Numerical quality control in computational materials...

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


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


“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




Method/Code based


Physical


8 / 22




Method/Code based


Physical


1K. Lejaeghere et al., Science 351 (2016)

8 / 22




Method/Code based


Physical


PBE lattice parameter of Si


8 / 22




Method/Code based


Physical


• 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




Method/Code based


Physical


∆i (a, b) =

√√√√∫ 1.06V0,i

0.94V0,i(Eb,i − Ea,i )

2 dV

0.12V0,i


8 / 22


• 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



(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










Excitingdevelopment


QuantumEspresso



QuantumEspresso









9 / 22










Excitingdevelopment


QuantumEspresso



QuantumEspresso








Results from differentapproaches/methods/

electronic structurecodes are identical.


9 / 22

Error estimation for FHI-aims








FHI-aims 81213tight numerical



FHI-aims 81213light numerical




10 / 22
















10 / 22















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.


10 / 22




Method/Code based

(e.g. Pseudopotential)

Physical


11 / 22




Method/Code based


Physical


• Basis set

• k-point grid

• Integration grids

• Real space cut-off

• Relativistic treatment

• Electrostatic Treatment

• . . .

11 / 22




Method/Code based


Physical


• Basis set

• k-point grid





• . . .

Settings can becode specific

11 / 22




Method/Code based


Physical


• Basis set

• k-point grid





• . . .


Convergence ismaterial specific

11 / 22




Method/Code based


Physical


• Basis set

• k-point grid





• . . .



Convergence isproperty specific

11 / 22




Method/Code based


Physical





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




Method/Code based


Physical





Challenge:How trustworthy and useful is data generated

for property A to investigate property B

11 / 22




Method/Code based


Physical





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


• 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


⇒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





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





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





Most fundamentalnumerical settings:

• Basis Sets


• k-points

• relativistictreatment

• Potential

13 / 22






• Basis Sets


• k-points


• Potential

FHI-aims

• light, tight,really tightdefaults

• basis set:minimal, tier1,tier2

13 / 22






• Basis Sets


• k-points


• Potential

FHI-aims

• light, tight,really tightdefaults

• basis set:minimal, tier1,tier2

13 / 22






• Basis Sets


• k-points


• Potential

VASP

• Low, Normaland Accurate

13 / 22






• Basis Sets


• k-points


• Potential

FHI-aims, VASP

• 4, 8, 16 k-points

per A−1

13 / 22






• Basis Sets


• k-points


• 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






• Basis Sets


• k-points


• Potential

VASP

• standard, hardand soft withdifferent semi-coretreatment forvalence states

13 / 22






• Basis Sets


• k-points


• Potential

⇒ 3× 4× 3× 2× 2× (71 + 82) = 22032

FHI-aims calculations

13 / 22






• Basis Sets


• k-points


• Potential

⇒= 10872 VASP calculations

13 / 22






• Basis Sets


• k-points


• Potential

Most fundamentalmaterials properties:

• Cohesive energy

• relative energy(Reference: 1%expanded cell)

• Unit Cell Volume

• Band Gap

13 / 22






• Basis Sets


• k-points


• 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%



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%



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]




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]




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%



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%




17 / 22


Elemental solids

10 8 6 4 2 0Ecoh (tight) [eV]

10

8

6

4

2

0

2

Ecoh (

really

tig

ht)

[eV

]




Ecoh (tight / really tight)

Binaries

9 8 7 6 5 4 3 2 1Ecoh (light) [eV]

8

6

4

2

0

Ecoh (

tight)

[eV

]





17 / 22


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%



∆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%



∆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%



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%




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

]





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

]




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%



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%



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

]





Binaries

0 1 2 3 4 5 6 7 8 9Gap (tight) [eV]

0

2

4

6

8

10

Gap (

really

tig

ht)

[eV

]





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

]





relaxed

10 8 6 4 2 0 2 4Ecoh (light) [eV]

10

8

6

4

2

0

2

Ecoh (

tight)

[eV

]





20 / 22


unrelaxed

100 0 100 200 300 400 500Ecoh (light) [eV]

100

0

100

200

300

400

500

Ecoh (

tight)

[eV

]





relaxed

10 8 6 4 2 0Ecoh (tight) [eV]

10

8

6

4

2

0

2

Ecoh (

really

tig

ht)

[eV

]




Ecoh (tight / really tight)

20 / 22


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

]




∆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

]




∆Ecoh (tight / really tight)

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unrelaxed

0 5 10 15 20 25Gap (light) [eV]

0

5

10

15

20

Gap (

tight)

[eV

]




Gap (light / tight)

relaxed

0 5 10 15 20 25Gap (tight) [eV]

0

5

10

15

20

Gap (

really

tig

ht)

[eV

]





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unrelaxed

0 1 2 3 4 5 6 7 8 9Gap (tight) [eV]

0

2

4

6

8

10

Gap (

really

tig

ht)

[eV

]





relaxed

0 2 4 6 8 10 12 14 16 18Gap (tight) [eV]

0

5

10

15

20

Gap (

really

tig

ht)

[eV

]





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Method/Code based


Physical


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Method/Code based


Physical


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


Numerical((e.g. k-points)


Method/Code based


Physical


Reference either hardto define and/or hard

to compute

21 / 22


Numerical((e.g. k-points)


Method/Code based


Physical


Reference either hardto define and/or hard

to compute

Systematic (unconverged) data production required!

21 / 22

Thank you for your attention.

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Date post:	24-Jul-2020
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Numerical quality control in computational materials...

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