Dialog Box: Custom Symmetry [Symmetry dialog, Input menu]
Note that proper use of this option absolutely depends on identification of the point or factor group, and possibly applying Pre-Calculation Rotations to bring the atoms and symmetry into standard orientation; both requirements are described below.
This option is used for old VIBRAT files (which should already have the correct factor group number), or for certain import file formats. It is intended primarily for space groups, but can also be used for crystallographic point groups. It cannot be used for non-crystallographic point groups. The symmetry is entered and stored in the form of general positions as given in the International Tables for X-ray Crystallography. These are sometimes given in reports on crystal structures (e.g. Wyckoff, Crystal Structures). Note however that often only the operations for special positions are given: VIBRATZ needs all the operations for the general position.
If you specify Centric, rather than acentric, and the Operations include center box is not checked, only half the symmetry operations should be entered. If the origin of coordinates is not on an inversion center, the Operations include center box must be checked and all the operations must be present. However, symmetry analysis will not generally be successful if the origin is not on a center, and the coordinates must be corrected; see below under Origin of Coordinates.
The Space-group symbol is for your reference only - it is not used directly by VIBRATZ. However, if you click on the Get Space Group Symbol button VIBRATZ will analyze the given operations and try to provide a valid space-group symbol. When you click on the Change Symmetry Option button, this will also cause an attempt to provide the correct space-group symbol.
The Point/factor group number must be correct for proper symmetry analysis. This number, as well as the point group symbol (which is for your reference only), may be filled in with the Get Space Group Symbol button, but this will succeed only if the current operations constitute a valid space group. If this fails, the number must be entered using the values from the table below.
Note also that the orientation of the symmetry operators must be consistent with the basis functions. For a number of space groups in their standard orientation, this is not the case, and it is necessary to apply Pre-Calculation Rotations to both input atoms and symmetry matrices. If you select a space-group with the Space-Group Symmetry option, the proper values are automatically entered in the Pre-Calculation Rotations dialog if necessary. You must enter these rotations manually, if needed, for the Custom Symmetry option. See the Space-Group Symmetry dialog for which space groups need rotation.
The Bravais lattice is in most cases the capital letter which begins the space-group symbol. However, VIBRATZ uses a somewhat different convention from the standard for trigonal crystals: if you are using hexagonal axes for a rhombohedral crystal (whose standard space group symbol will always begin with "R"), enter "R" - if you are using the primitive rhombohedral axes, enter "P". Enter "P" for a molecule.
In the Operations list, you must enter all the "symmetry operations" for the most general position in the structure, with one operator per line. "X, Y, Z;" will always be the first operator. Click on the Add Line button to add a line, or Revise to change a line, either of which will call up the Edit Symmetry Operation Line dialog.
Origin of Coordinates. The symmetry analysis in VIBRATZ requires that if a space- or point-group is centric (contains a center of inversion), the origin of coordinates must be on that center. In the International Tables, this is usually standard, but for 24 space groups in the orthorhombic, tetragonal and cubic systems, there is a choice of origins. In VIBRATZ, the first choice of origin, which is off the center of inversion, is denoted by adding ":1" to the standard symbol or number, and the second choice, on the center, is denoted with ":2". In Hall symbols, the origin is explicit. If you enter the symbol or number without extension ( ":1" or ":2" ), origin on the center (":2") is assumed.
When you use Custom symmetry, the choice of origin is not obvious, and if your atomic coordinates are for the first setting in one of these space groups you must correct the coordinates and symmetry in either of two ways. If you are using one of these settings, the Centric radio button should be selected, and the Operations include center box should be checked.
First, you can correct coordinates manually, using the increments x, y and z given in the Tables in the line "Origin at..., at x, y, z from centre". The symmetry operations entered in this dialog must also be completely changed - they must be taken from the second setting instead of the first.
Second, you can allow VIBRATZ to make the corrections. This must be done in an indirect way. After entering the original atomic coordinates and symmetry operations for the off-center setting in the Custom symmetry dialog, click the Change Symmetry Option button, and change to Space-Group symmetry. This should convert your symmetry Settings to a standard space-group symbol (first setting), then correct both the symbols and the atomic coordinates to the second setting. If you click on the Get Space-Group Symbol button, the symbols, Settings and atomic coordinates will be corrected, but the Custom symmetry option will be retained. Of course these conversions depend on your data being for the standard off-center (first) setting of one of the 24 space groups of this type in the Tables. Any non-standard off-center settings will have to be corrected manually.
Point/Factor group numbers
1. C1 - 1 9. D3 - 32 17. C3h - 6 25. D3d - 3m
2. Ci - 1 10. D4 - 422 18. C4h - 4/m 26. S4 - 4
3. Cs - m 11. D6 - 622 19. C6h - 6/m 27. S6 - 3
4. C2 - 2 12. C2v - mm2 20. D2h - mmm 28. T - 23
5. C3 - 3 13. C3v - 3m 21. D3h - 6m2 29. Th - m3
6. C4 - 4 14. C4v - 4mm 22. D4h - 4/mmm 30. Td - 43m
7. C6 - 6 15. C6v - 6mm 23. D6h - 6/mmm 31. O - 432
8. D2 - 222 16. C2h - 2/m 24. D2d - 42m 32. Oh - m3m
1. C1 - 1
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9. D3 - 32
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17. C3h - 6
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25. D3d - 3m
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2. Ci - 1
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10. D4 - 422
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18. C4h - 4/m
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26. S4 - 4
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3. Cs - m
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11. D6 - 622
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19. C6h - 6/m
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27. S6 - 3
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4. C2 - 2
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12. C2v - mm2
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20. D2h - mmm
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28. T - 23
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5. C3 - 3
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13. C3v - 3m
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21. D3h - 6m2
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29. Th - m3
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6. C4 - 4
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14. C4v - 4mm
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22. D4h - 4/mmm
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30. Td - 43m
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7. C6 - 6
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15. C6v - 6mm
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23. D6h - 6/mmm
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31. O - 432
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8. D2 - 222
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16. C2h - 2/m
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24. D2d - 42m
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32. Oh - m3m
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