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.