In the present paper, we examine the general applicability of different TiO2 model clusters to study of local chemical events on TiO2 sub-nanoparticles. Our previous DFT study of TiO2 activation through H adsorption and following deactivation by O2 adsorption using small amorphous Ti8O16 cluster were complemented by examination of rutile-type and spherical Ti15O30 nanoclusters. The obtained results were thoroughly compared with experimental data and results of related computational studies using other TiO2 models including periodic structures. It turned out that all considered model TiO2 model systems provide qualitatively similar results. It was shown that atomic hydrogen is adsorbed with negligible activation energy on surface O atoms, which is accompanied by the appearance of reduced Ti(3+) species and corresponding localized band gap 3d-Ti states. Oxygen molecule is adsorbed on Ti(3+) sites spontaneously forming molecular O2 (-) species by capturing an extra electron of Ti(3+) ion, which results in disappearance of Ti(3+) species and corresponding band gap states. Calculated g-tensor values of Ti(3+) and O2 (-) species agree well with the results of EPR studies and do not depend on the used TiO2 model cluster. Additionally, it was shown that the various cluster calculations provide results comparable with the calculations of periodic structures with respect to the modeling of chemical processes under study. As a whole, the present study approves the validity of molecular cluster approach to study of local chemical events on TiO2 sub-nanoparticles.