Crystal symmetry

Tolerance used in crystal symmetry search

Phonon calculation is based on the assumption that atoms have thier own equilibrium positions where forces on these atoms are zero. In addition, there is a unit cell that contains these atoms and the unit cell are repeated in the direct space, i.e., it forms a lattice. The lattice vectors (or basis vectors) and points of atoms in this unit cell give the information of the crystal structure.

The crystal structure may have a specific symmetry. The categorization of the crystal symmetried is achieved by the group theory about symmetry operations, and there are the 230 different space group types. In phonopy, the crystal symmetry is automatically analyzed from the input unit cell structure file that doesn’t contain the symmetry information. Symmetries are searched by attemping possible symmetry operations to the crystal structure and cheking if the crystal structure after the symmetry operation is overlapping to the original crystal structures. In this analysis, a tolerance of distance is used to tolerate small deviation of overlapping. This tolerance is the user’s choice. The default value is 1e-5.

Often we know the space group type of our crystal. Therefore it is recommended to check whether the space group type of the input unit cell is the correct one or not with very tight value such as --tolerance=1e-8 (SYMMETRY_TOLERANCE). If an input unit cell structure is naively distorted for which the distortion is about the same order of the chosen tolerance, inconsistency in symmetry handling may occur and it can result in a crash of the calculation or induce a strange calculation result. This can be checked by changing the tolerance value variously and watching the obtained space group type. If an input unit cell structure is distorted, different space group types are found with respect to the different tolerance values.

The detailed space group information is obtained by --symmetry option. As a result of using this option and the chosen tolerance value, BPOSCAR file is obtained. This is a standardized conventional unit cell (see https://spglib.github.io/spglib/definition.html#conventions-of-standardized-unit-cell), and its distortion against the crystal symmetry is very small. It is recommended to used this structure as the starting point of phonopy calculation.