# pymatgen.analysis.chemenv.coordination_environments.coordination_geometries module¶

This module contains the class describing the coordination geometries that can exist in a given structure. These “model” coordination geometries are described in the following articles :

• Pure Appl. Chem., Vol. 79, No. 10, pp. 1779–1799, 2007.

• Acta Cryst. A, Vol. 46, No. 1, pp. 1–11, 1990.

The module also contains descriptors of part of these geometries (plane of separation, …) that are used in the identification algorithms.

class AbstractChemenvAlgorithm(algorithm_type)[source]

Bases: monty.json.MSONable

Base class used to define a Chemenv algorithm used to identify the correct permutation for the computation of the Continuous Symmetry Measure.

Base constructor for ChemenvAlgorithm.

Parameters

algorithm_type (str) – Type of algorithm.

property algorithm_type[source]

Return the type of algorithm.

Returns: Type of the algorithm

abstract as_dict()[source]

A JSON serializable dict representation of the algorithm

class AllCoordinationGeometries(permutations_safe_override=False, only_symbols=None)[source]

Bases: dict

Class used to store all the reference “coordination geometries” (list with instances of the CoordinationGeometry classes)

Initializes the list of Coordination Geometries.

Parameters
• permutations_safe_override – Whether to use safe permutations.

• only_symbols – Whether to restrict the list of environments to be identified.

get_geometries(coordination=None, returned='cg')[source]

Returns a list of coordination geometries with the given coordination number.

Parameters
• coordination – The coordination number of which the list of coordination geometries are returned.

• returned – Type of objects in the list.

get_geometry_from_IUCr_symbol(IUCr_symbol)[source]

Returns the coordination geometry of the given IUCr symbol.

Parameters

IUCr_symbol – The IUCr symbol of the coordination geometry.

get_geometry_from_IUPAC_symbol(IUPAC_symbol)[source]

Returns the coordination geometry of the given IUPAC symbol.

Parameters

IUPAC_symbol – The IUPAC symbol of the coordination geometry.

get_geometry_from_mp_symbol(mp_symbol)[source]

Returns the coordination geometry of the given mp_symbol.

Parameters

mp_symbol – The mp_symbol of the coordination geometry.

get_geometry_from_name(name)[source]

Returns the coordination geometry of the given name.

Parameters

name – The name of the coordination geometry.

get_implemented_geometries(coordination=None, returned='cg', include_deactivated=False)[source]

Returns a list of the implemented coordination geometries with the given coordination number.

Parameters
• coordination – The coordination number of which the list of implemented coordination geometries are returned.

• returned – Type of objects in the list.

• include_deactivated – Whether to include CoordinationGeometry that are deactivated.

get_not_implemented_geometries(coordination=None, returned='mp_symbol')[source]

Returns a list of the implemented coordination geometries with the given coordination number.

Parameters
• coordination – The coordination number of which the list of implemented coordination geometries are returned.

• returned – Type of objects in the list.

get_symbol_cn_mapping(coordination=None)[source]

Return a dictionary mapping the symbol of a CoordinationGeometry to its coordination.

Parameters

coordination – Whether to restrict the dictionary to a given coordination.

Returns: Dictionary mapping the symbol of a CoordinationGeometry to its coordination.

get_symbol_name_mapping(coordination=None)[source]

Return a dictionary mapping the symbol of a CoordinationGeometry to its name.

Parameters

coordination – Whether to restrict the dictionary to a given coordination.

Returns: Dictionary mapping the symbol of a CoordinationGeometry to its name.

is_a_valid_coordination_geometry(mp_symbol=None, IUPAC_symbol=None, IUCr_symbol=None, name=None, cn=None)[source]

Checks whether a given coordination geometry is valid (exists) and whether the parameters are coherent with each other.

Parameters
• mp_symbol – The mp_symbol of the coordination geometry.

• IUPAC_symbol – The IUPAC_symbol of the coordination geometry.

• IUCr_symbol – The IUCr_symbol of the coordination geometry.

• name – The name of the coordination geometry.

• cn – The coordination of the coordination geometry.

pretty_print(type='implemented_geometries', maxcn=8, additional_info=None)[source]

Return a string with a list of the Coordination Geometries.

Parameters
• type – Type of string to be returned (all_geometries, all_geometries_latex_images, all_geometries_latex, implemented_geometries).

• maxcn – Maximum coordination.

Returns: String describing the list of coordination geometries.

class CoordinationGeometry(mp_symbol, name, alternative_names=None, IUPAC_symbol=None, IUCr_symbol=None, coordination=None, central_site=array([0.0, 0.0, 0.0]), points=None, solid_angles=None, permutations_safe_override=False, deactivate=False, faces=None, edges=None, algorithms=None, equivalent_indices=None, neighbors_sets_hints=None)[source]

Bases: object

Class used to store the ideal representation of a chemical environment or “coordination geometry”.

Initializes one “coordination geometry” according to [Pure Appl. Chem., Vol. 79, No. 10, pp. 1779–1799, 2007] and [Acta Cryst. A, Vol. 46, No. 1, pp. 1–11, 1990].

Parameters
• mp_symbol – Symbol used internally for the coordination geometry.

• name – Name of the coordination geometry.

• alternative_names – Alternative names for this coordination geometry.

• IUPAC_symbol – The IUPAC symbol of this coordination geometry.

• IUCr_symbol – The IUCr symbol of this coordination geometry.

• coordination – The coordination number of this coordination geometry (number of neighboring atoms).

• central_site – The coordinates of the central site of this coordination geometry.

• points – The list of the coordinates of all the points of this coordination geometry.

• solid_angles – The list of solid angles for each neighbor in this coordination geometry.

• permutations_safe_override – Computes all the permutations if set to True (overrides the plane separation algorithms or any other algorithm, for testing purposes)

• deactivate – Whether to deactivate this coordination geometry

• faces – List of the faces with their vertices given in a clockwise or anticlockwise order, for drawing purposes.

• edges – List of edges, for drawing purposes.

• algorithms – Algorithms used to identify this coordination geometry.

• equivalent_indices – The equivalent sets of indices in this coordination geometry (can be used to skip equivalent permutations that have already been performed).

• neighbors_sets_hints – Neighors sets hints for this coordination geometry.

CSM_SKIP_SEPARATION_PLANE_ALGO = 10.0[source]
property IUCr_symbol[source]

Returns the IUCr symbol of this coordination geometry.

property IUCr_symbol_str[source]

Returns a string representation of the IUCr symbol of this coordination geometry.

property IUPAC_symbol[source]

Returns the IUPAC symbol of this coordination geometry.

property IUPAC_symbol_str[source]

Returns a string representation of the IUPAC symbol of this coordination geometry.

class NeighborsSetsHints(hints_type, options)[source]

Bases: object

Class used to describe neighbors sets hints.

This allows to possibly get a lower coordination from a capped-like model polyhedron.

Parameters
• hints_type – type of hint (single, double or triple cap)

• options – options for the “hinting”, e.g. the maximum csm value beyond which no additional neighbors set could be found from a “cap hint”.

ALLOWED_HINTS_TYPES = ['single_cap', 'double_cap', 'triple_cap'][source]
as_dict()[source]

A JSON serializable dict representation of this NeighborsSetsHints

double_cap_hints(hints_info)[source]

Return hints for an additional neighbors set, i.e. the voronoi indices that constitute this new neighbors set, in case of a “Double cap” hint.

Parameters

hints_info – Info needed to build new “hinted” neighbors set.

Returns: Voronoi indices of the new “hinted” neighbors set.

classmethod from_dict(dd)[source]

Reconstructs the NeighborsSetsHints from its JSON serializable dict representation.

Parameters

dd – a JSON serializable dict representation of a NeighborsSetsHints.

hints(hints_info)[source]

Return hints for an additional neighbors set, i.e. the voronoi indices that constitute this new neighbors set.

Parameters

hints_info – Info needed to build new “hinted” neighbors set.

Returns: Voronoi indices of the new “hinted” neighbors set.

single_cap_hints(hints_info)[source]

Return hints for an additional neighbors set, i.e. the voronoi indices that constitute this new neighbors set, in case of a “Single cap” hint.

Parameters

hints_info – Info needed to build new “hinted” neighbors set.

Returns: Voronoi indices of the new “hinted” neighbors set.

triple_cap_hints(hints_info)[source]

Return hints for an additional neighbors set, i.e. the voronoi indices that constitute this new neighbors set, in case of a “Triple cap” hint.

Parameters

hints_info – Info needed to build new “hinted” neighbors set.

Returns: Voronoi indices of the new “hinted” neighbors set.

property algorithms[source]

Returns the list of algorithms that are used to identify this coordination geometry.

as_dict()[source]

A JSON serializable dict representation of this CoordinationGeometry.

property ce_symbol[source]

Returns the symbol of this coordination geometry.

property coordination_number[source]

Returns the coordination number of this coordination geometry.

property distfactor_max[source]

The maximum distfactor for the perfect CoordinationGeometry.

Returns: Maximum distfactor for the perfect CoordinationGeometry (usually 1.0 for symmetric polyhedrons).

edges(sites, permutation=None, input='sites')[source]

Returns the list of edges of this coordination geometry. Each edge is given as a list of its end vertices coordinates.

faces(sites, permutation=None)[source]

Returns the list of faces of this coordination geometry. Each face is given as a list of its vertices coordinates.

classmethod from_dict(dd)[source]

Reconstructs the CoordinationGeometry from its JSON serializable dict representation.

Parameters

dd – a JSON serializable dict representation of a CoordinationGeometry.

Returns: a CoordinationGeometry.

get_central_site()[source]

Returns the central site of this coordination geometry.

get_coordination_number()[source]

Returns the coordination number of this coordination geometry.

get_name()[source]

Returns the name of this coordination geometry.

get_pmeshes(sites, permutation=None)[source]

Returns the pmesh strings used for jmol to show this geometry.

is_implemented()[source]

Returns True if this coordination geometry is implemented.

property mp_symbol[source]

Returns the MP symbol of this coordination geometry.

property number_of_permutations[source]

Returns the number of permutations of this coordination geometry.

property pauling_stability_ratio[source]

Returns the theoretical Pauling stability ratio (rC/rA) for this environment.

ref_permutation(permutation)[source]

Returns the reference permutation for a set of equivalent permutations.

Can be useful to skip permutations that have already been performed.

Parameters

permutation – Current permutation

Returns: Reference permutation of the perfect CoordinationGeometry.

set_permutations_safe_override(permutations_safe_override)[source]

Setup ChemEnv so that a safe set of permutations are used.

Parameters

permutations_safe_override – Whether to use safe permutations.

solid_angles(permutation=None)[source]

Returns the list of “perfect” solid angles Each edge is given as a list of its end vertices coordinates.

class ExplicitPermutationsAlgorithm(permutations)[source]

Class representing the algorithm doing the explicit permutations for the calculation of the Continuous Symmetry Measure.

Initializes a separation plane for a given perfect coordination geometry.

Parameters

permutations – Permutations used for this algorithm.

property as_dict[source]

Return the JSON serializable dict representation of this ExplicitPermutationsAlgorithm algorithm.

Returns: a JSON serializable dict representation of this ExplicitPermutationsAlgorithm algorithm.

classmethod from_dict(dd)[source]

Reconstructs the ExplicitPermutationsAlgorithm algorithm from its JSON serializable dict representation.

Parameters

dd – a JSON serializable dict representation of an ExplicitPermutationsAlgorithm algorithm.

Returns: an ExplicitPermutationsAlgorithm algorithm.

property permutations[source]

Return the permutations to be performed for this algorithm.

Returns: Permutations to be performed.

class SeparationPlane(plane_points, mirror_plane=False, ordered_plane=False, point_groups=None, ordered_point_groups=None, explicit_permutations=None, minimum_number_of_points=None, explicit_optimized_permutations=None, multiplicity=None, other_plane_points=None)[source]

Class representing the algorithm using separation planes for the calculation of the Continuous Symmetry Measure.

Initializes a separation plane for a given perfect coordination geometry

Parameters
• plane_points – Indices of the points that are in the plane in the perfect structure (and should be found in the defective one as well).

• mirror_plane – True if the separation plane is a mirror plane, in which case there is a correspondence of the points in each point_group (can reduce the number of permutations).

• ordered_plane – True if the order of the points in the plane can be taken into account to reduce the number of permutations.

• point_groups – Indices of the points in the two groups of points separated by the plane.

• ordered_point_groups – Whether the order of the points in each group of points can be taken into account to reduce the number of permutations.

• explicit_permutations – Explicit permutations to be performed in this separation plane algorithm.

• minimum_number_of_points – Minimum number of points needed to initialize a separation plane for this algorithm.

• explicit_optimized_permutations – Optimized set of explicit permutations to be performed in this separation plane algorithm.

• multiplicity – Number of such planes in the model geometry.

• other_plane_points – Indices of the points that are in the plane in the perfect structure for the other planes. The multiplicity should be equal to the length of this list + 1 (“main” separation plane + the other ones).

property argsorted_ref_separation_perm[source]

“Arg sorted” ordered indices of the separation plane.

This is used in the identification of the final permutation to be used.

Returns: list of the “arg sorted” ordered indices of the separation plane.

property as_dict[source]

Return the JSON serializable dict representation of this SeparationPlane algorithm.

Returns: a JSON serializable dict representation of this SeparationPlane algorithm.

classmethod from_dict(dd)[source]

Reconstructs the SeparationPlane algorithm from its JSON serializable dict representation.

Parameters

dd – a JSON serializable dict representation of an SeparationPlane algorithm.

Returns: a SeparationPlane algorithm.

property permutations[source]

Permutations used for this separation plane algorithm.

Returns: List of permutations to be performed.

property ref_separation_perm[source]

Ordered indices of the separation plane.

Examples

For a separation plane of type 2|4|3, with plane_points indices [0, 3, 5, 8] and point_groups indices [1, 4] and [2, 7, 6], the list of ordered indices is : [0, 3, 5, 8, 1, 4, 2, 7, 6].

Returns: list of ordered indices of this separation plane.

safe_separation_permutations(ordered_plane=False, ordered_point_groups=None, add_opposite=False)[source]

Simple and safe permutations for this separation plane.

This is not meant to be used in production. Default configuration for ChemEnv does not use this method. :param ordered_plane: Whether the order of the points in the plane can be used to reduce the

number of permutations.

Parameters
• ordered_point_groups – Whether the order of the points in each point group can be used to reduce the number of permutations.

• add_opposite – Whether to add the permutations from the second group before the first group as well.

Returns: List of safe permutations.