Bayesian Error Estimation in Density-Functional Theory

Mortensen, Jens Jørgen; Kaasbjerg, Kristen; Frederiksen, Søren Lund; Nørskov, Jens K.; Sethna, James P.; Jacobsen, Karsten Wedel

doi:10.1103/physrevlett.95.216401

Cited by 188 publications

(185 citation statements)

References 36 publications

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“…[29] Alloy data will be uploaded next, and as more accurate exchange-correlation functionals become available, such data will be made available as well. This will include data for reactions on oxide, carbide, nitride and sulfide surfaces.…”

Section: Figure 1 Screenshots From the App Two Leftmost Panels: N 2mentioning

confidence: 99%

CatApp: A Web Application for Surface Chemistry and Heterogeneous Catalysis

et al. 2011

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We introduce a web application (CatApp) for looking up calculated reaction and activation energies for elementary coupling reactions occurring on metal surfaces. It provides access to reaction and activation energies for all reactions involving C-C, C-H, C-O, O-O, O-H, N-N, C-N, O-N, N-H splittingSolid catalysts form the backbone of the chemical industry and the hydrocarbon-based energy sector. Most catalysts and processes today are highly optimized, but there is still considerable room for improvements in reactivity and selectivity that would lower energy consumption and waste production. In addition there are tremendous challenges to catalysis science and engineering in developing a sustainable energy solutions. The ability to store solar energy as a fuel calls for new catalysts and so does the development of a sustainable chemical industry based on biomass and other non-fossil building blocks.The development of new catalysts could be accelerated significantly if we had access to systematic data for activation energies of elementary surface reactions. Once the key parameters determining the activity or selectivity of a certain process has been established though experiments or calculations, such a database would enable searches for new catalyst leads. Ideally, data would come from detailed, systematic experiments, but it is in general not possible to find such data. Electronic structure calculations provide a powerful alternative. The accuracy is not such that detailed predictions of absolute rates of elementary reaction steps can be made, but for classes of interesting catalysts (transition metals) it is possible to create systematic data with sufficient accuracy to predict trends in reactivity. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] In the present paper, we introduce such a set of calculated reaction energies and activation energies for a large number of elementary surface reactions on a series of metal single crystal surfaces including surfaces with defects such as steps. We will also introduce a simple web application (CatApp) that can be downloaded to access these data.

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Section: Figure 1 Screenshots From the App Two Leftmost Panels: N 2mentioning

confidence: 99%

CatApp: A Web Application for Surface Chemistry and Heterogeneous Catalysis

et al. 2011

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“…20 In this way, they found the prediction uncertainty on lattice parameters to increase as a function of the lattice parameter itself. Finally, Mortensen et al 21 extracted error estimates per element by varying the generalized-gradient approximation (GGA) functional itself according to a Gaussian distribution. This distribution was tuned to a least-squares fit of DFT-GGA cohesive energies to experimental results.…”

Section: Introductionmentioning

confidence: 99%

Is the error on first-principles volume predictions absolute or relative?

Lejaeghere

Vanduyfhuys

Verstraelen

et al. 2016

Computational Materials Science

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Many benchmarks of density-functional theory with respect to experiment suggest the error on predicted equilibrium volumes to scale with the volume. Relative volume errors are therefore often used as a decisive argument to select one exchange-correlation functional over another. We show that the error on the volume (after correcting for systematic deviations) is only approximately relative. A simple analytic model, validated by rigorous Monte Carlo simulations, reveals that a more accurate error estimate can be derived from the inverse of the bulk modulus. This insight is not only instrumental for the selection or design of suitable functionals. It also calls for a new attitude towards computational errors: to report computational errors on electronic-structure calculations, identify systematic deviations and distinguish between relative and absolute effects.

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“…use the errors for small calibration molecules with different functionals to estimate an error based upon the difference between two (or more in principle) is not perfect, but reasonable; it has been used in a slightly different form earlier with LDA and PW91 functionals [42]. In principle one might be able to do better with a Bayesian method as suggested by Mortensen et al [43]. The accuracy that we argue the calculations have, ~0.25 eV per 1x1 unit cell, is probably the best that can be achieved with current DFT methods.…”

Section: Discussionmentioning

confidence: 99%

The small unit cell reconstructions of SrTiO3(111)

et al. 2009

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We analyze the basic structural units of simple reconstructions of the (111) surface of SrTiO 3 using density functional calculations. The prime focus is to answer three questions: what is the most appropriate functional to use; how accurate are the energies; what are the dominant low-energy structures and where do they lie on the surface phase diagram. Using test calculations of representative small molecules we compare conventional GGA with higher-order methods such as the TPSS meta-GGA and on-site hybrid methods PBE0 and TPSSh, the later being the most accurate. There are large effects due to reduction of the metal d oxygen sp hybridization when using the hybrid methods which are equivalent to a dynamical GGA+U, which leads to rather substantial improvements in the atomization energies of simple calibration molecules, even though the d-electron density for titanium compounds is rather small. By comparing the errors of the different methods we are able to generate an estimate of the theoretical error, which is about 0.25eV per 1x1 unit cell, with changes of 0.5-1.0 eV per 1x1 cell with the more accurate method relative to conventional GGA. An analysis of the plausible structures reveals an unusual low-energy TiO 2 -rich configuration with an unexpected distorted trigonal biprismatic structure. This structure can act as a template for layers of either TiO or Ti 2 O 3 , consistent with experimental results as well as, in principle, Magnelli phases. The results also suggest that both the fracture surface and the stoichiometric SrTiO 3 (111) surface should spontaneously disproportionate into SrO and TiO 2 rich domains, and show that there are still surprises to be found for polar oxide surfaces.

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Bayesian Error Estimation in Density-Functional Theory

Cited by 188 publications

References 36 publications

CatApp: A Web Application for Surface Chemistry and Heterogeneous Catalysis

CatApp: A Web Application for Surface Chemistry and Heterogeneous Catalysis

Is the error on first-principles volume predictions absolute or relative?

The small unit cell reconstructions of SrTiO3(111)

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