusive hydrogen physisorption interaction. Here we report our findings from the investigation of the weak intermolecular interactions of adsorbed hydrogen molecules on MOF-linkers by using cluster models. Since physical interactions such as dispersion and polarization have a major contribution to attraction energy, our approach is to analyze the adsorption interaction using energy decomposition analysis (EDA) that distinguishes the contribution of the physical interactions from the charge-transfer (CT) "chemical" interaction. Surprisingly, it is found that CT from the adsorbent to the σ*(H2) orbital is present in all studied complexes and can contribute up to approximately -2 kJ/mol to the interaction. When metal ions are present, donation from the σ(H2) → metal Rydberg-like orbital, along with the adsorbent → σ*(H2) contribution, can contribute from -2 to -10 kJ/mol, depending on the coordination mode. To reach a sufficient adsorption enthalpy for practical usage, the hydrogen molecule must be substantially polarized. Ultimately, the ability of the metalated linker to polarize the hydrogen molecule is highly dependent on the geometry of the metal ion coordination site where a strong electrostatic dipole or quadrupole moment is required.