We have recently highlighted that H-SSZ-13, a highly siliceous zeolite (Si/Al = 11.6) with a chabazitic framework, is the most efficient zeolitic material for hydrogen storage [A. Zecchina, S. Bordiga, J. G. Vitillo, G. Ricchiardi, C. Lamberti, G. Spoto, M. Bjorgen and K. P. Lillerud, J. Am. Chem. Soc., 2005, 127, 6361]. The aim of this new study is thus to clarify both the role played by the acidic strength and by the density of the polarizing centers hosted in the same framework topology in the increase of the adsorptive capabilities of the chabazitic materials towards H2. To achieve this goal, the volumetric experiments of H2 uptake (performed at 77 K) and the transmission IR experiment of H2 adsorption at 15 K have been performed on H-SSZ-13, H-SAPO-34 (the isostructural silico-aluminophosphate material with the same Bronsted site density) and H-CHA (the standard chabazite zeolite: Si/Al = 2.1) materials. We have found that a H2 uptake improvement has been obtained by increasing the acidic strength of the Bronsted sites (moving from H-SAPO-34 to H-SSZ-13). Conversely, the important increase of the Bronsted sites density (moving from H-SSZ-13 to H-CHA) has played a negative role. This unexpected behavior has been explained as follows. The additional Bronsted sites are in mutual interaction via H-bonds inside the small cages of the chabazitic framework and for most of them the energetic cost needed to displace the adjacent OH ligand is higher than the adsorption enthalpy of the OH...H2 adduct. From our work it can be concluded that proton exchanged chabazitic frameworks represent, among zeolites, the most efficient materials for hydrogen storage. We have shown that a proper balance between available space (volume accessible to hydrogen), high contact surface, and specific interaction with strong and isolated polarizing centers are the necessary characteristics requested to design better materials for molecular H2 storage.