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Unlocking the Potential of Cerium Dioxide: How to Optimize DFT for CeO2 Studies

Learn about the challenges and solutions of working with Cerium Dioxide (CeO2) in DFT calculations, exploring its unique properties such as defects, bands, and polarons. Discover the intricacies of CeO2 and how to overcome computational hurdles to advance research in catalysis, fuel cells, and more.

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Unlocking the Potential of Cerium Dioxide: How to Optimize DFT for CeO2 Studies

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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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