Multiple configurations of the two excess 4f electrons on defective CeO2(111) : Origin and implications

Density-functional theory calculations have been carried out to systematically study single surface oxygen vacancies on ${\text{CeO}}_{2}(111)$. It is surprisingly found that multiple structures with the two excess electrons localized at different positions can exist. We show that the origin of the multiconfigurations of $4f$ electrons is a result of geometric relaxation on the surface and strong localization characteristic of $4f$ electrons in ceria. The importance of $4f$ electron structures is also presented and discussed. These results may possess implications for our understanding of materials with $f$ electrons.