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

Computational materials design

Falsig, Shen, Khan, Guo, Jones, Dahl, Bligaard, Topics in Catalysis (2013)

NO decomposition

Tuesday, May 21, 13

XC model compromise

Wellendorff, Lundgaard, Møgelhøj, Petzold, Landis, Nørskov, Bligaard, Jacobsen,Phys. Rev. B 85, 235149 (2012)

Tuesday, May 21, 13

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

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

Ensemble prediction in weather forecasting

http://www.wpc.ncep.noaa.gov/ensembletraining/

Tuesday, May 21, 13

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)

Tuesday, May 21, 13

Error-estimation ensemble

K. Kaasbjerg, Master Thesis, DTU (June 2005)

Tuesday, May 21, 13

Bulk Cu cohesive energy and structural energy difference

Skriver, PRB 31, 1909 (1985)

Mortensen, Kaasbjerg, Frederiksen, Nørskov, Sethna, Jacobsen,PRL 95, 216401 (2005)

Tuesday, May 21, 13

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

Tuesday, May 21, 13

Physisorption of n-Alkanes in ZSM-22

Brogaard, Moses, Nørskov, Catalysis Letters 142, 1057 (2012)

Tuesday, May 21, 13

BEEF-vdW error-estimation ensemble

Tuesday, May 21, 13

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()

Tuesday, May 21, 13

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

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

Tuesday, May 21, 13

CO adsorption on Rh(111)

Tuesday, May 21, 13

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

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

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

CollaboratorsKeld LundgaardKarsten W. JacobsenJens K. NørskovThomas Bligaard

Center for Atomic-scale Materials Design

Thanks!

OrganizationsCAMDSUNCAT

U.S. Department of EnergyOffice of Basic Energy Sciences

Tuesday, May 21, 13

Tuesday, May 21, 13

A meta-GGA functional: mBEEF

Wellendorff, Lundgaard, Jacobsen, Bligaard (2013)

Tuesday, May 21, 13

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

Tuesday, May 21, 13

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