A Hybrid Density Functional Theory Investigation of the \(({\text {CeO}}_2)_{6}\) Clusters in the Cationic, Neutral, and Anionic States

  • Mailde S. Ozório
  • Augusto C. H. Da Silva
  • Juarez L. F. Da SilvaEmail author
Original Paper


We report a quantum-chemistry investigation of the cationic, neutral, and anionic \(({\text {CeO}}_2)_{6}\) clusters to obtain an atom-level understanding of the effects induced by the release or addition of a single electron on the physical and chemical properties of small oxide clusters. Our ab initio calculations are based on density functional theory (DFT) within the hybrid Heyd–Scuseria–Ernzerhof (HSE06) and semilocal Perdew–Burke–Ernzerhof (PBE) functional. Compared with PBE, the HSE06 functional changes the relative stability of the neutral \(({\text {CeO}}_2)_{6}\) isomers, in particular, for structures with small total energy differences, e.g., about \(100 \, \text {meV/fu}\), which can be explained by the enhancement of the exchange interactions. The addition of an electron to the \(({\text {CeO}}_2)_{6}\) clusters change the oxidation state of a single \(\text {Ce}\) atom from + IV to + III, which drives a local distortion and the formation of a small polaron near to the \({\text {Ce}}^{\text{III}}\) cation. In contrast, the release of an electron induces the formation of a localized hole on one of the \(\text {O}\) atoms combined with local structural distortions. For the anionic and cationic clusters in the putative global minimum configurations, we found a strain energy induced by the distortion of 1.00 and 1.31 eV, respectively.


Cerium oxide Clusters Density functional theory 



density functional theory






Fritz–Haber Institute ab initio molecular simulations



The authors gratefully acknowledge support from FAPESP (São Paulo Research Foundation, Grant Number 2017/11631-2), Shell and the strategic importance of the support given by ANP (Brazils National Oil, Natural Gas and Biofuels Agency) through the R&D levy regulation. This study was financed in part by the National Counsel of Technological and Scientific Development (fellowships for Mailde S. Ozório and Augusto C. H. Da Silva). The authors acknowledge also the National Laboratory for Scientific Computing (LNCC/MCTI, Brazil) for providing HPC resources of the SDumont supercomputer, which have contributed to the research results reported within this paper. We acknowledges also the Advanced Scientific Computational Laboratory (University of São Paulo) and the infrastructure provided to our computer cluster by the São Carlos Center of Informatics, University of São Paulo.

Supplementary material

10876_2019_1728_MOESM1_ESM.pdf (15.5 mb)
Supplementary material 1 (PDF 154 kb)


  1. 1.
    Q. Fu, H. Saltsburg and M. Flytzani-Stephanopoulos (2003). Active nonmetallic Au and Pt species on ceria-based water-gas shift catalysts. Science301, 935–938.CrossRefGoogle Scholar
  2. 2.
    R. J. Gorte (2010). Ceria in catalysis: from automotive applications to the water-gas shift reaction. AlChE J. 56, 1126–1135.Google Scholar
  3. 3.
    A. F. Diwell, R. R. Rajaram, H. A. Shaw and T. J. Truex (1991). The role of ceria in three-way catalysts. Stud. Surf. Sci. Catal. 71, 139–152.CrossRefGoogle Scholar
  4. 4.
    A. Trovarelli Catalysis by ceria and related materials, 1st ed (World Scientific Publishing Company, Singapore, 2002).CrossRefGoogle Scholar
  5. 5.
    A. Beste and S. H. Overbury (2015). Pathways for ethanol dehydrogenation and dehydration catalyzed by ceria (111) and (100) surfaces. J. Phys. Chem. C2015, 2447–2455.CrossRefGoogle Scholar
  6. 6.
    Z.-X. Zhou, L.-N. Wang, Z.-Y. Li, S.-G. He and T.-M. Ma (2016). Oxidation of \({\text{ SO }}_{2}\) to \({\text{ SO }}_{3}\) by cerium oxide cluster cations \({\text{ Ce }}_{2} {\text{ O }}_{4}{}^{+}\) and \({\text{ Ce }}_{3} {\text{ O }}_{6}{}^{+}\). J. Phys. Chem. C120, 3843–3848.CrossRefGoogle Scholar
  7. 7.
    X.-L. Ding, X.-N. Wu, Y.-X. Zhao, J.-B. Ma and S.-G. He (2011). Double-oxygen-atom transfer in reactions of \({\text{ Ce }}_{m} {\text{ O }}_{2m} {}^{+}\) (m= 2–6) with \({\text{ C }}_{2} {\text{ H }}_{2}\). ChemPhysChem12, 2110–2117.CrossRefGoogle Scholar
  8. 8.
    S. Hirabayashi and M. Ichihashi (2013). Oxidation of CO and NO on composition-selected cerium oxide cluster cations. J. Phys. Chem. A117, 9005–9010.CrossRefGoogle Scholar
  9. 9.
    J. A. Felton, M. Ray, S. E. Waller, J. O. Kafader and C. C. Jarrold (2014). \({\text{ Ce }}_{x} {\text{ O }}_{y} - (\text{ x }= 2{-}3) + {\text{ D }}_2\text{ O }\) reactions: stoichiometric cluster formation from deuteroxide decomposition and anti-arrhenius behavior. J. Phys. Chem. A118, 9960–9969.CrossRefGoogle Scholar
  10. 10.
    I. E. Wachs and K. Routray (2012). Catalysis science of bulk mixed oxides. ACS Catal. 2, 1235–1246.CrossRefGoogle Scholar
  11. 11.
    M. V. Ganduglia-Pirovano, J. L. F. Da Silva and J. Sauer (2009). Density functional calculations of the structure of near-surface oxygen vacancies and electron localization \(\text{ CeO }_2\)(111). Phys. Rev. Lett. 102, 026101.CrossRefGoogle Scholar
  12. 12.
    L. Sun, X. Huang, L. Wang and A. Janotti (2017). Disentangling the role of small polarons and oxygen vacancies in \({\text{ CeO }}_{2}\). Phys. Rev. B95, 245101.CrossRefGoogle Scholar
  13. 13.
    J. L. F. Da Silva, M. V. Ganduglia-Pirovano, J. Sauer, V. Bayer and G. Kresse (2007). Hybrid functionals applied to rare-earth oxides: the example of ceria. Phys. Rev. B75, 045121.CrossRefGoogle Scholar
  14. 14.
    M. J. Piotrowski, P. Tereshchuk and J. L. F. Da Silva (2014). Theoretical investigation of small transition-metal clusters supported on the \({\text{ CeO }}_{2}\)(111) surface. J. Phys. Chem. C188, 21438–21446.CrossRefGoogle Scholar
  15. 15.
    P. Tereshchuk, R. L. H. Freire, C. G. Ungureanu, Y. Seminovski, A. Kiejna and J. L. F. Da Silva (2015). The role of charge transfer in the oxidation state change of Ce atoms in the \({\text{ TM }}_{13} - {\text{ CeO }}_{2}\)(111) systems (\(\text{ TM } = \text{ Pd }, \text{ Ag }, \text{ Pt }, \text{ Au }\)): A DFT+U investigation. Phys. Chem. Chem. Phys. 17, 13520–13530.CrossRefGoogle Scholar
  16. 16.
    T. Nagata, J. W. J. Wu, M. Nakano, K. Ohshimo and F. Misaizu (2019). Geometrical structures of gas-phase cerium oxide cluster cations studied by ion mobility mass spectrometry. J. Phys. Chem. C123, 16641–16650.CrossRefGoogle Scholar
  17. 17.
    S. T. Akin, S. G. Ard, B. E. Dye, H. F. Schaefer and M. A. Duncan (2016). Photodissociation of cerium oxide nanocluster cations. J. Phys. Chem. A120, 2313–2319.CrossRefGoogle Scholar
  18. 18.
    A. M. Burow, T. Wende, M. Sierka, R. Włodarczyk, J. Sauer, P. Claes, L. Jiang, G. Meijer, P. Lievens and K. R. Asmis (2011). Structures and vibrational spectroscopy of partially reduced gas-phase cerium oxide clusters. Phys. Chem. Chem. Phys. 13, 19393–19400.CrossRefGoogle Scholar
  19. 19.
    L. Zibordi-Besse, Y. Seminovski, I. Rosalino, D. Guedes-Sobrinho and J. L. F. D. Silva (2018). Physical and chemical properties of unsupported \(({\text{ MO }}_2)_{n}\) clusters for M = Ti, Zr, or \(\text{ Ce }\) and n = 1–15: a density functional theory study combined with the tree-growth scheme and euclidean similarity distance algorithm. J. Phys. Chem. C122, 27702–27712.CrossRefGoogle Scholar
  20. 20.
    C. Chuan, C. Hui-Lung, W. Meng-Hsiung, J. Shin-Pon, J.-G. Chang and C.-S. Chang (2008). Structural properties of \(({\text{ CeO }}_2)_{n}\) (n= 1–5) nanoparticle: molecular mechanics and first principle studies. Chin. J. Catal. 29, 1117–1121.CrossRefGoogle Scholar
  21. 21.
    S. F. Li, H. Lu, P. Li, Z. Yang and Z. X. Guo (2008). First-principles local density approximation (generalized gradient approximation) + U study of catalytic \({\text{ Ce }}_{n} {\text{ O }}_{m}\) clusters: U value differs from bulk. J. Chem. Phys. 128, 164718.CrossRefGoogle Scholar
  22. 22.
    J. Heyd, G. E. Scuseria and M. Ernzerhof (2003). Hybrid functionals based on a screened coulomb potential. J. Chem. Phys. 118, 8207–8215.CrossRefGoogle Scholar
  23. 23.
    J. P. Perdew, K. Burke and M. Ernzerhof (1996). Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868.CrossRefGoogle Scholar
  24. 24.
    V. Blum, R. Gehrke, F. Hanke, P. Havu, V. Havu, X. Ren, K. Reuter and M. Scheffler (2009). Ab initio molecular simulations with numeric atom-centered orbitals. Comput. Phys. Commun. 180, 2175–2196.CrossRefGoogle Scholar
  25. 25.
    V. Havu, V. Blum, P. Havu and M. Scheffler (2009). Efficient \(O(N)\) integration for all-electron electronic structure calculation using numeric basis functions. J. Comput. Phys. 228, 8367–8379.CrossRefGoogle Scholar
  26. 26.
    M. Chen and D. A. Dixon (2013). Tree growth—hybrid genetic algorithm for predicting the structure of small \(({\text{ TiO }}_2)_{n}\), \(n = 2-13\). Nanoclusters. J. Chem. Theory Comput. 9, 3189–3200.CrossRefGoogle Scholar
  27. 27.
    R. Gehrke and K. Reuter (2009). Assessing the efficiency of first-principles basin-hopping sampling. Phys. Rev. B79, 085412.CrossRefGoogle Scholar
  28. 28.
    H. M. Cezar, G. G. Rondina and J. L. F. Da Silva (2017). Parallel tempering monte carlo combined with clustering euclidean metric analysis to study the thermodynamic stability of Lennard–Jones nanoclusters. J. Chem. Phys. 146, 064114.CrossRefGoogle Scholar
  29. 29.
    J. Nocedal, J. Stephen and S. J. Wright Numerical optimization (Springer, Berlin, 2006).Google Scholar
  30. 30.
    J. L. F. Da Silva (2011). Effective coordination concept applied for phase change \((\text{ GeTe })_{m}~({\text{ Sb }}_2 {\text{ Te }}_3)_{n}\) compounds. J. Appl. Phys. 109, 023502.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Mailde S. Ozório
    • 1
  • Augusto C. H. Da Silva
    • 1
  • Juarez L. F. Da Silva
    • 1
    Email author
  1. 1.São Carlos Institute of ChemistryUniversity of São PauloSão CarlosBrazil

Personalised recommendations