### Setup of the unit cell symmetry

The symmetry of the system is another important input to Fleur. It is specified by providing a list of symmetry operations. Usually, these operations are generated by the input-generator by inspection of the cell and atomic input.

For certain calculations you might want to modify the operations and for example remove symmetry operations. While this is easily possible by removing operations from the list in inp.xml you should be careful not to remove operations that map equivalent atoms onto each other within an atom group. If you remove such operations you have to adjust the assignment of atoms to groups.

The usual way to specify symmetry operations is by using the corresponding '' XML tag.

      <symmetryOperations>
<symOp>
<row-1>1 0 0 .0000000000</row-1>
<row-2>0 1 0 .0000000000</row-2>
<row-3>0 0 1 .0000000000</row-3>
</symOp>
<symOp>
<row-1>-1 0 0 .0000000000</row-1>
<row-2>0 1 0 .0000000000</row-2>
<row-3>0 0 1 .0000000000</row-3>
</symOp>
<symOp>
<row-1>1 0 0 .0000000000</row-1>
<row-2>0 -1 0 .0000000000</row-2>
<row-3>0 0 1 .0000000000</row-3>
</symOp>
<symOp>
<row-1>-1 0 0 .0000000000</row-1>
<row-2>0 -1 0 .0000000000</row-2>
<row-3>0 0 1 .0000000000</row-3>
</symOp>
<symOp>
<row-1>0 -1 0 .5000000000</row-1>
<row-2>-1 0 0 .5000000000</row-2>
<row-3>0 0 1 .0000000000</row-3>
</symOp>
<symOp>
<row-1>0 -1 0 .5000000000</row-1>
<row-2>1 0 0 .5000000000</row-2>
<row-3>0 0 1 .0000000000</row-3>
</symOp>
<symOp>
<row-1>0 1 0 .5000000000</row-1>
<row-2>-1 0 0 .5000000000</row-2>
<row-3>0 0 1 .0000000000</row-3>
</symOp>
<symOp>
<row-1>0 1 0 .5000000000</row-1>
<row-2>1 0 0 .5000000000</row-2>
<row-3>0 0 1 .0000000000</row-3>
</symOp>
<symOp>
<row-1>1 0 0 .5000000000</row-1>
<row-2>0 1 0 .5000000000</row-2>
<row-3>0 0 -1 .0000000000</row-3>
</symOp>
<symOp>
<row-1>-1 0 0 .5000000000</row-1>
<row-2>0 1 0 .5000000000</row-2>
<row-3>0 0 -1 .0000000000</row-3>
</symOp>
<symOp>
<row-1>1 0 0 .5000000000</row-1>
<row-2>0 -1 0 .5000000000</row-2>
<row-3>0 0 -1 .0000000000</row-3>
</symOp>
<symOp>
<row-1>-1 0 0 .5000000000</row-1>
<row-2>0 -1 0 .5000000000</row-2>
<row-3>0 0 -1 .0000000000</row-3>
</symOp>
<symOp>
<row-1>0 -1 0 .0000000000</row-1>
<row-2>-1 0 0 .0000000000</row-2>
<row-3>0 0 -1 .0000000000</row-3>
</symOp>
<symOp>
<row-1>0 -1 0 .0000000000</row-1>
<row-2>1 0 0 .0000000000</row-2>
<row-3>0 0 -1 .0000000000</row-3>
</symOp>
<symOp>
<row-1>0 1 0 .0000000000</row-1>
<row-2>-1 0 0 .0000000000</row-2>
<row-3>0 0 -1 .0000000000</row-3>
</symOp>
<symOp>
<row-1>0 1 0 .0000000000</row-1>
<row-2>1 0 0 .0000000000</row-2>
<row-3>0 0 -1 .0000000000</row-3>
</symOp>
</symmetryOperations>

The symmetryOperations element allows to specify each symmetry operation directly. Each symmetry operation is given by a matrix of three rows and four columns, where the last column is a translation vector needed for nonsymmorphic symmetries. If the input file generator is invoked with the -explicit command line switch this form of declaring the symmetry operations is used in the inp.xml file.

Including the sym.xml file

As this list can be long it might be desired to provide the symmetry operations in a separate file. You can use the x-include option for this purpose.

#### Alternative options to specify the symmetry

Deprecated options to specify the symmetry

The options below are still in frequent use but should be considered as deprecated. We will remove them in future.

##### Symmetries in an external sym.out file
<symmetryFile filename="sym.out"/>

By providing the symmetryFile element the symmetry operations are read in from an external file. Typically this is the sym.out file written out by the input file generator. It is, of course, possible to change the filename with the associated attribute. At the moment the generation and usage of the sym.out file is the default for most inpgen runs.

##### Explicit specification of space-groups
<symmetry spgrp="p4m" invs="T" zrfs="T"/>

With the XML element symmetry it is possible to define the symmetries by providing one of the 2D space groups in the attribute spgrp and additionally providing information about the availability of inversion symmetry in invs and z reflection symmetry in zrfs. The applicable 2D space groups are (where the angles denote the number of centers for corresponding rotations):

name lattice 180° 120° 90° 60° reflection axes glide reflections
p1 oblique - - - - - -
p2 oblique 4 - - - - -
pmy
pgy
cmy
pmm rectangular 4 - - - 4 (in 2 perp. directions) -
pmg rectangular 2 - - - 2 (parallel) 2 (parallel, perp. to refl. axes)
pgg rectangular 2 - - - - 4 (in 2 perp. directions)
cmm rhombic 3 - - - 2 (in 2 perp. directions) 4 (in 2 perp. directions)
p4 square 2 - 2 - - -
p4m square 2 - 2 - 6 (2 horizontal, 2 vertical, 2 diagonal) 4 (in 2 perp. directions, not on refl. axes)
p4g square 2 - 2 - 4 (2 per diagonal) 6 (in 4 directions, not on refl. axes)
p3 hexagonal - 3 - - - -
p3m1 hexagonal - 3 - - 5 (in 3 directions) 8 (in 3 directions, in middle between refl. axes)
p31m hexagonal - 3 - - 3 (in 3 directions) 4 (in 3 directions, in middle between refl. axes)
p6 hexagonal 3 2 - 1 - -
p6m hexagonal 3 2 - 1 8 (in 6 directions) 12 (in 6 directions, in middle between refl. axes)
pm rectangular - - - - 2 (parallel) -
pg rectangular - - - - - 2 (parallel)
cm rhombic - - - - 2 (parallel) 2 (parallel to, in middle between refl. axes)