Recently, zeolites have been proposed as media for hydrogen by means of molecular adsorption. The interaction of a dihydrogen molecule on alkali metal ions in high-silica zeolites has been theoretically studied in cluster and periodic models at the B3-LYP level of theory. The cluster models have been obtained by embedding Li⁺, Na⁺, and K⁺ in aluminosilicate rings of different sizes (Si_n-1AlO_nH _2n, 4 ≤ n ≤ 6). The structure of Li, Na, and K-exchanged chabazite with Si/Al =11:1 has been adopted as the periodic model. In both cases, the hydrogen molecule interacts side-on with the cations, forming T-shaped complexes. The results have been compared with similar data obtained for bare cations and previous experimental studies. Furthermore, the necessity of employing correlated methods for a proper description of the interaction has been verified at the MP₂ level.