First-principles<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>LDA</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant="normal">U</mml:mi></mml:mrow></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>GGA</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant="normal">U</mml:mi></mml:mrow></mml:math>study of cerium oxides: Dependence on the effective U parameter

Loschen, Christoph; Carrasco, Javier; Neyman, Konstantin M.; Illas, Francesc

doi:10.1103/physrevb.75.035115

Cited by 657 publications

(138 citation statements)

References 53 publications

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“…In this study, we used the GGA (generalized gradient approximation) functional PBE developed by Perdew et al 46 The DFT+U (LDA+U and GGA+U) methods have been shown to overcome the inability of LDA and GGA to describe the localized Ce4f electrons in ceria with reduced cerium ions. 21,22 The choice of the U parameter value was explored in several previous studies 21,[47][48][49][50] and it has been noted (Ref. 50 and elsewhere) that LDA+U actually provides a better overall description of ceria than GGA+U.…”

Section: Methods a Computational Detailsmentioning

confidence: 99%

Many competing ceria (110) oxygen vacancy structures: From small to large supercells

Kullgren

Hermansson

Castleton

2012

The Journal of Chemical Physics

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We present periodic "DFT+U" studies of single oxygen vacancies on the CeO 2 (110) surface using a number of different supercells, finding a range of different local minimum structures for the vacancy and its two accompanying Ce(III) ions. We find three different geometrical structures in combination with a variety of different Ce(III) localization patterns, several of which have not been studied before. The desired trapping of electrons was achieved in a two-stage optimization procedure. We find that the surface oxygen nearest to the vacancy either moves within the plane towards the vacancy, or rises out of the surface into either a symmetric or an unsymmetric bridge structure. Results are shown in seven slab geometry supercells, p(2 × 1), p(2 × 2), p(2 × 3), p(3 × 2), p(2 × 4), p(4 × 2), and p(3 × 3), and indicate that the choice of supercell can affect the results qualitatively and quantitatively. An unsymmetric bridge structure with one nearest and one next-nearest neighbour Ce(III) ion (a combination of localizations not previously found) is the ground state in all (but one) of the supercells studied here, and the relative stability of other structures depends strongly on supercell size. Within any one supercell the formation energies of the different vacancy structures differ by up to 0.5 eV, but the same structure can vary by up to ∼1 eV between supercells. Furthermore, finite size scaling suggests that the remaining errors (compared to still larger supercells) can also be ∼1 eV for some vacancy structures.

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Section: Methods a Computational Detailsmentioning

confidence: 99%

Many competing ceria (110) oxygen vacancy structures: From small to large supercells

Kullgren

Hermansson

Castleton

2012

The Journal of Chemical Physics

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“…Obviously, in order to optimize the engineering applications of the NPs, one must have a complete understanding of the atomic scale processes responsible for the properties of the NPs. Consequently, there have been a number of atomistic computer simulations of the ceria NPs [10][11][12], in addition to, of course, the considerable body of literature on the modelling of point defect properties, including electronic structure of the bulk structure and surfaces [13][14][15]. However, available computer resources have usually constrained the size of the NPs which could be modelled to those somewhat smaller than even the 2 nm range.…”

Section: Introductionmentioning

confidence: 99%

Simulations of ceria nanoparticles

et al. 2015

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Atomistic computer simulations, using classical potential models, have been used to model ceria nanoparticles (NPs) with diameters of approximately 1 and 2 nm. Lattice expansion is observed in the stoichiometric 1 nm NP, consistent with experiment, indicating that reduction is not the primary driver for such expansion. Furthermore, on reduction, the 1 nm NP is found to distort significantly, offering a possible explanation for its reduced oxygen storage capacity compared to the 2 nm NP. Point defect calculations on the 2 nm NP indicate that while doping with La is energetically favourable, Fe incorporation is not.

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“…The difficulty to correctly model the electronic structure of Ce 2 O 3 with GGA had already been pointed out by Skorodumova et al 54 One proposed solution has been to apply a Hubbard U on the cerium f-electrons. 55 While fitting a U value for Ce is beyond the scope of this work, we indeed observe the reaction energy getting closer to the experimental data by applying a moderate U value (U = 3 eV) on the f electrons in Ce for both CeCrO 3 and CeAlO 3 (see Table I). The other f-containing elements (i.e., U and La) do not show as large discrepancies as Ce (with the exception of one uranium based compound Cs 2 UO 4 ).…”

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confidence: 96%

Accuracy of density functional theory in predicting formation energies of ternary oxides from binary oxides and its implication on phase stability

et al. 2012

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The evaluation of reaction energies between solids using density functional theory (DFT) is of practical importance in many technological fields and paramount in the study of the phase stability of known and predicted compounds. In this work, we present a comparison between reaction energies provided by experiments and computed by DFT in the generalized gradient approximation (GGA), using a Hubbard U parameter for some transition metal elements (GGA+U). We use a data set of 135 reactions involving the formation of ternary oxides from binary oxides in a broad range of chemistries and crystal structures. We find that the computational errors can be modeled by a normal distribution with a mean close to zero and a standard deviation of 24 meV/atom. The significantly smaller error compared to the more commonly reported errors in the formation energies from the elements is related to the larger cancellation of errors in energies when reactions involve chemically similar compounds. This result is of importance for phase diagram computations for which the relevant reaction energies are often not from the elements but from chemically close phases (e.g., ternary oxides vs binary oxides). In addition, we discuss the distribution of computational errors among chemistries and show that the use of a Hubbard U parameter is critical to the accuracy of reaction energies involving transition metals even when no major change in formal oxidation state is occurring.

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First-principlesLDA+UandGGA+Ustudy of cerium oxides: Dependence on the effective U parameter

Cited by 657 publications

References 53 publications

Many competing ceria (110) oxygen vacancy structures: From small to large supercells

Many competing ceria (110) oxygen vacancy structures: From small to large supercells

Simulations of ceria nanoparticles

Accuracy of density functional theory in predicting formation energies of ternary oxides from binary oxides and its implication on phase stability

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