Oxygen vacancies (VO's) are of paramount importance in influencing the properties and applications of ceria (CeO2). Yet, comprehending the distribution and nature of VO's poses a significant challenge due to the vast number of electronic configurations and intricate many-body interactions among VO's and polarons (Ce3+ ions). In this study, we established a cluster expansion model based on first-principles calculations and statistical learning to decouple the interactions among the Ce3+ ions and VO's, thereby circumventing the limitations associated with sampling electronic configurations. By separating these interactions, we identified specific electronic configurations characterized by the most favorable VO-Ce3+ attractions and the least favorable Ce3+-Ce3+/VO-VO repulsions, which are crucial in determining the stability of vacancy structures. Through more than 108 Metropolis Monte Carlo samplings of VO's and Ce3+ ions in the near surface of CeO2(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 VO 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.
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