Symmetry - Custom
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Dialog Box - called from: Symmetry Dialog

ATOMS can access all the standard orientations for space groups in the International Tables but there are still a few possibilities for alternate settings of symmetry elements with respect to structure axes which are not listed in the Tables. In some cases displacement, rotation or permutation of atomic coordinates may not be convenient, and it may be easier to enter the symmetry operations for the non-standard setting. These are sometimes given in reports on structures (e.g. Wyckoff, Crystal Structures). Note however that often only the operations for special positions are given: ATOMS needs all the operations for the general position.

The Symbol is for your reference only - it is not used by ATOMS, unless you click the Get Symbol button (below).

Get Symbol. This button will attempt to identify the space group from the operations, the lattice type and the centric/acentric setting. If the operations contain an inversion center or lattice centerings, they should be identified and can be removed at your option.

If you specify centric, rather than acentric, you must enter only half of the symmetry operations, related to any others by the center. The two sets or halves of the operations related by the center will have opposite signs on the x, y and z coordinates.

The Bravais lattice type is in most cases the capital letter which begins the space-group symbol. However, ATOMS 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.

If the group is monoclinic, you should specify which is the Unique axis. This is normally c for a molecule and b for a crystal. The angle specified in the Title/Axes dialog will then be applied correctly, the other two interaxial angles being set to 90 degrees.

In the Operations group, you must enter all the "symmetry operations" for the most general position in the structure. Click on the Add Operation button to add an operator, or Delete to remove an operator. The operation which is selected in the Operations list box is available for editing in the box to the right. Note that earlier versions of ATOMS allowed several operations per line; currently, there should be only one operation per line. Semicolons at the end of each operation (line) are optional.

It is assumed in the following that you will be using data listed in the International Tables, but this is only for purposes of illustration; if you find it necessary to enter the operations through this dialog, you will very likely be using data from another source. Reports on crystal structures, especially older ones, often list the relevant operations in the same format as the Tables.

In the Tables, the "Co-ordinates of equivalent positions" can be regarded as operations (or at least the operations can be easily derived from them). These coordinates occupy the middle of the page in each space-group entry in the Tables, and the general position is the uppermost group. The general position has the point symmetry 1, and the list of operations for this position always begins with "x,y,z;". The individual operations are separated in the Tables by semicolons.

Copy these operations, including the commas (semicolons optional), one per line. They are entered just as given in the Tables, except that a negative sign, indicated by a small bar over the letter in the Tables, must be indicated with a minus sign in front of the letter. The first operation, "x,y,z;" is present in all symmetry groups and must always be entered. Ignore the translations for non-primitive lattices (e.g. 0,0,0; 1/2,1/2,1/2) which may be listed in the Tables above the operations; these are taken care of if you enter the proper Bravais lattice symbol. Some older structure reports may include lattice-centering in the equivalent positions.

Important: if you have specified a centric space group with origin on the center of inversion, you should omit half the operations, which are related to the other half by the center (opposite signs for x, y and z coordinates). If you have difficulty making this separation, you can specify non-centric and enter all the operations. The Get Symbol button should detect a center of inversion on the origin, and remove it if desired.