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: [ <...> ]
                                       range: [ <...> ]
                                       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 have to be included. Most of the parameters have default values and do not have 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