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In this work, using the state-of-the-art first principles calculations basedon density functional theory, we found that the concentration as well ascoordination of surface oxygen vacancies with respect to each other werecritical for direct water-splitting reaction on the (001) surfaces of PbTiO$_3$and TiO$_2$. For the water-splitting reaction to happen on TiO$_2$-terminatedsurfaces, it is necessary to have two neighboring O-vacancies acting as activesites that host two adsorbing water molecules. However, eventual dissociationof O-H bonds is possible only in the presence of an additional nearest-neighborO-vacancy. Unfortunately, this necessary third vacancy inhibits the formationof molecular hydrogen by trapping the dissociated H atoms overTiO$_2$-teminated surfaces. Formation of up to 3 O-vacancies, is energeticallyless costly on both terminations of PbTiO$_3$ (001) surfaces compared with thatof TiO$_2$, the presence of Pb leads to weaker O bonds over these surfaces.Molecular hydrogen formation is more favorable over the PbO-terminated surfaceof PbTiO$_3$, requiring only two neighboring oxygen vacancies. However,hydrogen molecule is retained near the surface by weak van der Waals forces.Our study indicates two barriers leading to low productivity of direct watersplitting processes. First and foremost, there is an entropic barrier imposedby the requirement of at least two nearest-neighbor O-vacancies, stericallyhindering the process. Furthermore, there are also enthalpic barriers offormation over TiO$_2$-terminated surfaces, or removal of H$_2$ molecules fromthe PbO-terminated surface.

Elucidating the barriers on direct water splitting: Key role of oxygen vacancy density and coordination over PbTiO$_3$ and TiO$_2$