# Crystal symmetry

## Contents

# Crystal symmetry¶

## Tolerance used in crystal symmetry search¶

Phonon calculation is based on the assumption that atoms have their 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 symmetrized 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 attempting
possible symmetry operations to the crystal structure and checking 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.