Reactions of the "naked" and MgO(100) supported Zr2Pd2 cluster with nitrogen and four hydrogen molecules were studied at the density functional level using the periodic slab approach (VASP). It was shown that adsorption of the Zr2Pd2 clusteron the MgO(100) surface does not change its gas-phase geometry and electronic structure significantly. In spite of this the N-2 coordination to the MgO(100)-supported Zr2Pd2 cluster, I/MgO, is found to be almost 30 kcal/mol less favorable than for the "naked" one. The addition of the first H-2 molecule to the resulting II/MgO, that is, II/MgO + H-2 -> IV/MgO reaction, proceeds with a relatively small, 9.0 kcal/mol, barrier and is exothermic by 8.3 kcal/mol. The same reaction for the "naked" Zr2Pd2 cluster requires a slightly larger barrier (10.1 kcal/mol) and is highly exothermic (by 23.3 kcal/mol). The interaction of the H-2 Molecule with the intermediate IV/MgO (i.e., the second H-2 molecule addition to II/MgO) requires larger energy barrier, 23.3 kcal/mol vs 8.8 kcal/mol for the "naked" cluster, and is exothermic by 20.5 kcal/mol (vs 18.2 kcal/mol reported for the "naked" Zr2Pd2 cluster). The addition of the H-2 molecule to VII/MgO and VI (i.e., the third H-2 molecule addition to II/MgO and II, respectively) requires similar barriers, 12.0 versus 16.8 kcal/mol, respectively, but is highly exothermic for the supported cluster compared to the "naked" one, 13.6 versus 0.1 kcal/mol. The addition of the fourth H-2 molecule occurs with almost twice larger barrier for the "naked" cluster compared to the adsorbed species, 30.7 versus 15.9 kcal/mol. Furthermore, this reaction step is endothermic (by 11.4 kcal/mol) for the gas-phase cluster but exothermic by 7.8 kcal/mol for the adsorbed cluster. Dissociation of the formed hydrazine molecule from the on-surface complex X/MgO and the "naked" complex X requires 19.1 and 26.3 kcal/mol, respectively. Thus, the Zr2Pd2 adsorption on the MgO(100) surface facilitates its reaction with N-2 and four H-2 molecules, as well as formation of hydrazine from the hydrogen and nitrogen molecules. The reported differences in the reactivity of the "naked" and MgO adsorbed Zr2Pd2 clusters were explained by analyzing the nature of the H-2 addition steps in these systems.