The problem of various cationic positions in zeolites with high Si/Al ratio in the framework is discussed. The statistical distribution of aluminum in the lattice of pentasils makes probable appearance of the structures with distant placing of two aluminum atoms. Cations, localized at such sites, should be very strong Lewis acids that are highly active in different chemical reactions. An example of such a site is considered for two Zn2+ ions stabilized in the zeolite fragment represented by two adjacent five-membered rings sharing the common edge. DFT calculations of molecular and dissociative hydrogen adsorption by such sites are in agreement with experimental results. Adsorption of dihydrogen by zinc ion at such sites results in an unusually large low-frequency shift of H - H stretching vibrations indicating essential activation of adsorbed H-2 molecule. The calculated path of heterolytic dissociative adsorption of dihydrogen and of the proton migration to the distantly placed basic oxygen of such acid-base pair are in agreement with the previously published DRIFT experimental data.