Density functional theory studies of the structure and electronic structure of pure and defective low index surfaces of ceria

We present periodic density functional theory (DFT) calculations of bulk ceria and its low index surfaces (1 1 1), (1 1 0) and (1 0 0). We find that the surface energies increase in the order (1 1 1) > (1 1 0) > (1 0 0), while the magnitude of the surface relaxations follows the inverse order. The electronic properties of the bulk and surfaces are analysed by means of the electronic density of states and the electron density. We demonstrate that the bonding in pure ceria is partially covalent and analysis of the resulting electronic states confirms the presence of localised Ce 4f states above the Fermi level. The surface atoms show only a small change in the charge distribution in comparison to the bulk and from the DOS the main differences are due to the changes in the oxygen 2p and cerium 5 d states. Investigation of the atomic and electronic structure of an oxygen vacancy on the (1 0 0) surface shows the problems DFT can have with the description of strongly localised systems, wrongly predicting electron delocalisation over all of the cerium atoms in the simulation cell. We demonstrate an improvement in the description of the strongly correlated cerium 4f states in partially reduced ceria by applying the DFT+U methodology, which leads to the appearance of a new gap state between the valence band and the empty Ce 4f band. Analysis of the partial charge density shows that these states are localised on the CeIII ions neighbouring the oxygen vacancy. In terms of classical defect chemistry, the vacancy is bound by two neighbouring CeIII ions, which have been reduced from CeIV, i.e. VO··+2CeCe′. The remaining Ce ions are in the CeIV oxidation state. The localisation of Ce 4f electrons modifies the predicted structure of the defective surface.