Active-Site Ensemble for the Reverse Water-Gas Shift Reaction over Pd/TiO₂: Two Is Better than One or More

Determining whether the active-site ensemble number for a given reaction is a single atom, dual atom, or subnanocluster remains a challenge for both experimental and theoretical studies. This work presents a systematic theoretical study, employing density functional theory and mean-field microkinetic modeling, on the reverse water-gas shift (rWGS) reaction over the anatase TiO₂-supported Pd cluster, Pd/A-TiO₂ (n = 1, 2, 3, 4) to explore the optimal active ensemble number required for rWGS. Our results show that Pd₂ shows the best catalytic activity for rWGS, while neither Pd₁ nor Pd₃(Pd₄) demonstrates high catalytic activity. This is due to either the limited active sites for carboxyl formation, as observed with Pd₁, or excessively strong binding of H* species, which hinders the carboxyl formation, as seen with Pd₃ (or Pd₄). We found that Pd₂with the most stable position for [COOH* + H*] species along the rWGS reaction energy diagrams, which maybe one of the possible reasons for its high rWGS catalytic activity. Moreover, H* binding energy can be used as a descriptor of rWGS activity, in line with the Sabatier principle, neither too strong nor too weak binding is favorable. It is hoped that the present findings can be extended to other reaction types, such as the water-gas shift (WGS) reaction, where Pd₂ may outperform either a single Pd atom or small Pd clusters.