# space group symmetry operations (property)
This page documents an [OPTIMADE](https://www.optimade.org/) [Property Definition](https://schemas.optimade.org/#definitions). See [https://schemas.optimade.org/](https://schemas.optimade.org/) for more information.
**ID: [`https://schemas.optimade.org/defs/v1.2/properties/optimade/structures/space_group_symmetry_operations_xyz`](https://schemas.optimade.org/defs/v1.2/properties/optimade/structures/space_group_symmetry_operations_xyz.md)**
**Definition name:** `space_group_symmetry_operations_xyz`
**Property name:** space group symmetry operations
**Description:** A list of symmetry operations given as general position x, y and z coordinates in algebraic form.
**Type:** list
**Requirements/Conventions**:
- MUST be `null` if the property `nperiodic_dimensions` is equal to 0.
- Each symmetry operation is described by a string that gives that symmetry operation in Jones' faithful representation (Bradley & Cracknell, 1972: pp. 35-37), adapted for computer string notation.
- The letters `x`, `y` and `z` that are typesetted with overbars in printed text represent coordinate values multiplied by -1 and are encoded as `-x`, `-y` and `-z`, respectively.
- The syntax of the string representing a symmetry operation MUST conform to regular expressions given in the OPTIMADE specification appendix 'The Symmetry Operation String Regular Expressions'.
- The interpretation of the strings MUST follow the conventions of the IUCr CIF core dictionary (IUCr, 2023).
- In particular, this property MUST explicitly provide all symmetry operations needed to generate all the atoms in the unit cell from the atoms in the asymmetric unit, for the setting used.
- This symmetry operation set MUST always include the `x,y,z` identity operation.
- The symmetry operations are to be applied to fractional atom coordinates.
- In case only Cartesian coordinates are available, these Cartesian coordinates must be converted to fractional coordinates before the application of the provided symmetry operations.
- If the symmetry operation list is present, it MUST be compatible with other space group specifications (e.g. the ITC space group number, the Hall symbol, the Hermann-Mauguin symbol) if these are present.
**Notes**:
- The list of space group symmetry operations applies to the whole periodic array of atoms and together with the lattice translations given in the `lattice_vectors` property provides the necessary information to reconstruct all atom site positions of the periodic material.
- Thus, the symmetry operations described in this property are only applicable to material models with at least one periodic dimension.
- This property is not meant to represent arbitrary symmetries of molecules, non-periodic (finite) collections of atoms or non-crystallographic symmetry.
**Explained examples**:
- Space group operations for the space group with ITC number 3 (H-M symbol `P 2`, extended H-M symbol `P 1 2 1`, Hall symbol `P 2y`): `["x,y,z", "-x,y,-z"]`
- Space group operations for the space group with ITC number 5 (H-M symbol `C 2`, extended H-M symbol `C 1 2 1`, Hall symbol `C 2y`): `["x,y,z", "-x,y,-z", "x+1/2,y+1/2,z", "-x+1/2,y+1/2,-z"]`
**Bibliographic References**
- Bradley, C. J. and Cracknell, A. P. (1972) The Mathematical Theory of Symmetry in Solids. Oxford, Clarendon Press (paperback edition 2010) 745 p. [ISBN 978-0-19-958258-7](https://isbnsearch.org/isbn/9780199582587>).
- IUCr (2023) Core dictionary (coreCIF) version 2.4.5; data name `_space_group_symop_operation_xyz`. Available from: [https://www.iucr.org/__data/iucr/cifdic_html/1/cif_core.dic/Ispace_group_symop_operation_xyz.html](https://www.iucr.org/__data/iucr/cifdic_html/1/cif_core.dic/Ispace_group_symop_operation_xyz.html) [Accessed 2023-06-18T16:46+03:00].
**Examples:**
- `["x,y,z", "-x,y,-z"]`
- `["x,y,z", "-x,y,-z", "x+1/2,y+1/2,z", "-x+1/2,y+1/2,-z"]`
**Formats:** [[JSON](space_group_symmetry_operations_xyz.json)] [[MD](space_group_symmetry_operations_xyz.md)]
**JSON definition:**
``` json
{
"$id": "https://schemas.optimade.org/defs/v1.2/properties/optimade/structures/space_group_symmetry_operations_xyz",
"$schema": "https://schemas.optimade.org/meta/v1.2/optimade/property_definition.json",
"title": "space group symmetry operations",
"x-optimade-type": "list",
"x-optimade-definition": {
"label": "space_group_symmetry_operations_xyz_optimade_structures",
"kind": "property",
"version": "1.2.0",
"format": "1.2",
"name": "space_group_symmetry_operations_xyz"
},
"type": [
"array",
"null"
],
"description": "A list of symmetry operations given as general position x, y and z coordinates in algebraic form.\n\n**Requirements/Conventions**:\n\n- MUST be `null` if the property `nperiodic_dimensions` is equal to 0.\n- Each symmetry operation is described by a string that gives that symmetry operation in Jones' faithful representation (Bradley & Cracknell, 1972: pp. 35-37), adapted for computer string notation.\n- The letters `x`, `y` and `z` that are typesetted with overbars in printed text represent coordinate values multiplied by -1 and are encoded as `-x`, `-y` and `-z`, respectively.\n- The syntax of the string representing a symmetry operation MUST conform to regular expressions given in the OPTIMADE specification appendix 'The Symmetry Operation String Regular Expressions'.\n- The interpretation of the strings MUST follow the conventions of the IUCr CIF core dictionary (IUCr, 2023).\n- In particular, this property MUST explicitly provide all symmetry operations needed to generate all the atoms in the unit cell from the atoms in the asymmetric unit, for the setting used.\n- This symmetry operation set MUST always include the `x,y,z` identity operation.\n- The symmetry operations are to be applied to fractional atom coordinates.\n- In case only Cartesian coordinates are available, these Cartesian coordinates must be converted to fractional coordinates before the application of the provided symmetry operations.\n- If the symmetry operation list is present, it MUST be compatible with other space group specifications (e.g. the ITC space group number, the Hall symbol, the Hermann-Mauguin symbol) if these are present.\n\n**Notes**:\n\n- The list of space group symmetry operations applies to the whole periodic array of atoms and together with the lattice translations given in the `lattice_vectors` property provides the necessary information to reconstruct all atom site positions of the periodic material.\n- Thus, the symmetry operations described in this property are only applicable to material models with at least one periodic dimension.\n- This property is not meant to represent arbitrary symmetries of molecules, non-periodic (finite) collections of atoms or non-crystallographic symmetry.\n\n**Explained examples**:\n\n- Space group operations for the space group with ITC number 3 (H-M symbol `P 2`, extended H-M symbol `P 1 2 1`, Hall symbol `P 2y`): `[\"x,y,z\", \"-x,y,-z\"]`\n- Space group operations for the space group with ITC number 5 (H-M symbol `C 2`, extended H-M symbol `C 1 2 1`, Hall symbol `C 2y`): `[\"x,y,z\", \"-x,y,-z\", \"x+1/2,y+1/2,z\", \"-x+1/2,y+1/2,-z\"]`\n\n**Bibliographic References**\n\n- Bradley, C. J. and Cracknell, A. P. (1972) The Mathematical Theory of Symmetry in Solids. Oxford, Clarendon Press (paperback edition 2010) 745 p. [ISBN 978-0-19-958258-7](https://isbnsearch.org/isbn/9780199582587>).\n- IUCr (2023) Core dictionary (coreCIF) version 2.4.5; data name `_space_group_symop_operation_xyz`. Available from: [https://www.iucr.org/__data/iucr/cifdic_html/1/cif_core.dic/Ispace_group_symop_operation_xyz.html](https://www.iucr.org/__data/iucr/cifdic_html/1/cif_core.dic/Ispace_group_symop_operation_xyz.html) [Accessed 2023-06-18T16:46+03:00].",
"examples": [
[
"x,y,z",
"-x,y,-z"
],
[
"x,y,z",
"-x,y,-z",
"x+1/2,y+1/2,z",
"-x+1/2,y+1/2,-z"
]
],
"x-optimade-unit": "unapplicable",
"items": {
"$id": "https://schemas.optimade.org/defs/v1.2/properties/optimade/common/space_group_symmetry_operation_xyz",
"title": "space group symmetry operation",
"x-optimade-type": "string",
"x-optimade-definition": {
"label": "space_group_symmetry_operation_xyz_optimade_common",
"kind": "property",
"version": "1.2.0",
"format": "1.2",
"name": "space_group_symmetry_operation_xyz"
},
"type": [
"string"
],
"description": "A single symmetry operation.\n\n**Requirements/Conventions**:\n\n- The symmetry operation is described in Jones' faithful representation (Bradley & Cracknell, 1972: pp. 35-37), adapted for computer string notation.\n- The interpretation of the string MUST follow the conventions of the IUCr CIF core dictionary (IUCr, 2023).\n- The letters `x`, `y` and `z` that are typesetted with overbars in printed text represent coordinate values multiplied by -1 and are encoded as `-x`, `-y` and `-z`, respectively.\n- The syntax of the string representing a symmetry operation MUST conform to regular expressions given in the OPTIMADE specification appendix 'The Symmetry Operation String Regular Expressions'.\n\n**Bibliographic References**\n\n- Bradley, C. J. and Cracknell, A. P. (1972) The Mathematical Theory of Symmetry in Solids. Oxford, Clarendon Press (paperback edition 2010) 745 p. [ISBN 978-0-19-958258-7](https://isbnsearch.org/isbn/9780199582587>).\n- IUCr (2023) Core dictionary (coreCIF) version 2.4.5; data name `_space_group_symop_operation_xyz`. Available from: [https://www.iucr.org/__data/iucr/cifdic_html/1/cif_core.dic/Ispace_group_symop_operation_xyz.html](https://www.iucr.org/__data/iucr/cifdic_html/1/cif_core.dic/Ispace_group_symop_operation_xyz.html) [Accessed 2023-06-18T16:46+03:00].",
"examples": [
"x,y,z",
"-x,y,-z"
],
"x-optimade-unit": "inapplicable"
}
}
```