The reactivity of coordinatively unsaturated centers of aluminum oxide clusters, found for example in extraframework aluminum species of steamed zeolites, was examined theoretically on the example of the reaction of a hydrogen molecule with dialuminum hydroxide clusters (HO)(2)(H2O)(n)Al-O-Al(OH)(2)(H2O) (1). In the cluster, one aluminum atom is tricoordinated and the other is tetracoordinated (2, n = 0), or both aluminum atoms are tetracoordinated (3, n = 1). The system studied is also a model for transitional aluminas, in which two or three tetracoordinated aluminum centers can occur next to each other. Density functional theory calculations with electron correlation at the B3LYP/6-31G** level have identified a complex with physisorbed hydrogen and a complex with chemisorbed hydrogen in each case. Each of them was more stable than the corresponding complex formed by the corresponding one-aluminum cluster. The transition structures for chemisorption were identified. The reaction coordinate for chemisorption revealed that the reaction is a case of metal ion catalysis, rather than an acid-base reaction with heterolytic dissociation of hydrogen. The potential energy barrier (PEB) for hydrogen chemisorption was lower for the two-Al clusters than for the one-Al clusters. The chemisorption on a silicon-aluminum cluster, (HO)(2)(H2O)Al-O-Si(OH)(3) was also found to occur, but it had a higher FEB than for the corresponding two-aluminum cluster. Thus, zeolites can also exchange hydrogen, albeit less effectively than alumina, whereas the extraframework aluminum species in steamed zeolites should exchange hydrogen easier than the intact zeolite.