The rate constants of H-2 formation on five models of silicate nanoclusters with varying degrees of hydroxylation, (Mg4Si4O12)(H2O)(N), were computed over a wide temperature range [180-2000 K]. We tested nine combinations of density functional methods and basis sets for their suitability for calculating reaction energies and barrier heights, and we computed the minimum energy H + H -> H-2 reaction paths on each nanocluster. Subsequently, we computed the rate constants employing three semiclassical approaches that take into account tunneling and nonclassical reflection effects by means of the zero curvature tunneling (ZCT), the small curvature tunneling (SCT), and the one-dimensional semiclassical transition state theory (SCTST) methods, which all provided comparable results. Our investigations show that the H-2 formation process following the Langmuir-Hinshelwood (LH) mechanism is more efficient on the hydroxylated (N = 1-4) nanoclusters than on the bare (N = 0) one due to relatively higher reaction barrier height on the latter. H-2 formation is found to have the smallest barrier and the most exothermic reaction for the moderately hydroxylated (Mg4S4O12)(H2O)(2) nanocluster for all nine considered methods. Overall, we conclude that all the considered nanoclusters are very efficient catalyzing grains for H-2 formation in the physical conditions of the interstellar medium (ISM) with pyroxene nanosilicates having moderate to high hydroxylation being more efficient than bare nanograins.