Using density-functional theory with the HSE06 (Heyd-Scuseria-Ernzerhof) hybrid

functional as well as the DFT+U approach (where U was a Hubbard-like term

describing on-site Coulomb interactions), sub-surface vacancies with (2 x 2)

periodicity were found to be energetically more favorable by 0.45 (HSE06), 0.47

[PBE+U (Perdew-Burke-Ernzerhof functional)], and 0.22eV [LDA+U (local

density approximation)]. The excess electrons localized not on Ce ions, which were

the nearest neighbors to the defect, but instead on those that were next-nearest

neighbors. The excess-electron distribution and the preference for sub-surface

vacancies were explained in terms of defect-induced lattice relaxation effects.

Density-Functional Calculations of the Structure of Near-Surface Oxygen

Vacancies and Electron Localization on CeO2(111). M.V.Ganduglia-Pirovano,

J.L.Da Silva, J.Sauer: Physical Review Letters , 2009, 102[2], 026101