This page documents an OPTIMADE Property Definition. See https://schemas.optimade.org/ for more information.
ID: https://schemas.anyterial.se/defs/v0.1/properties/symmetry/wyckoff_position
Definition name: wyckoff_position
Property name: Wyckoff position
Description: Information related to a Wyckoff position in a space-group setting.
Type: dictionary
Wyckoff positions represent symmetry-equivalent sites partitioned by multiplicity and site symmetry in a given space group. The property is a dictionary containing information about the multiplicity, oriented site-symmetry symbol, representative coordinate, full orbit, and orbit factorized modulo centering translations.
Requirements/Conventions:
It MUST be a dictionary with the following keys:
letter: REQUIRED; String. Wyckoff letter for this position in the setting.
multiplicity: REQUIRED; Integer.
Multiplicity of the Wyckoff position in the conventional cell.
It MUST equal the length of orbit.
sitesym: REQUIRED; String. Oriented site-symmetry symbol.
hasfreedom: REQUIRED; List of booleans. Flags indicating whether each fractional coordinate has a free parameter.
first_orbit: REQUIRED; String.
First representative coordinate expression used by the generator.
It MUST equal the xyz field of orbit[0].
orbit: REQUIRED; List. Full orbit as a list of affine transformations from Wyckoff-position parameters to fractional coordinates. The first item is the canonical representative whose degrees of freedom can be chosen to place it inside the asymmetric unit.
orbit_mod_centering: REQUIRED; List.
Orbit representatives modulo centering translations, represented in the same form as orbit.
Examples:
{"letter": "e", "multiplicity": 2, "sitesym": "1", "hasfreedom": [true, true, true], "first_orbit": "x,y,z", "orbit": [{"matrix": [["1", "0", "0"], ["0", "1", "0"], ["0", "0", "1"]], "vector": ["0", "0", "0"], "xyz": "x,y,z"}, {"matrix": [["-1", "0", "0"], ["0", "1", "0"], ["0", "0", "-1"]], "vector": ["0", "0", "0"], "xyz": "-x,y,-z"}], "orbit_mod_centering": [{"matrix": [["1", "0", "0"], ["0", "1", "0"], ["0", "0", "1"]], "vector": ["0", "0", "0"], "xyz": "x,y,z"}, {"matrix": [["-1", "0", "0"], ["0", "1", "0"], ["0", "0", "-1"]], "vector": ["0", "0", "0"], "xyz": "-x,y,-z"}]}JSON definition:
{
"$id": "https://schemas.anyterial.se/defs/v0.1/properties/symmetry/wyckoff_position",
"$schema": "https://schemas.optimade.org/meta/v1.3/optimade/property_definition.json",
"title": "Wyckoff position",
"x-optimade-type": "dictionary",
"x-optimade-definition": {
"kind": "property",
"version": "0.1.0",
"format": "1.3",
"name": "wyckoff_position",
"label": "wyckoff_position_symmetry"
},
"x-optimade-unit": "inapplicable",
"type": [
"object",
"null"
],
"description": "Information related to a Wyckoff position in a space-group setting.\n\nWyckoff positions represent symmetry-equivalent sites partitioned by multiplicity and site symmetry in a given space group.\nThe property is a dictionary containing information about the multiplicity, oriented site-symmetry symbol, representative coordinate, full orbit, and orbit factorized modulo centering translations.\n\n**Requirements/Conventions**:\n\n- It MUST be a dictionary with the following keys:\n\n - **letter**: REQUIRED; String.\n Wyckoff letter for this position in the setting.\n\n - **multiplicity**: REQUIRED; Integer.\n Multiplicity of the Wyckoff position in the conventional cell.\n It MUST equal the length of `orbit`.\n\n - **sitesym**: REQUIRED; String.\n Oriented site-symmetry symbol.\n\n - **hasfreedom**: REQUIRED; List of booleans.\n Flags indicating whether each fractional coordinate has a free parameter.\n\n - **first\\_orbit**: REQUIRED; String.\n First representative coordinate expression used by the generator.\n It MUST equal the `xyz` field of `orbit[0]`.\n\n - **orbit**: REQUIRED; List.\n Full orbit as a list of affine transformations from Wyckoff-position parameters to fractional coordinates.\n The first item is the canonical representative whose degrees of freedom can be chosen to place it inside the asymmetric unit.\n\n - **orbit\\_mod\\_centering**: REQUIRED; List.\n Orbit representatives modulo centering translations, represented in the same form as `orbit`.",
"properties": {
"letter": {
"$id": "https://schemas.optimade.org/defs/v1.3/properties/optimade/structures/wyckoff_positions",
"title": "Wyckoff positions",
"x-optimade-type": "list",
"x-optimade-definition": {
"label": "wyckoff_positions_optimade_structures",
"kind": "property",
"version": "1.3.0",
"format": "1.2",
"name": "wyckoff_positions"
},
"x-optimade-dimensions": {
"names": [
"dim_sites"
],
"sizes": [
null
]
},
"type": [
"array",
"null"
],
"description": "A list of Wyckoff symbols of sites (where values for sites are specified with the same order of the property `cartesian_site_positions` and/or `fractional_site_positions`).\n\n**Requirements/Conventions**:\n\n- MUST have length equal to the number of sites in the structure (first dimension of the list properties `cartesian_site_positions` and/or `fractional_site_positions`).\n- If provided, MUST list a single letter (`a`-`z` or `\u03b1`) Wyckoff position for each site in the structure according to the International Tables for Crystallography vol. A (IUCr, 2016).\n\n**Bibliographic References**:\n\n- IUCr (2016). International Tables for Crystallography vol. A. Space-group Symmetry, Ed. M. I. Aroyo, 6-th edition. Chichester, John Wiley & Sons.",
"x-optimade-unit": "inapplicable",
"items": {
"$id": "https://schemas.optimade.org/defs/v1.3/properties/optimade/common/wyckoff_position",
"title": "Wyckoff position",
"x-optimade-type": "string",
"x-optimade-definition": {
"label": "wyckoff_position_optimade_common",
"kind": "property",
"version": "1.3.0",
"format": "1.2",
"name": "wyckoff_position"
},
"description": "The Wyckoff symbol for a site.",
"x-optimade-unit": "inapplicable",
"type": [
"string"
],
"maxLength": 1,
"enum": [
"a",
"b",
"c",
"d",
"e",
"f",
"g",
"h",
"i",
"j",
"k",
"l",
"m",
"n",
"o",
"p",
"q",
"r",
"s",
"t",
"u",
"v",
"w",
"x",
"y",
"z",
"\u03b1"
]
}
},
"multiplicity": {
"x-optimade-type": "integer",
"x-optimade-unit": "inapplicable",
"x-compatible": [
"https://www.iucr.org/__data/iucr/cifdic_html/3/CORE_DIC/Ispace_group_Wyckoff.multiplicity.html"
],
"type": [
"integer",
"null"
],
"description": "Multiplicity of the Wyckoff position in the conventional cell."
},
"sitesym": {
"x-optimade-type": "string",
"x-optimade-unit": "inapplicable",
"x-compatible": [
"https://www.iucr.org/__data/iucr/cifdic_html/3/CORE_DIC/Ispace_group_Wyckoff.site_symmetry.html"
],
"type": [
"string",
"null"
],
"description": "The site-symmetry symbol for the subgroup of the space group that leaves the point fixed.\nThe symmetry direction is determined by the Hermann-Mauguin symbol of the space group, as given in International Tables for Crystallography Volume A, Section 2.2.12 (2006)."
},
"hasfreedom": {
"x-optimade-type": "list",
"x-optimade-unit": "inapplicable",
"x-optimade-dimensions": {
"names": [
"dim_lattice"
],
"sizes": [
3
]
},
"type": [
"array",
"null"
],
"description": "A list of three booleans indicating whether each fractional coordinate contains a free parameter.",
"items": {
"x-optimade-type": "boolean",
"x-optimade-unit": "inapplicable",
"type": [
"boolean"
],
"description": "A boolean indicating if the corresponding coordinate is free."
}
},
"first_orbit_ita": {
"x-optimade-type": "string",
"x-optimade-unit": "inapplicable",
"type": [
"string",
"null"
],
"description": "Representative coordinate expression following the source convention in the International Tables of Crystallography Volume A (2006), when distinct from `first_orbit`."
},
"first_orbit": {
"x-optimade-type": "string",
"x-optimade-unit": "inapplicable",
"type": [
"string",
"null"
],
"description": "Representative coordinate expression for the Wyckoff position chosen such that the degrees of freedom can be chosen to place it inside the asymmetric unit obtained from cctbx.\nThis value MUST equal the `xyz` field of `orbit[0]`; it is repeated here as a directly queryable convenience field."
},
"orbit": {
"x-optimade-type": "list",
"x-optimade-unit": "inapplicable",
"type": [
"array",
"null"
],
"description": "Full orbit of the Wyckoff position.\nEach item is an affine transformation from the Wyckoff-position parameter vector `(x, y, z)` to one fractional coordinate in the orbit.\nThe matrix part may be singular because special Wyckoff positions can constrain or identify parameters.",
"items": {
"$id": "https://schemas.anyterial.se/defs/v0.1/properties/symmetry/affine_transformation",
"title": "Affine transformation",
"x-optimade-type": "dictionary",
"x-optimade-definition": {
"kind": "property",
"version": "0.1.0",
"format": "1.3",
"name": "affine_transformation",
"label": "affine_transformation_symmetry"
},
"x-optimade-unit": "inapplicable",
"type": [
"object",
"null"
],
"description": "An affine transformation acting on fractional crystallographic coordinates.\n\nAn affine transformation is a geometric transformation preserving points, straight lines, and parallelism (collinearity), but may not preserve Euclidean distances and angles.\nThe transformation is represented by a 3 by 3 matrix and a 3-vector, both serialized with exact string entries.\nThe transformation may, for example, represent an operation within one setting, a setting transform, a subgroup embedding, a normalizer representative, or a parametric coordinate map for a Wyckoff-position orbit representative.\nWhen used as a parametric coordinate map, the matrix may be singular because special Wyckoff positions can constrain or identify parameters.\n\n**Requirements/Conventions**:\n\n- It MUST be a dictionary with the following keys:\n\n - **matrix**: REQUIRED; Exact 3x3 matrix.\n Matrix part of the affine transformation.\n It MUST be represented as a list of three row lists, each containing three exact rational entries represented as strings.\n\n - **vector**: REQUIRED; List of 3 Fractions (String).\n Translation or origin-shift vector of the affine transformation in fractional coordinates.\n\n - **xyz**: OPTIONAL; String.\n Coordinate expression for the affine transformation in `x,y,z` notation when available.\n\n - **det**: OPTIONAL; Integer.\n Determinant of `matrix` when the generator emits it.\n\n - **is\\_orthogonal**: OPTIONAL; Boolean.\n Whether `matrix` is orthogonal in the exact representation used by the generator.",
"properties": {
"matrix": {
"x-optimade-type": "list",
"x-optimade-unit": "inapplicable",
"x-optimade-dimensions": {
"names": [
"dim_lattice",
"dim_lattice"
],
"sizes": [
3,
3
]
},
"type": [
"array",
"null"
],
"description": "Exact 3 by 3 matrix part of the affine transformation.",
"items": {
"x-optimade-type": "list",
"x-optimade-unit": "inapplicable",
"x-optimade-dimensions": {
"names": [
"dim_lattice"
],
"sizes": [
3
]
},
"type": [
"array"
],
"description": "One row of the exact 3 by 3 matrix.",
"items": {
"$id": "https://schemas.anyterial.se/defs/v0.1/properties/core/fraction",
"title": "Fraction",
"x-optimade-type": "string",
"x-optimade-definition": {
"label": "fraction_core",
"kind": "property",
"version": "0.1.0",
"format": "1.3",
"name": "fraction"
},
"type": [
"string",
"null"
],
"description": "A numerical representation formed as the quotient of two numbers represented as a string.",
"examples": [
"2/3",
"5/42",
"10",
"0"
],
"x-optimade-unit": "inapplicable"
}
}
},
"vector": {
"x-optimade-type": "list",
"x-optimade-unit": "inapplicable",
"x-optimade-dimensions": {
"names": [
"dim_lattice"
],
"sizes": [
3
]
},
"type": [
"array",
"null"
],
"description": "Exact fractional-coordinate vector part of the affine transformation.",
"items": {
"$id": "https://schemas.anyterial.se/defs/v0.1/properties/core/fraction",
"title": "Fraction",
"x-optimade-type": "string",
"x-optimade-definition": {
"label": "fraction_core",
"kind": "property",
"version": "0.1.0",
"format": "1.3",
"name": "fraction"
},
"type": [
"string",
"null"
],
"description": "A numerical representation formed as the quotient of two numbers represented as a string.",
"examples": [
"2/3",
"5/42",
"10",
"0"
],
"x-optimade-unit": "inapplicable"
}
},
"xyz": {
"$id": "https://schemas.anyterial.se/defs/v0.1/properties/symmetry/op_xyz",
"title": "Operation xyz",
"x-optimade-type": "string",
"x-compatibility": [
"https://schemas.optimade.org/defs/v1.2/properties/optimade/common/symmetry_operation_xyz",
"https://www.iucr.org/__data/iucr/cifdic_html/2/cif_sym.dic/Ispace_group_symop.operation_xyz.html"
],
"x-optimade-definition": {
"kind": "property",
"version": "0.1.0",
"format": "1.3",
"name": "op_xyz",
"label": "op_xyz_symmetry"
},
"x-optimade-unit": "inapplicable",
"type": [
"string",
"null"
],
"description": "Coordinate operation expressed in the algebraic xyz form, also known as Jones' faithful representation (Bradley & Cracknell, 1972: pp. 35-37; adapted for computer strings).\n\nThe following definition is adapted from (and meant to be compatible with) the IUCr symCIF version 1.0.1 dictionary definition of `_space_group_symop.operation_xyz` referenced to: International Tables for Crystallography (2002). Volume A, Space-group symmetry, edited by Th. Hahn, 5th. ed. (Kluwer Academic Publishers).\nIt is available at: https://www.iucr.org/__data/iucr/cifdic_html/2/cif_sym.dic/Ispace_group_symop.operation_xyz.html\n\nIf W is a matrix representation of the rotational part of the symmetry operation defined by the positions and signs of x, y and z, and w is a column of translations defined by the fractions, an equivalent position X' is generated from a given position X by the equation: X' = WX + w.",
"x-undef-pattern": "^([-+]?[xyz]([-+][xyz])?([-+](1/2|[12]/3|[1-3]/4|[1-5]/6))?|[-+]?(1/2|[12]/3|[1-3]/4|[1-5]/6)([-+][xyz]([-+][xyz])?)?),([-+]?[xyz]([-+][xyz])?([-+](1/2|[12]/3|[1-3]/4|[1-5]/6))?|[-+]?(1/2|[12]/3|[1-3]/4|[1-5]/6)([-+][xyz]([-+][xyz])?)?),([-+]?[xyz]([-+][xyz])?([-+](1/2|[12]/3|[1-3]/4|[1-5]/6))?|[-+]?(1/2|[12]/3|[1-3]/4|[1-5]/6)([-+][xyz]([-+][xyz])?)?)$",
"examples": [
"-x,-y,z",
"x,1/2-y,1/2+z"
]
},
"det": {
"x-optimade-type": "integer",
"x-optimade-unit": "inapplicable",
"type": [
"integer",
"null"
],
"description": "Determinant of the matrix part when emitted by the generator."
},
"is_orthogonal": {
"x-optimade-type": "boolean",
"x-optimade-unit": "inapplicable",
"type": [
"boolean",
"null"
],
"description": "Whether the matrix part is orthogonal."
}
},
"examples": [
{
"matrix": [
[
"-1",
"0",
"0"
],
[
"0",
"-1",
"0"
],
[
"0",
"0",
"1"
]
],
"vector": [
"0",
"0",
"0"
],
"xyz": "-x,-y,z",
"det": 1,
"is_orthogonal": true
}
]
}
},
"orbit_mod_centering": {
"x-optimade-type": "list",
"x-optimade-unit": "inapplicable",
"type": [
"array",
"null"
],
"description": "Representatives of the Wyckoff-position orbit modulo centering translations.\nEach item has the same affine-transformation representation as an item in `orbit`.",
"items": {
"$id": "https://schemas.anyterial.se/defs/v0.1/properties/symmetry/affine_transformation",
"title": "Affine transformation",
"x-optimade-type": "dictionary",
"x-optimade-definition": {
"kind": "property",
"version": "0.1.0",
"format": "1.3",
"name": "affine_transformation",
"label": "affine_transformation_symmetry"
},
"x-optimade-unit": "inapplicable",
"type": [
"object",
"null"
],
"description": "An affine transformation acting on fractional crystallographic coordinates.\n\nAn affine transformation is a geometric transformation preserving points, straight lines, and parallelism (collinearity), but may not preserve Euclidean distances and angles.\nThe transformation is represented by a 3 by 3 matrix and a 3-vector, both serialized with exact string entries.\nThe transformation may, for example, represent an operation within one setting, a setting transform, a subgroup embedding, a normalizer representative, or a parametric coordinate map for a Wyckoff-position orbit representative.\nWhen used as a parametric coordinate map, the matrix may be singular because special Wyckoff positions can constrain or identify parameters.\n\n**Requirements/Conventions**:\n\n- It MUST be a dictionary with the following keys:\n\n - **matrix**: REQUIRED; Exact 3x3 matrix.\n Matrix part of the affine transformation.\n It MUST be represented as a list of three row lists, each containing three exact rational entries represented as strings.\n\n - **vector**: REQUIRED; List of 3 Fractions (String).\n Translation or origin-shift vector of the affine transformation in fractional coordinates.\n\n - **xyz**: OPTIONAL; String.\n Coordinate expression for the affine transformation in `x,y,z` notation when available.\n\n - **det**: OPTIONAL; Integer.\n Determinant of `matrix` when the generator emits it.\n\n - **is\\_orthogonal**: OPTIONAL; Boolean.\n Whether `matrix` is orthogonal in the exact representation used by the generator.",
"properties": {
"matrix": {
"x-optimade-type": "list",
"x-optimade-unit": "inapplicable",
"x-optimade-dimensions": {
"names": [
"dim_lattice",
"dim_lattice"
],
"sizes": [
3,
3
]
},
"type": [
"array",
"null"
],
"description": "Exact 3 by 3 matrix part of the affine transformation.",
"items": {
"x-optimade-type": "list",
"x-optimade-unit": "inapplicable",
"x-optimade-dimensions": {
"names": [
"dim_lattice"
],
"sizes": [
3
]
},
"type": [
"array"
],
"description": "One row of the exact 3 by 3 matrix.",
"items": {
"$id": "https://schemas.anyterial.se/defs/v0.1/properties/core/fraction",
"title": "Fraction",
"x-optimade-type": "string",
"x-optimade-definition": {
"label": "fraction_core",
"kind": "property",
"version": "0.1.0",
"format": "1.3",
"name": "fraction"
},
"type": [
"string",
"null"
],
"description": "A numerical representation formed as the quotient of two numbers represented as a string.",
"examples": [
"2/3",
"5/42",
"10",
"0"
],
"x-optimade-unit": "inapplicable"
}
}
},
"vector": {
"x-optimade-type": "list",
"x-optimade-unit": "inapplicable",
"x-optimade-dimensions": {
"names": [
"dim_lattice"
],
"sizes": [
3
]
},
"type": [
"array",
"null"
],
"description": "Exact fractional-coordinate vector part of the affine transformation.",
"items": {
"$id": "https://schemas.anyterial.se/defs/v0.1/properties/core/fraction",
"title": "Fraction",
"x-optimade-type": "string",
"x-optimade-definition": {
"label": "fraction_core",
"kind": "property",
"version": "0.1.0",
"format": "1.3",
"name": "fraction"
},
"type": [
"string",
"null"
],
"description": "A numerical representation formed as the quotient of two numbers represented as a string.",
"examples": [
"2/3",
"5/42",
"10",
"0"
],
"x-optimade-unit": "inapplicable"
}
},
"xyz": {
"$id": "https://schemas.anyterial.se/defs/v0.1/properties/symmetry/op_xyz",
"title": "Operation xyz",
"x-optimade-type": "string",
"x-compatibility": [
"https://schemas.optimade.org/defs/v1.2/properties/optimade/common/symmetry_operation_xyz",
"https://www.iucr.org/__data/iucr/cifdic_html/2/cif_sym.dic/Ispace_group_symop.operation_xyz.html"
],
"x-optimade-definition": {
"kind": "property",
"version": "0.1.0",
"format": "1.3",
"name": "op_xyz",
"label": "op_xyz_symmetry"
},
"x-optimade-unit": "inapplicable",
"type": [
"string",
"null"
],
"description": "Coordinate operation expressed in the algebraic xyz form, also known as Jones' faithful representation (Bradley & Cracknell, 1972: pp. 35-37; adapted for computer strings).\n\nThe following definition is adapted from (and meant to be compatible with) the IUCr symCIF version 1.0.1 dictionary definition of `_space_group_symop.operation_xyz` referenced to: International Tables for Crystallography (2002). Volume A, Space-group symmetry, edited by Th. Hahn, 5th. ed. (Kluwer Academic Publishers).\nIt is available at: https://www.iucr.org/__data/iucr/cifdic_html/2/cif_sym.dic/Ispace_group_symop.operation_xyz.html\n\nIf W is a matrix representation of the rotational part of the symmetry operation defined by the positions and signs of x, y and z, and w is a column of translations defined by the fractions, an equivalent position X' is generated from a given position X by the equation: X' = WX + w.",
"x-undef-pattern": "^([-+]?[xyz]([-+][xyz])?([-+](1/2|[12]/3|[1-3]/4|[1-5]/6))?|[-+]?(1/2|[12]/3|[1-3]/4|[1-5]/6)([-+][xyz]([-+][xyz])?)?),([-+]?[xyz]([-+][xyz])?([-+](1/2|[12]/3|[1-3]/4|[1-5]/6))?|[-+]?(1/2|[12]/3|[1-3]/4|[1-5]/6)([-+][xyz]([-+][xyz])?)?),([-+]?[xyz]([-+][xyz])?([-+](1/2|[12]/3|[1-3]/4|[1-5]/6))?|[-+]?(1/2|[12]/3|[1-3]/4|[1-5]/6)([-+][xyz]([-+][xyz])?)?)$",
"examples": [
"-x,-y,z",
"x,1/2-y,1/2+z"
]
},
"det": {
"x-optimade-type": "integer",
"x-optimade-unit": "inapplicable",
"type": [
"integer",
"null"
],
"description": "Determinant of the matrix part when emitted by the generator."
},
"is_orthogonal": {
"x-optimade-type": "boolean",
"x-optimade-unit": "inapplicable",
"type": [
"boolean",
"null"
],
"description": "Whether the matrix part is orthogonal."
}
},
"examples": [
{
"matrix": [
[
"-1",
"0",
"0"
],
[
"0",
"-1",
"0"
],
[
"0",
"0",
"1"
]
],
"vector": [
"0",
"0",
"0"
],
"xyz": "-x,-y,z",
"det": 1,
"is_orthogonal": true
}
]
}
}
},
"examples": [
{
"letter": "e",
"multiplicity": 2,
"sitesym": "1",
"hasfreedom": [
true,
true,
true
],
"first_orbit": "x,y,z",
"orbit": [
{
"matrix": [
[
"1",
"0",
"0"
],
[
"0",
"1",
"0"
],
[
"0",
"0",
"1"
]
],
"vector": [
"0",
"0",
"0"
],
"xyz": "x,y,z"
},
{
"matrix": [
[
"-1",
"0",
"0"
],
[
"0",
"1",
"0"
],
[
"0",
"0",
"-1"
]
],
"vector": [
"0",
"0",
"0"
],
"xyz": "-x,y,-z"
}
],
"orbit_mod_centering": [
{
"matrix": [
[
"1",
"0",
"0"
],
[
"0",
"1",
"0"
],
[
"0",
"0",
"1"
]
],
"vector": [
"0",
"0",
"0"
],
"xyz": "x,y,z"
},
{
"matrix": [
[
"-1",
"0",
"0"
],
[
"0",
"1",
"0"
],
[
"0",
"0",
"-1"
]
],
"vector": [
"0",
"0",
"0"
],
"xyz": "-x,y,-z"
}
]
}
]
}