Space-Group Symmetry
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Dialog Box: Space-Group Symmetry [Symmetry Dialog, Input menu]

Space-group symmetry is generated using licensed excerpts from the SGInfo program of Ralf Grosse-Kunstleve. You can specify the space group in any of three ways: 1) the Hermann-Maughin (H-M) or International symbol; 2) the Hall symbol (S.R. Hall: Acta Cryst., A37, 517, 1981); or 3) the number of the group in the International Tables for X-ray Crystallography.

International Tables Volume. You have the option of using the older version of the Tables (called the Second Edition: various revisions and reprints from 1952 to 1979) in which the symmetry information was in Volume I, or the newer version (1983 onwards) in which it is in Volume A. The principal difference between the two versions is that in the older one the unique axis of a monoclinic group is assumed to be the c-axis, whereas in the newer one it is assumed to be the b-axis. Thus entering the symbol P2/m gives two different orientations depending on the volume selected. You can always specify the setting by entering the long form of the symbol, i.e. P_2/m_1_1, P_1_2/m_1 or P_1_1_2/m. Of course, for the first two of these examples you would have to use the Pre-Calculation Rotations to attain the standard orientation, which is unique axis parallel to c.

The H-M symbol can be typed into the edit box in either short form or long form, with or without spaces or underscores between positions. However, it is usually safer to select the symbol from the list box at the bottom, which gives the standard-form symbols for all the space-groups. Clicking the Select button copies the relevant data to the edit boxes at the top; it does not actually generate the symmetry. Symmetry generation is done after you click OK - this may take a few seconds.

If the space group you select does not appear to be consistent with your choice of axes, a warning box appears, but in most cases consistency is not required. Select the rhombohedral setting for trigonal crystals by adding :R to the end of the symbol in the case of H-M symbols, or asterisk (*) in the case of Hall symbols. The choice of rhombohedral vs. primitive cell should agree with the type of axes entered in the Title/Axes dialog. If you select the rhombohedral setting and then switch to the Custom symmetry option, the lattice type will be P; it will be R if the axes are hexagonal.

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.

If your atomic coordinates are for the first setting in one of these space groups, you can either correct the coordinates manually, using the increments x, y and z given in the Tables in the line "Origin at..., at x, y, z from centre" and enter the symbol for the second setting (add extension ":2" to symbol or number), or you can enter the original coordinates and allow VIBRATZ to make the corrections to the atomic coordinates (add extension ":1" to symbol or number).

Orientation. Certain orientations of the symmetry elements are required by the basis functions used for symmetry analysis, and some standard space-group settings may not be consistent with these settings. VIBRATZ will usually detect such cases, and supply appropriate rotations for the Pre-Calculation Rotations dialog.

VIBRATZ requires any unique axis to be the z-axis or crystallographic c-axis, whereas the standard orientation for monoclinic crystals is the unique axis is usually b, which is by default parallel to y. Thus monoclinic crystals in the standard second setting should be rotated 90 degrees on x. If the unique axis is a, a rotation of 90 degrees on y should be entered

Some trigonal, tetragonal and hexagonal space groups have either of two different orientations of the symmetry elements with respect to the axes. In some cases, only one of the orientations is consistent with the basis functions used for symmetry analysis used in VIBRATZ. Specifically, space groups in the point or factor group D2d, of the type P4m2 (where P and m may be replaced by other symbols), must be rotated by 45 degrees. Space groups in the point or factor group D3h, of the type P62m, and of the point or factor group C3v of the type P3m1, must be rotated by 30 degrees. Space groups of the type P42m, P6m2 and P31m do not require rotation.

Space groups in the point or factor groups D3 and D3d also may take two different orientations, but either orientation is valid without rotation. However, the Raman components which appear in the E species are different depending on the orientation.

See Orientation for more information about orientations and rotations.

Non-standard settings. Often non-standard settings can be attained by selecting a space group, then switching to the Custom Symmetry option. It is especially easy to change the Bravais lattice type. For example, for the space group C(bar)1, select P(bar)1 then switch to the the Custom Symmetry option and change the Bravais lattice to C.