title: Tuning LDA+U for electron localization and structure at oxygen vacancies in ceria.
abstract: We examine the real space structure and the electronic structure (particularly Ce4f electron localization) of oxygen vacancies in CeO(2) (ceria) as a function of U in density functional theory studies with the rotationally invariant forms of the LDA+U and GGA+U functionals. The four nearest neighbor Ce ions always relax outwards, with those not carrying localized Ce4f charge moving furthest. Several quantification schemes show that the charge starts to become localized at U approximately 3 eV and that the degree of localization reaches a maximum at approximately 6 eV for LDA+U or at approximately 5.5 eV for GGA+U. For higher U it decreases rapidly as charge is transferred onto second neighbor O ions and beyond. The localization is never into atomic corelike states; at maximum localization about 80-90% of the Ce4f charge is located on the two nearest neighboring Ce ions. However, if we look at the total atomic charge we find that the two ions only make a net gain of (0.2-0.4)e each, so localization is actually very incomplete, with localization of Ce4f electrons coming at the expense of moving other electrons off the Ce ions. We have also revisited some properties of defect-free ceria and find that with LDA+U the crystal structure is actually best described with U=3-4 eV, while the experimental band structure is obtained with U=7-8 eV. (For GGA+U the lattice parameters worsen for U>0 eV, but the band structure is similar to LDA+U.) The best overall choice is U approximately 6 eV with LDA+U and approximately 5.5 eV for GGA+U, since the localization is most important, but a consistent choice for both CeO(2) and Ce(2)O(3), with and without vacancies, is hard to find.
authors.affiliation: Department of Physics and Measurement Technology (IFM), Linköping University, SE-58183 Linköping, Sweden. christopher.castleton@mkem.uu.se
authors.forename: C W M
authors.initials: CW
authors.lastname: Castleton
authors.forename: J
authors.initials: J
authors.lastname: Kullgren
authors.forename: K
authors.initials: K
authors.lastname: Hermansson