and something else…
Mikkel Strange (but presented by Karsten W. Jacobsen)
European Centre of Excellence (CoE)
Overview of current projects• Creating a big database for:
DFT + Excited states + Molecular dynamics (writing parsers)
• Error bars in DFT calculations (finite basis set) Useful for comparing calculations, or not?
• Self-consistent hybrid functionals
Outline
• Brief overview of the NOMAD project.
• “Parsers” that converts output from electronic structure codes to a common format
• “Error bars” from basis and k-point sampling
• Self-consistent hybrid functionals in GPAW
NOMAD overview
• Virtual reality (fx: exciton (r,r’)) • Remote visualisation
(structures, wave-functions, etc)
• Stores your data for at least 10 years
• Advanced analysis tools (machine learning etc)
3,027,865 calculations today
Nomad: Producing dataRepository:
output files from all codes are
welcome (file.gpw)
Archive:common data
format (contains
everything that is in the output files)
50 most cited codes (GPAW, VASP, Gaussian,
ASAP…)
Conversion
http://nomad-repository.eu/cms/
Big data analytics Materials Encyclopedia
…
Nomad: Producing dataParsers done at DTU for: • GPAW | works • MOPAC | works • ASAP | works • ATK | not started • GROMACS | created
All data should be parsed: Structures Energies
Electron density Wave functions
SCF iteration time Force field information
Constraints …Start uploading your
favourite GPAW gpw filescome June 15th!
Error bars project
Next step: something about the error due to:• finite basis set • k-point sampling • other numerical settings?
Should be useful for judging the quality of data in the NOMAD database
RESEARCH ARTICLE SUMMARY◥
DFT METHODS
Reproducibility in density functionaltheory calculations of solidsKurt Lejaeghere,* Gustav Bihlmayer, Torbjörn Björkman, Peter Blaha, Stefan Blügel,Volker Blum, Damien Caliste, Ivano E. Castelli, Stewart J. Clark, Andrea Dal Corso,Stefano de Gironcoli, Thierry Deutsch, John Kay Dewhurst, Igor Di Marco, Claudia Draxl,Marcin Dułak, Olle Eriksson, José A. Flores-Livas, Kevin F. Garrity, Luigi Genovese,Paolo Giannozzi, Matteo Giantomassi, Stefan Goedecker, Xavier Gonze, Oscar Grånäs,E. K. U. Gross, Andris Gulans, François Gygi, D. R. Hamann, Phil J. Hasnip,N. A. W. Holzwarth, Diana Iuşan, Dominik B. Jochym, François Jollet, Daniel Jones,Georg Kresse, Klaus Koepernik, Emine Küçükbenli, Yaroslav O. Kvashnin,Inka L. M. Locht, Sven Lubeck, Martijn Marsman, Nicola Marzari, Ulrike Nitzsche,Lars Nordström, Taisuke Ozaki, Lorenzo Paulatto, Chris J. Pickard, Ward Poelmans,Matt I. J. Probert, Keith Refson, Manuel Richter, Gian-Marco Rignanese, Santanu Saha,Matthias Scheffler, Martin Schlipf, Karlheinz Schwarz, Sangeeta Sharma,Francesca Tavazza, Patrik Thunström, Alexandre Tkatchenko, Marc Torrent,David Vanderbilt, Michiel J. van Setten, Veronique Van Speybroeck, John M.Wills,Jonathan R. Yates, Guo-Xu Zhang, Stefaan Cottenier*
INTRODUCTION:The reproducibility of resultsis one of the underlying principles of science. Anobservation canonly be accepted by the scientificcommunity when it can be confirmed by inde-pendent studies. However, reproducibility doesnot come easily. Recent works have painfullyexposed cases where previous conclusionswerenot upheld. The scrutiny of the scientific com-munity has also turned to research involvingcomputer programs, finding that reproducibil-ity depends more strongly on implementationthan commonly thought. These problems areespecially relevant for property predictions ofcrystals and molecules, which hinge on precisecomputer implementations of the governingequation of quantum physics.
RATIONALE:Thiswork focuses ondensity func-tional theory (DFT), a particularly popular quan-
tum method for both academic and industrialapplications. More than 15,000 DFT papers arepublished each year, and DFT is now increas-ingly used in an automated fashion to buildlarge databases or applymultiscale techniqueswith limited human supervision. Therefore, thereproducibility of DFT results underlies thescientific credibility of a substantial fraction ofcurrent work in the natural and engineeringsciences. A plethora of DFT computer codesare available, many of them differing consid-erably in their details of implementation, andeach yielding a certain “precision” relative toother codes. How is one to decide formore thana few simple cases which code predicts the cor-rect result, and which does not? We devised aprocedure to assess the precision of DFT meth-ods and used this to demonstrate reproduci-bility among many of the most widely used
DFT codes. The essential part of this assessmentis a pairwise comparison of a wide range ofmethodswith respect to their predictions of theequations of state of the elemental crystals. Thiseffort required the combined expertise of a largegroup of code developers and expert users.
RESULTS:We calculated equation-of-state datafor four classes of DFT implementations, total-ing 40 methods. Most codes agree very well,with pairwise differences that are comparableto those between different high-precision exper-
iments. Even in the case ofpseudization approaches,which largely depend ontheatomic potentials used,a similar precision can beobtainedaswhenusing thefull potential. The remain-
ing deviations are due to subtle effects, such asspecific numerical implementations or the treat-ment of relativistic terms.
CONCLUSION: Our work demonstrates thatthe precision of DFT implementations can bedetermined, even in the absence of one absolutereference code. Although this was not the case 5to 10 years ago,most of the commonlyused codesand methods are now found to predict essen-tially identical results. The established precisionof DFT codes not only ensures the reproducibilityof DFT predictions but also puts several past andfuture developments on a firmer footing. Anynewly developedmethodology can nowbe testedagainst the benchmark to verify whether itreaches the same level of precision. NewDFT ap-plications can be shown to have used a suffi-ciently precise method.Moreover, high-precisionDFT calculations are essential for developing im-provements to DFTmethodology, such as newdensity functionals, whichmay further increasethe predictive power of the simulations.▪
RESEARCH
SCIENCE sciencemag.org 25 MARCH 2016 • VOL 351 ISSUE 6280 1415
The list of author affiliations is available in the full article online.*Corresponding author. E-mail: [email protected] (K.L.);[email protected] (S.C.)Cite this article as K. Lejaeghere et al., Science 351, aad3000(2016). DOI: 10.1126/science.aad3000
Recent DFTmethods yield reproducible results.Whereas older DFT implementations predict different values (red darts), codes have now evolved tomutual agreement (green darts).The scoreboard illustrates the good pairwise agreement of four classes of DFT implementations (horizontal direction)with all-electron results (vertical direction). Each number reflects the average difference between the equations of state for a given pair of methods,withthe green-to-red color scheme showing the range from the best to the poorest agreement.
ON OUR WEB SITE◥
Read the full articleat http://dx.doi.org/10.1126/science.aad3000..................................................
on
June
1, 2
016
http
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ienc
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.org
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Delta DFT:DFT codes can be converged to good agreement
Error bars projectSome simple questions
• Is convergence with k-points and basis set independent?
• Can we give error estimates?
Error bars project
1 225
H
LiH
3 225
Li
LiF
11 225
Na
Nacl
19 225
K
KCl
37 225
Rb
RbCl
55 225
Cs
CsCl
87
Fr
4 216
Be
BeS
12 225
Mg
MgO
20 225
Ca
CaO
38 225
Sr
SrO
56 225
Ba
BaO
88 225
Ra
RaF
21 225
Sc
ScS
39 225
Y
YN
57-71
La-Lu
Lanthanide
89-103
Ac-Lr
Actinide
22 225
Ti
TiN
40 225
Zr
ZrC
72 225
Hf
HfC
104
Rf
23 225
V
VC
41 225
Nb
NbC
73 225
Ta
TaC
105
Db
24 225
Cr
CrN
42 187
Mo
MoC
74 187
W
WC
106
Sg
25 225
Mn
MnS
43 14
Tc
TcO2
75 221
Re
ReO
107
Bh
26 225
Fe
FeO
44 136
Ru
RuO
76 187
Os
BOs
108
Hs
27 225
Co
CoO
45 136
Rh
RhO
77 136
Ir
IrO
109
Mt
28 225
Ni
NiO
46 131
Pd
PdO
78 131
Pt
PtO
110
Ds
29 216
Cu
CuBr
47 225
Ag
AgCl
79 224
Au
Au2S
111
Rg
30 216
Zn
ZnO
48 225
Cd
CdO
80 225
Hg
HgF
112
Uub
31 216
Ga
GaP
13 216
Al
AlP
5 194
B
BN
49 216
In
InP
81 225
Tl
TlCl
113
Uut
6 225
C
TiC
14 216
Si
SiC
32 160
Ge
TeGe
50 62
Sn
SnS
82 225
Pb
PbS
114
Uuq
7 225
N
VN
15 216
P
InP
33 216
As
GaAS
51 216
Sb
InSb
83 215
Bi
BiF5
115
Uup
8 225
O
CdO
16 216
S
ZnS
34 186
Se
CdSe
52 216
Te
ZnTe
84 225
Po
PoO
116
Uuh
9 225
F
NaF
17 216
Cl
CuCl
35 225
Br
KBr
53 225
I
LiI
85
At
117
Uus
10
Ne
2
He
18
Ar
36
Kr
54
Xe
86
Rn
118
Uuo
1
2
3
4
5
6
7
1 IA
2 IIA
3 IIIA 4 IVB 5 VB 6 VIB 7 VIIB 8 VIIIB 9 VIIIB 10 VIIIB 11 IB 12 IIB
13 IIIA 14 IVA 15 VA 16 VIA 17 VIIA
18 VIIIA
57 176
La
LaCl
58 225
Ce
CeN
59 225
Pr
PrN
60 225
Nd
NdN
61 164
Pm
PmO2
62 225
Sm
SmN
63 225
Eu
EuN
64 225
Gd
GdN
65 225
Tb
TbN
66 225
Dy
DyN
67 225
Ho
HoN
68 225
Er
ErN
69 225
Tm
TmN
70 225
Yb
YbN
71 225
Lu
Lu
89 176
Ac
AcCl
90 225
Th
ThC
91
Pa
92
U
93
Np
94
Pu
95
Am
96
Cm
97
Bk
98
Cf
99
Es
100
Fm
101
Md
102
No
103
LrZ Spacegroup
Symbol
Binary solid
notused
Periodic Table of Chemical Elements for Binary solids
Codes: GPAW | PW | DTU
VASP | PW | TU Graz Exciting | LAPW | HU Berlin
AIMS | NAO | FHI Berlin
Properties:Structures Energies
Band gaps
Functional: PBE and LDA 90 Binary solids 73 Elemental (from ∆DFT) -> ~5000 calculations
(+ random systems from the NOMAD database)
Error bars projectTotal energies (binaries): light vs really tight basis
AIMS
-12 -10 -8 -6 -4 -2 0Etot (Ec=400eV) (eV)
-12
-10
-8
-6
-4
-2
0
E tot
(Ec=
1600
eV) (
eV)
kdens=4, error: 7.08%kdens=6, error: 7.07%kdens=8, error: 7.07%
GPAW
Error from k-point sampling looks “small” compared to basis set
Error bars projectTotal energies (binaries)
Things really improve at Ecut = 600eV!
MAE: Mean absolute error MAXAE: Max absolute error MAPE: Mean absolute percentage error
Error bars projectCohesive energies (binaries)
Energy differences benefit from error cancelation
MAE: Mean absolute error MAXAE: Max absolute error MAPE: Mean absolute percentage error
Error bars project
N
O
F
Elemental solids
N, O and F are the bad guys!
Error bars projectBinaries without
N, O and F
N, O and F are the bad guys!
Binaries
Error bars project
400 800 1200Ecut (eV)
1
10
100
1000
E tot
abs
erro
r (m
eV)
Mean | binariesMax | binariesMean | monomersMax | monomers Max abs error for binaries
and elemental solids similar
Simple error estimate suggestion:simply use the error for the worst element.
Error bars projectIs convergence with basis set and k-points independent?
E(kpts, basis) = F1(kpts) + F2(basis)
Å Å
400 eV 1600 eV
4 5 6 7 8kdens
-0.15
-0.1
-0.05
0
0.05
∆E t
ot(1
600e
V) - ∆
E tot
(400
eV) (
eV)
�Etot
(⇢k
) = Etot
(⇢k
= 8)� Etot
(⇢k
) Independent or not?
Error bars projectAlso need to look at: - band gaps - structures…
Self-consistent hybrid functionals (HSE, PBE0, …)
Challenges:• Slow (compared to GGA) • Convergence is
supposed to be difficult
Currently in GPAW• Non-SC with PW and k-points • SC with FD Gamma point only
VASP tells you to use: Damped “molecular dynamics”
Self-consistent hybrid functionals (HSE, PBE0, …)
Challenges:• Convergence is difficult
hg|ĥ|g0iHamiltonian in PW basis
We are trying with damped molecular dynamics but also brute force:
ĥHF = t̂+ v̂H + v̂F + ...
Should be stable, but limited in supercell size
Thank you for the attention!