The dissociative chemisorption of molecular hydrogen on charged and neutral aluminum clusters A112X (X = Mg, Al, Si) was investigated using DFT and a modified G3(MP2)-RAD procedure. Reaction barriers and enthalpies were determined for both neutral and sigly charged clusters. The lowest barrier for dissociative adsorption of H2 on a neutral cluster was found for the Al12Mg cluster, whereas the highest barrier was found to be on the closed-shell Al12Si. The interaction of H2 with Al13+ is found to proceed via an association complex that is 0.07 eV lower in energy than the isolated species and from which the barrier to H2 dissociative adsorption is only 0.16 eV. The most exothermic reaction of H2 with Al12X occurs for the Al13+/H2 system. In comparison, reactions with the closed-shell Al13- and Al12Si clusters are found to be endothermic. The barriers for H2 desorption from the dihydrogenated clusters are generally quite substantial.