Group Settings¶

For the output 3D structures, PyXtal uses the conventional standard cell (same as Bilbao). Below are the links for each set.

One can conveniently access the list of crystallographic point groups, 1D rod, 2D layer groups and 3D space groups by changing the dim flag.

>>> from pyxtal.symmetry import Group
>>> g=Group.list_groups(dim=0)
point_group
1           C1
2           Ci
3           C2
...
56          Ih
57          C*
58         C*h

Space Group¶

By default, pyxtal follows the standard according to the Volume A of International Tables for Crystallography. They are defined as: unique axis b setting, cell choice 1 for monoclinic groups, hexagonal axes setting for rhombohedral groups, and origin choice 2 (origin in -1) for the centrosymmetric groups listed with respect to two origins. The relation between the standard space group and hall numbers are shown as follows,

pyxtal_hall_numbers = [
1,   2,   3,   6,   9,   18,  21,  30,  39,  57,  60,  63,  72,  81,  90,
108, 109, 112, 115, 116, 119, 122, 123, 124, 125, 128, 134, 137, 143, 149,
155, 161, 164, 170, 173, 176, 182, 185, 191, 197, 203, 209, 212, 215, 218,
221, 227, 229, 230, 234, 239, 245, 251, 257, 263, 266, 269, 275, 279, 284,
290, 292, 298, 304, 310, 313, 316, 323, 334, 336, 337, 338, 341, 343, 349,
350, 351, 352, 353, 354, 355, 356, 357, 358, 360, 362, 363, 365, 366, 367,
368, 369, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382,
383, 384, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 395, 396, 397,
398, 399, 400, 401, 403, 405, 406, 407, 409, 411, 412, 413, 415, 417, 418,
419, 421, 423, 424, 425, 427, 429, 430, 431, 432, 433, 435, 436, 438, 439,
440, 441, 442, 443, 444, 446, 447, 448, 449, 450, 452, 454, 455, 456, 457,
458, 460, 462, 463, 464, 465, 466, 467, 468, 469, 470, 471, 472, 473, 474,
475, 476, 477, 478, 479, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489,
490, 491, 492, 493, 494, 496, 497, 499, 500, 501, 502, 503, 504, 505, 506,
507, 508, 509, 510, 511, 512, 513, 514, 515, 516, 517, 519, 520, 522, 523,
524, 526, 528, 529, 530]

However, in some programs like Spglib, when converting from space group to Hall numbers, the first description of the space-group type in International Tables for Crystallography) is chosen. In this case, the Hall number 525 (instead of 526) will be chosen for the space group 227.

spglib_hall_numbers = [
1,   2,   3,   6,   9,   18,  21,  30,  39,  57,  60,  63,  72,  81,  90,
108, 109, 112, 115, 116, 119, 122, 123, 124, 125, 128, 134, 137, 143, 149,
155, 161, 164, 170, 173, 176, 182, 185, 191, 197, 203, 209, 212, 215, 218,
221, 227, 228, 230, 233, 239, 245, 251, 257, 263, 266, 269, 275, 278, 284,
290, 292, 298, 304, 310, 313, 316, 322, 334, 335, 337, 338, 341, 343, 349,
350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 361, 363, 364, 366, 367,
368, 369, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382,
383, 384, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 395, 396, 397,
398, 399, 400, 401, 402, 404, 406, 407, 408, 410, 412, 413, 414, 416, 418,
419, 420, 422, 424, 425, 426, 428, 430, 431, 432, 433, 435, 436, 438, 439,
440, 441, 442, 443, 444, 446, 447, 448, 449, 450, 452, 454, 455, 456, 457,
458, 460, 462, 463, 464, 465, 466, 467, 468, 469, 470, 471, 472, 473, 474,
475, 476, 477, 478, 479, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489,
490, 491, 492, 493, 494, 495, 497, 498, 500, 501, 502, 503, 504, 505, 506,
507, 508, 509, 510, 511, 512, 513, 514, 515, 516, 517, 518, 520, 521, 523,
524, 525, 527, 529, 530]

Layer Group¶

For 2D structures, we use unique axis c for monoclinic layer groups 3-7, and unique axis a for layer groups 8-18. When two origin choices are available, we use origin choice 1. We always choose c as the non-periodic axis.

Rod Group¶

For 1D structures, we use unique axis a for monoclinic Rod groups 3-7, and unique axis c for Rod groups 8-12. When two settings are available for a group, we use the 1st setting. We always choose c as the periodic axis.

Point Group¶

For point group structures, we use unique axis c for all groups except the polyhedral groups T, Th, O, Td, Oh, I, and Ih. For all of these groups, we place the 2-fold rotation about the z axis and a 3-fold rotation about the (x,x,x) axis. For I and Ih, we use a 5-fold rotation about the axis (1, \(\tau\), 0), where \(\tau\) is the golden ratio 1.618.

All supported point groups, listed by number:

1: C1	2: Ci	3: C2	4: Cs
5: C2h	6: D2	7: C2v	8: D2h
9: C4	10: S4	11: C4h	12: D4
13: C4v	14: D2d	15: D4h	16: C3
17: C3i	18: D3	19: C3v	20: D3d
21: C6	22: C3h	23: C6h	24: D6
25: C6v	26: D3h	27: D6h	28: T
29: Th	30: O	31: Td	32: Oh
33: C5	34: C7	35: C8	36: D5
37: D7	38: D8	39: C5v	40: C7v
41: C8v	42: C5h	43: D5h	44: D7h
45: D8h	46: D4d	47: D5d	48: D6d
49: D7d	50: D8d	51: S6	52: S8
53: S10	54: S12	55: I	56: Ih
57: C*	58: C*h

In addition to the 32 crystallographic point group , we add the following finite non-crystallographic point groups:

Cn, Cnh, Cnv, Sn, Cni, Dn, Dnh, Dnd.

where n should be replaced by an integer. I and Ih, which are the icosahedral and full icosahedral groups, are particularly useful (Buckminsterfullerene, for example has point group symmetry Ih). Finally, the infinite rotational and dihedral point groups C* and C*h can be used for generating linear structures. C*h will have mirror symmetry, while C* will not.