Can oxygen vacancies in ceria surfaces be measured by O1s photoemission spectroscopy?

X-ray photoemission spectroscopy is a standard technique for materials characterization and the O 1s binding energy is commonly measured for oxides. Here we use density functional theory calculations to investigate how the O 1s binding energy in CeO2(111) is influenced by the presence of oxygen vacancies. The case with point vacancies in CeO2(111) is compared to complete reduction to Ce2O3. Reduction of CeO2 by oxygen vacancies is found to have a minor effect on the O 1s binding energy. The O 1s binding energy is instead clearly changed when the character of the chemical bond for the considered oxygen atom is modified by, for example, the formation of OH-groups or carbonates.


Introduction
Physical and chemical properties of oxide surfaces may depend strongly on the presence of oxygen vacancies. For reducible oxides such as CeO 2 , oxygen vacancies create occupied states in the band-gap, which modifies optical and catalytic properties [1]. Thus, to establish structure-function relationships, it is desirable to know if vacancies are present. X-ray photoemission spectroscopy (XPS) is the standard technique for chemical analysis [2], which has been used to make conclusions regarding the presence of vacancies in different oxides by measuring shifts in O 1s binding energy, see e.g. references [3][4][5][6][7]. The assigned shift is commonly about 1-2 eV * Authors to whom any correspondence should be addressed.
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. to higher binding energies than the O 1s binding energy in the bulk oxide. The assignment of shifts in O 1s binding energies to oxygen vacancies is based on the assumption that the presence of vacancies changes the electrostatic potential for the oxygen anions that are left in the system.
Core level shifts (CLS) of O 1s has also been used to make conclusions regarding oxygen vacancies in CeO 2 . For CeO 2 , vacancy induced shifts have been reported in the range from 1 to 2.5 eV [8][9][10][11][12][13]. For example, in reference [10], the interaction of oxidized and partially reduced CeO 2 with water was studied by a range of techniques including synchrotronradiation photoelectron spectroscopy. The O 1s binding energy for oxygen atoms in the bulk of CeO 2−x (with x = 0.16) was measured to be 529.7 eV. An O 1s binding energy feature at 532.0 eV was for this system assigned to oxygen atoms close to Ce 3+ , resulting in a shift of 2.3 eV.
It should be noted that the literature on shifts of the O 1s binding energies in the presence of oxygen vacancies is not consistent and measurements have also been reported with no or minor shifts [14][15][16][17][18]. Early studies measured a shift of only 0.3 eV for vacancies in CeO 2 [14] and, similarly, a small shift of 0.2 eV between CeO 2 and the fully reduced phase Ce 2 O 3 has been reported [15]. In reference [18], the reduction of a CeO 2 (111)/Ru(0001) surface by atomic hydrogen was investigated by means of scanning tunneling microscopy and x-ray photoelectron spectroscopy. Exposing the sample to atomic hydrogen resulted initially to the formation of OH trimers and eventually to H 2 O formation and desorption leading to oxygen vacancies. The presence of oxygen vacancies did not result in additional peaks in the O 1s spectrum although signatures of the vacancies were visible in the Ce 3d spectrum [18].
We have recently studied the effect of oxygen vacancies on O 1s CLS for different oxides including CeO 2 (111) [19] using density functional theory (DFT) calculations. The calculations did not reveal any O 1s shift owing to vacancies. However, the calculations were restricted to point defects in the most stable surfaces without the possibility of structural transformations, which could induce changes in the Madelung potential and, thus, a possible shifts in the O 1s binding energy.
The unclear situation without a consensus whether signatures of oxygen vacancies are visible in the O 1s core level spectrum of reduced ceria have motivated us to further explore the issue with DFT calculations. Here we consider O 1s CLS for CeO 2 (111), CeO 2 (111) with vacancies and Ce 2 O 3 (0001) together with hydroxyl-and carbonate-groups on CeO 2 (111). We find that vacancies are not visible as shifts in the O 1s spectrum. Chemical reasons for observed shifts could instead be the presence of contaminants giving rise to hydroxyl-and carbonate-groups.

Computational method
The Vienna ab initio Simulation Package [20][21][22][23] was used to perform DFT calculations. The plane augmented wave (PAW) method [24,25] was used to model the interaction between the valence electrons and the cores. Electrons treated in the valence were 1s 1 for H, 2s 2 2p 2 for C, 2s 2 2p 4 for O and 5s 2 5p 6 5d 1 4f 1 6s 2 for Ce. The exchange-correlation functional according to Perdew, Burke and Ernzerhof [26] augmented with a Hubbard-U correction for Ce 4f states [27] was used to account for exchange and correlation effects. The Hubbard-U correction is required to localize the Ce 4f states and we used a value of 4.5 eV, which has been used previously [28]. The Kohn-Sham orbitals were expanded with plane waves using a 450 eV cut-off. A Monkhorst-Pack scheme [29,30] was used to generate k-points for a numerical integration over the Brillouin zone. Slabs of CeO 2 (111) and Ce 2 O 3 (0001) were considered and the repeated slabs were separated by at least 15 Å of vacuum. All structures were optimized using the method of conjugate gradients until the largest force was smaller than 0.03 eV Å −1 .
The CLS were calculated as total energy differences with a core hole either in the surface or in the center of the slab. This method includes complete screening of the core hole [31] and is based on the assumptions that the photo-emission process is fast with respect to the lifetime of the core hole, that the system remains in the ground state (with the constraint of a core hole), and that structural changes are small. The core holes were obtained by removing one electron from the O 1s shell in the PAW potential.
The presence of a core hole means that the system is ionized. However, periodic boundary conditions requires neutral supercells. The charge neutrality could be maintained either by adding an extra electron to the valence or by applying a compensating jellium background. The addition of an extra electron could be done for metallic systems, where the character of the occupied and unoccupied states are similar [32]. As ceria has a band gap, the CLS were here calculated by the use of a negatively charged homogeneous jellium background.

Structural models
The considered bulk structures are shown in figure 1. The bulk structure of CeO 2 is of fluorite type, with four Ce 4+ cations and eight O 2− anions. The four Ce 4+ cations are eight-fold coordinated, whereas the oxygen are four-fold coordinated. The optimized lattice parameter is a = 5.49 Å, which agrees with previous DFT studies [1,33] and the experimental value of 5.41 Å. Ce 2 O 3 has an hexagonal structure with two Ce 4+ cations and three O 2− anions. The two cerium atoms are sevenfold coordinated. Two of the oxygen atoms are four-fold coordinated, whereas the third oxygen atom is six-fold coordinated. The optimized lattice parameters are a = b = 3.92 Å and c = 6.16 Å, which agrees with previous DFT-reports [34,35]. The experimental lattice parameters are a = b = 3.89 Å and c = 6.06 Å.
One important difference between stoichiometric and reduced ceria is that the 4f-states are partially occupied for Ce 2 O 3 . The density of states (DOS) for the two bulk structures are shown in figure 2. The oxidation state of the cerium atoms in CeO 2 is +4, meaning that the 4f states are empty. In the DOS, the empty 4f-states are 2.2 eV above the Fermi energy. The states below the Fermi energy are of O 2p character. The 4f-states become occupied for Ce 2 O 3 , forming states at the Fermi energy. The occupation of 4f-states is linked with a change in the oxidation state of the cerium atoms from +4 to +3. The occupied 4f-states are split from the unoccupied 4fstates, which are located about 2.4 eV above the Fermi energy.  CeO 2 is a closed-shell electronic system in the absence of vacancies. When vacancies are formed, electrons occupy the 4f-states in a ferromagnetic (FM) or anti-ferromagnetic (AFM) fashion. The FM and AFM solutions for CeO 2 (111) with vacancies are in our calculations close to degenerate. For Ce 2 O 3 (0001), the AFM configuration is preferred with alternating spin-up and spin-down Ce 3+ layers. The magnetic ordering was obtained by analyzing the magnetization.

O 1s core level shifts for the surface models
To investigate the possibility to measure shifts in the O 1s binding energies between pristine CeO 2 , partially or completely reduced CeO 2 , we calculated O 1s CLS for CeO 2 (111), CeO 2 (111) with oxygen vacancies, Ce 2 O 3 (0001) and the interface system. The shifts are calculated as the total energy difference between the system with a core-hole in the atom of interest and a core-hole in the bulk. The atoms that are selected to represent the bulk are shown in figure 3. A CeO 2 -reference is chosen for the interface model (C). The results are presented in table 1.
The shifts for surface oxygen atoms in both CeO 2 (111) and Ce 2 O 3 (0001) are negative. For CeO 2 (111), the shift for the top most oxygen atoms are −0.47 eV, whereas the subsurface atoms have shifts of only −0.02 eV. The surface CLS is only slightly affected by the presence of an oxygen vacancy. In Ce 2 O 3 (0001), the oxygen atoms have different coordination, being either four or six-fold coordinated. The reference is in this case considered to be an average between fourand six-fold coordinated bulk atoms. The O 1s binding energy of the two types of atoms differ by 0.19 eV. The CLS for a surface atom in Ce 2 O 3 (0001) is calculated to be −0.17 eV, whereas the sub-surface atoms have a shift of −0.14 eV. The smaller CLS for Ce 2 O 3 (0001) as compared to CeO 2 (111) is consistent with previous calculations for irreducible oxides such as MgO (100), which show small negative shifts [19]. For the interface system (C), the CLS have been calculated with respect to the bulk of the CeO 2 (111) slab, as shown in figure 3. The shifts for surface atoms of the Ce 2 O 3 (0001) part are positive, being 0.34 eV and 0.29 eV for the surface and sub-surface atoms, respectively. Thus, for this system where ceria is completely reduced (maximum number of vacancies), the shifts in O 1s binding energies are clearly smaller than the experimentally assigned shifts of 1-2.5 eV [8][9][10][11][12][13].
One important contribution to the CLS is the electronic screening where the creation of the core-hole attracts additional charge to the core-excited atom. We have investigated the screening by performing a Bader charge analysis [36]. The charge on the anions of CeO 2 (111) is calculated to be 7.2 electrons, whereas the charge on a core excited atom is about 7.8 electrons. Thus, the core hole attracts 0.6 electrons. The Bader analysis for Ce 2 O 3 (0001) shows a charge of 7.35 electrons. The corresponding charge in the presence of a core-hole is 7.9 electrons. In this case, the core-hole attracts about 0.5 electrons. The Bader charges for the interface system are consistent with the results for the pristine surfaces. As the 2s 2 2p 6 configuration of an oxygen anion constitutes a closed shell, this is also the formal screening configuration for a core excited oxygen atom in an oxide. The reason why the charge screening for reduced ceria is lower than for the stoichiometric case is that the oxygen anions in Ce 2 O 3 are closer to the 2s 2 2p 6 configuration in the unexcited state.

Effects of adsorbates
As oxygen vacancies do not result in large positive shifts, we have studied whether the observed experimental CLS could originate from different adsorbates on stoichiometric ceria. The reference atom is in this case a bulk CeO 2 atom, as for the pristine model system A. The considered adsorbates are OH groups produced by dissociated H 2 , water and adsorbed CO 2 forming CO 2− 3 . The considered structures and the corresponding CLS are shown in figure 4.
The presence of oxygen vacancies results in the change of oxidation state of two cerium atoms. The stable configuration  in presence of a vacancy corresponds to Ce 3+ atoms in next nearest neighbor position with respect to the vacancy [37]. The presence of OH groups is investigated with H 2 dissociated in an homolytic fashion. The adsorption of OH groups also leads to the formations of two Ce 3+ atoms. The adsorption energy is −1.17 eV per H, which is in agreement with previous results [38]. Water can on CeO 2 (111) coexist in molecular form and as a hydroxyl-pair [39]. The two OH-groups are bonded through a hydrogen bond in the hydroxyl-pair. The adsorption energy of the hydroxyl-pair is calculated to be −0.56 eV. Molecular water is adsorbed with an adsorption energy of −0.53 eV, which agrees with previous work [39]. The adsorption energy of CO 2 forming a carbonate is −0.61 eV, which also agrees with previous work [40]. The calculated CLS shows that the shift for the oxygen vacancy is close to the shift for the pristine case, suggesting that such shift is difficult to observe in an XPS experiment. On the contrary, the O 1s shift for the OH group is 2.44 eV and the shift from water in the form of the hydroxyl-pair, is between 0.97 and 1.07 eV. The calculated shifts agree with experimental results where a O 1s shift around 1.75 eV was assigned to the presence of OH groups, and a shift around 3.2 eV was assigned to molecular water [41].
The difference between the shifts of the OH groups formed by H 2 dissociation and water in hydroxyl pair form, originates from the presence of a hydrogen bond between the OH groups. In fact, when the OH group on a cerium atom is placed far from the lattice OH group, the shift increases from about 1 eV to about 2 eV. The carbonate structure results in two CLS at 1.57 eV and 1.78 eV, respectively. The larger shift corresponds to the oxygen atom in the lattice.
The O 1s CLS obtained for OH and carbonate adsorbates could potentially explain the experimental shifts attributed to oxygen vacancies. Our calculations agree with experimental literature where minor shifts have been attributed to oxygen vacancies, and instead pronounced shifts have been attributed to OH groups [14][15][16][17][18]41]. The calculated shifts for OHgroups are in the range where assignments have been done to oxygen vacancies [8][9][10][11][12][13].

Conclusions
We have used DFT calculations to investigate O 1s CLS for CeO 2 (111) with the goal to elucidate whether oxygen vacancies result in measurable shifts. The origin of measured O 1s shifts is important when establishing structurefunction relationships. The pristine surface was investigated together with CeO 2 (111) including vacancies, completely reduced Ce 2 O 3 (0001) and hydroxyl-and carbonate-groups on CeO 2 (111). We do not find any substantial O 1s shifts related to reduced ceria. Clear shifts are instead calculated in the presence of adsorbates. Experimentally, shifts in the O 1s binding energy of 1-2.5 eV have previously been assigned to oxygen atoms coordinated to Ce 3+ formed by the presence of oxygen vacancies. Our calculations indicate that such shifts instead could be due to contaminations, such as H 2 , H 2 O and CO 2 .

Acknowledgments
Financial support from the Knut and Alice Wallenberg Foundation through the project 'Atomistic design of catalysts' (No: KAW 2015.0058) and the Swedish Research Council (2020-05191) is gratefully acknowledged. The calculations have been performed at C3SE (Göteborg) and PDC (Stockholm) through a SNIC Grant. The Competence Centre for Catalysis is hosted by Chalmers University of Technology and financially supported by the Swedish Energy Agency and the member companies AB Volvo, ECAPS AB, Johnson Matthey AB, Preem AB, Scania CV AB, and Umicore Denmark Aps.

Data availability statement
The data generated and/or analysed during the current study are not publicly available for legal/ethical reasons but are available from the corresponding author on reasonable request.