Decoupling many-body interactions in the CeO 2 (111) oxygen vacancy structure with statistical learning and cluster expansion.

Oxygen vacancies (V _O 's) are of paramount importance in influencing the properties and applications of ceria (CeO ₂ ). Yet, comprehending the distribution and nature of V _O 's poses a significant challenge due to the vast number of electronic configurations and intricate many-body interactions among V _O 's and polarons (Ce ³⁺ ions). In this study, we established a cluster expansion model based on first-principles calculations and statistical learning to decouple the interactions among the Ce ³⁺ ions and V _O 's, thereby circumventing the limitations associated with sampling electronic configurations. By separating these interactions, we identified specific electronic configurations characterized by the most favorable V _O -Ce ³⁺ attractions and the least favorable Ce ³⁺ -Ce ³⁺ /V _O -V _O repulsions, which are crucial in determining the stability of vacancy structures. Through more than 10 ⁸ Metropolis Monte Carlo samplings of V _O 's and Ce ³⁺ ions in the near surface of CeO ₂ (111), we explored potential configurations within an 8 × 8 supercell. Our findings revealed that oxygen vacancies tend to aggregate and are abundant in the third oxygen layer with an elevated V _O concentration primarily due to extensive geometric relaxation, an aspect previously overlooked. This work introduces a novel theoretical framework for unraveling the complex vacancy structures in metal oxides, with potential applications in redox and catalytic chemistry.