exchange-correlation functionals with error estimation
TRANSCRIPT
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Jess WellendorffSUNCAT Center for Interface Science and CatalysisSLAC National Accelerator Laboratory
Electronic structure calculations with the GPAW code: Users and developers meetingTechnical University of Denmark, May 21-23, 2013
Development and applications of ensembleerror-estimation xc functionals in computationalsurface science
Tuesday, May 21, 13
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Computational materials design
Falsig, Shen, Khan, Guo, Jones, Dahl, Bligaard, Topics in Catalysis (2013)
NO decomposition
Tuesday, May 21, 13
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XC model compromise
Wellendorff, Lundgaard, Møgelhøj, Petzold, Landis, Nørskov, Bligaard, Jacobsen,Phys. Rev. B 85, 235149 (2012)
Tuesday, May 21, 13
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Ammonia synthesis on Ru
XC = x⋅RPBE + (1 - x )⋅PW91
Honkala et al., Science 307, 555 (2005)
x → 0:- barriers decrease.- adsorption energies increase.
- N2 dissociation becomes muchfaster, but the coverage of free sites also decrease.- total rate is rather insensitive.
Tuesday, May 21, 13
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XC = x⋅RPBE + (1 - x )⋅PW91
Honkala et al., Science 307, 555 (2005)
x → 0:- barriers decrease.- adsorption energies increase.
- N2 dissociation becomes muchfaster, but the coverage of free sites also decrease.- total rate is rather insensitive.
Questions:- What is the influence on scientific conclusions of inherent variations in DFT predictions?- How can we reliably estimate the errors of GGA-DFT?
Ammonia synthesis on Ru
Tuesday, May 21, 13
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Ensemble prediction in weather forecasting
http://www.wpc.ncep.noaa.gov/ensembletraining/
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Ensemble XC functionals
GGA XC model space
Probability distribution for the model parameters
Quadratic cost function to be minimized
Mortensen, Kaasbjerg, Frederiksen, Nørskov, Sethna, Jacobsen,PRL 95, 216401 (2005)
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Error-estimation ensemble
K. Kaasbjerg, Master Thesis, DTU (June 2005)
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Bulk Cu cohesive energy and structural energy difference
Skriver, PRB 31, 1909 (1985)
Mortensen, Kaasbjerg, Frederiksen, Nørskov, Sethna, Jacobsen,PRL 95, 216401 (2005)
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BEEF-vdW density functional
0.19
eV0.
59eV
0.90
eV0.
27eV
0.24
eV0.
28eV
1.44
eV0.
21eV
G3
0.16
eV0.
11eV
0.40
eV0.
38eV
0.18
eV0.
20eV
0.45
eV
CE27
0.26
eV0.
27eV
0.33
eV0.
35eV
0.28
eV0.
31eV
0.37
eV0.
17eV
DBH24/08
0.29
eV0.
26eV
0.30
eV0.
33eV
0.39
eV0.
40eV
0.26
eV0.
15eV
RE42
0.45
eV0.
58eV
0.27
eV0.
37eV
0.60
eV0.
64eV
0.25
eVSol27Ec
0.08
A0.
11A
0.06
A0.
04A
0.12
A0.
14A
0.08
A
Sol27Lc
50m
eV13
8m
eV76
meV
92m
eV52
meV
33m
eV10
meV
111
meV
S22x5
Scaled MAD BEEF-vdWRPBE
PBErevTPSS
vdW-DFvdW-DF2
optB88-vdWB3LYP
GGA+vdW model space
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Physisorption of n-Alkanes in ZSM-22
Brogaard, Moses, Nørskov, Catalysis Letters 142, 1057 (2012)
Tuesday, May 21, 13
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BEEF-vdW error-estimation ensemble
Tuesday, May 21, 13
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It’s really fast and simple!
>>> from gpaw import GPAW>>> from ase.dft.bee import BEEF_Ensemble
>>> calc = GPAW(gpw)>>> ens = BEEF_Ensemble(calc)>>> de = ens.get_ensemble_energies()
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It’s really fast and simple!
>>> from gpaw import GPAW>>> from ase.dft.bee import BEEF_Ensemble
>>> calc = GPAW(gpw)>>> ens = BEEF_Ensemble(calc)>>> de = ens.get_ensemble_energies()
GPAW:non-self-consistent xc contributions
Tuesday, May 21, 13
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It’s really fast and simple!
>>> from gpaw import GPAW>>> from ase.dft.bee import BEEF_Ensemble
>>> calc = GPAW(gpw)>>> ens = BEEF_Ensemble(calc)>>> de = ens.get_ensemble_energies()
VASP, Quantum Espresso: Johannes Voss @ SUNCAT
GPAW:non-self-consistent xc contributions
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CO adsorption on Rh(111)
Tuesday, May 21, 13
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Sensitivity of reactivity volcanos: NO decomposition
What is the probability that a certain metal/alloy will be more active than Pt for direct NO decomposition?
Khan, Lundgaard, Wellendorff, Nørskov, Jacobsen, Bligaard (2013)
Distributions of ensemble predictions relative to Pt(111)
Tuesday, May 21, 13
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Sensitivity of reactivity volcanos: NO decomposition
What is the probability that a certain metal/alloy will be more active than Pt for direct NO decomposition?
Tuesday, May 21, 13
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Summary and outlook
- A BEEF ensemble of xc functionals offers a systematic and quantitative framework for assessing the sensitivity of scientific conclusions within the chosen XC model space, e.g., GGA+vdW.
- Probabilistic volcano plots should be particularly useful in computational catalysis.
- Work continues in the SUNCAT theory group towards ensemble functionals for surface science that include
metaGGA exchange, non-local correlation, and screened exact exchange.
Tuesday, May 21, 13
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CollaboratorsKeld LundgaardKarsten W. JacobsenJens K. NørskovThomas Bligaard
Center for Atomic-scale Materials Design
Thanks!
OrganizationsCAMDSUNCAT
U.S. Department of EnergyOffice of Basic Energy Sciences
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A meta-GGA functional: mBEEF
Wellendorff, Lundgaard, Jacobsen, Bligaard (2013)
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Non-covalent interactions: electrostatics vs. dispersion
GGAs and MGGAs can capture hydrogen bonding quite well, but higher-level theory is needed for long-range dispersion, e.g. non-local correlation functionals or RPA.
S66x8 data set: Rezac Riley, Hobza, J. Chem. Theory Comput. 7, 2427 (2011)
Disp/Elec = 0.29 Disp/Elec = 3.44
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Non-covalent interactions: electrostatics vs. dispersion
Disp/Elec = 0.29 Disp/Elec = 3.44
In progress: mBEEF-vdW
S66x8 data set: Rezac Riley, Hobza, J. Chem. Theory Comput. 7, 2427 (2011)
GGAs and MGGAs can capture hydrogen bonding quite well, but higher-level theory is needed for long-range dispersion, e.g. non-local correlation functionals or RPA.
Tuesday, May 21, 13