7. Appendices

7.1. Block hierarchy

In order to make orientation in parameters and blocks of the input.uspex file more visual and convenient, we have prepared an example code template. This template consists of blocks and all parameters or nested blocks of each level.

{
   optimizer:
            {
            type: GlobalOptimizer
            target:
                     {
                     type: Atomistic
                     conditions: { externalPressure: <...> }
                     compositionSpace:
                                       {
                                       symbols: [ <...> ]
                                       blocks: [ <...> ]
                                       ranges: [ <...> ]
                                       minAt: <...>
                                       maxAt: <...>
                                       }
                     ionDistances:
                                 {
                                  < ... >
                                 }
                     cellUtility:
                                 {
                                 dim: < ... >
                                 thickness: < ... >         #if dim=2
                                 axis: ( <...> )
                                 supercellDegree:  <...>    #if dim=2
                                 cellParameters: { <...> }
                                 cellVolume: <...>
                                 cellVectors: <...>
                                 }
                     radialDistributionUtility:
                                                {
                                                Rmax: <...>
                                                delta: <...>
                                                sigma: <...>
                                                tolerance: <...>
                                                }
                     randSym:
                              {
                              nsym: '<...>'
                              splitInto: [ <...> ]
                              }
                     permutation:
                                 {
                                 howManySwaps: <...>
                                 specificSwaps: <...>
                                 }
                     transmutation:
                                 {
                                 howManyTrans: <...>
                                 }
                     softmodemutation:
                                 {
                                 degree: <...>
                                 }
                     randSymPyXtal:
                                 {
                                 nsym: '<...>'
                                 }
                     environmentUtility:
                                       {
                                       environments:  [substrate]
                                       }
                     seeds:
                           {
                           generations: <...>
                           seedsFolders: [ <...> ]
                           }
                     }

            optType: <...>
            selection:
                     {
                     type: USPEXClassic
                     popSize: <...>
                     initialPopSize: <...>
                     bestFrac: <...>
                     howManyDiverse: <...>
                     optType: ( <...> )
                     fractions:
                              {
                              heredity: ( <...> )
                              softModeMutation: ( <...> )
                              randSym: ( <...> )
                              randTop: ( <...> )
                              permutation: ( <...> )
                              randSymPyXtal: ( <...> )
                              }
                     }
            }

   stages: [ <...> ]
   numParallelCalcs: <...>
   numGenerations: <...>
   stopCrit: <...>

   output:
         {
         columns: [ <...>
                  ]
         }
   outputRefreshDelay: <...>
}

#define < external code >
{type : <...>, commandExecutable : '<...>', goptions : ' <...> '}

#define substrate
 {
 type: <...>
 file: '<...>'
 pbc: (<...>)
 bufferThickness: <...>
 }

 #define < Task Manager >
 {
 type: <...>
 header: '<...>'
 }

Note

This is just a template with every possible parameter, however, depending on the selected values in parameters or blocks, some of them do not hav to be included. Most of the parameters have default values and do not hav to be included.

7.2. List of space groups

1

\(P1\)

2

\(P-1\)

3

\(P2\)

4

\(P2_1\)

5

\(C2(A2)\ast\)

6

\(Pm\)

7

\(Pc(Pa)\ast\)

8

\(Cm(Am)\ast\)

9

\(Cc(Aa)\ast\)

10

\(P2/m\)

11

\(P2_1/m\)

12

\(C2/m(a2/m)\ast\)

13

\(P2/c (P2/a)\ast\)

14

\(P2_1/c (P2_1/a)\ast\)

15

\(C2/c (A2/a)\ast\)

16

\(P222\)

17

\(P222_1\)

18

\(P2_12_12\)

19

\(P2_12_12_1\)

20

\(C222_1\)

21

\(C222\)

22

\(F222\)

23

\(I222\)

24

\(I2_12_12_1\)

25

\(Pmm2\)

26

\(Pmc2_1\)

27

\(P cc2\)

28

\(Pma2\)

29

\(Pca2_1\)

30

\(Pnc2\)

31

\(Pmn2_1\)

32

\(Pba2\)

33

\(Pna2_1\)

34

\(Pnn2\)

35

\(Cmm2\)

36

\(Cmc2_1\)

37

\(Ccc2\)

38

\(Amm2 (C2mm)\ast\)

39

\(Aem2 (C2mb)\ast\)

40

\(Ama2 (C2cm)\ast\)

41

\(Aea2 (C2cb)\ast\)

42

\(Fmm2\)

43

\(Fdd2\)

44

\(Imm2\)

45

\(Iba2\)

46

\(Ima2\)

47

\(Pmmm\)

48

\(P nnn\)

49

\(Pccm\)

50

\(Pban\)

51

\(Pmma\)

52

\(Pnna\)

53

\(Pmna\)

54

\(Pcca\)

55

\(Pbam\)

56

\(P ccn\)

57

\(Pbcm\)

58

\(Pnnm\)

59

\(Pmmn\)

60

\(P bcn\)

61

\(Pbca\)

62

\(Pnma\)

63

\(Cmcm\)

64

\(Cmce(Cmca)\ast\)

65

\(Cmmm\)

66

\(Cccm\)

67

\(Cmme (Cmma)\ast\)

68

\(Ccce (Ccca)\ast\)

69

\(Fmmm\)

70

\(Fddd\)

71

\(Immm\)

72

\(Ibam\)

73

\(Ibca\)

74

\(Imma\)

75

\(P4\)

76

\(P4_1\)

77

\(P4_2\)

78

\(P4_3\)

79

\(I4\)

80

\(I4_1\)

81

\(P-4\)

82

\(I-4\)

83

\(P4/m\)

84

\(P42/m\)

85

\(P4/n\)

86

\(P4_2/n\)

87

\(I4/m\)

88

\(I4_1/a\)

89

\(P422\)

90

\(P42_12\)

91

\(P4_122\)

92

\(P4_12_12\)

93

\(P4_222\)

94

\(P4_22_12\)

95

\(P4_322\)

96

\(P4_32_12\)

97

\(I422\)

98

\(I4_122\)

99

\(P4mm\)

100

\(P4bm\)

101

\(P4_2cm\)

102

\(P4_2nm\)

103

\(P4cc\)

104

\(P4nc\)

105

\(P4_2mc\)

106

\(P4_2bc\)

107

\(I4mm\)

108

\(I4cm\)

109

\(I4_1md\)

110

\(I4_1cd\)

111

\(P-42m\)

112

\(P-42c\)

113

\(P-42_1m\)

114

\(P-42_1c\)

115

\(P-4m2\)

116

\(P-4c2\)

117

\(P-4b2\)

118

\(P-4b2\)

119

\(I-4m2\)

120

\(I-4c2\)

121

\(I-42m\)

122

\(I-42d\)

123

\(P4/mmm\)

124

\(P4/mcc\)

125

\(P4/nbm\)

126

\(P4/nnc\)

127

\(P4/mbm\)

128

\(P4/mnc\)

129

\(P4/nmm\)

130

\(P4/ncc\)

131

\(P4_2/mmc\)

132

\(P42/mcm\)

133

\(P4_2/nbc\)

134

\(P4_2/nnm\)

135

\(P4_2/mbc\)

136

\(P4_2/mnm\)

137

\(P4_2/nmc\)

138

\(P4_2/ncm\)

139

\(I4/mmm\)

140

\(I4/mcm\)

141

\(I4_1/amd\)

142

\(I4_1/acd\)

143

\(P3\)

144

\(P3_1\)

145

\(P3_2\)

146

\(R3\)

147

\(P-3\)

148

\(R-3\)

149

\(P312\)

150

\(P321\)

151

\(P3_112\)

152

\(P3_121\)

153

\(P3_212\)

154

\(P3_221\)

155

\(R32\)

156

\(P3m1\)

157

\(P31m\)

158

\(P3c1\)

159

\(P31c\)

160

\(R3m\)

161

\(R3c\)

162

\(P-31m\)

163

\(P-31c\)

164

\(P-3m1\)

165

\(P-3c1\)

166

\(R-3m\)

167

\(R-3c\)

168

\(P6\)

169

\(P6_1\)

170

\(P6_5\)

171

\(P6_2\)

172

\(P6_4\)

173

\(P6_3\)

174

\(P-6\)

175

\(P6/m\)

176

\(P6_3/m\)

177

\(P622\)

178

\(P6_122\)

179

\(P6_522\)

180

\(P6_222\)

181

\(P6_422\)

182

\(P6_322\)

183

\(P6mm\)

184

\(P6cc\)

185

\(P6_3cm\)

186

\(P6_3mc\)

187

\(P-6m2\)

188

\(P-6c2\)

189

\(P-62m\)

190

\(P-62c\)

191

\(P6/mmm\)

192

\(P6/mcc\)

193

\(P6_3/mcm\)

194

\(P6_3/mmc\)

195

\(P23\)

196

\(F23\)

197

\(I23\)

198

\(P2_13\)

199

\(I2_13\)

200

\(Pm-3\)

201

\(Pn-3\)

202

\(Fm-3\)

203

\(Fd-3\)

204

\(Im-3\)

205

\(Pa-3\)

206

\(Ia-3\)

207

\(P432\)

208

\(P4_232\)

209

\(F432\)

210

\(F4_132\)

211

\(I432\)

212

\(P4_332\)

213

\(P4_132\)

214

\(I4_132\)

215

\(P-43m\)

216

\(F-43m\)

217

\(I-43m\)

218

\(P-43n\)

219

\(F-43c\)

220

\(I-43d\)

221

\(Pm-3m\)

222

\(Pn-3n\)

223

\(Pm-3n\)

224

\(Pn-3m\)

225

\(P1\)

226

\(P-1\)

227

\(P2\)

228

\(P2_1\)

229

\(Im-3m\)

230

\(Ia-3d\)

\({\ast}\) In parentheses we give non-standard space groups used in the code.

7.3. List of layer groups

Triclinic

1

\(p1\)

2

\(p-1\)

Monoclinic / inclined

3

\(p112\)

4

\(p11m\)

5

\(p11a\)

6

\(p112/m\)

7

\(p112/a\)

Monoclinic / orthogonal

8

\(p211\)

9

\(p2_11\)

10

\(c211\)

11

\(pm11\)

12

\(pb11\)

13

\(cm11\)

14

\(p2/m11\)

15

\(p2_1/m11\)

16

\(p2/b11\)

17

\(p2_1/b11\)

18

\(c2/m11\)

Orthorhombic

19

\(p222\)

20

\(p2_22\)

21

\(p2_12_12\)

22

\(c222\)

25

\(pmm2\)

24

\(pma2\)

25

\(pba2\)

26

\(cmm2\)

27

\(pm2m\)

28

\(pm2_1b\)

29

\(pm2_1m\)

30

\(pb2b\)

31

\(pm2a\)

32

\(pm2_1a\)

33

\(pb2_1a\)

34

\(pb2n\)

35

\(cm2m\)

36

\(cm2e\)

37

\(pmmm\)

38

\(pmaa\)

39

\(pban\)

40

\(pmam\)

41

\(pmma\)

42

\(pman\)

43

\(pbaa\)

44

\(pbam\)

45

\(pbma\)

46

\(pmmn\)

47

\(cmmm\)

48

\(cmme\)

Tetragonal

49

\(p4\)

50

\(p-4\)

51

\(p4/m\)

52

\(p4/n\)

53

\(p422\)

54

\(p42_12\)

55

\(p4mm\)

56

\(p4bn\)

57

\(p-4m2\)

58

\(p-42_1m\)

59

\(p-4m2\)

60

\(p-4b2\)

61

\(p4/mmm\)

62

\(p4/nbm\)

63

\(p/4mbn\)

64

\(p4/nmm\)

Trigonal

65

\(p3\)

66

\(p-3\)

67

\(p312\)

68

\(p321\)

69

\(p3m1\)

70

\(p31m\)

71

\(p-31m\)

72

\(p-3m1\)

Hexagonal

73

\(p6\)

74

\(p-6\)

75

\(p6/m\)

76

\(p622\)

77

\(p6mm\)

78

\(p-m2\)

79

\(p-62m\)

80

\(p6/mmm\)

7.4. List of plane groups

Number

Group

1

p1

2

p2

3

pm

4

pg

5

cm

6

pmm

7

pmg

8

pgg

9

cmm

10

p4

11

p4m

12

p4g

13

p3

14

p3m1

15

p31m

16

p6

17

p6m

7.5. List of point groups

List of all crystallographic and the most important non-crystallographic point groups in Schönflies and Hermann-Mauguin (international) notations.

Crystallographic point groups:

Hermann-Maugin

Schönflies

In USPEX

1

C\(_1\)

C1 or E

2

C\(_2\)

C2

222

D\(_2\)

D2

4

C\(_4\)

C4

3

C\(_3\)

C3

6

C\(_6\)

C6

23

T

T

\(\overline{1}\)

S\(_2\)

S2

M

C\(_{1h}\)

Ch1

mm2

C\(_{2v}\)

Cv2

\(\overline{2}\)

S\(_4\)

S4

\(\overline{3}\)

S\(_6\)

S6

\(\overline{6}\)

C\(_{3h}\)

Ch3

m\(\overline{3}\)

T\(_h\)

Th

2/m

C\(_{2h}\)

Ch2

mmm

D\(_{2h}\)

Dh2

4/m

C\(_{4h}\)

Ch4

32

D\(_3\)

D3

6/m

C\(_{6h}\)

Ch6

432

O

O

422

D\(_4\)

D4

3m

C\(_{3v}\)

Cv3

622

D\(_6\)

D6

\(\overline{4}\)3m

T\(_d\)

Td

4mm

C\(_{4v}\)

Cv4

\(\overline{3}\)m

D\(_{3d}\)

Dd3

6mm

C\(_{6v}\)

Cv6

m\(\overline{3}\)m

O\(_h\)

Oh

\(\overline{4}\)2m

D\(_{2d}\)

Dd2

\(\overline{6}\)2m

D\(_{3h}\)

Dh3

4/mmm

D\(_{4h}\)

Dh4

6/mmm

D\(_{6h}\)

Dh6

m\(\overline{3}\)m

O\(_h\)

Oh

Important non-crystallographic point groups

Hermann-Maugin

Schönflies

In USPEX

5

C\(_5\)

C5

5/m

S\(_5\)

S5

\(\overline{5}\)

S\(_{10}\)

S10

5m

Cv\(_{5v}\)

Cv5

\(\overline{10}\)

Ch\(_{5h}\)

Ch5

52

D\(_5\)

D5

\(\overline{5}\)m

D\(_{5d}\)

Dd5

\(\overline{10}\)2m

D\(_{5h}\)

Dh5

532

I

I

5\(\overline{3}\)m

I\(_h\)

Ih

7.6. Table of univalent covalent radii used in USPEX

Table of covalent radii (in \(\text{Å}\)) used in USPEX (for hardness calculations, etc.):

Z

Element

radius

Z

Element

radius

Z

Element

radius

1

H

0.31

30

Zn

1.22

63

Eu

1.98

2

He

0.28

31

Ga

1.22

64

Gd

1.96

3

Li

1.28

32

Ge

1.20

65

Tb

1.94

4

Be

0.96

33

As

1.19

66

Dy

1.92

5

B

0.84

34

Se

1.20

67

Ho

1.92

6

C \(sp^3\)

0.76

35

Br

1.20

68

Er

1.89

C \(sp^2\)

0.73

36

Kr

1.16

69

Tm

1.90

C \(sp\)

0.69

37

Rb

2.20

70

Yb

1.87

7

N

0.71

38

Sr

1.95

71

Lu

1.87

8

O

0.66

39

Y

1.90

72

Hf

1.75

9

F

0.57

40

Zr

1.75

73

Ta

1.70

10

Ne

0.58

41

Nb

1.64

74

W

1.62

11

Na

1.66

42

Mo

1.54

75

Re

1.51

12

Mg

1.41

43

Tc

1.47

76

Os

1.44

13

Al

1.21

44

Ru

1.46

77

Ir

1.41

14

Si

1.11

45

Rh

1.42

78

Pt

1.36

15

P

1.07

46

Pd

1.39

79

Au

1.36

16

S

1.05

47

Ag

1.45

80

Hg

1.32

17

Cl

1.02

48

Cd

1.44

81

Tl

1.45

18

Ar

1.06

49

In

1.42

82

Pb

1.46

19

K

2.03

50

Sn

1.39

83

Bi

1.48

20

Ca

1.76

51

Sb

1.39

84

Po

1.40

21

Sc

1.70

52

Te

1.38

85

At

1.50

22

Ti

1.60

53

I

1.39

86

Rn

1.50

23

V

1.53

54

Xe

1.40

87

Fr

2.60

24

Cr

1.39

55

Cs

2.44

88

Ra

2.21

25

Mn l.s.

1.39

56

Ba

2.15

89

Ac

2.15

h.s

1.61

57

La

2.07

90

Th

2.06

26

Fe l.s

1.32

58

Ce

2.04

91

Pa

2.00

h.s.

1.52

59

Pr

2.03

92

U

1.96

27

Co l.s.

1.26

60

Nd

2.01

93

Np

1.90

h.s.

1.50

61

Pm

1.99

94

Pu

1.87

28

Ni

1.24

62

Sm

1.98

95

Am

1.80

29

Cu

1.32

96

Cm

1.69

Source: Cordero et al., Dalton Trans. 2832-2838, 2008 22.

7.7. Table of default chemical valences used in USPEX

Table of chemical valences used in USPEX (for hardness calculations, etc.):

Z

Element

valence

Z

Element

valence

Z

Element

valence

1

H

1

35

Br

1

69

Tm

3

2

He

0.5

36

Kr

0.5

70

Yb

3

3

Li

1

37

Rb

1

71

Lu

3

4

Be

2

38

Sr

2

72

Hf

4

5

B

3

39

Y

3

73

Ta

5

6

C

4

40

Zr

4

74

W

4

7

N

3

41

Nb

5

75

Re

4

8

O

2

42

Mo

4

76

Os

4

9

F

1

43

Tc

4

77

Ir

4

10

Ne

0.5

44

Ru

4

78

Pt

4

11

Na

1

45

Rh

4

79

Au

1

12

Mg

2

46

Pd

4

80

Hg

2

13

Al

3

47

Ag

1

81

Tl

3

14

Si

4

48

Cd

2

82

Pb

4

15

P

3

49

In

3

83

Bi

3

16

S

2

50

Sn

4

84

Po

2

17

Cl

1

51

Sb

3

85

At

1

18

Ar

0.5

52

Te

2

86

Rn

0.5

19

K

1

53

I

1

87

Fr

1

20

Ca

2

54

Xe

0.5

88

Ra

2

21

Sc

3

55

Cs

1

89

Ac

3

22

Ti

4

56

Ba

2

90

Th

4

23

V

4

57

La

3

91

Pa

4

24

Cr

3

58

Ce

4

92

U

4

25

Mn

4

59

Pr

3

93

Np

4

26

Fe

3

60

Nd

3

94

Pu

4

27

Co

3

61

Pm

3

95

Am

4

28

Ni

2

62

Sm

3

96

Cm

4

29

Cu

2

63

Eu

3

97

Bk

4

30

Zn

2

64

Gd

3

98

Cf

4

31

Ga

3

65

Tb

3

99

Es

4

32

Ge

4

66

Dy

3

100

FM

4

33

As

3

67

Ho

3

101

Md

4

34

Se

2

68

Er

3

102

No

4

7.8. Table of default goodBonds used in USPEX

Table of default goodBonds used in USPEX (for hardness calculations, etc.):

Z

Element

goodBonds

Z

Element

goodBonds

Z

Element

goodBonds

1

H

0.20

35

Br

0.10

69

Tm

0.20

2

He

0.05

36

Kr

0.05

70

Yb

0.20

3

Li

0.10

37

Rb

0.05

71

Lu

0.20

4

Be

0.20

38

Sr

0.10

72

Hf

0.30

5

B

0.30

39

Y

0.20

73

Ta

0.40

6

C

0.50

40

Zr

0.30

74

W

0.30

7

N

0.50

41

Nb

0.35

75

Re

0.30

8

O

0.30

42

Mo

0.30

76

Os

0.30

9

F

0.10

43

Tc

0.30

77

Ir

0.30

10

Ne

0.05

44

Ru

0.30

78

Pt

0.30

11

Na

0.05

45

Rh

0.30

79

Au

0.05

12

Mg

0.10

46

Pd

0.30

80

Hg

0.10

13

Al

0.20

47

Ag

0.05

81

Tl

0.20

14

Si

0.30

48

Cd

0.10

82

Pb

0.30

15

P

0.30

49

In

0.20

83

Bi

0.20

16

S

0.20

50

Sn

0.30

84

Po

0.20

17

Cl

0.10

51

Sb

0.20

85

At

0.10

18

Ar

0.05

52

Te

0.20

86

Rn

0.05

19

K

0.05

53

I

0.10

87

Fr

0.05

20

Ca

0.10

54

Xe

0.05

88

Ra

0.10

21

Sc

0.20

55

Cs

0.05

89

Ac

0.20

22

Ti

0.30

56

Ba

0.10

90

Th

0.30

23

V

0.30

57

La

0.20

91

Pa

0.30

24

Cr

0.25

58

Ce

0.30

92

U

0.30

25

Mn

0.30

59

Pr

0.20

93

Np

0.30

26

Fe

0.25

60

Nd

0.20

94

Pu

0.30

27

Co

0.25

61

Pm

0.20

95

Am

0.30

28

Ni

0.15

62

Sm

0.20

96

Cm

0.30

29

Cu

0.10

63

Eu

0.20

97

Bk

0.30

30

Zn

0.10

64

Gd

0.20

98

Cf

0.30

31

Ga

0.25

65

Tb

0.20

99

Es

0.30

32

Ge

0.50

66

Dy

0.20

100

FM

0.30

33

As

0.35

67

Ho

0.20

101

Md

0.30

34

Se

0.20

68

Er

0.20

102

No

0.30