This page documents an OPTIMADE Property Definition. See https://schemas.optimade.org/ for more information.
ID: https://schemas.anyterial.se/defs/v0.1/properties/pointgroups/character_table_complex
Definition name: character_table_complex
Property name: Complex character table
Description: Complex irreducible character table of the crystallographic point group.
Type: list
Rows correspond to complex irreducible representations and columns follow the order of conjugacy_classes.
Characters are exact complex rational values stored as dictionaries with re and im fraction strings, so that they round-trip without floating-point loss.
Examples:
[{"label": "A", "dimension": 1, "characters": [1], "frobenius_schur_indicator": 1, "label_markup": {"latex": "A", "unicode": "A"}}][{"label": "Ag", "dimension": 1, "characters": [1, 1], "frobenius_schur_indicator": 1, "label_markup": {"latex": "A_{g}", "unicode": "Ag"}}, {"label": "Au", "dimension": 1, "characters": [1, -1], "frobenius_schur_indicator": 1, "label_markup": {"latex": "A_{u}", "unicode": "Au"}}]JSON definition:
{
"$id": "https://schemas.anyterial.se/defs/v0.1/properties/pointgroups/character_table_complex",
"$schema": "https://schemas.optimade.org/meta/v1.3/optimade/property_definition.json",
"title": "Complex character table",
"$comment": "Generated from data-generators JSON-LD fields without external definition URLs.",
"x-optimade-type": "list",
"x-optimade-definition": {
"kind": "property",
"version": "0.1.0",
"format": "1.3",
"name": "character_table_complex",
"label": "character_table_complex_pointgroups"
},
"type": [
"array",
"null"
],
"description": "Complex irreducible character table of the crystallographic point group.\n\nRows correspond to complex irreducible representations and columns follow the order of `conjugacy_classes`.\nCharacters are exact complex rational values stored as dictionaries with `re` and `im` fraction strings, so that they round-trip without floating-point loss.",
"x-optimade-unit": "inapplicable",
"items": {
"x-optimade-type": "dictionary",
"type": [
"object",
"null"
],
"description": "One row of a point-group character table.",
"properties": {
"label": {
"x-optimade-type": "string",
"type": [
"string",
"null"
],
"description": "Irreducible-representation label.",
"x-optimade-unit": "inapplicable"
},
"label_markup": {
"$id": "https://schemas.anyterial.se/defs/v0.1/properties/core/string_markups",
"title": "String markups",
"x-optimade-type": "dictionary",
"x-optimade-definition": {
"kind": "property",
"version": "0.1.0",
"format": "1.3",
"name": "string_markups",
"label": "string_markups_core"
},
"x-optimade-unit": "inapplicable",
"type": [
"object",
"null"
],
"description": "Strings with alternate markup and/or encoding for display rendering.\n\nThe object is intended for display-oriented variants only, a sibling property should be used for canonical plain string value.\n\n**Requirements/Conventions**:\n\n- It MUST be a dictionary with the following keys:\n\n - **html**: OPTIONAL; String.\n HTML rendering of the sibling string, using inline HTML elements where needed for typographic structure such as subscripts, superscripts, overlines, fractions, and line breaks.\n\n - **latex**: OPTIONAL; String.\n LaTeX rendering of the sibling string, suitable for use with a LaTeX or MathJax-like renderer.\n\n - **unicode**: OPTIONAL; String.\n Unicode rendering of the sibling string, using Unicode code points for display features where practical.",
"properties": {
"html": {
"x-optimade-type": "string",
"x-optimade-unit": "inapplicable",
"type": [
"string",
"null"
],
"description": "HTML rendering of the sibling string."
},
"latex": {
"x-optimade-type": "string",
"x-optimade-unit": "inapplicable",
"type": [
"string",
"null"
],
"description": "LaTeX rendering of the sibling string."
},
"unicode": {
"x-optimade-type": "string",
"x-optimade-unit": "inapplicable",
"type": [
"string",
"null"
],
"description": "Unicode rendering of the sibling string."
}
},
"examples": [
{
"html": "<i>P</i> 2<sub>1</sub>/<i>c</i>",
"latex": "\\mathit{P}\\,2_{1}/c",
"unicode": "P2\u2081/c"
}
]
},
"dimension": {
"x-optimade-type": "integer",
"type": [
"integer",
"null"
],
"description": "Dimension of the irreducible representation.",
"x-optimade-unit": "inapplicable"
},
"characters": {
"x-optimade-type": "list",
"type": [
"array",
"null"
],
"description": "Characters for the conjugacy classes in table order.",
"items": {
"x-optimade-type": "dictionary",
"type": [
"object",
"null"
],
"description": "One complex character value represented as exact real and imaginary parts.",
"x-optimade-unit": "inapplicable",
"properties": {
"re": {
"x-optimade-type": "string",
"type": [
"string",
"null"
],
"description": "Exact real part represented as a string.",
"x-optimade-unit": "inapplicable"
},
"im": {
"x-optimade-type": "string",
"type": [
"string",
"null"
],
"description": "Exact imaginary part represented as a string.",
"x-optimade-unit": "inapplicable"
}
}
},
"x-optimade-unit": "inapplicable"
},
"frobenius_schur_indicator": {
"x-optimade-type": "integer",
"type": [
"integer",
"null"
],
"description": "Frobenius-Schur indicator of the representation.",
"x-optimade-unit": "inapplicable"
},
"basis_linear": {
"x-optimade-type": "list",
"type": [
"array",
"null"
],
"description": "Linear basis functions transforming as this representation.",
"items": {
"x-optimade-type": "string",
"type": [
"string",
"null"
],
"description": "One basis function.",
"x-optimade-unit": "inapplicable"
},
"x-optimade-unit": "inapplicable"
},
"basis_rotation": {
"x-optimade-type": "list",
"type": [
"array",
"null"
],
"description": "Rotational basis functions transforming as this representation.",
"items": {
"x-optimade-type": "string",
"type": [
"string",
"null"
],
"description": "One rotational basis function.",
"x-optimade-unit": "inapplicable"
},
"x-optimade-unit": "inapplicable"
},
"basis_quadratic": {
"x-optimade-type": "list",
"type": [
"array",
"null"
],
"description": "Quadratic basis functions transforming as this representation.",
"items": {
"x-optimade-type": "string",
"type": [
"string",
"null"
],
"description": "One quadratic basis function.",
"x-optimade-unit": "inapplicable"
},
"x-optimade-unit": "inapplicable"
}
},
"x-optimade-unit": "inapplicable"
},
"examples": [
[
{
"label": "A",
"dimension": 1,
"characters": [
1
],
"frobenius_schur_indicator": 1,
"label_markup": {
"latex": "A",
"unicode": "A"
}
}
],
[
{
"label": "Ag",
"dimension": 1,
"characters": [
1,
1
],
"frobenius_schur_indicator": 1,
"label_markup": {
"latex": "A_{g}",
"unicode": "Ag"
}
},
{
"label": "Au",
"dimension": 1,
"characters": [
1,
-1
],
"frobenius_schur_indicator": 1,
"label_markup": {
"latex": "A_{u}",
"unicode": "Au"
}
}
]
]
}