Oxygen-Vacancy Dynamics and Entanglement with Polaron Hopping at the Reduced CeO_{2}(111) Surface

The migration of oxygen vacancies (V_{O}) in ceria-based systems is crucial to their functionality in applications. Yet, although the V_{O}'s structure and the distribution of the Ce^{3+} polarons at the CeO_{2}(111) surface has received extensive attention, the dynamic behaviors of V_{O}'s and polarons are not fully understood. By combining density functional theory calculations and ab initio molecular dynamics simulations, we show that the movements of V_{O}'s and polarons exhibit very distinct entanglement characteristics within a temperature range of 300-900 K, and that the positions of the Ce^{3+} polarons play a key role in the V_{O} migration. Long-distance vacancy migration occurs at moderate temperatures when the "suitable" Ce^{3+} distribution remains long enough to promote oxygen migration. This study provides microscopic insight into the interplay between the electronic and ionic charge transport in ceria that will be beneficial for the rational design of conductive ceria-based materials.