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Why is CeO 2 interesting? Why is CeO 2 awkward? What can we do about it….

How To Get DFT To Work for CeO 2 Christopher Castleton 1 , Jolla Kullgren 2 , Carsten Müller 3 , David Muñoz Ramo 4 , Amy Green 1 & Kersti Hermansson 2 1. Nottingham Trent University, UK 2. Uppsala University, Sweden 3. Free University Berlin, Germany 4. University College London, UK.

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Why is CeO 2 interesting? Why is CeO 2 awkward? What can we do about it….

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  1. How To Get DFT To Work for CeO2Christopher Castleton1, Jolla Kullgren2, Carsten Müller3, David Muñoz Ramo4 , Amy Green1 & Kersti Hermansson21. Nottingham Trent University, UK2. Uppsala University, Sweden3. Free University Berlin, Germany4. University College London, UK • Why is CeO2 interesting? • Why is CeO2 awkward? • What can we do about it…. • …. and a little of what we have done about it!

  2. Cerium Dioxide (CeO2, Ceria) Flourite Structure • Uses: Catalysis (esp car exhausts) • Fuel cells • Gas sensors • Replacement for SiO2 in CMOS • VOMost common defect • Create & remove easily • => “oxygen storage capacity”. • Anticipate double donor => VO+2 • …… but actually form as neutral VO+0….. • Ce2O3Can continuously remove oxygen to reach Ce2O3.

  3. Bands and Polarons in Ceria • Bands: Empty Ce:4f band lies between valence & conduction. • Localization: Electrons entering this localize on individual Ce ions. • => Local lattice distortion => a self trapped “polaron”. • Conductivity: Thermally activated polaron “hopping” …….. not band-like.

  4. Bands and Polarons in Ceria • Bands: Empty Ce:4f band lies between valence & conduction. • Localization: Electrons entering this localize on individual Ce ions. • => Local lattice distortion => a self trapped “polaron”. • Conductivity: Thermally activated polaron “hopping” …….. not band-like. • VO+0 “Donated” electrons stay very local. VO

  5. Bands and Polarons in Ceria • Bands: Empty Ce:4f band lies between valence & conduction. • Localization: Electrons entering this localize on individual Ce ions. • => Local lattice distortion => a self trapped “polaron”. • Conductivity: Thermally activated polaron “hopping” …….. not band-like. • VO+0 “Donated” electrons stay very local. • Ce2O3 One localized Ce:4f electron per Ce.

  6. Why is CeO2 Awkward? • Core e- : US-PP fails!1 Need PAW, with relatively hard Ce potential • or a small core ECP with an atomic basis.2 • Otherwise you get “ghost states.” • Functionals: LDA & GGA fail! • Supercells: Choice often controls the results…. • Localization: Many possible…. 1: Kresse et al. PRB 72, 237101 (2005) 2: Kullgren et al. JCP 132, 054110 (2010)

  7. Neutral VO: LDA vs LDA+U • Pure LDA: Ce4f electrons not localized. • LDA+U ≈ 6eV, Ce4f localized, level in gap1. • U choice is a compromise: Ce2O3 & some CeO2 gaps want smaller U, • other gaps larger… 1: Castleton et al. JCP 127, 244704 (2007)

  8. CeO2: LDA+U vs GGA+U • For ceria, GGA worsens LDA’s balance of correlation & exchange errors so • LDA beats GGA & LDA+U beats GGA+U

  9. CeO2 Hybrid Functionals • Mix Hartree Fock (exact exchange, NO correlation) • with LDA/GGA (partial exchange, partial correlation). • B3LYP has been popular for molecules, so … • Question: Does B3LYP work OK for ceria, & hence for molecules on ceria?1 • LDA+U does best.1 • B3LYP is better hybrid for electronic properties1 • PBE0 is better hybrid for structural properties1 1: Kullgren et al. JCP 132, 054110 (2010)

  10. Polarons in Ceria (II) • Can we study the dynamics of “free” polarons? • Using LDA+U => Maybe ….1 • Expt: ~0.5 eV 1: Castleton, Green et al. in preparation.

  11. Ceria (110) surface vacancies • Oxygens on (110) are paired. • Remove one, & the other moves, but previous authors didn’t agree how. Kullgren et al. Submitted to JCP

  12. Localization Patterns • Oxygens on (110) are paired. • Remove one, & the other moves, but previous work didn’t agree how. • The problem was, where do the Ce 4f electrons localize. • => many possibilities, all within about ~0.5 eV! • 1+2, 3+4, 3+6, 4+9, 7+8 => Bridge • 1+3, 1+4, 1+8, 3+5, => Distorted • 1+2 metastable alternative => In plane 1+4 4 • New Problem: • Energies of some patterns change by up to ~1 eV between different supercells. 1 Kullgren et al. Submitted to JCP

  13. NOT doing defect calculations. Problems with Supercells. => an infinite, ordered array of interacting “defects”. Question: How big are the errors compared to infinite supercell / lone vacancy?

  14. VASP, PAW, LDA, 200 eV planewave cut Assessing Supercell Errors. • Can assess errors by scaling with 1/L (supercell size). • In bulk: Errors ~ 1/L (length) & ~ 1/L3 (volume) • Effect on energetics can be VERY significant. Castleton et al. Modeling Simul. Mater. Sci. Eng. 17 084003 (2009)

  15. Ceria (110) surface supercells • Can’t manage p(4x4) supercell, so must • Check effect of defect images in x and y directions separately: Errors in p(2x2): X => 0.2 – 1.0 eV y => 0.0 – 0.1 eV When combined, the optimal localization changes: 4 4 1 3

  16. Summary • CeO2 • Interesting, but hard to treat, due to Ce 4f electron localization both times! • Core Electrons: • No US-PP, need small core PAW • Functionals: • LDA+U is best. • For hybrids B3LYP is better for electronic properties • PBE0 is better for structural properties • Surface Vacancies & Polarons: • Electron localization especially complex. • Supercells of a few 10s or 100s of atoms often cause errors of several eV.

  17. Core Electrons • Treat core electrons only as an average field (PAW or ECP) • ECP: 46 electrons in the core has a ghost state: need 28 electron ECPs. • PAW: 46 electrons in the core has a ghost state: need 28 electron ECPs.

  18. Band gaps U values

  19. InP Defects Scaling

  20. InP Defects Scaling (Neutral)

  21. CeO2: LDA vs LDA+U • Pure LDA: Ce4f electrons not localized. • LDA+U ≈ 6eV, Ce4f localized, level in gap. • Choice not unique: Ce2O3 & some CeO2 gaps want smaller, other gaps larger… • Sledgehammer method: Messes with other electrons & worsens O2p => Ce5d gap. • Pure LDA is best if have no Ce4f electrons!

  22. CeO2 Hybrid Functionals • Mix Hartree Fock (exact exchange, NO correlation) • with LDA/GGA (partial exchange, partial correlation). • B3LYP has been popular for molecules, so … • Question: Does B3LYP work OK for ceria, & hence for molecules on ceria?1 Ce2O3 1: Kullgren et al. JCP 132, 054110 (2010)

  23. Hybrid Functionals • Mix Hartree Fock (exact exchange, NO correlation) • with LDA/GGA (partial exchange, partial correlation). • B3LYP has been popular for molecules, so … • Question: Does B3LYP work OK for ceria, & hence for molecules on ceria?1 • LDA+U does best.1 • B3LYP is better hybrid for electronic properties1 • PBE0 is better hybrid for structural properties1 1: Kullgren et al. JCP 132, 054110 (2010)

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