## Symmetry operation rule

Symmetry operation in space group is treated by a transformation matrix, i.e., symrel, and a translation vector, i.e., tnons. The center of symmetry operation is always the origin of the crystal coordinates. The translation is not always required for the non-symmorphic operations since there are symmorphic operations whose center are not at the origin. In such a case, the symmetry operation is represented by the combination of the symmetry operation matrix and the translation vector. In the code, the symmetry operation is used beyond these mentioned above and is also used for the structure which is not a primitive structure, e.g. supercell. The symmetry of this structure contains pure translations inside the cell and cannot be determined its space group. When we use the symmetry operation in the code, symrel and tnons are used as follows. In forward operation,
xred_new(:) = matmul(symrel(:,:), xred(:)) + tnons(:),
where xred is an atom position in reduced coordinates. In backward operation,
xred_new(:) = matmul(symrel(:,:), xred(:) - tnons(:)).
Be careful not to change the order of xred and tnons.

togo 2009-02-12