Production of hydrogen by splitting water in thermochemical water-splitting cycles, such as the sulfur-based group that employs the catalytic decomposition of sulfuric acid into SO2 and O2 is of considerable interest. Most of these processes occur at high temperatures (T > 1,000 K) and exposes catalysts to the extreme conditions such as steam, oxygen, and acid vapor that severely damage these catalysts within a short time. To develop an understanding of the factors that cause catalyst deactivation, we performed density-functional-theory (DFT)-based first-principles calculations and computer simulations for transition metal (TM) particles positioned on the two types of substrate (gamma-alumina and TiO2-rutile). We found that the catalytic activity of the considered systems is defined by several factors, namely: (i) The efficiency of detaching oxygen atoms from the sulfur-containing species; (ii) The ability of the cluster to eliminate oxygen from its surface, in order to regain the catalytically active sites and to continue the process; (iii) The ability of the cluster to keep its size to avoid sintering (that reduces the number of low-coordinated catalytically active sites at the surface of the cluster). We found that the clusters of Pd and Pt are more efficient (at T > 1,000 K) in eliminating oxygen from the surface than the clusters of other TM's considered (Rh, Ir, Ru, and Os). However, the sintering of Rh, Ir, Ru, and Os clusters is significantly suppressed in comparison with the sintering of Pd and Pt clusters of the same size. At the present, we are searching (experimentally and theoretically) for the most optimal combination of the structure, size, and composition of TM nanoparticles, for which the catalytic activity of sulfuric acid decomposition will be the highest.