pymatgen.analysis.dimensionality — pymatgen 2020.7.3 documentation

# Source code for pymatgen.analysis.dimensionality

    """
    This module provides functions to get the dimensionality of a structure.

    A number of different algorithms are implemented. These are based on the
    following publications:

    get_dimensionality_larsen:
      - P. M. Larsen, M. Pandey, M. Strange, K. W. Jacobsen. Definition of a
        scoring parameter to identify low-dimensional materials components.
        Phys. Rev. Materials 3, 034003 (2019).

    get_dimensionality_cheon:
      - Cheon, G.; Duerloo, K.-A. N.; Sendek, A. D.; Porter, C.; Chen, Y.; Reed,
        E. J. Data Mining for New Two- and One-Dimensional Weakly Bonded Solids
        and Lattice-Commensurate Heterostructures. Nano Lett. 2017.

    get_dimensionality_gorai:
      - Gorai, P., Toberer, E. & Stevanovic, V. Computational Identification of
        Promising Thermoelectric Materials Among Known Quasi-2D Binary Compounds.
        J. Mater. Chem. A 2, 4136 (2016).
    """

    import itertools
    import copy

    import numpy as np

    from collections import defaultdict

    from networkx.readwrite import json_graph

    from pymatgen.analysis.graphs import MoleculeGraph, StructureGraph
    from pymatgen.core.lattice import get_integer_index
    from pymatgen.core.structure import Structure, Molecule
    from pymatgen.core.periodic_table import Specie
    from pymatgen.core.surface import SlabGenerator
    from pymatgen.analysis.local_env import JmolNN
    from pymatgen.analysis.structure_analyzer import get_max_bond_lengths
    from pymatgen.symmetry.analyzer import SpacegroupAnalyzer

    __author__ = "Alex Ganose, Gowoon Cheon, Prashun Gorai"

    def get_dimensionality_larsen(bonded_structure):
        """
        Gets the dimensionality of a bonded structure.

        The dimensionality of the structure is the highest dimensionality of all
        structure components. This method is very robust and can handle
        many tricky structures, regardless of structure type or improper connections
        due to periodic boundary conditions.

        Requires a StructureGraph object as input. This can be generated using one
        of the NearNeighbor classes. For example, using the CrystalNN class::

            bonded_structure = CrystalNN().get_bonded_structure(structure)

        Based on the modified breadth-first-search algorithm described in:

        P. M. Larsen, M. Pandey, M. Strange, K. W. Jacobsen. Definition of a
        scoring parameter to identify low-dimensional materials components.
        Phys. Rev. Materials 3, 034003 (2019).

        Args:
            bonded_structure (StructureGraph): A structure with bonds, represented
                as a pymatgen structure graph. For example, generated using the
                CrystalNN.get_bonded_structure() method.

        Returns:
            (int): The dimensionality of the structure.
        """
        return max([c['dimensionality'] for c in
                    get_structure_components(bonded_structure)])

    def get_structure_components(bonded_structure, inc_orientation=False,
                                 inc_site_ids=False, inc_molecule_graph=False):
        """
        Gets information on the components in a bonded structure.

        Correctly determines the dimensionality of all structures, regardless of
        structure type or improper connections due to periodic boundary conditions.

        Requires a StructureGraph object as input. This can be generated using one
        of the NearNeighbor classes. For example, using the CrystalNN class::

            bonded_structure = CrystalNN().get_bonded_structure(structure)

        Based on the modified breadth-first-search algorithm described in:

        P. M. Larsen, M. Pandey, M. Strange, K. W. Jacobsen. Definition of a
        scoring parameter to identify low-dimensional materials components.
        Phys. Rev. Materials 3, 034003 (2019).

        Args:
            bonded_structure (StructureGraph): A structure with bonds, represented
                as a pymatgen structure graph. For example, generated using the
                CrystalNN.get_bonded_structure() method.
            inc_orientation (bool, optional): Whether to include the orientation
                of the structure component. For surfaces, the miller index is given,
                for one-dimensional structures, the direction of the chain is given.
            inc_site_ids (bool, optional): Whether to include the site indices
                of the sites in the structure component.
            inc_molecule_graph (bool, optional): Whether to include MoleculeGraph
                objects for zero-dimensional components.

        Returns:
            (list of dict): Information on the components in a structure as a list
            of dictionaries with the keys:

            - "structure_graph": A pymatgen StructureGraph object for the
                component.
            - "dimensionality": The dimensionality of the structure component as an
                int.
            - "orientation": If inc_orientation is `True`, the orientation of the
                component as a tuple. E.g. (1, 1, 1)
            - "site_ids": If inc_site_ids is `True`, the site indices of the
                sites in the component as a tuple.
            - "molecule_graph": If inc_molecule_graph is `True`, the site a
                MoleculeGraph object for zero-dimensional components.
        """
        import networkx as nx  # optional dependency therefore not top level import

        comp_graphs = (bonded_structure.graph.subgraph(c) for c in
                       nx.weakly_connected_components(bonded_structure.graph))

        components = []
        for graph in comp_graphs:
            dimensionality, vertices = calculate_dimensionality_of_site(
                bonded_structure, list(graph.nodes())[0], inc_vertices=True)

            component = {'dimensionality': dimensionality}

            if inc_orientation:
                if dimensionality in [1, 2]:
                    vertices = np.array(vertices)

                    g = vertices.sum(axis=0) / vertices.shape[0]

                    # run singular value decomposition
                    _, _, vh = np.linalg.svd(vertices - g)

                    # get direction (first column is best fit line,
                    # 3rd column is unitary norm)
                    index = 2 if dimensionality == 2 else 0
                    orientation = get_integer_index(vh[index, :])
                else:
                    orientation = None

                component['orientation'] = orientation

            if inc_site_ids:
                component['site_ids'] = tuple(graph.nodes())

            if inc_molecule_graph and dimensionality == 0:
                component['molecule_graph'] = zero_d_graph_to_molecule_graph(
                    bonded_structure, graph)

            component_structure = Structure.from_sites(
                [bonded_structure.structure[n] for n in sorted(graph.nodes())])

            sorted_graph = nx.convert_node_labels_to_integers(
                graph, ordering="sorted")
            component_graph = StructureGraph(
                component_structure,
                graph_data=json_graph.adjacency_data(sorted_graph))
            component['structure_graph'] = component_graph

            components.append(component)
        return components

    def calculate_dimensionality_of_site(bonded_structure, site_index,
                                         inc_vertices=False):
        """
        Calculates the dimensionality of the component containing the given site.

        Implements directly the modified breadth-first-search algorithm described in
        Algorithm 1 of:

        P. M. Larsen, M. Pandey, M. Strange, K. W. Jacobsen. Definition of a
        scoring parameter to identify low-dimensional materials components.
        Phys. Rev. Materials 3, 034003 (2019).

        Args:
            bonded_structure (StructureGraph): A structure with bonds, represented
                as a pymatgen structure graph. For example, generated using the
                CrystalNN.get_bonded_structure() method.
            site_index (int): The index of a site in the component of interest.
            inc_vertices (bool, optional): Whether to return the vertices (site
                images) of the component.

        Returns:
            (int or tuple): If inc_vertices is False, the dimensionality of the
            component will be returned as an int. If inc_vertices is true, the
            function will return a tuple of (dimensionality, vertices), where
            vertices is a list of tuples. E.g. [(0, 0, 0), (1, 1, 1)].
        """

        def neighbours(comp_index):
            return [(s.index, s.jimage) for s
                    in bonded_structure.get_connected_sites(comp_index)]

        def rank(vertices):
            if len(vertices) == 0:
                return -1
            elif len(vertices) == 1:
                return 0
            else:
                vertices = np.array(list(vertices))
                return np.linalg.matrix_rank(vertices[1:] - vertices[0])

        def rank_increase(seen, candidate):

            rank0 = len(seen) - 1
            rank1 = rank(seen.union({candidate}))
            return rank1 > rank0

        connected_sites = {i: neighbours(i) for i in
                           range(bonded_structure.structure.num_sites)}

        seen_vertices = set()
        seen_comp_vertices = defaultdict(set)

        queue = [(site_index, (0, 0, 0))]
        while len(queue) > 0:
            comp_i, image_i = queue.pop(0)

            if (comp_i, image_i) in seen_vertices:
                continue
            seen_vertices.add((comp_i, image_i))

            if not rank_increase(seen_comp_vertices[comp_i], image_i):
                continue

            seen_comp_vertices[comp_i].add(image_i)

            for comp_j, image_j in connected_sites[comp_i]:

                image_j = tuple(np.add(image_j, image_i))

                if (comp_j, image_j) in seen_vertices:
                    continue

                if rank_increase(seen_comp_vertices[comp_j], image_j):
                    queue.append((comp_j, image_j))

        if inc_vertices:
            return (rank(seen_comp_vertices[site_index]),
                    list(seen_comp_vertices[site_index]))
        else:
            return rank(seen_comp_vertices[site_index])

    def zero_d_graph_to_molecule_graph(bonded_structure, graph):
        """
        Converts a zero-dimensional networkx Graph object into a MoleculeGraph.

        Implements a similar breadth-first search to that in
        calculate_dimensionality_of_site().

        Args:
            bonded_structure (StructureGraph): A structure with bonds, represented
                as a pymatgen structure graph. For example, generated using the
                CrystalNN.get_bonded_structure() method.
            graph (nx.Graph): A networkx `Graph` object for the component of
                interest.

        Returns:
            (MoleculeGraph): A MoleculeGraph object of the component.
        """
        import networkx as nx
        seen_indices = []
        sites = []

        start_index = list(graph.nodes())[0]
        queue = [(start_index, (0, 0, 0),
                  bonded_structure.structure[start_index])]
        while len(queue) > 0:
            comp_i, image_i, site_i = queue.pop(0)

            if comp_i in [x[0] for x in seen_indices]:
                raise ValueError("Graph component is not 0D")

            seen_indices.append((comp_i, image_i))
            sites.append(site_i)

            for site_j in bonded_structure.get_connected_sites(
                    comp_i, jimage=image_i):

                if ((site_j.index, site_j.jimage) not in seen_indices and
                        (site_j.index, site_j.jimage, site_j.site) not in queue):
                    queue.append((site_j.index, site_j.jimage, site_j.site))

        # sort the list of indices and the graph by index to make consistent
        indices_ordering = np.argsort([x[0] for x in seen_indices])
        sorted_sites = np.array(sites, dtype=object)[indices_ordering]
        sorted_graph = nx.convert_node_labels_to_integers(graph, ordering="sorted")
        mol = Molecule([s.specie for s in sorted_sites],
                       [s.coords for s in sorted_sites])
        mol_graph = MoleculeGraph.with_edges(mol, nx.Graph(sorted_graph).edges())

        return mol_graph

    def get_dimensionality_cheon(structure_raw, tolerance=0.45,
                                 ldict=JmolNN().el_radius, standardize=True, larger_cell=False):
        """
        Algorithm for finding the dimensions of connected subunits in a structure.
        This method finds the dimensionality of the material even when the material
        is not layered along low-index planes, or does not have flat
        layers/molecular wires.

        Author: "Gowoon Cheon"
        Email: "gcheon@stanford.edu"

        See details at :

        Cheon, G.; Duerloo, K.-A. N.; Sendek, A. D.; Porter, C.; Chen, Y.; Reed,
        E. J. Data Mining for New Two- and One-Dimensional Weakly Bonded Solids and
        Lattice-Commensurate Heterostructures. Nano Lett. 2017.

        Args:
            structure_raw (Structure): A pymatgen Structure object.
            tolerance (float): length in angstroms used in finding bonded atoms.
                Two atoms are considered bonded if (radius of atom 1) + (radius of
                atom 2) + (tolerance) < (distance between atoms 1 and 2). Default
                value = 0.45, the value used by JMol and Cheon et al.
            ldict (dict): dictionary of bond lengths used in finding bonded atoms.
                Values from JMol are used as default
            standardize: works with conventional standard structures if True. It is
                recommended to keep this as True.
            larger_cell: tests with 3x3x3 supercell instead of 2x2x2. Testing with
                2x2x2 supercell is faster but misclssifies rare interpenetrated 3D
                 structures. Testing with a larger cell circumvents this problem

        Returns:
            (str): dimension of the largest cluster as a string. If there are ions
            or molecules it returns 'intercalated ion/molecule'
        """
        if standardize:
            structure = SpacegroupAnalyzer(structure_raw).get_conventional_standard_structure()
        else:
            structure = structure_raw
        structure_save = copy.copy(structure_raw)
        connected_list1 = find_connected_atoms(structure, tolerance=tolerance, ldict=ldict)
        max1, min1, clusters1 = find_clusters(structure, connected_list1)
        if larger_cell:
            structure.make_supercell([[3, 0, 0], [0, 3, 0], [0, 0, 3]])
            connected_list3 = find_connected_atoms(structure, tolerance=tolerance, ldict=ldict)
            max3, min3, clusters3 = find_clusters(structure, connected_list3)
            if min3 == min1:
                if max3 == max1:
                    dim = '0D'
                else:
                    dim = 'intercalated molecule'
            else:
                dim = np.log2(float(max3) / max1) / np.log2(3)
                if dim == int(dim):
                    dim = str(int(dim)) + 'D'
                else:
                    return
        else:
            structure.make_supercell([[2, 0, 0], [0, 2, 0], [0, 0, 2]])
            connected_list2 = find_connected_atoms(structure, tolerance=tolerance, ldict=ldict)
            max2, min2, clusters2 = find_clusters(structure, connected_list2)
            if min2 == 1:
                dim = 'intercalated ion'
            elif min2 == min1:
                if max2 == max1:
                    dim = '0D'
                else:
                    dim = 'intercalated molecule'
            else:
                dim = np.log2(float(max2) / max1)
                if dim == int(dim):
                    dim = str(int(dim)) + 'D'
                else:
                    structure = copy.copy(structure_save)
                    structure.make_supercell([[3, 0, 0], [0, 3, 0], [0, 0, 3]])
                    connected_list3 = find_connected_atoms(structure, tolerance=tolerance, ldict=ldict)
                    max3, min3, clusters3 = find_clusters(structure, connected_list3)
                    if min3 == min2:
                        if max3 == max2:
                            dim = '0D'
                        else:
                            dim = 'intercalated molecule'
                    else:
                        dim = np.log2(float(max3) / max1) / np.log2(3)
                        if dim == int(dim):
                            dim = str(int(dim)) + 'D'
                        else:
                            return
        return dim

    def find_connected_atoms(struct, tolerance=0.45, ldict=JmolNN().el_radius):
        """
        Finds bonded atoms and returns a adjacency matrix of bonded atoms.

        Author: "Gowoon Cheon"
        Email: "gcheon@stanford.edu"

        Args:
            struct (Structure): Input structure
            tolerance: length in angstroms used in finding bonded atoms. Two atoms
                are considered bonded if (radius of atom 1) + (radius of atom 2) +
                (tolerance) < (distance between atoms 1 and 2). Default
                value = 0.45, the value used by JMol and Cheon et al.
            ldict: dictionary of bond lengths used in finding bonded atoms. Values
                from JMol are used as default

        Returns:
            (np.ndarray): A numpy array of shape (number of atoms, number of atoms);
            If any image of atom j is bonded to atom i with periodic boundary
            conditions, the matrix element [atom i, atom j] is 1.
        """
        n_atoms = len(struct.species)
        fc = np.array(struct.frac_coords)
        fc_copy = np.repeat(fc[:, :, np.newaxis], 27, axis=2)
        neighbors = np.array(list(itertools.product([0, 1, -1], [0, 1, -1], [0, 1, -1]))).T
        neighbors = np.repeat(neighbors[np.newaxis, :, :], 1, axis=0)
        fc_diff = fc_copy - neighbors
        species = list(map(str, struct.species))
        # in case of charged species
        for i, item in enumerate(species):
            if item not in ldict.keys():
                species[i] = str(Specie.from_string(item).element)
        latmat = struct.lattice.matrix
        connected_matrix = np.zeros((n_atoms, n_atoms))

        for i in range(n_atoms):
            for j in range(i + 1, n_atoms):
                max_bond_length = ldict[species[i]] + ldict[species[j]] + tolerance
                frac_diff = fc_diff[j] - fc_copy[i]
                distance_ij = np.dot(latmat.T, frac_diff)
                # print(np.linalg.norm(distance_ij,axis=0))
                if sum(np.linalg.norm(distance_ij, axis=0) < max_bond_length) > 0:
                    connected_matrix[i, j] = 1
                    connected_matrix[j, i] = 1
        return connected_matrix

    def find_clusters(struct, connected_matrix):
        """
        Finds bonded clusters of atoms in the structure with periodic boundary
        conditions.

        If there are atoms that are not bonded to anything, returns [0,1,0]. (For
        faster computation time)

        Author: "Gowoon Cheon"
        Email: "gcheon@stanford.edu"

        Args:
            struct (Structure): Input structure
            connected_matrix: Must be made from the same structure with
                find_connected_atoms() function.

        Returns:
            max_cluster: the size of the largest cluster in the crystal structure
            min_cluster: the size of the smallest cluster in the crystal structure
            clusters: list of bonded clusters found here, clusters are formatted as
            sets of indices of atoms
        """
        n_atoms = len(struct.species)
        if n_atoms == 0:
            return [0, 0, 0]
        if 0 in np.sum(connected_matrix, axis=0):
            return [0, 1, 0]

        cluster_sizes = []
        clusters = []
        visited = [False for item in range(n_atoms)]
        connected_matrix += np.eye(len(connected_matrix))

        def visit(atom, atom_cluster):
            visited[atom] = True
            new_cluster = set(np.where(connected_matrix[atom] != 0)[0]).union(atom_cluster)
            atom_cluster = new_cluster
            for new_atom in atom_cluster:
                if not visited[new_atom]:
                    visited[new_atom] = True
                    atom_cluster = visit(new_atom, atom_cluster)
            return atom_cluster

        for i in range(n_atoms):
            if not visited[i]:
                atom_cluster = set()
                cluster = visit(i, atom_cluster)
                clusters.append(cluster)
                cluster_sizes.append(len(cluster))

        max_cluster = max(cluster_sizes)
        min_cluster = min(cluster_sizes)
        return [max_cluster, min_cluster, clusters]

    def get_dimensionality_gorai(structure, max_hkl=2, el_radius_updates=None,
                                 min_slab_size=5, min_vacuum_size=5,
                                 standardize=True, bonds=None):
        """
        This method returns whether a structure is 3D, 2D (layered), or 1D (linear
        chains or molecules) according to the algorithm published in Gorai, P.,
        Toberer, E. & Stevanovic, V. Computational Identification of Promising
        Thermoelectric Materials Among Known Quasi-2D Binary Compounds. J. Mater.
        Chem. A 2, 4136 (2016).

        Note that a 1D structure detection might indicate problems in the bonding
        algorithm, particularly for ionic crystals (e.g., NaCl)

        Users can change the behavior of bonds detection by passing either
        el_radius_updates to update atomic radii for auto-detection of max bond
        distances, or bonds to explicitly specify max bond distances for atom pairs.
        Note that if you pass both, el_radius_updates are ignored.

        Args:
            structure: (Structure) structure to analyze dimensionality for
            max_hkl: (int) max index of planes to look for layers
            el_radius_updates: (dict) symbol->float to update atomic radii
            min_slab_size: (float) internal surface construction parameter
            min_vacuum_size: (float) internal surface construction parameter
            standardize (bool): whether to standardize the structure before
                analysis. Set to False only if you already have the structure in a
                convention where layers / chains will be along low <hkl> indexes.
            bonds ({(specie1, specie2): max_bond_dist}: bonds are
                    specified as a dict of tuples: float of specie1, specie2
                    and the max bonding distance. For example, PO4 groups may be
                    defined as {("P", "O"): 3}.

        Returns: (int) the dimensionality of the structure - 1 (molecules/chains),
            2 (layered), or 3 (3D)

        """
        if standardize:
            structure = SpacegroupAnalyzer(structure). \
                get_conventional_standard_structure()

        if not bonds:
            bonds = get_max_bond_lengths(structure, el_radius_updates)

        num_surfaces = 0
        for h in range(max_hkl):
            for k in range(max_hkl):
                for l in range(max_hkl):
                    if max([h, k, l]) > 0 and num_surfaces < 2:
                        sg = SlabGenerator(structure, (h, k, l),
                                           min_slab_size=min_slab_size,
                                           min_vacuum_size=min_vacuum_size)
                        slabs = sg.get_slabs(bonds)
                        for _ in slabs:
                            num_surfaces += 1

        return 3 - min(num_surfaces, 2)