numerical quality control in computational materials...
TRANSCRIPT
Numerical quality control in computationalmaterials databases
Bjorn Bieniek1, Mansur Sahid1, Christian Carbogno1,
Luca Ghiringhelli1, and Matthias Scheffler1
1Fritz-Haber-Institut der MPG - Berlin
Hands-on Workshop &Humboldt-Kolleg
Isafahan Technical UniversityIran
May 10th, 20161 / 22
Once upon a time....
1https://de.wikipedia.org/wiki/Computer 2 / 22
Electronic structure theory invaluable in material science
• number of publicatiosn peryear including DFTcalculations tripled in thelast 10 years
• 70+ electronic structurecodes based on DFT
3 / 22
Electronic structure theory invaluable in material science
2000 2002 2004 2006 2008 2010 2012 20140
5000
10000
15000
20000
25000
slope=1596
"DFT"-Publications per year
• number of publicatiosn peryear including DFTcalculations tripled in thelast 10 years
• 70+ electronic structurecodes based on DFT
3 / 22
Many different codes
4 / 22
Many different codes
• Potential
- All-ellectron, Pseudopotential,Ultra-soft-Pseudopotential,...
• Basis set
- Gaussian, Plain Wave, Numerical atomicorbitals, Slater type,...
• ...
4 / 22
DFT codes are user friendly
1https://de.wikipedia.org/wiki/Rechnen
5 / 22
Electronic structure theory invaluable in material science
“Predicting crystal structure by merging datamining with quantum mechanics”
• code/method: VASP
• xc-functional: GGA (PW91)
• 2500 k-points/number of atoms
• 405eV cut off
Fischer et al.,Nat. Mat. 8, 641, (2006)
“Combined Electronic Structure andEvolutionary Search Approach toMaterials Design”
• code/method: LMTO
• xc-functional: GGA (PW91)
• 2000 k-points in BZ
Jøhannesson et al., Phys. Rev. Lett.
88 (25), 255506, (2002)
“Assessing the ThermoelectricProperties of Sintered Compoundsvia High-Throughput Ab-InitioCalculations”
• code/method: VASP
• xc-functional: GGA(PBE)
• 2500-3000 per recipr.atom
• ∆E=1meV per atom
Wang et al., Phys. Rev. X 1 (2),
021012, (2011)
6 / 22
Data available in repositories
• NoMaD - Novel Materials Discovery,
http://nomad-repository.eu
• Materials Project,
https://www.materialsproject.org
• Computational Materials Repository,
https://wiki.fysik.dtu.dk/cmr
• Harvard Clean Energy Project,
https://cepdb.molecularspace.org
• AiiDA (infrastructure for at. sim.),
http://www.aiida.net
• Aflowlib,
http://www.aflowlib.org
7 / 22
Error classification
Numerical(e.g. k-points)
Model based(e.g. System size)
Method/Code based
(e.g. Pseudo potential)
Physical
(e.g. xc-functional)
8 / 22
Error classification
Numerical(e.g. k-points)
Model based(e.g. System size)
Method/Code based
(e.g. Pseudo potential)
Physical
(e.g. xc-functional)
8 / 22
Error classification
Numerical(e.g. k-points)
Model based(e.g. System size)
Method/Code based
(e.g. Pseudo potential)
Physical
(e.g. xc-functional)
1K. Lejaeghere et al., Science 351 (2016)
8 / 22
Error classification
Numerical(e.g. k-points)
Model based(e.g. System size)
Method/Code based
(e.g. Pseudo potential)
Physical
(e.g. xc-functional)
PBE lattice parameter of Si
1K. Lejaeghere et al., Science 351 (2016)
8 / 22
Error classification
Numerical(e.g. k-points)
Model based(e.g. System size)
Method/Code based
(e.g. Pseudo potential)
Physical
(e.g. xc-functional)
• 71 elemental crystals
• PBE xc-functional
• ”ultimate” numerical settingse.g. FHI-aims:
• really tight +tier2
• 16 k-points per A−1
• ”scaled zora” rel. treatment
• Birch-Murnaghan Equation-of-state1K. Lejaeghere et al., Science 351 (2016)
8 / 22
Error classification
Numerical(e.g. k-points)
Model based(e.g. System size)
Method/Code based
(e.g. Pseudo potential)
Physical
(e.g. xc-functional)
∆i (a, b) =
√√√√∫ 1.06V0,i
0.94V0,i(Eb,i − Ea,i )
2 dV
0.12V0,i
1K. Lejaeghere et al., Science 351 (2016)
8 / 22
Error classification
• Pairwise comparison of 15 solid state codes
• 40 different potentials or basis set types
• E(V) curves of 71 elemental crystals at the DFT-PBE level
Code Version Basis Electron treatment ∆-value [meV/atom] Authors
Wien2k 13.1 LAPW/APW+lo all-electron 0 S. Cottenier
FHI-aims 81213tier2 numerical
orbitalsall-electron
(atomic ZORA relativity)0.2 ASE
Excitingdevelopment
versionLAPW+xlo all-electron 0.2 Exciting
QuantumEspresso
5.1 plane wavesSSSP Accuracy
(mixed NC/USP/PAW)0.3
QuantumEspresso
Elk 3.1.5 APW+lo all-electron 0.3 Elk
VASP 5.2.12 plane wavesPAW 2015
GW-ready (5.4)0.4 K. Lejaeghere
FHI-aims 81213tier2 numerical
orbitalsall-electron
(scaled ZORA relativity)0.4 ASE
CASTEP plane waves plane waves OTFG CASTEP 9.0 0.5 CASTEP
1K. Lejaeghere et al., Science 351 (2016) and https://molmod.ugent.be/deltacodesdft
9 / 22
Error classification
• Pairwise comparison of 15 solid state codes
• 40 different potentials or basis set types
• E(V) curves of 71 elemental crystals at the DFT-PBE level
Code Version Basis Electron treatment ∆-value [meV/atom] Authors
Wien2k 13.1 LAPW/APW+lo all-electron 0 S. Cottenier
FHI-aims 81213tier2 numerical
orbitalsall-electron
(atomic ZORA relativity)0.2 ASE
Excitingdevelopment
versionLAPW+xlo all-electron 0.2 Exciting
QuantumEspresso
5.1 plane wavesSSSP Accuracy
(mixed NC/USP/PAW)0.3
QuantumEspresso
Elk 3.1.5 APW+lo all-electron 0.3 Elk
VASP 5.2.12 plane wavesPAW 2015
GW-ready (5.4)0.4 K. Lejaeghere
FHI-aims 81213tier2 numerical
orbitalsall-electron
(scaled ZORA relativity)0.4 ASE
CASTEP plane waves plane waves OTFG CASTEP 9.0 0.5 CASTEP
1K. Lejaeghere et al., Science 351 (2016) and https://molmod.ugent.be/deltacodesdft
9 / 22
Error classification
• Pairwise comparison of 15 solid state codes
• 40 different potentials or basis set types
• E(V) curves of 71 elemental crystals at the DFT-PBE level
Code Version Basis Electron treatment ∆-value [meV/atom] Authors
Wien2k 13.1 LAPW/APW+lo all-electron 0 S. Cottenier
FHI-aims 81213tier2 numerical
orbitalsall-electron
(atomic ZORA relativity)0.2 ASE
Excitingdevelopment
versionLAPW+xlo all-electron 0.2 Exciting
QuantumEspresso
5.1 plane wavesSSSP Accuracy
(mixed NC/USP/PAW)0.3
QuantumEspresso
Elk 3.1.5 APW+lo all-electron 0.3 Elk
VASP 5.2.12 plane wavesPAW 2015
GW-ready (5.4)0.4 K. Lejaeghere
FHI-aims 81213tier2 numerical
orbitalsall-electron
(scaled ZORA relativity)0.4 ASE
CASTEP plane waves plane waves OTFG CASTEP 9.0 0.5 CASTEP
Results from differentapproaches/methods/
electronic structurecodes are identical.
1K. Lejaeghere et al., Science 351 (2016) and https://molmod.ugent.be/deltacodesdft
9 / 22
Error estimation for FHI-aims
Code Version Basis Electron treatment ∆-value [meV/atom] Authors
FHI-aims 81213tier2 numerical
orbitalsall-electron
(atomic ZORA relativity)0.2 ASE
FHI-aims 81213tier2 numerical
orbitalsall-electron
(scaled ZORA relativity)0.4 ASE
FHI-aims 81213tight numerical
orbitalsall-electron
(atomic ZORA relativity)0.6 ASE
FHI-aims 81213light numerical
orbitalsall-electron
(scaled ZORA relativity)2.4 ASE
1K. Lejaeghere et al., Science 351 (2016) and https://molmod.ugent.be/deltacodesdft
10 / 22
Error estimation for FHI-aims
Code Version Basis Electron treatment ∆-value [meV/atom] Authors
FHI-aims 81213tier2 numerical
orbitalsall-electron
(atomic ZORA relativity)0.2 ASE
FHI-aims 81213tier2 numerical
orbitalsall-electron
(scaled ZORA relativity)0.4 ASE
FHI-aims 81213tight numerical
orbitalsall-electron
(atomic ZORA relativity)0.6 ASE
FHI-aims 81213light numerical
orbitalsall-electron
(scaled ZORA relativity)2.4 ASE
1K. Lejaeghere et al., Science 351 (2016) and https://molmod.ugent.be/deltacodesdft
10 / 22
Error estimation for FHI-aims
Code Version Basis Electron treatment ∆-value [meV/atom] Authors
FHI-aims 81213tier2 numerical
orbitalsall-electron
(atomic ZORA relativity)0.2 ASE
FHI-aims 81213tier2 numerical
orbitalsall-electron
(scaled ZORA relativity)0.4 ASE
FHI-aims 81213tight numerical
orbitalsall-electron
(atomic ZORA relativity)0.6 ASE
FHI-aims 81213light numerical
orbitalsall-electron
(scaled ZORA relativity)2.4 ASE
1 194
H
0.06
3 166
Li
0.47
11 166
Na
0.66
19 229
K
5.42
37 229
Rb
13.88
55 229
Cs
9.53
4 194
Be
4.05
12 194
Mg
0.54
20 225
Ca
0.71
38 225
Sr
2.35
56 229
Ba
5.17
21 194
Sc
0.68
39 194
Y
0.31
22 194
Ti
0.18
40 194
Zr
0.58
72 194
Hf
0.57
Z Spacegroup
Symbol
∆-value inmeV/at.
1K. Lejaeghere et al., Science 351 (2016) and https://molmod.ugent.be/deltacodesdft
10 / 22
Error classification
Numerical(e.g. k-points)
Model based(e.g. System size)
Method/Code based
(e.g. Pseudopotential)
Physical
(e.g. xc-functional)
11 / 22
Error classification
Numerical(e.g. k-points)
Model based(e.g. System size)
Method/Code based
(e.g. Pseudopotential)
Physical
(e.g. xc-functional)
• Basis set
• k-point grid
• Integration grids
• Real space cut-off
• Relativistic treatment
• Electrostatic Treatment
• . . .
11 / 22
Error classification
Numerical(e.g. k-points)
Model based(e.g. System size)
Method/Code based
(e.g. Pseudopotential)
Physical
(e.g. xc-functional)
• Basis set
• k-point grid
• Integration grids
• Real space cut-off
• Relativistic treatment
• Electrostatic Treatment
• . . .
Settings can becode specific
11 / 22
Error classification
Numerical(e.g. k-points)
Model based(e.g. System size)
Method/Code based
(e.g. Pseudopotential)
Physical
(e.g. xc-functional)
• Basis set
• k-point grid
• Integration grids
• Real space cut-off
• Relativistic treatment
• Electrostatic Treatment
• . . .
Settings can becode specific
Convergence ismaterial specific
11 / 22
Error classification
Numerical(e.g. k-points)
Model based(e.g. System size)
Method/Code based
(e.g. Pseudopotential)
Physical
(e.g. xc-functional)
• Basis set
• k-point grid
• Integration grids
• Real space cut-off
• Relativistic treatment
• Electrostatic Treatment
• . . .
Settings can becode specific
Convergence ismaterial specific
Convergence isproperty specific
11 / 22
Error classification
Numerical(e.g. k-points)
Model based(e.g. System size)
Method/Code based
(e.g. Pseudopotential)
Physical
(e.g. xc-functional)
Convergence isproperty specific
Settings can becode specific
Convergence ismaterial specific
2 4 6 8 10 12 14 16 18 20k{x, y, z} [#]
10-6
10-5
10-4
10-3
10-2
10-1
100
Etot(
k)-E
ref (
k=3
0)
[Å]
Etot vs. k for ZnO (zincblend)
2 4 6 8 10 12 14 16 18 20k{x, y, z} [#]
1.0
1.5
2.0
2.5
3.0
a -
4.6
16
[Å]
1e 4a vs. k for ZnO (zincblend)
11 / 22
Error classification
Numerical(e.g. k-points)
Model based(e.g. System size)
Method/Code based
(e.g. Pseudopotential)
Physical
(e.g. xc-functional)
Convergence isproperty specific
Settings can becode specific
Convergence ismaterial specific
Challenge:How trustworthy and useful is data generated
for property A to investigate property B
11 / 22
Error classification
Numerical(e.g. k-points)
Model based(e.g. System size)
Method/Code based
(e.g. Pseudopotential)
Physical
(e.g. xc-functional)
Convergence isproperty specific
Settings can becode specific
Convergence ismaterial specific
Challenge:How trustworthy and useful is data generated
for property A to investigate property B
Wei Liu et al., Phys. Chem. Let.
(2016) 7 (6), 1022-1027S. Wang et al., Phys. Rev. X
1, 021012 (2011)
L. Pithan et al., Cryst. Growth,
2015, 15 (3), pp 13191324
11 / 22
How trustworthy and useful is data generated forproperty A to investigate property B?
• The community largelyagrees on the definition ofnumerical convergence
• Brute-force numericalconvergence achievable forsimple realistic systems
• Convergence studies aretypically not included inpublications
• Convergence studies aretypically not uploaded torepositories and databases
12 / 22
How trustworthy and useful is data generated forproperty A to investigate property B?
• The community largelyagrees on the definition ofnumerical convergence
• Brute-force numericalconvergence achievable forsimple realistic systems
• Convergence studies aretypically not included inpublications
• Convergence studies aretypically not uploaded torepositories and databases
⇒Build a numerical convergencedata base as a reference
12 / 22
How trustworthy and useful is data generated forproperty A to investigate property B?
⇒Build a numerical convergencedata base as a reference
Flexible and Adaptive
• calculations areset up using ASE
• scripts are easilyextended andadapted for othercodes
Automatic evaluation
• Simple statistics(average error,minimum, maximum,standard deviation)
• overview plots
Big-Data ready
• storage in SQLdatabases
• easy retrieval formachine learningapplications
12 / 22
Numerical convergence data base
Simple Set of Materials
• Elemental solids
• Test Set fromliterature search
• 71 elemental crystals
13 / 22
Numerical convergence data base
Simple Set of Materials
• Elemental solids
• Test Set fromliterature search
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
Criteria for defining the representative set of solids:
• One crystal structure for each chemical element
• Binary
• No duplicates
• Few atoms per unit cell
• Realistic materials known in literature 13 / 22
Numerical convergence data base
Simple Set of Materials
• Elemental solids
• Test Set fromliterature search
11 Na NaCl doi: 10.1063/1.166133612 Mg MgO doi: 10.1080/0141861021015576213 Al AlP doi: 10.1002/crat.217019091714 Si SiC doi: 10.1016/S0925-8388(98)00994-315 P InP doi: Inorg. Mater. 22.3 (1986)16 S ZnS doi: 10.1016/j.ssc.2006.05.04317 Cl CuCl doi: 10.1107/S0365110X64003401
Criteria for defining the representative set of solids:
• One crystal structure for each chemical element
• Binary
• No duplicates
• Few atoms per unit cell
• Realistic materials known in literature
13 / 22
Numerical convergence data base
Simple Set of Materials
• Elemental solids
• Test Set fromliterature search
Most fundamentalnumerical settings:
• Basis Sets
• Integration grids
• k-points
• relativistictreatment
• Potential
13 / 22
Numerical convergence data base
Simple Set of Materials
• Elemental solids
• Test Set fromliterature search
Most fundamentalnumerical settings:
• Basis Sets
• Integration grids
• k-points
• relativistictreatment
• Potential
FHI-aims
• light, tight,really tightdefaults
• basis set:minimal, tier1,tier2
13 / 22
Numerical convergence data base
Simple Set of Materials
• Elemental solids
• Test Set fromliterature search
Most fundamentalnumerical settings:
• Basis Sets
• Integration grids
• k-points
• relativistictreatment
• Potential
FHI-aims
• light, tight,really tightdefaults
• basis set:minimal, tier1,tier2
13 / 22
Numerical convergence data base
Simple Set of Materials
• Elemental solids
• Test Set fromliterature search
Most fundamentalnumerical settings:
• Basis Sets
• Integration grids
• k-points
• relativistictreatment
• Potential
VASP
• Low, Normaland Accurate
13 / 22
Numerical convergence data base
Simple Set of Materials
• Elemental solids
• Test Set fromliterature search
Most fundamentalnumerical settings:
• Basis Sets
• Integration grids
• k-points
• relativistictreatment
• Potential
FHI-aims, VASP
• 4, 8, 16 k-points
per A−1
13 / 22
Numerical convergence data base
Simple Set of Materials
• Elemental solids
• Test Set fromliterature search
Most fundamentalnumerical settings:
• Basis Sets
• Integration grids
• k-points
• relativistictreatment
• Potential
FHI-aims• Atomic ZORA
~pZORA = ~p ·c2
2c2 − v· ~p
• scaled ZORA
εscaledl =
εatomicl
1 +
⟨ψl |~p c2
(2c2−v)2 |~p|ψl
⟩
13 / 22
Numerical convergence data base
Simple Set of Materials
• Elemental solids
• Test Set fromliterature search
Most fundamentalnumerical settings:
• Basis Sets
• Integration grids
• k-points
• relativistictreatment
• Potential
VASP
• standard, hardand soft withdifferent semi-coretreatment forvalence states
13 / 22
Numerical convergence data base
Simple Set of Materials
• Elemental solids
• Test Set fromliterature search
Most fundamentalnumerical settings:
• Basis Sets
• Integration grids
• k-points
• relativistictreatment
• Potential
⇒ 3× 4× 3× 2× 2× (71 + 82) = 22032
FHI-aims calculations
13 / 22
Numerical convergence data base
Simple Set of Materials
• Elemental solids
• Test Set fromliterature search
Most fundamentalnumerical settings:
• Basis Sets
• Integration grids
• k-points
• relativistictreatment
• Potential
⇒= 10872 VASP calculations
13 / 22
Numerical convergence data base
Simple Set of Materials
• Elemental solids
• Test Set fromliterature search
Most fundamentalnumerical settings:
• Basis Sets
• Integration grids
• k-points
• relativistictreatment
• Potential
Most fundamentalmaterials properties:
• Cohesive energy
• relative energy(Reference: 1%expanded cell)
• Unit Cell Volume
• Band Gap
13 / 22
Numerical convergence data base
Simple Set of Materials
• Elemental solids
• Test Set fromliterature search
Most fundamentalnumerical settings:
• Basis Sets
• Integration grids
• k-points
• relativistictreatment
• Potential
Most fundamentalmaterials properties:
• Cohesive energy
• relative energy(Reference: 1%expanded cell)
• Unit Cell Volume
• Band Gap
⇒ easily extensible
13 / 22
4 Codes / Methods
• FHI-aims (All-electron, NAO)
- Bjorn Bieniek, Mansur Said, Christian Carbogno,Luca Ghiringhelli, Matthias Scheffler
• Exicting (All-electron, LAPW+lxo)
- Andris Gulans, Claudia Draxl
• VASP (PAW, plain waves)
- Elisabeth Wruss, Oliver Hofmann
• GPAW (PAW, plain waves)
- Jens Jørgen Mortensen, Kristian Sommer Thygesen
14 / 22
Results
Elemental solids
15 / 22
Results
Binaries
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
15 / 22
Results - Unit cell Volume
Elemental solids
0 50 100 150 200 250 300 350 400
Volume (light) [Å3]
0
100
200
300
400
Volu
me (
tight)
[Å
3]
elemental solids, Vol., k-density: 4 / 4 pt·Å, error: 10.56%
elemental solids, Vol., k-density: 8 / 8 pt·Å, error: 5.48%
elemental solids, Vol., k-density: 16 / 16 pt·Å, error: 5.28%
Volume (light / tight)
Binaries
0 50 100 150 200 250 300 350
Volume (light) [Å3]
0
50
100
150
200
250
300
350
400
Volu
me (
tight)
[Å
3]
binaries, Vol., k-density: 4 / 4 pt·Å, error: 0.05%
binaries, Vol., k-density: 8 / 8 pt·Å, error: 0.28%
binaries, Vol., k-density: 16 / 16 pt·Å, error: 0.78%
Volume (light / tight)
16 / 22
Results - Unit cell Volume
Elemental solids
0 50 100 150 200 250 300 350 400
Volume (tight) [Å3]
0
100
200
300
400
Volu
me (
really
tig
ht)
[Å
3]
elemental solids, Vol., k-density: 4 / 4 pt·Å, error: 1.23%
elemental solids, Vol., k-density: 8 / 8 pt·Å, error: 2.39%
elemental solids, Vol., k-density: 16 / 16 pt·Å, error: 0.31%
Volume (tight / really tight)
Binaries
0 50 100 150 200 250 300 350
Volume (tight) [Å3]
0
50
100
150
200
250
300
350
400
Volu
me (
really
tig
ht)
[Å
3]
binaries, Vol., k-density: 4 / 4 pt·Å, error: 0.74%
binaries, Vol., k-density: 8 / 8 pt·Å, error: 0.98%
binaries, Vol., k-density: 16 / 16 pt·Å, error: 0.04%
Volume (tight / really tight)
16 / 22
Results - Cohesive energy
Elemental solids
10 8 6 4 2 0 2 4Ecoh (light) [eV]
10
8
6
4
2
0
2
Ecoh (
tight)
[eV
]
elemental solids, Ecoh, k-density: 4 / 4 pt·Å, error: 36.37%
elemental solids, Ecoh, k-density: 8 / 8 pt·Å, error: 36.3%
elemental solids, Ecoh, k-density: 16 / 16 pt·Å, error: 36.3%
Ecoh (light / tight)
Binaries
9 8 7 6 5 4 3 2 1Ecoh (light) [eV]
8
6
4
2
0
Ecoh (
tight)
[eV
]
binaries, Ecoh, k-density: 4 / 4 pt·Å, error: 6.93%
binaries, Ecoh, k-density: 8 / 8 pt·Å, error: 6.94%
binaries, Ecoh, k-density: 16 / 16 pt·Å, error: 6.94%
Ecoh (light / tight)
17 / 22
Results - Cohesive energy
Elemental solids
10 8 6 4 2 0Ecoh (tight) [eV]
10
8
6
4
2
0
2
Ecoh (
really
tig
ht)
[eV
]
elemental solids, Ecoh, k-density: 4 / 4 pt·Å, error: 0.02%
elemental solids, Ecoh, k-density: 8 / 8 pt·Å, error: 0.02%
elemental solids, Ecoh, k-density: 16 / 16 pt·Å, error: 0.04%
Ecoh (tight / really tight)
Binaries
9 8 7 6 5 4 3 2 1Ecoh (light) [eV]
8
6
4
2
0
Ecoh (
tight)
[eV
]
binaries, Ecoh, k-density: 4 / 4 pt·Å, error: 0.01%
binaries, Ecoh, k-density: 8 / 8 pt·Å, error: 0.01%
binaries, Ecoh, k-density: 16 / 16 pt·Å, error: 0.01%
Ecoh (light / tight)
17 / 22
Results - Cohesive energy
Elemental solids
10 8 6 4 2 0Ecoh (tight) [eV]
10-6
10-5
10-4
10-3
10-2
10-1
100
∆Ecoh (
really
tig
ht)
[eV
]
elemental solids, ∆Ecoh, k-density: 4 / 4 pt·Å, error: 0.02%
elemental solids, ∆Ecoh, k-density: 8 / 8 pt·Å, error: 0.02%
elemental solids, ∆Ecoh, k-density: 16 / 16 pt·Å, error: 0.04%
∆Ecoh (tight / really tight)
Binaries
9 8 7 6 5 4 3 2 1Ecoh (light) [eV]
10-4
10-3
10-2
10-1
100
∆Ecoh (
tight)
[eV
]
binaries, ∆Ecoh, k-density: 4 / 4 pt·Å, error: 0.01%
binaries, ∆Ecoh, k-density: 8 / 8 pt·Å, error: 0.01%
binaries, ∆Ecoh, k-density: 16 / 16 pt·Å, error: 0.01%
∆Ecoh (light / tight)
17 / 22
Results - Relative energy
Elemental solids
0.0000 0.0005 0.0010 0.0015 0.0020 0.0025rel. E (light) [eV]
10-4
10-3
10-2
10-1
∆re
l. E
(ti
ght)
[eV
]
elemental solids, ∆rel. E, k-density: 4 / 4 pt·Å, error: 1827.82%
elemental solids, ∆rel. E, k-density: 8 / 8 pt·Å, error: 1219.07%
elemental solids, ∆rel. E, k-density: 16 / 16 pt·Å, error: 1354.9%
rel. E=Ecoh(101%Vol.)-Ecoh(100%Vol.) (light / tight)
Binaries
0.0000 0.0005 0.0010 0.0015 0.0020 0.0025rel. E (light) [eV]
10-5
10-4
10-3
∆re
l. E
(ti
ght)
[eV
]
binaries, ∆rel. E, k-density: 4 / 4 pt·Å, error: 81.84%
binaries, ∆rel. E, k-density: 8 / 8 pt·Å, error: 67.69%
binaries, ∆rel. E, k-density: 16 / 16 pt·Å, error: 66.69%
rel. E=Ecoh(101%Vol.)-Ecoh(100%Vol.) (light / tight)
18 / 22
Results - Relative energy
Elemental solids
0.0000 0.0005 0.0010 0.0015 0.0020 0.0025rel. E (light) [eV]
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
101
∆re
l. E
(ti
ght)
[eV
]
elemental solids, ∆rel. E, k-density: 4 / 4 pt·Å, error: 3364.85%
elemental solids, ∆rel. E, k-density: 8 / 8 pt·Å, error: 24.63%
elemental solids, ∆rel. E, k-density: 16 / 16 pt·Å, error: 41.0%
rel. E=Ecoh(101%Vol.)-Ecoh(100%Vol.) (light / tight)
Binaries
0.0000 0.0005 0.0010 0.0015 0.0020 0.0025rel. E (tight) [eV]
10-6
10-5
10-4
10-3
∆re
l. E
(re
ally
tig
ht)
[eV
]
binaries, ∆rel. E, k-density: 4 / 4 pt·Å, error: 7.93%
binaries, ∆rel. E, k-density: 8 / 8 pt·Å, error: 13.77%
binaries, ∆rel. E, k-density: 16 / 16 pt·Å, error: 14.65%
rel. E=Ecoh(101%Vol.)-Ecoh(100%Vol.) (tight / really tight)
18 / 22
Results - Band Gaps
Elemental solids
0 5 10 15 20 25Gap (tight) [eV]
0
5
10
15
20
Gap (
really
tig
ht)
[eV
]
elemental solids, Gap, k-density: 4 / 4 pt·Å, error: 104.3%
elemental solids, Gap, k-density: 8 / 8 pt·Å, error: 46.69%
elemental solids, Gap, k-density: 16 / 16 pt·Å, error: 7.93%
Gap (tight / really tight)
Binaries
0 1 2 3 4 5 6 7 8 9Gap (light) [eV]
0
2
4
6
8
10
Gap (
tight)
[eV
]
binaries, Gap, k-density: 4 / 4 pt·Å, error: 9.17%
binaries, Gap, k-density: 8 / 8 pt·Å, error: 4.58%
binaries, Gap, k-density: 16 / 16 pt·Å, error: 3.62%
Gap (light / tight)
19 / 22
Results - Band Gaps
Elemental solids
0 2 4 6 8 10 12 14 16 18Gap (tight) [eV]
0
5
10
15
20
Gap (
really
tig
ht)
[eV
]
elemental solids, Gap, k-density: 4 / 4 pt·Å, error: 0.47%
elemental solids, Gap, k-density: 8 / 8 pt·Å, error: 0.65%
elemental solids, Gap, k-density: 16 / 16 pt·Å, error: 0.75%
Gap (tight / really tight)
Binaries
0 1 2 3 4 5 6 7 8 9Gap (tight) [eV]
0
2
4
6
8
10
Gap (
really
tig
ht)
[eV
]
binaries, Gap, k-density: 4 / 4 pt·Å, error: 0.15%
binaries, Gap, k-density: 8 / 8 pt·Å, error: 0.24%
binaries, Gap, k-density: 16 / 16 pt·Å, error: 0.24%
Gap (tight / really tight)
19 / 22
Results - Elemental solids
unrelaxed
100 0 100 200 300 400 500Ecoh (light) [eV]
100
0
100
200
300
400
500
Ecoh (
tight)
[eV
]
elemental solids, Ecoh, k-density: 4 / 4 pt·Å, error: 32.01%
elemental solids, Ecoh, k-density: 8 / 8 pt·Å, error: 31.76%
elemental solids, Ecoh, k-density: 16 / 16 pt·Å, error: 31.76%
Ecoh (light / tight)
relaxed
10 8 6 4 2 0 2 4Ecoh (light) [eV]
10
8
6
4
2
0
2
Ecoh (
tight)
[eV
]
elemental solids, Ecoh, k-density: 4 / 4 pt·Å, error: 36.37%
elemental solids, Ecoh, k-density: 8 / 8 pt·Å, error: 36.3%
elemental solids, Ecoh, k-density: 16 / 16 pt·Å, error: 36.3%
Ecoh (light / tight)
20 / 22
Results - Elemental solids
unrelaxed
100 0 100 200 300 400 500Ecoh (light) [eV]
100
0
100
200
300
400
500
Ecoh (
tight)
[eV
]
elemental solids, Ecoh, k-density: 4 / 4 pt·Å, error: 0.02%
elemental solids, Ecoh, k-density: 8 / 8 pt·Å, error: 0.02%
elemental solids, Ecoh, k-density: 16 / 16 pt·Å, error: 0.02%
Ecoh (light / tight)
relaxed
10 8 6 4 2 0Ecoh (tight) [eV]
10
8
6
4
2
0
2
Ecoh (
really
tig
ht)
[eV
]
elemental solids, Ecoh, k-density: 4 / 4 pt·Å, error: 0.02%
elemental solids, Ecoh, k-density: 8 / 8 pt·Å, error: 0.02%
elemental solids, Ecoh, k-density: 16 / 16 pt·Å, error: 0.04%
Ecoh (tight / really tight)
20 / 22
Results - Elemental solids
unrelaxed
100 0 100 200 300 400 500Ecoh (light) [eV]
10-5
10-4
10-3
10-2
10-1
100
101
102
∆Ecoh (
tight)
[eV
]
elemental solids, ∆Ecoh, k-density: 4 / 4 pt·Å, error: 0.02%
elemental solids, ∆Ecoh, k-density: 8 / 8 pt·Å, error: 0.02%
elemental solids, ∆Ecoh, k-density: 16 / 16 pt·Å, error: 0.02%
∆Ecoh (light / tight)
relaxed
10 8 6 4 2 0Ecoh (tight) [eV]
10-6
10-5
10-4
10-3
10-2
10-1
100
∆Ecoh (
really
tig
ht)
[eV
]
elemental solids, ∆Ecoh, k-density: 4 / 4 pt·Å, error: 0.02%
elemental solids, ∆Ecoh, k-density: 8 / 8 pt·Å, error: 0.02%
elemental solids, ∆Ecoh, k-density: 16 / 16 pt·Å, error: 0.04%
∆Ecoh (tight / really tight)
20 / 22
Results - Elemental solids
unrelaxed
0 5 10 15 20 25Gap (light) [eV]
0
5
10
15
20
Gap (
tight)
[eV
]
elemental solids, Gap, k-density: 4 / 4 pt·Å, error: 11.08%
elemental solids, Gap, k-density: 8 / 8 pt·Å, error: 13.59%
elemental solids, Gap, k-density: 16 / 16 pt·Å, error: 5.61%
Gap (light / tight)
relaxed
0 5 10 15 20 25Gap (tight) [eV]
0
5
10
15
20
Gap (
really
tig
ht)
[eV
]
elemental solids, Gap, k-density: 4 / 4 pt·Å, error: 104.3%
elemental solids, Gap, k-density: 8 / 8 pt·Å, error: 46.69%
elemental solids, Gap, k-density: 16 / 16 pt·Å, error: 7.93%
Gap (tight / really tight)
20 / 22
Results - Elemental solids
unrelaxed
0 1 2 3 4 5 6 7 8 9Gap (tight) [eV]
0
2
4
6
8
10
Gap (
really
tig
ht)
[eV
]
binaries, Gap, k-density: 4 / 4 pt·Å, error: 0.15%
binaries, Gap, k-density: 8 / 8 pt·Å, error: 0.24%
binaries, Gap, k-density: 16 / 16 pt·Å, error: 0.24%
Gap (tight / really tight)
relaxed
0 2 4 6 8 10 12 14 16 18Gap (tight) [eV]
0
5
10
15
20
Gap (
really
tig
ht)
[eV
]
elemental solids, Gap, k-density: 4 / 4 pt·Å, error: 0.47%
elemental solids, Gap, k-density: 8 / 8 pt·Å, error: 0.65%
elemental solids, Gap, k-density: 16 / 16 pt·Å, error: 0.75%
Gap (tight / really tight)
20 / 22
Error classification
Numerical(e.g. k-points)
Model based(e.g. System size)
Method/Code based
(e.g. Pseudopotential)
Physical
(e.g. xc-functional)
21 / 22
Error classification
Numerical(e.g. k-points)
Model based(e.g. System size)
Method/Code based
(e.g. Pseudopotential)
Physical
(e.g. xc-functional)
Reference well defined and accessible:
• The scientific community largely agrees on thedefinition of a “numerically convergedcalculation”.
• Typically, a brute force convergence ofnumerical parameters can be achieved forsimple, but realistic systems.
21 / 22
Error classification
Numerical((e.g. k-points)
Model based(e.g. System size)
Method/Code based
(e.g. Pseudo potential)
Physical
(e.g. xc-functional)
Reference either hardto define and/or hard
to compute
21 / 22
Error classification
Numerical((e.g. k-points)
Model based(e.g. System size)
Method/Code based
(e.g. Pseudo potential)
Physical
(e.g. xc-functional)
Reference either hardto define and/or hard
to compute
Systematic (unconverged) data production required!
21 / 22
Thank you for your attention.
22 / 22