Comment on 'Oxygen Vacancy Ordering and Electron Localization in

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Reply to “Comment on ‘Oxygen Vacancy Ordering and Electron Localization in CeO: Hybrid Functional Study'” 2

Xiaoping Han, Noureddine Amrane, Zongsheng Zhang, and Maamar Benkraouda J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b02945 • Publication Date (Web): 29 Aug 2017 Downloaded from http://pubs.acs.org on August 30, 2017

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The Journal of Physical Chemistry

Reply to “Comment on ‘Oxygen Vacancy Ordering and Electron Localization in CeO2: Hybrid Functional Study’ ”

Xiaoping Han,1 Noureddine Amrane,1 Zongsheng Zhang,2 and Maamar Benkraouda1,*

1

Department of Physics, United Arab Emirates University, Al-Ain, P.O.Box 15551, U.A.E. 2

College of International Education, North University of China, Taiyuan 030051, China

* E-mail: [email protected] Tel: +971 (0)3 7136742

ACS Paragon Plus 1 Environment


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Recently, we reported a Heyd-Scuseria-Enrzerhof (HSE)1 hybrid functional study of oxygen vacancy ordering and electron localization in bulk CeO2, with the aim to obtain an atomic-level insight into the multiple oxygen vacancies in CeO2 and the associated effects on the photocatalytic, photovoltaic and magnetic properties properties.2 Our main conclusions are that oxygen vacancies energetically prefer to order in the direction, and that such vacancy ordering and the caused electron localization may profoundly influence the photocatalytic, photovoltaic and magnetic properties. In a comment,3 Ganduglia-Pirovano et al. questioned three points in our paper: (i) the localization of two excess electrons left behind by oxygen removal, (ii) the associated lattice relaxation and (iii) the missing of the citations to some previous works. In this reply we try to address these comments and explain why there are evident discrepancies between our results and theirs. Regarding the excess charge localization, Ganduglia-Pirovano et al. think two excess charges should localize on two second-nearest Ce ions to the oxygen vacancy and reduce them into Ce3+ ions, and disagree with our results (where the two excess charges were found to localize on two Ce ions nearest to the oxygen vacancy). Theoretically, this pair of Ce3+ ions can be the first neighbor (1N), second neighbor (2N) or third neighbor (3N) to the vacancy, and so on. In order to identify the most stable configuration of Ce3+ ions, we use the approach of predetermining the Ce3+ sites (as described in Ref. 4) to inspect all possible configurations of Ce3+ ions in the case of a single vacancy, and their respective energies are listed in Table 1 (note, the configurations with 4N and beyond are strongly disfavored because of their much higher energies). Clearly, the 1N1N configuration is the most stable, with 17 meV less than the 2N-2N case. It is consistent with several recent reports5-11 but different from other ones (i.e., the 2N-2N configuration is the most stable).

4,12-15

Apparently, no general agreement on the excess charge localization has been

achieved, considering that related experimental results are yet to be desired. In our opinion, the first factor responsible for the discrepancy is attributed to the different lattice relaxation schemes used. In our case, a full relaxation scheme has been used, i.e., the


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relaxation on the shape, volume and atomic positions. The different spin configurations of Ce3+ ions have also been taken into account and compared. As expected, there is little difference between the optimized structures with a single vacancy using the limited relaxation (fixed volume and shape) and full relaxation. However, the influence of the full relaxation on the systems with di-vacancy and four vacancies is not negligible with respect to the limited relaxation. The full relaxation not only causes their volume to expand a bit but also drives the cubic structures to have slight distortion, leading to the decrease in total energy for the systems of vacancy pair (by 0.21 eV) and four linear vacancies (by 0.45 eV) along the direction in contrast with the limited relaxation. We use the full relaxation to selectively perform the studies on the configurations in vacancy pair (VV331-13) and line (Line3131-03), which were thought to be the most stable in the investigated configurations by the authors of Ref. 3, and compare their total energies with the corresponding stable configurations in our original paper. The results show that our configurations are more stable, with the energies of 21 and 28 meV less than theirs, respectively. Simultaneously, the Ce3+-O-Ce3+ angles are also influenced by the full relaxation. The vacancy formation drives the nearest Ce ions to move away from the vacancy site and the O ions (first neighbors to vacancy within the oxygen sublattice) to move toward the vacancy site, but the distortions simultaneously take place. This leads to the results different from those obtained by Ganduglia-Pirovano et al. Considering that most theoretical works did not involve the relaxation of the cell shape, we have done additional optimizations on the structures with di-vacancy and four linear vacancies in the direction with the shape fixed and the volume and atomic positions relaxed. The results show the increase in total energy for the systems of vacancy pair (by 51 meV) and four linear vacancies (by 86 meV) along the direction in contrast with the full relaxation. The same scheme is also used to optimize the configurations in vacancy pair (VV331-13) and line (Line313103),

and it is found that VV331-13 and Line3131-03 are more stable than the corresponding

configurations in our original paper, although just with the energy differences of no more than 20



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meV. Therefore, it is the full relaxation that directly takes effect. Another factor inducing the discrepancy is the different functionals used: the HSE and GGA+U. To better illustrate this point, we have added some calculations and compare the results of the stoichiometric CeO2 obtained using the GGA+U and HSE functionals. Their calculated results of the lattice constant and band gap are shown in Fig. 1. One can see that the band gaps with U between 8 and 9 eV are close to the experimental value of 3.0 eV16 while the lattice constants with U of over 5 eV are evidently bigger than the experimental value (5.41 Å17). In strong contrast, the HSE method produces the lattice constant of 5.40 Å and the band gap of 3.07 eV (both excellently agreeing with the corresponding experimental values), exhibiting a reliable theoretical description of CeO2. Such different lattice parameters obtained using GGA+U and HSE are very likely to induce the different localized charge distributions, as suggested by Arapn et al.18 In addition, the influence of the multiple self-consistent solutions in GGA+U should be brought into sharp focus, which varies with the U value, the initial orbital occupancy, lattice geometry, and minimization algorithms used for the calculations.12,19,20 As shown above, we have cited the references4,12-15 , which we have overseen in our original paper, and made comparison between their results and ours. It is worth stressing that these references used the approach of predetermining the positions of Ce3+ ions to search for the most stable configuration of Ce3+ sites. Though this approach is physically grounded, it still has its own limitation: Manually fixing the positions of excess charges is bound to affect the finally optimized structures and hence the associated energetics. In this respect, we did not use it to inspect each Ce3+ configuration in our original paper. Instead, if the ionic relaxation can be fully performed, the resultant structures are likely to avoid or improve the above limitation. In conclusion, we thank the authors of Ref. 3 for pointing out the need to improve our results and descriptions. We hope our explanations and additional calculations can answer their comments and provide further understanding of our conclusions.


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ACKNOWLEDGEMENT This work was supported by United Arab Emirates University through the University Program for Advanced Research (no: 31S109-UPAR). Part of computing time was provided by North University of China.



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REFERENCES (1) Heyd, S.; Scuseria, G. E.; Ernzerhof, M. Hybrid Functionals Based on a Screened Coulomb Potential. J. Chem. Phys. 2003, 118, 8207. (2) Han, X.; Amrane, N.; Zhang, Z.; Benkraouda, M. Oxygen Vacancy Ordering and Electron Localization in CeO2: Hybrid Functional Study. J. Phys. Chem. C 2016, 120, 13325-13331. (3) Ganduglia-Pirovano, M. V.; Murgida, G. E.; Ferrari, V.; Llois, A. M. Comment on “Oxygen Vacancy Ordering and Electron Localization in CeO2: Hybrid Functional Study”. accepted J. Phys. Chem. C (4) Murgida, G. E.; Ferrari, V.; Ganduglia-Pirovano, M. V.; Llois, A. M. Ordering of Oxygen Vacancies and Excess Charge Localization in Bulk Ceria: A DFT+U Study, Phys. Rev. B 2014, 90, 115120. (5) Paier, J.; Penschke, C.; Sauer, J. Oxygen Defects and Surface Chemistry of Ceria: Quantum Chemical Studies Compared to Experiment, Chem. Rev. 2013, 113, 3949-3985. (6) Plata, J. J.; Marquez, A. M.; Sanz, J. F. Communication: Improving the Density Functional Theory+U Description of CeO2 by Including the Contribution of the O 2p Electrons. J. Chem. Phys. 2012, 136, 041101. (7) Hellman, O.; Skorodumova, N. V.; Simak, S. I. Charge Redistribution Mechanisms of Ceria Reduction. Phys. Rev. Lett. 2012, 108, 135504. (8) Molinari, M.; Parker, S. C.; Sayle, D. C.; Islam, M. S. Water Adsorption and Its Effect on the Stability of Low Index Stoichiometric and Reduced Surfaces of Ceria. J. Phys. Chem. C 2012, 116, 7073-7082. (9) Keating, P. R. L.; Scanlon, D. O.; Morgan, B. J.; Galea, N. M.; Watson, G. W. Analysis of Intrinsic Defects in CeO2 Using a Koopmans-Like GGA+U Approach. J. Phys. Chem. C 2012, 116, 2443-2452. (10) Kehoe, A. B.; Scanlon, D. O.; Watson, G. W. Role of Lattice Distortions in the Oxygen Storage Capacity of Divalently Doped CeO2. Chem. Mater. 2011, 23, 4464-4468.


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(11) Dholabhai, P. P.; Adams, J. B.; Crozier, P.; Sharma R. Oxygen Vacancy Migration in Ceria and Pr-doped Ceria: a DFT+U Study. J. Chem. Phys. 2010, 132, 094104. (12) Allen, J. P.; Watson, G. W. Occupation Matrix Control of d- and f-electron Localisations Using DFT + U. Phys. Chem. Chem. Phys. 2014, 16, 21016-21031. (13) Murgida G. E.; Ganduglia-Pirovano, M. V. Evidence for Subsurface Ordering of Oxygen Vacancies on the Reduced CeO2(111) Surface Using Density-Functional and Statistical Calculations. Phys. Rev. Lett. 2013, 110, 246101. (14) Pan, Y.; Nilius, N.; Freund, H. J.; Paier, J.; Penschke, C.; Sauer, J. Titration of Ce3+ Ions in the CeO2(111) Surface by Au Adatoms. Phys. Rev. Lett. 2013, 111, 206101. (15) Plata, J. J.; Marquez, A. M.; Sabz, J. F. Transport Properties in the CeO2–x(111) Surface: From Charge Distribution to Ion-Electron Collaborative Migration. J. Phys. Chem. C 2013, 117, 25497-25503. (16) Wuilloud, E.; Delley, B.; Schneider, W. D.; Baer, Y. Spectroscopic Evidence for Localized and Extended f-Symmetry States in CeO2. Phys. Rev. Lett. 1984, 53, 202. (17) Gschneider, K. A.; Eyring, L. Handbook on the Physics and Chemistry of Rare Earths; North-Holland: Amsterdam, Netherlands, 1979. (18) Arapan, S.; Simak, S. I.; Skorodumova, N. V. Volume-dependent Electron Localizationin Ceria. Phys. Rev. B 2015, 91, 125108. (19) Dorado, B.; Freyss, M.; Amadom, B.; Bertolus, M.; Jomard, G.; Garcia, P. Advances in firstprinciples modelling of point defects in UO2: f electron correlations and the issue of local energy minima. J. Phys.: Condens. Matter 2013, 25, 333201. (20) Meredig, B.; Thompson, A.; Hansen, H. A.; Wolverton, C.; van de Walle, A. Method for locating low-energy solutions within DFT+U. Phys. Rev. B 2010, 82, 195128.



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Table 1. The relative energy or vacancy formation energy for a single vacancy in 2×2×2 supercell of CeO2 for different Ce3+ distributions using HSE approach. Here nN-mN represents a pair of Ce3+ ions which are n-th and m-th nearest to the oxygen vacancy. For each nN-mN, up to the third nearest distances (1N, 2N and 3N) between Ce3+ ions (Ce3+-Ce3+) are considered in the Ce sublattice. Here we set the energy of 1N-1N configuration as a reference. Ce3+-Ce3+

Energy (eV)

1N-1N

1N

0

1N-2N

2N

0.097

1N-3N

1N

0.072

3N

0.164

1N

0.017

2N

0.086

3N

0.112

2N-3N

2N

0.189

3N-3N

1N

0.216

3N

0.375

2N-2N


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FIG. 1. Effect of U on the lattice constant a (a) and band gap (b) of CeO2. The Hubbard correction is applied to the 4f electrons. The dot lines represent the corresponding experimental values. For the sake of comparison, the corresponding HSE values are marked using red squares.


Comment on 'Oxygen Vacancy Ordering and Electron Localization in

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