pymatgen.analysis.structure_matcher module

This module provides classes to perform fitting of structures.

class AbstractComparator

Bases: MSONable

Abstract Comparator class. A Comparator defines how sites are compared in a structure.

abstract are_equal(sp1, sp2) → bool

Defines how the species of two sites are considered equal. For example, one can consider sites to have the same species only when the species are exactly the same, i.e., Fe2+ matches Fe2+ but not Fe3+. Or one can define that only the element matters, and all oxidation state information are ignored.

Parameters:

• sp1 – First species. A dict of {specie/element: amt} as per the definition in Site and PeriodicSite.

• sp2 – Second species. A dict of {specie/element: amt} as per the definition in Site and PeriodicSite.

Returns:

Boolean indicating whether species are considered equal.

as_dict()

Returns:

MSONable dict

classmethod from_dict(d)

Parameters:

d – Dict representation

Returns:

Comparator.

abstract get_hash(composition)

Defines a hash to group structures. This allows structures to be grouped efficiently for comparison. The hash must be invariant under supercell creation. (e.g. composition is not a good hash, but fractional_composition might be). Reduced formula is not a good formula, due to weird behavior with fractional occupancy.

Composition is used here instead of structure because for anonymous matches it is much quicker to apply a substitution to a composition object than a structure object.

Parameters:

composition (Composition) – composition of the structure

Returns:

A hashable object. Examples can be string formulas, integers etc.

class ElementComparator

Bases: AbstractComparator

A Comparator that matches elements. i.e. oxidation states are ignored.

are_equal(sp1, sp2) → bool

True if element:amounts are exactly the same, i.e., oxidation state is not considered.

Parameters:

• sp1 – First species. A dict of {specie/element: amt} as per the definition in Site and PeriodicSite.

• sp2 – Second species. A dict of {specie/element: amt} as per the definition in Site and PeriodicSite.

Returns:

Boolean indicating whether species are the same based on element and amounts.

get_hash(composition)

Returns: Fractional element composition

class FrameworkComparator

Bases: AbstractComparator

A Comparator that matches sites, regardless of species.

are_equal(sp1, sp2) → bool

True if there are atoms on both sites.

Parameters:

• sp1 – First species. A dict of {specie/element: amt} as per the definition in Site and PeriodicSite.

• sp2 – Second species. A dict of {specie/element: amt} as per the definition in Site and PeriodicSite.

Returns:

True always

get_hash(composition)

No hash possible

class OccupancyComparator

Bases: AbstractComparator

A Comparator that matches occupancies on sites, irrespective of the species of those sites.

are_equal(sp1, sp2) → bool

Parameters:

• sp1 – First species. A dict of {specie/element: amt} as per the definition in Site and PeriodicSite.

• sp2 – Second species. A dict of {specie/element: amt} as per the definition in Site and PeriodicSite.

Returns:

True if sets of occupancies (amt) are equal on both sites.

get_hash(composition)

Parameters:

composition – Composition.

Returns:

1. Difficult to define sensible hash

class OrderDisorderElementComparator

Bases: AbstractComparator

A Comparator that matches sites, given some overlap in the element composition

are_equal(sp1, sp2) → bool

True if there is some overlap in composition between the species

Parameters:

• sp1 – First species. A dict of {specie/element: amt} as per the definition in Site and PeriodicSite.

• sp2 – Second species. A dict of {specie/element: amt} as per the definition in Site and PeriodicSite.

Returns:

True always

get_hash(composition)

Returns: Fractional composition

class SpeciesComparator

Bases: AbstractComparator

A Comparator that matches species exactly. The default used in StructureMatcher.

are_equal(sp1, sp2) → bool

True if species are exactly the same, i.e., Fe2+ == Fe2+ but not Fe3+.

Parameters:

• sp1 – First species. A dict of {specie/element: amt} as per the definition in Site and PeriodicSite.

• sp2 – Second species. A dict of {specie/element: amt} as per the definition in Site and PeriodicSite.

Returns:

Boolean indicating whether species are equal.

get_hash(composition)

Returns: Fractional composition

class SpinComparator

Bases: AbstractComparator

A Comparator that matches magnetic structures to their inverse spins. This comparator is primarily used to filter magnetically ordered structures with opposite spins, which are equivalent.

are_equal(sp1, sp2) → bool

True if species are exactly the same, i.e., Fe2+ == Fe2+ but not Fe3+. and the spins are reversed. i.e., spin up maps to spin down, and vice versa.

Parameters:

• sp1 – First species. A dict of {specie/element: amt} as per the definition in Site and PeriodicSite.

• sp2 – Second species. A dict of {specie/element: amt} as per the definition in Site and PeriodicSite.

Returns:

Boolean indicating whether species are equal.

get_hash(composition)

Returns: Fractional composition

class StructureMatcher(ltol: float = 0.2, stol: float = 0.3, angle_tol: float = 5, primitive_cell: bool = True, scale: bool = True, attempt_supercell: bool = False, allow_subset: bool = False, comparator: AbstractComparator | None = None, supercell_size: Literal['num_sites', 'num_atoms', 'volume'] = 'num_sites', ignored_species: Sequence[str | Element | Species | DummySpecies] = ())

Bases: MSONable

Class to match structures by similarity.

Algorithm:

1. Given two structures: s1 and s2

2. Optional: Reduce to primitive cells.

3. If the number of sites do not match, return False

4. Reduce to s1 and s2 to Niggli Cells

5. Optional: Scale s1 and s2 to same volume.

6. Optional: Remove oxidation states associated with sites

7. Find all possible lattice vectors for s2 within shell of ltol.

8. For s1, translate an atom in the smallest set to the origin

9. For s2: find all valid lattices from permutations of the list of lattice vectors (invalid if: det(Lattice Matrix) < half volume of original s2 lattice)

10. For each valid lattice:

    1. If the lattice angles of are within tolerance of s1, basis change s2 into new lattice.

    2. For each atom in the smallest set of s2:

       i. Translate to origin and compare fractional sites in structure within a fractional tolerance. ii. If true:

       ia. Convert both lattices to Cartesian and place both structures on an average lattice ib. Compute and return the average and max rms displacement between the two structures normalized by the average free length per atom

       if fit function called:

       if normalized max rms displacement is less than stol. Return True

       if get_rms_dist function called:

       if normalized average rms displacement is less than the stored rms displacement, store and continue. (This function will search all possible lattices for the smallest average rms displacement between the two structures)

Parameters:

• ltol (float) – Fractional length tolerance. Default is 0.2.

• stol (float) – Site tolerance. Defined as the fraction of the average free length per atom := ( V / Nsites ) ** (1/3) Default is 0.3.

• angle_tol (float) – Angle tolerance in degrees. Default is 5 degrees.

• primitive_cell (bool) – If true: input structures will be reduced to primitive cells prior to matching. Default to True.

• scale (bool) – Input structures are scaled to equivalent volume if true; For exact matching, set to False.

• attempt_supercell (bool) – If set to True and number of sites in cells differ after a primitive cell reduction (divisible by an integer) attempts to generate a supercell transformation of the smaller cell which is equivalent to the larger structure.

• allow_subset (bool) – Allow one structure to match to the subset of another structure. Eg. Matching of an ordered structure onto a disordered one, or matching a delithiated to a lithiated structure. This option cannot be combined with attempt_supercell, or with structure grouping.

• comparator (Comparator) –

  A comparator object implementing an equals method that declares equivalency of sites. Default is SpeciesComparator, which implies rigid species mapping, i.e., Fe2+ only matches Fe2+ and not Fe3+.

  Other comparators are provided, e.g., ElementComparator which matches only the elements and not the species.

  The reason why a comparator object is used instead of supplying a comparison function is that it is not possible to pickle a function, which makes it otherwise difficult to use StructureMatcher with Python’s multiprocessing.

• supercell_size (str or list) – Method to use for determining the size of a supercell (if applicable). Possible values are ‘num_sites’, ‘num_atoms’, ‘volume’, or an element or list of elements present in both structures.

• ignored_species (list) – A list of ions to be ignored in matching. Useful for matching structures that have similar frameworks except for certain ions, e.g., Li-ion intercalation frameworks. This is more useful than allow_subset because it allows better control over what species are ignored in the matching.

as_dict()

Returns:

MSONable dict

fit(struct1: Structure, struct2: Structure, symmetric: bool = False, skip_structure_reduction: bool = False) → bool

Fit two structures.

Parameters:

• struct1 (Structure) – 1st structure

• struct2 (Structure) – 2nd structure

• symmetric (bool) – Defaults to False If True, check the equality both ways. This only impacts a small percentage of structures

• skip_structure_reduction (bool) – Defaults to False If True, skip to get a primitive structure and perform Niggli reduction for struct1 and struct2

Returns:

True if the structures are equivalent

Return type:

bool

fit_anonymous(struct1: Structure, struct2: Structure, niggli: bool = True, skip_structure_reduction: bool = False) → bool

Performs an anonymous fitting, which allows distinct species in one structure to map to another. E.g., to compare if the Li2O and Na2O structures are similar.

Parameters:

• struct1 (Structure) – 1st structure

• struct2 (Structure) – 2nd structure

• niggli (bool) – If true, perform Niggli reduction for struct1 and struct2

• skip_structure_reduction (bool) – Defaults to False If True, skip to get a primitive structure and perform Niggli reduction for struct1 and struct2

Returns:

Whether a species mapping can map struct1 to stuct2

Return type:

True/False

classmethod from_dict(d)

Parameters:

d – Dict representation

Returns:

StructureMatcher

get_all_anonymous_mappings(struct1, struct2, niggli=True, include_dist=False)

Performs an anonymous fitting, which allows distinct species in one structure to map to another. Returns a dictionary of species substitutions that are within tolerance

Parameters:

• struct1 (Structure) – 1st structure

• struct2 (Structure) – 2nd structure

• niggli (bool) – Find niggli cell in preprocessing

• include_dist (bool) – Return the maximin distance with each mapping

Returns:

list of species mappings that map struct1 to struct2.

get_best_electronegativity_anonymous_mapping(struct1: Structure, struct2: Structure) → dict | None

Performs an anonymous fitting, which allows distinct species in one structure to map to another. E.g., to compare if the Li2O and Na2O structures are similar. If multiple substitutions are within tolerance this will return the one which minimizes the difference in electronegativity between the matches species.

Parameters:

• struct1 (Structure) – 1st structure

• struct2 (Structure) – 2nd structure

Returns:

Mapping of struct1 species to struct2 species

Return type:

min_mapping (dict)

get_mapping(superset, subset)

Calculate the mapping from superset to subset.

Parameters:

• superset (Structure) – Structure containing at least the sites in subset (within the structure matching tolerance)

• subset (Structure) – Structure containing some of the sites in superset (within the structure matching tolerance)

Returns:

numpy array such that superset.sites[mapping] is within matching tolerance of subset.sites or None if no such mapping is possible

get_rms_anonymous(struct1, struct2)

Performs an anonymous fitting, which allows distinct species in one structure to map to another. E.g., to compare if the Li2O and Na2O structures are similar.

Parameters:

• struct1 (Structure) – 1st structure

• struct2 (Structure) – 2nd structure

Returns:

(min_rms, min_mapping) min_rms is the minimum rms distance, and min_mapping is the corresponding minimal species mapping that would map struct1 to struct2. (None, None) is returned if the minimax_rms exceeds the threshold.

get_rms_dist(struct1, struct2)

Calculate RMS displacement between two structures

Parameters:

• struct1 (Structure) – 1st structure

• struct2 (Structure) – 2nd structure

Returns:

rms displacement normalized by (Vol / nsites) ** (1/3) and maximum distance between paired sites. If no matching lattice is found None is returned.

get_s2_like_s1(struct1, struct2, include_ignored_species=True)

Performs transformations on struct2 to put it in a basis similar to struct1 (without changing any of the inter-site distances)

Parameters:

• struct1 (Structure) – Reference structure

• struct2 (Structure) – Structure to transform.

• include_ignored_species (bool) – Defaults to True, the ignored_species is also transformed to the struct1 lattice orientation, though obviously there is no direct matching to existing sites.

Returns:

A structure object similar to struct1, obtained by making a supercell, sorting, and translating struct2.

get_supercell_matrix(supercell, struct) → ndarray | None

Returns the matrix for transforming struct to supercell. This can be used for very distorted ‘supercells’ where the primitive cell is impossible to find

get_transformation(struct1, struct2)

Returns the supercell transformation, fractional translation vector, and a mapping to transform struct2 to be similar to struct1.

Parameters:

• struct1 (Structure) – Reference structure

• struct2 (Structure) – Structure to transform.

Returns:

supercell matrix vector (numpy.ndarray(3)): fractional translation vector mapping (list(int or None)):

The first len(struct1) items of the mapping vector are the indices of struct1’s corresponding sites in struct2 (or None if there is no corresponding site), and the other items are the remaining site indices of struct2.

Return type:

supercell (numpy.ndarray(3, 3))

group_structures(s_list, anonymous=False)

Given a list of structures, use fit to group them by structural equality.

Parameters:

• s_list ([Structure]) – List of structures to be grouped

• anonymous (bool) – Whether to use anonymous mode.

Returns:

A list of lists of matched structures Assumption: if s1 == s2 but s1 != s3, than s2 and s3 will be put in different groups without comparison.