Electronic and Atomistic Structures of Clean and Reduced Ceria Surfaces Stefano Fabris,* ,† Gianpaolo Vicario, ‡ Gabriele Balducci, ‡ Stefano de Gironcoli, † and Stefano Baroni † INFM-CNR DEMOCRITOS National Simulation Center and SISSAsScuola Internazionale Superiore di Studi AVanzati, Via Beirut 2-4, I-34014 Trieste, Italy, and Chemistry Department and Center of Excellence for Nanostructured Materials, UniVersita ` di Trieste, Via Giorgieri 1, 34127 Trieste, Italy ReceiVed: March 7, 2005; In Final Form: October 13, 2005 The atomistic and electronic structures of oxygen vacancies on the (111) and (110) surfaces of ceria are studied by means of periodic density functional calculations. The removal of a neutral surface oxygen atom leaves back two excess electrons that are shown to localize on two cerium ions neighboring the defect. The resulting change of valency of these Ce ions (Ce 4+ f Ce 3+ ) originates from populating tightly bound Ce 4f states and is modeled by adding a Hubbard U term to the traditional energy functionals. The calculated atomistic and electronic structures of the defect-free and reduced surfaces are shown to agree with spectroscopic and microscopic measurements. The preferential defect segregation and the different chemical reactivity of the (111) and (110) surfaces are discussed in terms of energetics and features in the electronic structure. I. Introduction Ceria-based catalysts are presently used to abate pollutants from combustion exhausts and are believed to be key materials in the future hydrogen production technology. 1-3 The role of the oxide substrate in traditional catalysts is passive, in that it merely provides a resistant support for the chemically active noble metals. Supports based on the reducible oxide ceria (CeO 2 ), instead, participate actively in surface chemical reactions (typically oxidations and reductions) by easily releasing oxygen on demand at the reaction sites, acting therefore effectively as an oxygen buffer. 4 The improvement in the conversion ef- ficiency thus achieved is traced back to the presence of surface oxygen vacancies. 1 Their formation, i.e., the release of oxygen from the lattice, entails an excess of two electrons per vacancy, which localize into the f-states of Ce 4+ ions, reducing them to Ce 3+ . 1,4,5 Knowing the local structure, clustering properties, and mobility of these defects is therefore of paramount importance for understanding their role in binding catalytic species and in enhancing both the reactivity of supported noble metals and the oxygen storage capacity. 2,6,7 Microscopy techniques demonstrate that oxygen vacancies are present on the most stable (111) and (110) surfaces of ceria, either isolated or aggregated in extended defect clusters. 8-12 However, the resolution of these analyses cannot address the atomistic details of the defect structures. Spectroscopic tech- niques do show that oxygen defects strongly modify the electronic structure (i.e., change of valency of the cerium ions upon reduction), but they lack spatial resolution. 13-15 Theoretical modeling can provide new insight into both the atomistic and electronic structures of reduced ceria surfaces. Traditional approaches, based on either empirical potentials or standard implementations of the Hartree-Fock 16 (HF) or density functional 17-19 theories (DFT), have so far failed to provide a proper account of the multiple valency character of Ce, i.e., the change of valency Ce 4+ f Ce 3+ of the Ce ions upon reduction. The change of formal valency of Ce is determined by electron localization effects which break the symmetry of geometrically equivalent Ce ions. The main drawback of previous DFT calculations of reduced ceria was to miss such broken-symmetry solutions, therefore describing reduced ceria as a band conductor. The addition of a Hubbard-U term in the density functional substantially penalizes the metallic solution stabilizing the physical, insulating one. The resulting level of theorysusually denoted as LDA+U (or GGA+U, DFT+U, in brief)sprovides a unified modeling framework for pure (CeO 2 and Ce 2 O 3 ) and defective (CeO 2-x ) ceria structures. 20 This approach is now applied to the study of crystalline defects segregated to ceria surfaces. Defect-free ceria surfaces have been studied by classical interatomic potentials 21-26 and by ab initio methods in the HF approximation 16 or within DFT. 27,28 All these calculations predict the higher stability of the (111) surface with respect to other low-index surfaces, such as the (110) or the polar (001) one. The previous ab initio analysis 28 of the reduced (111) and (110) surfaces predicts that the electrons compensating for the oxygen vacancies would not be localized on the neighboring Ce atoms only but would rather be spread over the outermost three atomic layers. This study also indicates that the most stable site for the formation of a surface vacancy is in the topmost atomic layer for the (110) surface, while it would be in the atomic O layer underneath the surface for (111). We show that calculations based on the DFT+U method provide a different picture for the same reduced ceria surfaces. Nolan et al. 29 have recently applied the DFT+U method to the study of the pure (111) and (110) surfaces and of the reduced (001) surface. In general, this method is known to rely on the choice of a set of localized orbitals, which is to some extend arbitrary, and on a specific value for the parameter U. Both factors can in principle deteriorate the ab initio character of DFT calculations. To reduce the level of arbitrariness and to enhance the predictive power of the calculations we find that by identifying the localized orbitals which define the Hubbard-U term with † INFM-CNR DEMOCRITOS National Simulation Center and SISSAs Scuola Internazionale Superiore di Studi Avanzati. ‡ Chemistry Department and Center of Excellence for Nanostructured Materials, Universita ` di Trieste. 22860 J. Phys. Chem. B 2005, 109, 22860-22867 10.1021/jp0511698 CCC: $30.25 © 2005 American Chemical Society Published on Web 11/12/2005