The storage of hydrogen (H$_2$) is of economic and ecological relevance,\nbecause it could potentially replace petroleum-based fuels. However, H$_2$\nstorage at mild condition remains one of the bottlenecks for its widespread\nusage. In order to devise successful H$_2$ storage strategies, there is a need\nfor a fundamental understanding of the weak and elusive hydrogen interactions\nat the quantum mechanical level. One of the most promising strategies for\nstorage at mild pressure and temperature is physisorption. Porous materials are\nspecially effective at physisorption, however the process at the quantum level\nhas been under-studied. Here, we present quantum calculations to study the\ninteraction of H$_2$ with building units of porous materials. We report 240\nH$_2$ complexes made of different transition metal (Tm) atoms, chelating\nligands, spins, oxidation states, and geometrical configurations. We found that\nboth the dispersion and electrostatics interactions are the major contributors\nto the interaction energy between H$_2$ and the transition metal complexes. The\nbinding energy for some of these complexes is in the range of at least 10\nkJ/mol for many interactions sites, which is one of these main requirements for\npractical H$_2$ storage. Thus, these results are of fundamental nature for\npractical H$_2$ storage in porous materials.\n