Due to its fully reversible nature, H(2) storage by molecular adsorption could represent an advantage with respect to dissociative processes, where kinetic effects during the charging and discharging processes are present. A drawback of this strategy is represented by the extremely weak interactions that require low temperature and high pressure. High surface area materials hosting polarizing sites can represent a viable way toward more favorable working conditions. Of these, in this contribution, we have studied hydrogen adsorption in a series of zeolites using volumetric techniques and infrared spectroscopy at 15 K. We have found that in H-SSZ-13 zeolite the cooperative role played by high surface area, internal wall topology, and presence of high binding energy sites (protons) allows hydrogen to densify inside the nanopores at favorable temperature and pressure conditions.