  Oxygen vacancies (VO's) are of paramount importance in influencing the
properties and applications of ceria (CeO2). Yet, comprehending the
distribution and nature of the 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+'s). In this study, we employed a combination of
LASSO regression in machine learning, in conjunction with a cluster expansion
model and first-principles calculations to decouple the interactions among the
Ce3+'s 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 Ce3+-Ce3+/VO-VO repulsions, which are crucial in
determining the stability of vacancy structures. Through more than 10^8
Metropolis Monte Carlo samplings of Vo's and Ce3+ in the near-surface of
CeO2(111), we explored potential configurations within an 8x8 supercell. Our
findings revealed that oxygen vacancies tend to aggregate and are most abundant
in the third oxygen layer, primarily due to extensive geometric relaxation-an
aspect previously overlooked. This behavior is notably dependent on the
concentration of Vo. This work introduces a novel theoretical framework for
unraveling the complex vacancy structures in metal oxides, with potential
applications in redox and catalytic chemistry.
