Many competing ceria (110) oxygen vacancy structures: From small to large supercells

Abstract

We present periodic "DFT+U" studies of single oxygen vacancies on the CeO 2 (110) surface using a number of different supercells, finding a range of different local minimum structures for the vacancy and its two accompanying Ce(III) ions. We find three different geometrical structures in combination with a variety of different Ce(III) localization patterns, several of which have not been studied before. The desired trapping of electrons was achieved in a two-stage optimization procedure. We find that the surface oxygen nearest to the vacancy either moves within the plane towards the vacancy, or rises out of the surface into either a symmetric or an unsymmetric bridge structure. Results are shown in seven slab geometry supercells, p(2 × 1), p(2 × 2), p(2 × 3), p(3 × 2), p(2 × 4), p(4 × 2), and p(3 × 3), and indicate that the choice of supercell can affect the results qualitatively and quantitatively. An unsymmetric bridge structure with one nearest and one next-nearest neighbour Ce(III) ion (a combination of localizations not previously found) is the ground state in all (but one) of the supercells studied here, and the relative stability of other structures depends strongly on supercell size. Within any one supercell the formation energies of the different vacancy structures differ by up to 0.5 eV, but the same structure can vary by up to ∼1 eV between supercells. Furthermore, finite size scaling suggests that the remaining errors (compared to still larger supercells) can also be ∼1 eV for some vacancy structures.

Disentangling the role of small polarons and oxygen vacancies in CeO2

“…Some researchers reported that the two excess electrons prefer to localize on two Ce atoms that are the nearest neighbor (NN) to the vacancy [15,16,29,30,[34][35][36][37][38][39], while others [40,41,42] suggested that having the Ce 3+ on the next-nearest neighbor (NNN) sites is energetically more favorable over the NN configuration.…”

“…For the oxygen vacancy, the excess electrons are localized on individual Ce atoms, turning two Ce 4+ into two Ce 3+ species, which, by Coulomb attraction, sit near to the vacancy [29][30][31][32][33][34][35][36][37][38][39][40][41][42]. The results of DFT+U studies are largely dependent on the U value, bringing some uncertainty to the results and raising questions on what value of U should be used to describe the properties of perfect and reduced CeO 2 .…”

“…The DFT+U method has also been employed to study the electronic properties of CeO 2 and the impact of oxygen vacancies [29,30,[33][34][35][36][37][38][39][40][41][42]. In this approach, an extra on-site Coulomb interaction is added to the Ce 4f states, leading to a split between occupied and unoccupied states.…”

“…There have appeared numerous studies of bulk CeO 2 based on DFT calculations, many focusing on the oxygen vacancy [10][11][12][13][14][15][16][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42]. DFT calculations using the local density approximation (LDA) or the generalized gradient approximation (GGA) for the exchange-correlation term underestimate the separation between the top of the valence band (O 2p band) and the empty Ce 4f bands in CeO 2 by ~35 % [16,[31][32][33].…”

The nature of oxygen states on the surfaces of CeO2 and La-doped CeO2

“…[5] The most commonly studied defect on CeO 2 surfaces is the O vacancy, due to its importance for describing catalysis of CeO 2 . [15][16][17][18] Upon the formation of a neutral O vacancy, excess electrons are localized onto Ce(IV) ions, reducing them to Ce(III). In Kröger-Vink notation this is given as:…”