PLUTON92 and PLATON Manual

Space Group Symmetry

Space group symmetry is handled in PLATON with a general space group symmetry management routine that permits the specification of the symmetry either explicitly in terms of the general equivalent positions as presented in the International Tables or implicitly in terms of space group generators. The generators for all space groups in theirstandard setting and some commonly used non-standard settings are also implicitly retrievable by the program from internal tables on the basis of the specified name of the space group (e.g. R-3m)
For example, the symmetry for space group number 19 P212121 may be specified either as:

     LATT P A
     SYMM X,Y,Z
     SYMM 1/2 + X, 1/2 - Y, -Z
     SYMM -X, 1/2 + Y, 1/2 - Z
     SYMM 1/2 - X, - Y, 1/2 + Z
or
     LATT P A
     SYMM 1/2 + X, 1/2 - Y, -Z
     SYMM -X, 1/2 + Y, 1/2 - Z
or
     SPGR P212121

A LATT card should precede any SYMM card in order that the symmetry arrays are initialized to either, by default, a primitive non-centrosymmetric lattice or to the specified lattice type:

(P/A/B/C/I/F) and (A)Centric type (A/C).

The general equivalent positions should be given as specified in International Tables and should have the centre of symmetry at the origin, in the case that the space group is centrosymmetric. The symmetry operation SYMM X,Y,Z is always implicitly assumed as the first symmetry operation and needs not be given although any redundancy in the symmetry input will be ignored.

Note: Rhombohedral lattice types (in hexagonal setting) should be specified explicitly using an extra symmetry generator. Thus the generators for space group R3 are:

     LATT P A
     SYMM -Y, X-Y, Z
     SYMM 1/3+X, 2/3+Y, 2/3+Z

The same space group on rhombohedral axes should be specified as R3R.
The translation part may be specified either as a ratio or as a real (e.g. 1/4 or 0.25).
Monoclinic-b is taken as the standard setting for monoclinic space groups. Other settings are to be specified by the full space group name: e.g. P112 for the monoclinic-c setting of P2.

Non-standard orthorhombic settings such as space group A2aa may be handled by specifying Ccc2 -cba on the SPGR card (see International Tables Vol A). In fact the program automatically modifies the input line accordingly for non-standard settings (see table below). The standard setting symmetry is than transformed accordingly.

Note: Symmetry may also be presented in the SHELXL93 style. However, a LATT card should always be supplied since the default symmetry of PLATON is always P1 whereas SHELX93 defaults to P-1.

They space group names are in accordance with the usage in the CAMBRIDGE CRYSTALLOGRAPHIC DATA BASE files.