pymatgen.analysis.structure_analyzer — pymatgen 2020.7.3 documentation

# Source code for pymatgen.analysis.structure_analyzer

    # coding: utf-8
    # Copyright (c) Pymatgen Development Team.
    # Distributed under the terms of the MIT License.

    """
    This module provides classes to perform topological analyses of structures.
    """

    __author__ = "Shyue Ping Ong, Geoffroy Hautier, Sai Jayaraman"
    __copyright__ = "Copyright 2011, The Materials Project"

    from math import pi, acos
    import numpy as np
    import itertools
    import collections

    from monty.dev import deprecated

    from warnings import warn
    from scipy.spatial import Voronoi
    from pymatgen import PeriodicSite
    from pymatgen import Element, Specie, Composition
    from pymatgen.util.num import abs_cap
    from pymatgen.symmetry.analyzer import SpacegroupAnalyzer
    from pymatgen.core.surface import SlabGenerator
    from pymatgen.analysis.local_env import VoronoiNN, JmolNN

    def average_coordination_number(structures, freq=10):
        """
        Calculates the ensemble averaged Voronoi coordination numbers
        of a list of Structures using VoronoiNN.
        Typically used for analyzing the output of a Molecular Dynamics run.

        Args:
            structures (list): list of Structures.
            freq (int): sampling frequency of coordination number [every freq steps].

        Returns:
            Dictionary of elements as keys and average coordination numbers as values.
        """
        coordination_numbers = {}
        for spec in structures[0].composition.as_dict().keys():
            coordination_numbers[spec] = 0.0
        count = 0
        for t in range(len(structures)):
            if t % freq != 0:
                continue
            count += 1
            vnn = VoronoiNN()
            for atom in range(len(structures[0])):
                cn = vnn.get_cn(structures[t], atom, use_weights=True)
                coordination_numbers[structures[t][atom].species_string] += cn
        elements = structures[0].composition.as_dict()
        for el in coordination_numbers:
            coordination_numbers[el] = coordination_numbers[el] / elements[
                el] / count
        return coordination_numbers

    class VoronoiAnalyzer:
        """
        Performs a statistical analysis of Voronoi polyhedra around each site.
        Each Voronoi polyhedron is described using Schaefli notation.
        That is a set of indices {c_i} where c_i is the number of faces with i
        number of vertices.  E.g. for a bcc crystal, there is only one polyhedron
        notation of which is [0,6,0,8,0,0,...].
        In perfect crystals, these also corresponds to the Wigner-Seitz cells.
        For distorted-crystals, liquids or amorphous structures, rather than one-type,
        there is a statistical distribution of polyhedra.
        See ref: Microstructure and its relaxation in Fe-B amorphous system
        simulated by molecular dynamics,
            Stepanyuk et al., J. Non-cryst. Solids (1993), 159, 80-87.
        """

        def __init__(self, cutoff=5.0, qhull_options="Qbb Qc Qz"):
            """
            Args:
                cutoff (float): cutoff distance to search for neighbors of a given atom
                    (default = 5.0)
                qhull_options (str): options to pass to qhull (optional)
            """
            self.cutoff = cutoff
            self.qhull_options = qhull_options

        def analyze(self, structure, n=0):
            """
            Performs Voronoi analysis and returns the polyhedra around atom n
            in Schlaefli notation.

            Args:
                structure (Structure): structure to analyze
                n (int): index of the center atom in structure

            Returns:
                voronoi index of n: <c3,c4,c6,c6,c7,c8,c9,c10>
                    where c_i denotes number of facets with i vertices.
            """
            center = structure[n]
            neighbors = structure.get_sites_in_sphere(center.coords, self.cutoff)
            neighbors = [i[0] for i in sorted(neighbors, key=lambda s: s[1])]
            qvoronoi_input = np.array([s.coords for s in neighbors])
            voro = Voronoi(qvoronoi_input, qhull_options=self.qhull_options)
            vor_index = np.array([0, 0, 0, 0, 0, 0, 0, 0])

            for key in voro.ridge_dict:
                if 0 in key:  # This means if the center atom is in key
                    if -1 in key:  # This means if an infinity point is in key
                        raise ValueError("Cutoff too short.")
                    else:
                        try:
                            vor_index[len(voro.ridge_dict[key]) - 3] += 1
                        except IndexError:
                            # If a facet has more than 10 edges, it's skipped here.
                            pass
            return vor_index

        def analyze_structures(self, structures, step_freq=10,
                               most_frequent_polyhedra=15):
            """
            Perform Voronoi analysis on a list of Structures.
            Note that this might take a significant amount of time depending on the
            size and number of structures.

            Args:
                structures (list): list of Structures
                cutoff (float: cutoff distance around an atom to search for
                    neighbors
                step_freq (int): perform analysis every step_freq steps
                qhull_options (str): options to pass to qhull
                most_frequent_polyhedra (int): this many unique polyhedra with
                    highest frequences is stored.

            Returns:
                A list of tuples in the form (voronoi_index,frequency)
            """
            voro_dict = {}
            step = 0
            for structure in structures:
                step += 1
                if step % step_freq != 0:
                    continue

                v = []
                for n in range(len(structure)):
                    v.append(str(self.analyze(structure, n=n).view()))
                for voro in v:
                    if voro in voro_dict:
                        voro_dict[voro] += 1
                    else:
                        voro_dict[voro] = 1
            return sorted(voro_dict.items(),
                          key=lambda x: (x[1], x[0]),
                          reverse=True)[:most_frequent_polyhedra]

        @staticmethod
        def plot_vor_analysis(voronoi_ensemble):
            """
            Plot the Voronoi analysis.

            :param voronoi_ensemble:
            :return: matplotlib.pyplot
            """
            t = zip(*voronoi_ensemble)
            labels = t[0]
            val = list(t[1])
            tot = np.sum(val)
            val = [float(j) / tot for j in val]
            pos = np.arange(len(val)) + .5  # the bar centers on the y axis
            import matplotlib.pyplot as plt
            plt.figure()
            plt.barh(pos, val, align='center', alpha=0.5)
            plt.yticks(pos, labels)
            plt.xlabel('Count')
            plt.title('Voronoi Spectra')
            plt.grid(True)
            return plt

    class RelaxationAnalyzer:
        """
        This class analyzes the relaxation in a calculation.
        """

        def __init__(self, initial_structure, final_structure):
            """
            Please note that the input and final structures should have the same
            ordering of sites. This is typically the case for most computational
            codes.

            Args:
                initial_structure (Structure): Initial input structure to
                    calculation.
                final_structure (Structure): Final output structure from
                    calculation.
            """
            if final_structure.formula != initial_structure.formula:
                raise ValueError("Initial and final structures have different " +
                                 "formulas!")
            self.initial = initial_structure
            self.final = final_structure

        def get_percentage_volume_change(self):
            """
            Returns the percentage volume change.

            Returns:
                Volume change in percentage, e.g., 0.055 implies a 5.5% increase.
            """
            initial_vol = self.initial.lattice.volume
            final_vol = self.final.lattice.volume
            return final_vol / initial_vol - 1

        def get_percentage_lattice_parameter_changes(self):
            """
            Returns the percentage lattice parameter changes.

            Returns:
                A dict of the percentage change in lattice parameter, e.g.,
                {'a': 0.012, 'b': 0.021, 'c': -0.031} implies a change of 1.2%,
                2.1% and -3.1% in the a, b and c lattice parameters respectively.
            """
            initial_latt = self.initial.lattice
            final_latt = self.final.lattice
            d = {l: getattr(final_latt, l) / getattr(initial_latt, l) - 1
                 for l in ["a", "b", "c"]}
            return d

        def get_percentage_bond_dist_changes(self, max_radius=3.0):
            """
            Returns the percentage bond distance changes for each site up to a
            maximum radius for nearest neighbors.

            Args:
                max_radius (float): Maximum radius to search for nearest
                   neighbors. This radius is applied to the initial structure,
                   not the final structure.

            Returns:
                Bond distance changes as a dict of dicts. E.g.,
                {index1: {index2: 0.011, ...}}. For economy of representation, the
                index1 is always less than index2, i.e., since bonding between
                site1 and siten is the same as bonding between siten and site1,
                there is no reason to duplicate the information or computation.
            """
            data = collections.defaultdict(dict)
            for inds in itertools.combinations(list(range(len(self.initial))), 2):
                (i, j) = sorted(inds)
                initial_dist = self.initial[i].distance(self.initial[j])
                if initial_dist < max_radius:
                    final_dist = self.final[i].distance(self.final[j])
                    data[i][j] = final_dist / initial_dist - 1
            return data

    class VoronoiConnectivity:
        """
        Computes the solid angles swept out by the shared face of the voronoi
        polyhedron between two sites.
        """
        def __init__(self, structure, cutoff=10):
            """
            Args:
                structure (Structure): Input structure
                cutoff (float) Cutoff distance.
            """
            self.cutoff = cutoff
            self.s = structure
            recp_len = np.array(self.s.lattice.reciprocal_lattice.abc)
            i = np.ceil(cutoff * recp_len / (2 * pi))
            offsets = np.mgrid[-i[0]:i[0] + 1, -i[1]:i[1] + 1, -i[2]:i[2] + 1].T
            self.offsets = np.reshape(offsets, (-1, 3))
            # shape = [image, axis]
            self.cart_offsets = self.s.lattice.get_cartesian_coords(self.offsets)

        @property
        def connectivity_array(self):
            """
            Provides connectivity array.

            Returns:
                connectivity: An array of shape [atomi, atomj, imagej]. atomi is
                the index of the atom in the input structure. Since the second
                atom can be outside of the unit cell, it must be described
                by both an atom index and an image index. Array data is the
                solid angle of polygon between atomi and imagej of atomj
            """
            # shape = [site, axis]
            cart_coords = np.array(self.s.cart_coords)
            # shape = [site, image, axis]
            all_sites = cart_coords[:, None, :] + self.cart_offsets[None, :, :]
            vt = Voronoi(all_sites.reshape((-1, 3)))
            n_images = all_sites.shape[1]
            cs = (len(self.s), len(self.s), len(self.cart_offsets))
            connectivity = np.zeros(cs)
            vts = np.array(vt.vertices)
            for (ki, kj), v in vt.ridge_dict.items():
                atomi = ki // n_images
                atomj = kj // n_images

                imagei = ki % n_images
                imagej = kj % n_images

                if imagei != n_images // 2 and imagej != n_images // 2:
                    continue

                if imagei == n_images // 2:
                    # atomi is in original cell
                    val = solid_angle(vt.points[ki], vts[v])
                    connectivity[atomi, atomj, imagej] = val

                if imagej == n_images // 2:
                    # atomj is in original cell
                    val = solid_angle(vt.points[kj], vts[v])
                    connectivity[atomj, atomi, imagei] = val

                if -10.101 in vts[v]:
                    warn('Found connectivity with infinite vertex. '
                         'Cutoff is too low, and results may be '
                         'incorrect')
            return connectivity

        @property
        def max_connectivity(self):
            """
            returns the 2d array [sitei, sitej] that represents
            the maximum connectivity of site i to any periodic
            image of site j
            """
            return np.max(self.connectivity_array, axis=2)

        def get_connections(self):
            """
            Returns a list of site pairs that are Voronoi Neighbors, along
            with their real-space distances.
            """
            con = []
            maxconn = self.max_connectivity
            for ii in range(0, maxconn.shape[0]):
                for jj in range(0, maxconn.shape[1]):
                    if maxconn[ii][jj] != 0:
                        dist = self.s.get_distance(ii, jj)
                        con.append([ii, jj, dist])
            return con

        def get_sitej(self, site_index, image_index):
            """
            Assuming there is some value in the connectivity array at indices
            (1, 3, 12). sitei can be obtained directly from the input structure
            (structure[1]). sitej can be obtained by passing 3, 12 to this function

            Args:
                site_index (int): index of the site (3 in the example)
                image_index (int): index of the image (12 in the example)
            """
            atoms_n_occu = self.s[site_index].species
            lattice = self.s.lattice
            coords = self.s[site_index].frac_coords + self.offsets[image_index]
            return PeriodicSite(atoms_n_occu, coords, lattice)

    def solid_angle(center, coords):
        """
        Helper method to calculate the solid angle of a set of coords from the
        center.

        Args:
            center (3x1 array): Center to measure solid angle from.
            coords (Nx3 array): List of coords to determine solid angle.

        Returns:
            The solid angle.
        """
        o = np.array(center)
        r = [np.array(c) - o for c in coords]
        r.append(r[0])
        n = [np.cross(r[i + 1], r[i]) for i in range(len(r) - 1)]
        n.append(np.cross(r[1], r[0]))
        vals = []
        for i in range(len(n) - 1):
            v = -np.dot(n[i], n[i + 1]) \
                / (np.linalg.norm(n[i]) * np.linalg.norm(n[i + 1]))
            vals.append(acos(abs_cap(v)))
        phi = sum(vals)
        return phi + (3 - len(r)) * pi

    def get_max_bond_lengths(structure, el_radius_updates=None):
        """
        Provides max bond length estimates for a structure based on the JMol
        table and algorithms.

        Args:
            structure: (structure)
            el_radius_updates: (dict) symbol->float to update atomic radii

        Returns: (dict) - (Element1, Element2) -> float. The two elements are
            ordered by Z.
        """
        # jmc = JMolCoordFinder(el_radius_updates)
        jmnn = JmolNN(el_radius_updates=el_radius_updates)

        bonds_lens = {}
        els = sorted(structure.composition.elements, key=lambda x: x.Z)

        for i1 in range(len(els)):
            for i2 in range(len(els) - i1):
                bonds_lens[els[i1], els[i1 + i2]] = jmnn.get_max_bond_distance(
                    els[i1].symbol, els[i1 + i2].symbol)

        return bonds_lens

    @deprecated(message=("find_dimension has been moved to"
                         "pymatgen.analysis.dimensionality.get_dimensionality_gorai"
                         " this method will be removed in pymatgen v2019.1.1."))
    def get_dimensionality(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)

    def contains_peroxide(structure, relative_cutoff=1.1):
        """
        Determines if a structure contains peroxide anions.

        Args:
            structure (Structure): Input structure.
            relative_cutoff: The peroxide bond distance is 1.49 Angstrom.
                Relative_cutoff * 1.49 stipulates the maximum distance two O
                atoms must be to each other to be considered a peroxide.

        Returns:
            Boolean indicating if structure contains a peroxide anion.
        """
        ox_type = oxide_type(structure, relative_cutoff)
        if ox_type == "peroxide":
            return True
        else:
            return False

    class OxideType:
        """
        Separate class for determining oxide type.
        """

        def __init__(self, structure, relative_cutoff=1.1):
            """
            Args:
                structure: Input structure.
                relative_cutoff: Relative_cutoff * act. cutoff stipulates the max.
                    distance two O atoms must be from each other. Default value is
                    1.1. At most 1.1 is recommended, nothing larger, otherwise the
                    script cannot distinguish between superoxides and peroxides.
            """
            self.structure = structure
            self.relative_cutoff = relative_cutoff
            self.oxide_type, self.nbonds = self.parse_oxide()

        def parse_oxide(self):
            """
            Determines if an oxide is a peroxide/superoxide/ozonide/normal oxide.

            Returns:
                oxide_type (str): Type of oxide
                ozonide/peroxide/superoxide/hydroxide/None.
                nbonds (int): Number of peroxide/superoxide/hydroxide bonds in
                structure.
            """
            structure = self.structure
            relative_cutoff = self.relative_cutoff
            o_sites_frac_coords = []
            h_sites_frac_coords = []
            lattice = structure.lattice

            if isinstance(structure.composition.elements[0], Element):
                comp = structure.composition
            elif isinstance(structure.composition.elements[0], Specie):
                elmap = collections.defaultdict(float)
                for site in structure:
                    for species, occu in site.species.items():
                        elmap[species.element] += occu
                comp = Composition(elmap)
            if Element("O") not in comp or comp.is_element:
                return "None", 0

            for site in structure:
                syms = [sp.symbol for sp in site.species.keys()]
                if "O" in syms:
                    o_sites_frac_coords.append(site.frac_coords)
                if "H" in syms:
                    h_sites_frac_coords.append(site.frac_coords)

            if h_sites_frac_coords:
                dist_matrix = lattice.get_all_distances(o_sites_frac_coords,
                                                        h_sites_frac_coords)
                if np.any(dist_matrix < relative_cutoff * 0.93):
                    return "hydroxide", len(
                        np.where(dist_matrix < relative_cutoff * 0.93)[0]) / 2.0
            dist_matrix = lattice.get_all_distances(o_sites_frac_coords,
                                                    o_sites_frac_coords)
            np.fill_diagonal(dist_matrix, 1000)
            is_superoxide = False
            is_peroxide = False
            is_ozonide = False
            if np.any(dist_matrix < relative_cutoff * 1.35):
                bond_atoms = np.where(dist_matrix < relative_cutoff * 1.35)[0]
                is_superoxide = True
            elif np.any(dist_matrix < relative_cutoff * 1.49):
                is_peroxide = True
                bond_atoms = np.where(dist_matrix < relative_cutoff * 1.49)[0]
            if is_superoxide:
                if len(bond_atoms) > len(set(bond_atoms)):
                    is_superoxide = False
                    is_ozonide = True
            try:
                nbonds = len(set(bond_atoms))
            except UnboundLocalError:
                nbonds = 0.0
            if is_ozonide:
                str_oxide = "ozonide"
            elif is_superoxide:
                str_oxide = "superoxide"
            elif is_peroxide:
                str_oxide = "peroxide"
            else:
                str_oxide = "oxide"
            if str_oxide == "oxide":
                nbonds = comp["O"]
            return str_oxide, nbonds

    def oxide_type(structure, relative_cutoff=1.1, return_nbonds=False):
        """
        Determines if an oxide is a peroxide/superoxide/ozonide/normal oxide

        Args:
            structure (Structure): Input structure.
            relative_cutoff (float): Relative_cutoff * act. cutoff stipulates the
                max distance two O atoms must be from each other.
            return_nbonds (bool): Should number of bonds be requested?
        """

        ox_obj = OxideType(structure, relative_cutoff)
        if return_nbonds:
            return ox_obj.oxide_type, ox_obj.nbonds
        else:
            return ox_obj.oxide_type

    def sulfide_type(structure):
        """
        Determines if a structure is a sulfide/polysulfide

        Args:
            structure (Structure): Input structure.

        Returns:
            (str) sulfide/polysulfide/sulfate
        """
        structure = structure.copy()
        structure.remove_oxidation_states()
        s = Element("S")
        comp = structure.composition
        if comp.is_element or s not in comp:
            return None

        finder = SpacegroupAnalyzer(structure, symprec=0.1)
        symm_structure = finder.get_symmetrized_structure()
        s_sites = [sites[0] for sites in symm_structure.equivalent_sites if
                   sites[0].specie == s]

        def process_site(site):

            # in an exceptionally rare number of structures, the search
            # radius needs to be increased to find a neighbor atom
            search_radius = 4
            neighbors = []
            while len(neighbors) == 0:
                neighbors = structure.get_neighbors(site, search_radius)
                search_radius *= 2
                if search_radius > max(structure.lattice.abc) * 2:
                    break

            neighbors = sorted(neighbors, key=lambda n: n.nn_distance)
            dist = neighbors[0].nn_distance
            coord_elements = [nn.specie for nn in neighbors
                              if nn.nn_distance < dist + 0.4][:4]
            avg_electroneg = np.mean([e.X for e in coord_elements])
            if avg_electroneg > s.X:
                return "sulfate"
            elif avg_electroneg == s.X and s in coord_elements:
                return "polysulfide"
            else:
                return "sulfide"

        types = set([process_site(site) for site in s_sites])
        if "sulfate" in types:
            return None
        elif "polysulfide" in types:
            return "polysulfide"
        else:
            return "sulfide"