pymatgen.core.structure — pymatgen 2020.7.3 documentation

# Source code for pymatgen.core.structure

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

    """
    This module provides classes used to define a non-periodic molecule and a
    periodic structure.
    """

    import math
    import os
    import json
    import collections
    import itertools
    from abc import ABCMeta, abstractmethod
    import random
    import warnings
    from fnmatch import fnmatch
    import re
    import functools
    from typing import Dict, List, Tuple, Optional, Union, Iterator, Set, Sequence, Iterable
    import numpy as np

    from tabulate import tabulate

    from monty.dev import deprecated
    from monty.io import zopen
    from monty.json import MSONable

    from pymatgen.core.operations import SymmOp
    from pymatgen.core.lattice import Lattice, get_points_in_spheres
    from pymatgen.core.periodic_table import Element, Specie, get_el_sp, DummySpecie
    from pymatgen.core.sites import Site, PeriodicSite
    from pymatgen.core.bonds import CovalentBond, get_bond_length
    from pymatgen.core.composition import Composition
    from pymatgen.util.coord import get_angle, all_distances, \
        lattice_points_in_supercell
    from pymatgen.core.units import Mass, Length

    __author__ = "Shyue Ping Ong"
    __copyright__ = "Copyright 2011, The Materials Project"
    __version__ = "2.0"
    __maintainer__ = "Shyue Ping Ong"
    __email__ = "shyuep@gmail.com"
    __status__ = "Production"
    __date__ = "Sep 23, 2011"

    class Neighbor(Site):
        """
        Simple Site subclass to contain a neighboring atom that skips all the
        unnecessary checks for speed. Can be
        used as a fixed-length tuple of size 3 to retain backwards compatibility
        with past use cases.

            (site, nn_distance, index).

        In future, usage should be to call attributes, e.g., Neighbor.index,
        Neighbor.distance, etc.
        """

        def __init__(self,
                     species: Composition,
                     coords: np.ndarray,
                     properties: dict = None,
                     nn_distance: float = 0.0,
                     index: int = 0):
            """
            :param species: Same as Site
            :param coords: Same as Site, but must be fractional.
            :param properties: Same as Site
            :param nn_distance: Distance to some other Site.
            :param index: Index within structure.
            """
            self.coords = coords
            self._species = species
            self.properties = properties or {}
            self.nn_distance = nn_distance
            self.index = index

        def __len__(self):
            """
            Make neighbor Tuple-like to retain backwards compatibility.
            """
            return 3

        def __getitem__(self, i: int):  # type: ignore
            """
            Make neighbor Tuple-like to retain backwards compatibility.

            :param i:
            :return:
            """
            return (self, self.nn_distance, self.index)[i]

    class PeriodicNeighbor(PeriodicSite):
        """
        Simple PeriodicSite subclass to contain a neighboring atom that skips all
        the unnecessary checks for speed. Can be used as a fixed-length tuple of
        size 4 to retain backwards compatibility with past use cases.

            (site, distance, index, image).

        In future, usage should be to call attributes, e.g., PeriodicNeighbor.index,
        PeriodicNeighbor.distance, etc.
        """

        def __init__(self,
                     species: Composition,
                     coords: np.ndarray,
                     lattice: Lattice,
                     properties: dict = None,
                     nn_distance: float = 0.0,
                     index: int = 0,
                     image: tuple = (0, 0, 0)):
            """
            :param species: Same as PeriodicSite
            :param coords: Same as PeriodicSite, but must be fractional.
            :param lattice: Same as PeriodicSite
            :param properties: Same as PeriodicSite
            :param nn_distance: Distance to some other Site.
            :param index: Index within structure.
            :param image: PeriodicImage
            """
            self._lattice = lattice
            self._frac_coords = coords
            self._species = species
            self.properties = properties or {}
            self.nn_distance = nn_distance
            self.index = index
            self.image = image

        @property  # type: ignore
        def coords(self):
            """
            :return: Cartesian coords.
            """
            return self._lattice.get_cartesian_coords(self._frac_coords)

        def __len__(self):
            """
            Make neighbor Tuple-like to retain backwards compatibility.
            """
            return 4

        def __getitem__(self, i: int):  # type: ignore
            """
            Make neighbor Tuple-like to retain backwards compatibility.

            :param i:
            :return:
            """
            return (self, self.nn_distance, self.index, self.image)[i]

    class SiteCollection(collections.abc.Sequence, metaclass=ABCMeta):
        """
        Basic SiteCollection. Essentially a sequence of Sites or PeriodicSites.
        This serves as a base class for Molecule (a collection of Site, i.e., no
        periodicity) and Structure (a collection of PeriodicSites, i.e.,
        periodicity). Not meant to be instantiated directly.
        """

        # Tolerance in Angstrom for determining if sites are too close.
        DISTANCE_TOLERANCE = 0.5

        @property
        @abstractmethod
        def sites(self) -> Tuple[Union[Site, PeriodicSite]]:
            """
            Returns a tuple of sites.
            """

        @abstractmethod
        def get_distance(self, i: int, j: int) -> float:
            """
            Returns distance between sites at index i and j.

            Args:
                i: Index of first site
                j: Index of second site

            Returns:
                Distance between sites at index i and index j.
            """

        @property
        def distance_matrix(self) -> np.ndarray:
            """
            Returns the distance matrix between all sites in the structure. For
            periodic structures, this is overwritten to return the nearest image
            distance.
            """
            return all_distances(self.cart_coords, self.cart_coords)

        @property
        def species(self) -> List[Composition]:
            """
            Only works for ordered structures.
            Disordered structures will raise an AttributeError.

            Returns:
                ([Specie]) List of species at each site of the structure.
            """
            return [site.specie for site in self]

        @property
        def species_and_occu(self) -> List[Composition]:
            """
            List of species and occupancies at each site of the structure.
            """
            return [site.species for site in self]

        @property
        def ntypesp(self) -> int:
            """Number of types of atoms."""
            return len(self.types_of_specie)

        @property
        def types_of_specie(self) -> Tuple[Union[Element, Specie, DummySpecie]]:
            """
            List of types of specie.
            """
            # Cannot use set since we want a deterministic algorithm.
            types = []  # type: List[Union[Element, Specie, DummySpecie]]
            for site in self:
                for sp, v in site.species.items():
                    if v != 0:
                        types.append(sp)
            return tuple(set(types))  # type: ignore

        def group_by_types(self) -> Iterator[Union[Site, PeriodicSite]]:
            """Iterate over species grouped by type"""
            for t in self.types_of_specie:
                for site in self:
                    if site.specie == t:
                        yield site

        def indices_from_symbol(self, symbol: str) -> Tuple[int, ...]:
            """
            Returns a tuple with the sequential indices of the sites
            that contain an element with the given chemical symbol.
            """
            return tuple((i for i, specie in enumerate(self.species)
                          if specie.symbol == symbol))

        @property
        def symbol_set(self) -> Tuple[str]:
            """
            Tuple with the set of chemical symbols.
            Note that len(symbol_set) == len(types_of_specie)
            """
            return tuple(sorted(specie.symbol for specie in self.types_of_specie))  # type: ignore

        @property  # type: ignore
        def atomic_numbers(self) -> Tuple[int]:
            """List of atomic numbers."""
            return tuple(site.specie.Z for site in self)  # type: ignore

        @property
        def site_properties(self) -> Dict[str, List]:
            """
            Returns the site properties as a dict of sequences. E.g.,
            {"magmom": (5,-5), "charge": (-4,4)}.
            """
            props = {}  # type: Dict[str, List]
            prop_keys = set()  # type: Set[str]
            for site in self:
                prop_keys.update(site.properties.keys())

            for k in prop_keys:
                props[k] = [site.properties.get(k, None) for site in self]
            return props

        def __contains__(self, site):
            return site in self.sites

        def __iter__(self):
            return self.sites.__iter__()

        def __getitem__(self, ind):
            return self.sites[ind]

        def __len__(self):
            return len(self.sites)

        def __hash__(self):
            # for now, just use the composition hash code.
            return self.composition.__hash__()

        @property
        def num_sites(self) -> int:
            """
            Number of sites.
            """
            return len(self)

        @property
        def cart_coords(self):
            """
            Returns a np.array of the cartesian coordinates of sites in the
            structure.
            """
            return np.array([site.coords for site in self])

        @property
        def formula(self) -> str:
            """
            (str) Returns the formula.
            """
            return self.composition.formula

        @property
        def composition(self) -> Composition:
            """
            (Composition) Returns the composition
            """
            elmap = collections.defaultdict(float)  # type: Dict[Specie, float]
            for site in self:
                for species, occu in site.species.items():
                    elmap[species] += occu
            return Composition(elmap)

        @property
        def charge(self) -> float:
            """
            Returns the net charge of the structure based on oxidation states. If
            Elements are found, a charge of 0 is assumed.
            """
            charge = 0
            for site in self:
                for specie, amt in site.species.items():
                    charge += getattr(specie, "oxi_state", 0) * amt
            return charge

        @property
        def is_ordered(self) -> bool:
            """
            Checks if structure is ordered, meaning no partial occupancies in any
            of the sites.
            """
            return all((site.is_ordered for site in self))

        def get_angle(self, i: int, j: int, k: int) -> float:
            """
            Returns angle specified by three sites.

            Args:
                i: Index of first site.
                j: Index of second site.
                k: Index of third site.

            Returns:
                Angle in degrees.
            """
            v1 = self[i].coords - self[j].coords
            v2 = self[k].coords - self[j].coords
            return get_angle(v1, v2, units="degrees")

        def get_dihedral(self, i: int, j: int, k: int, l: int) -> float:
            """
            Returns dihedral angle specified by four sites.

            Args:
                i: Index of first site
                j: Index of second site
                k: Index of third site
                l: Index of fourth site

            Returns:
                Dihedral angle in degrees.
            """
            v1 = self[k].coords - self[l].coords
            v2 = self[j].coords - self[k].coords
            v3 = self[i].coords - self[j].coords
            v23 = np.cross(v2, v3)
            v12 = np.cross(v1, v2)
            return math.degrees(math.atan2(np.linalg.norm(v2) * np.dot(v1, v23),
                                           np.dot(v12, v23)))

        def is_valid(self, tol: float = DISTANCE_TOLERANCE) -> bool:
            """
            True if SiteCollection does not contain atoms that are too close
            together. Note that the distance definition is based on type of
            SiteCollection. Cartesian distances are used for non-periodic
            Molecules, while PBC is taken into account for periodic structures.

            Args:
                tol (float): Distance tolerance. Default is 0.5A.

            Returns:
                (bool) True if SiteCollection does not contain atoms that are too
                close together.
            """
            if len(self.sites) == 1:
                return True
            all_dists = self.distance_matrix[np.triu_indices(len(self), 1)]
            return bool(np.min(all_dists) > tol)

        @abstractmethod
        def to(self, fmt: str = None, filename: str = None):
            """
            Generates well-known string representations of SiteCollections (e.g.,
            molecules / structures). Should return a string type or write to a file.
            """

        @classmethod
        @abstractmethod
        def from_str(cls, input_string: str, fmt: str):
            """
            Reads in SiteCollection from a string.
            """

        @classmethod
        @abstractmethod
        def from_file(cls, filename: str):
            """
            Reads in SiteCollection from a filename.
            """

        def add_site_property(self, property_name: str, values: List):
            """
            Adds a property to a site.

            Args:
                property_name (str): The name of the property to add.
                values (list): A sequence of values. Must be same length as
                    number of sites.
            """
            if len(values) != len(self.sites):
                raise ValueError("Values must be same length as sites.")
            for site, val in zip(self.sites, values):
                site.properties[property_name] = val

        def remove_site_property(self, property_name):
            """
            Adds a property to a site.

            Args:
                property_name (str): The name of the property to add.
            """
            for site in self.sites:
                del site.properties[property_name]

        def replace_species(self, species_mapping: Dict[str, str]):
            """
            Swap species.

            Args:
                species_mapping (dict): dict of species to swap. Species can be
                    elements too. E.g., {Element("Li"): Element("Na")} performs
                    a Li for Na substitution. The second species can be a
                    sp_and_occu dict. For example, a site with 0.5 Si that is
                    passed the mapping {Element('Si): {Element('Ge'):0.75,
                    Element('C'):0.25} } will have .375 Ge and .125 C.
            """

            species_mapping = {get_el_sp(k): v
                               for k, v in species_mapping.items()}
            sp_to_replace = set(species_mapping.keys())
            sp_in_structure = set(self.composition.keys())
            if not sp_in_structure.issuperset(sp_to_replace):
                warnings.warn(
                    "Some species to be substituted are not present in "
                    "structure. Pls check your input. Species to be "
                    "substituted = %s; Species in structure = %s"
                    % (sp_to_replace, sp_in_structure))

            for site in self.sites:
                if sp_to_replace.intersection(site.species):
                    c = Composition()
                    for sp, amt in site.species.items():
                        new_sp = species_mapping.get(sp, sp)
                        try:
                            c += Composition(new_sp) * amt
                        except Exception:
                            c += {new_sp: amt}
                    site.species = c

        def add_oxidation_state_by_element(self, oxidation_states: Dict[str, float]):
            """
            Add oxidation states.

            Args:
                oxidation_states (dict): Dict of oxidation states.
                    E.g., {"Li":1, "Fe":2, "P":5, "O":-2}
            """
            try:
                for site in self.sites:
                    new_sp = {}
                    for el, occu in site.species.items():
                        sym = el.symbol
                        new_sp[Specie(sym, oxidation_states[sym])] = occu
                    site.species = Composition(new_sp)
            except KeyError:
                raise ValueError("Oxidation state of all elements must be "
                                 "specified in the dictionary.")

        def add_oxidation_state_by_site(self, oxidation_states: List[float]):
            """
            Add oxidation states to a structure by site.

            Args:
                oxidation_states (list): List of oxidation states.
                    E.g., [1, 1, 1, 1, 2, 2, 2, 2, 5, 5, 5, 5, -2, -2, -2, -2]
            """
            if len(oxidation_states) != len(self.sites):
                raise ValueError("Oxidation states of all sites must be "
                                 "specified.")
            for site, ox in zip(self.sites, oxidation_states):
                new_sp = {}
                for el, occu in site.species.items():
                    sym = el.symbol
                    new_sp[Specie(sym, ox)] = occu
                site.species = Composition(new_sp)

        def remove_oxidation_states(self):
            """
            Removes oxidation states from a structure.
            """
            for site in self.sites:
                new_sp = collections.defaultdict(float)
                for el, occu in site.species.items():
                    sym = el.symbol
                    new_sp[Element(sym)] += occu
                site.species = Composition(new_sp)

        def add_oxidation_state_by_guess(self, **kwargs):
            """
            Decorates the structure with oxidation state, guessing
            using Composition.oxi_state_guesses()

            Args:
                **kwargs: parameters to pass into oxi_state_guesses()
            """
            oxid_guess = self.composition.oxi_state_guesses(**kwargs)
            oxid_guess = oxid_guess or [{e.symbol: 0 for e in self.composition}]
            self.add_oxidation_state_by_element(oxid_guess[0])

        def add_spin_by_element(self, spins: Dict[str, float]):
            """
            Add spin states to a structure.

            Args:
                spins (dict): Dict of spins associated with elements or species,
                    e.g. {"Ni":+5} or {"Ni2+":5}
            """
            for site in self.sites:
                new_sp = {}
                for sp, occu in site.species.items():
                    sym = sp.symbol
                    oxi_state = getattr(sp, "oxi_state", None)
                    new_sp[Specie(sym, oxidation_state=oxi_state,
                                  properties={'spin': spins.get(str(sp), spins.get(sym, None))})] = occu
                site.species = Composition(new_sp)

        def add_spin_by_site(self, spins: List[float]):
            """
            Add spin states to a structure by site.

            Args:
                spins (list): List of spins
                    E.g., [+5, -5, 0, 0]
            """
            if len(spins) != len(self.sites):
                raise ValueError("Spin of all sites must be "
                                 "specified in the dictionary.")

            for site, spin in zip(self.sites, spins):
                new_sp = {}
                for sp, occu in site.species.items():
                    sym = sp.symbol
                    oxi_state = getattr(sp, "oxi_state", None)
                    new_sp[Specie(sym, oxidation_state=oxi_state,
                                  properties={'spin': spin})] = occu
                site.species = Composition(new_sp)

        def remove_spin(self):
            """
            Removes spin states from a structure.
            """
            for site in self.sites:
                new_sp = collections.defaultdict(float)
                for sp, occu in site.species.items():
                    oxi_state = getattr(sp, "oxi_state", None)
                    new_sp[Specie(sp.symbol, oxidation_state=oxi_state)] += occu
                site.species = new_sp

        def extract_cluster(self, target_sites: List[Site], **kwargs):
            r"""
            Extracts a cluster of atoms based on bond lengths

            Args:
                target_sites ([Site]): List of initial sites to nucleate cluster.
                **kwargs: kwargs passed through to CovalentBond.is_bonded.

            Returns:
                [Site/PeriodicSite] Cluster of atoms.
            """
            cluster = list(target_sites)
            others = [site for site in self if site not in cluster]
            size = 0
            while len(cluster) > size:
                size = len(cluster)
                new_others = []
                for site in others:
                    for site2 in cluster:
                        if CovalentBond.is_bonded(site, site2, **kwargs):
                            cluster.append(site)
                            break
                    else:
                        new_others.append(site)
                others = new_others
            return cluster

    class IStructure(SiteCollection, MSONable):
        """
        Basic immutable Structure object with periodicity. Essentially a sequence
        of PeriodicSites having a common lattice. IStructure is made to be
        (somewhat) immutable so that they can function as keys in a dict. To make
        modifications, use the standard Structure object instead. Structure
        extends Sequence and Hashable, which means that in many cases,
        it can be used like any Python sequence. Iterating through a
        structure is equivalent to going through the sites in sequence.
        """

        def __init__(self,
                     lattice: Union[List, np.ndarray, Lattice],
                     species: Sequence[Union[str, Element, Specie, DummySpecie, Composition]],
                     coords: Sequence[Sequence[float]],
                     charge: float = None,
                     validate_proximity: bool = False,
                     to_unit_cell: bool = False,
                     coords_are_cartesian: bool = False,
                     site_properties: dict = None):
            """
            Create a periodic structure.

            Args:
                lattice (Lattice/3x3 array): The lattice, either as a
                    :class:`pymatgen.core.lattice.Lattice` or
                    simply as any 2D array. Each row should correspond to a lattice
                    vector. E.g., [[10,0,0], [20,10,0], [0,0,30]] specifies a
                    lattice with lattice vectors [10,0,0], [20,10,0] and [0,0,30].
                species ([Specie]): Sequence of species on each site. Can take in
                    flexible input, including:

                    i.  A sequence of element / specie specified either as string
                        symbols, e.g. ["Li", "Fe2+", "P", ...] or atomic numbers,
                        e.g., (3, 56, ...) or actual Element or Specie objects.

                    ii. List of dict of elements/species and occupancies, e.g.,
                        [{"Fe" : 0.5, "Mn":0.5}, ...]. This allows the setup of
                        disordered structures.
                coords (Nx3 array): list of fractional/cartesian coordinates of
                    each species.
                charge (int): overall charge of the structure. Defaults to behavior
                    in SiteCollection where total charge is the sum of the oxidation
                    states.
                validate_proximity (bool): Whether to check if there are sites
                    that are less than 0.01 Ang apart. Defaults to False.
                to_unit_cell (bool): Whether to map all sites into the unit cell,
                    i.e., fractional coords between 0 and 1. Defaults to False.
                coords_are_cartesian (bool): Set to True if you are providing
                    coordinates in cartesian coordinates. Defaults to False.
                site_properties (dict): Properties associated with the sites as a
                    dict of sequences, e.g., {"magmom":[5,5,5,5]}. The sequences
                    have to be the same length as the atomic species and
                    fractional_coords. Defaults to None for no properties.
            """
            if len(species) != len(coords):
                raise StructureError("The list of atomic species must be of the"
                                     " same length as the list of fractional"
                                     " coordinates.")

            if isinstance(lattice, Lattice):
                self._lattice = lattice
            else:
                self._lattice = Lattice(lattice)

            sites = []
            for i, sp in enumerate(species):
                prop = None
                if site_properties:
                    prop = {k: v[i]
                            for k, v in site_properties.items()}

                sites.append(
                    PeriodicSite(sp, coords[i], self._lattice,
                                 to_unit_cell,
                                 coords_are_cartesian=coords_are_cartesian,
                                 properties=prop))
            self._sites = tuple(sites)
            if validate_proximity and not self.is_valid():
                raise StructureError(("Structure contains sites that are ",
                                      "less than 0.01 Angstrom apart!"))
            self._charge = charge

        @classmethod
        def from_sites(cls,
                       sites: List[PeriodicSite],
                       charge: float = None,
                       validate_proximity: bool = False,
                       to_unit_cell: bool = False):
            """
            Convenience constructor to make a Structure from a list of sites.

            Args:
                sites: Sequence of PeriodicSites. Sites must have the same
                    lattice.
                charge: Charge of structure.
                validate_proximity (bool): Whether to check if there are sites
                    that are less than 0.01 Ang apart. Defaults to False.
                to_unit_cell (bool): Whether to translate sites into the unit
                    cell.

            Returns:
                (Structure) Note that missing properties are set as None.
            """
            if len(sites) < 1:
                raise ValueError("You need at least one site to construct a %s" %
                                 cls)
            prop_keys = []  # type: List[str]
            props = {}
            lattice = sites[0].lattice
            for i, site in enumerate(sites):
                if site.lattice != lattice:
                    raise ValueError("Sites must belong to the same lattice")
                for k, v in site.properties.items():
                    if k not in prop_keys:
                        prop_keys.append(k)
                        props[k] = [None] * len(sites)
                    props[k][i] = v
            for k, v in props.items():
                if any((vv is None for vv in v)):
                    warnings.warn("Not all sites have property %s. Missing values "
                                  "are set to None." % k)
            return cls(lattice, [site.species for site in sites],
                       [site.frac_coords for site in sites],
                       charge=charge,
                       site_properties=props,
                       validate_proximity=validate_proximity,
                       to_unit_cell=to_unit_cell)

        @classmethod
        def from_spacegroup(cls,
                            sg: str,
                            lattice: Union[List, np.ndarray, Lattice],
                            species: Sequence[Union[str, Element, Specie, DummySpecie, Composition]],
                            coords: Sequence[Sequence[float]],
                            site_properties: Dict[str, Sequence] = None,
                            coords_are_cartesian: bool = False,
                            tol: float = 1e-5):
            """
            Generate a structure using a spacegroup. Note that only symmetrically
            distinct species and coords should be provided. All equivalent sites
            are generated from the spacegroup operations.

            Args:
                sg (str/int): The spacegroup. If a string, it will be interpreted
                    as one of the notations supported by
                    pymatgen.symmetry.groups.Spacegroup. E.g., "R-3c" or "Fm-3m".
                    If an int, it will be interpreted as an international number.
                lattice (Lattice/3x3 array): The lattice, either as a
                    :class:`pymatgen.core.lattice.Lattice` or
                    simply as any 2D array. Each row should correspond to a lattice
                    vector. E.g., [[10,0,0], [20,10,0], [0,0,30]] specifies a
                    lattice with lattice vectors [10,0,0], [20,10,0] and [0,0,30].
                    Note that no attempt is made to check that the lattice is
                    compatible with the spacegroup specified. This may be
                    introduced in a future version.
                species ([Specie]): Sequence of species on each site. Can take in
                    flexible input, including:

                    i.  A sequence of element / specie specified either as string
                        symbols, e.g. ["Li", "Fe2+", "P", ...] or atomic numbers,
                        e.g., (3, 56, ...) or actual Element or Specie objects.

                    ii. List of dict of elements/species and occupancies, e.g.,
                        [{"Fe" : 0.5, "Mn":0.5}, ...]. This allows the setup of
                        disordered structures.
                coords (Nx3 array): list of fractional/cartesian coordinates of
                    each species.
                coords_are_cartesian (bool): Set to True if you are providing
                    coordinates in cartesian coordinates. Defaults to False.
                site_properties (dict): Properties associated with the sites as a
                    dict of sequences, e.g., {"magmom":[5,5,5,5]}. The sequences
                    have to be the same length as the atomic species and
                    fractional_coords. Defaults to None for no properties.
                tol (float): A fractional tolerance to deal with numerical
                   precision issues in determining if orbits are the same.
            """
            from pymatgen.symmetry.groups import SpaceGroup
            try:
                i = int(sg)
                sgp = SpaceGroup.from_int_number(i)
            except ValueError:
                sgp = SpaceGroup(sg)

            if isinstance(lattice, Lattice):
                latt = lattice
            else:
                latt = Lattice(lattice)

            if not sgp.is_compatible(latt):
                raise ValueError(
                    "Supplied lattice with parameters %s is incompatible with "
                    "supplied spacegroup %s!" % (latt.parameters, sgp.symbol)
                )

            if len(species) != len(coords):
                raise ValueError(
                    "Supplied species and coords lengths (%d vs %d) are "
                    "different!" % (len(species), len(coords))
                )

            frac_coords = np.array(coords, dtype=np.float) if not coords_are_cartesian else \
                latt.get_fractional_coords(coords)

            props = {} if site_properties is None else site_properties

            all_sp = []  # type: List[Union[str, Element, Specie, DummySpecie, Composition]]
            all_coords = []  # type: List[List[float]]
            all_site_properties = collections.defaultdict(list)  # type: Dict[str, List]
            for i, (sp, c) in enumerate(zip(species, frac_coords)):
                cc = sgp.get_orbit(c, tol=tol)
                all_sp.extend([sp] * len(cc))
                all_coords.extend(cc)
                for k, v in props.items():
                    all_site_properties[k].extend([v[i]] * len(cc))

            return cls(latt, all_sp, all_coords,
                       site_properties=all_site_properties)

        @classmethod
        def from_magnetic_spacegroup(
                cls,
                msg: Union[str, 'MagneticSpaceGroup'],  # type: ignore  # noqa: F821
                lattice: Union[List, np.ndarray, Lattice],
                species: Sequence[Union[str, Element, Specie, DummySpecie, Composition]],
                coords: Sequence[Sequence[float]],
                site_properties: Dict[str, Sequence],
                coords_are_cartesian: bool = False,
                tol: float = 1e-5):
            """
            Generate a structure using a magnetic spacegroup. Note that only
            symmetrically distinct species, coords and magmoms should be provided.]
            All equivalent sites are generated from the spacegroup operations.

            Args:
                msg (str/list/:class:`pymatgen.symmetry.maggroups.MagneticSpaceGroup`):
                    The magnetic spacegroup.
                    If a string, it will be interpreted as one of the notations
                    supported by MagneticSymmetryGroup, e.g., "R-3'c" or "Fm'-3'm".
                    If a list of two ints, it will be interpreted as the number of
                    the spacegroup in its Belov, Neronova and Smirnova (BNS) setting.
                lattice (Lattice/3x3 array): The lattice, either as a
                    :class:`pymatgen.core.lattice.Lattice` or
                    simply as any 2D array. Each row should correspond to a lattice
                    vector. E.g., [[10,0,0], [20,10,0], [0,0,30]] specifies a
                    lattice with lattice vectors [10,0,0], [20,10,0] and [0,0,30].
                    Note that no attempt is made to check that the lattice is
                    compatible with the spacegroup specified. This may be
                    introduced in a future version.
                species ([Specie]): Sequence of species on each site. Can take in
                    flexible input, including:
                    i.  A sequence of element / specie specified either as string
                    symbols, e.g. ["Li", "Fe2+", "P", ...] or atomic numbers,
                    e.g., (3, 56, ...) or actual Element or Specie objects.

                    ii. List of dict of elements/species and occupancies, e.g.,
                        [{"Fe" : 0.5, "Mn":0.5}, ...]. This allows the setup of
                        disordered structures.
                coords (Nx3 array): list of fractional/cartesian coordinates of
                    each species.
                site_properties (dict): Properties associated with the sites as a
                    dict of sequences, e.g., {"magmom":[5,5,5,5]}. The sequences
                    have to be the same length as the atomic species and
                    fractional_coords. Unlike Structure.from_spacegroup(),
                    this argument is mandatory, since magnetic moment information
                    has to be included. Note that the *direction* of the supplied
                    magnetic moment relative to the crystal is important, even if
                    the resulting structure is used for collinear calculations.
                coords_are_cartesian (bool): Set to True if you are providing
                    coordinates in cartesian coordinates. Defaults to False.
                tol (float): A fractional tolerance to deal with numerical
                    precision issues in determining if orbits are the same.
            """
            from pymatgen.electronic_structure.core import Magmom
            from pymatgen.symmetry.maggroups import MagneticSpaceGroup

            if 'magmom' not in site_properties:
                raise ValueError('Magnetic moments have to be defined.')

            magmoms = [Magmom(m) for m in site_properties['magmom']]

            if not isinstance(msg, MagneticSpaceGroup):
                msg = MagneticSpaceGroup(msg)  # type: ignore

            if isinstance(lattice, Lattice):
                latt = lattice
            else:
                latt = Lattice(lattice)

            if not msg.is_compatible(latt):
                raise ValueError(
                    "Supplied lattice with parameters %s is incompatible with "
                    "supplied spacegroup %s!" % (latt.parameters, msg.sg_symbol)
                )

            if len(species) != len(coords):
                raise ValueError(
                    "Supplied species and coords lengths (%d vs %d) are "
                    "different!" % (len(species), len(coords))
                )

            if len(species) != len(magmoms):
                raise ValueError(
                    "Supplied species and magmom lengths (%d vs %d) are "
                    "different!" % (len(species), len(magmoms))
                )

            frac_coords = coords if not coords_are_cartesian else latt.get_fractional_coords(coords)

            all_sp = []  # type: List[Union[str, Element, Specie, DummySpecie, Composition]]
            all_coords = []  # type: List[List[float]]
            all_magmoms = []  # type: List[float]
            all_site_properties = collections.defaultdict(list)  # type: Dict[str, List]
            for i, (sp, c, m) in enumerate(zip(species, frac_coords, magmoms)):
                cc, mm = msg.get_orbit(c, m, tol=tol)
                all_sp.extend([sp] * len(cc))
                all_coords.extend(cc)
                all_magmoms.extend(mm)
                for k, v in site_properties.items():
                    if k != 'magmom':
                        all_site_properties[k].extend([v[i]] * len(cc))

            all_site_properties['magmom'] = all_magmoms

            return cls(latt, all_sp, all_coords,
                       site_properties=all_site_properties)

        @property
        def charge(self):
            """
            Overall charge of the structure
            """
            if self._charge is None:
                return super().charge
            return self._charge

        @property
        def distance_matrix(self):
            """
            Returns the distance matrix between all sites in the structure. For
            periodic structures, this should return the nearest image distance.
            """
            return self.lattice.get_all_distances(self.frac_coords,
                                                  self.frac_coords)

        @property
        def sites(self):
            """
            Returns an iterator for the sites in the Structure.
            """
            return self._sites

        @property
        def lattice(self):
            """
            Lattice of the structure.
            """
            return self._lattice

        @property
        def density(self):
            """
            Returns the density in units of g/cc
            """
            m = Mass(self.composition.weight, "amu")
            return m.to("g") / (self.volume * Length(1, "ang").to("cm") ** 3)

        def get_space_group_info(self, symprec=1e-2, angle_tolerance=5.0):
            """
            Convenience method to quickly get the spacegroup of a structure.

            Args:
                symprec (float): Same definition as in SpacegroupAnalyzer.
                    Defaults to 1e-2.
                angle_tolerance (float): Same definition as in SpacegroupAnalyzer.
                    Defaults to 5 degrees.

            Returns:
                spacegroup_symbol, international_number
            """
            # Import within method needed to avoid cyclic dependency.
            from pymatgen.symmetry.analyzer import SpacegroupAnalyzer
            a = SpacegroupAnalyzer(self, symprec=symprec,
                                   angle_tolerance=angle_tolerance)
            return a.get_space_group_symbol(), a.get_space_group_number()

        def matches(self, other, anonymous=False, **kwargs):
            """
            Check whether this structure is similar to another structure.
            Basically a convenience method to call structure matching.

            Args:
                other (IStructure/Structure): Another structure.
                **kwargs: Same **kwargs as in
                    :class:`pymatgen.analysis.structure_matcher.StructureMatcher`.

            Returns:
                (bool) True is the structures are similar under some affine
                transformation.
            """
            from pymatgen.analysis.structure_matcher import StructureMatcher
            m = StructureMatcher(**kwargs)
            if not anonymous:
                return m.fit(self, other)
            return m.fit_anonymous(self, other)

        def __eq__(self, other):
            if other is self:
                return True
            if other is None:
                return False
            if len(self) != len(other):
                return False
            if self.lattice != other.lattice:
                return False
            for site in self:
                if site not in other:
                    return False
            return True

        def __ne__(self, other):
            return not self.__eq__(other)

        def __hash__(self):
            # For now, just use the composition hash code.
            return self.composition.__hash__()

        def __mul__(self, scaling_matrix):
            """
            Makes a supercell. Allowing to have sites outside the unit cell

            Args:
                scaling_matrix: A scaling matrix for transforming the lattice
                    vectors. Has to be all integers. Several options are possible:

                    a. A full 3x3 scaling matrix defining the linear combination
                       the old lattice vectors. E.g., [[2,1,0],[0,3,0],[0,0,
                       1]] generates a new structure with lattice vectors a' =
                       2a + b, b' = 3b, c' = c where a, b, and c are the lattice
                       vectors of the original structure.
                    b. An sequence of three scaling factors. E.g., [2, 1, 1]
                       specifies that the supercell should have dimensions 2a x b x
                       c.
                    c. A number, which simply scales all lattice vectors by the
                       same factor.

            Returns:
                Supercell structure. Note that a Structure is always returned,
                even if the input structure is a subclass of Structure. This is
                to avoid different arguments signatures from causing problems. If
                you prefer a subclass to return its own type, you need to override
                this method in the subclass.
            """
            scale_matrix = np.array(scaling_matrix, np.int16)
            if scale_matrix.shape != (3, 3):
                scale_matrix = np.array(scale_matrix * np.eye(3), np.int16)
            new_lattice = Lattice(np.dot(scale_matrix, self._lattice.matrix))

            f_lat = lattice_points_in_supercell(scale_matrix)
            c_lat = new_lattice.get_cartesian_coords(f_lat)

            new_sites = []
            for site in self:
                for v in c_lat:
                    s = PeriodicSite(
                        site.species, site.coords + v,
                        new_lattice, properties=site.properties,
                        coords_are_cartesian=True, to_unit_cell=False,
                        skip_checks=True)
                    new_sites.append(s)

            new_charge = self._charge * np.linalg.det(scale_matrix) if self._charge else None
            return Structure.from_sites(new_sites, charge=new_charge)

        def __rmul__(self, scaling_matrix):
            """
            Similar to __mul__ to preserve commutativeness.
            """
            return self.__mul__(scaling_matrix)

        @property
        def frac_coords(self):
            """
            Fractional coordinates as a Nx3 numpy array.
            """
            return np.array([site.frac_coords for site in self._sites])

        @property
        def volume(self):
            """
            Returns the volume of the structure.
            """
            return self._lattice.volume

        def get_distance(self, i, j, jimage=None):
            """
            Get distance between site i and j assuming periodic boundary
            conditions. If the index jimage of two sites atom j is not specified it
            selects the jimage nearest to the i atom and returns the distance and
            jimage indices in terms of lattice vector translations if the index
            jimage of atom j is specified it returns the distance between the i
            atom and the specified jimage atom.

            Args:
                i (int): Index of first site
                j (int): Index of second site
                jimage: Number of lattice translations in each lattice direction.
                    Default is None for nearest image.

            Returns:
                distance
            """
            return self[i].distance(self[j], jimage)

        def get_sites_in_sphere(self, pt: np.array, r: float,
                                include_index: bool = False,
                                include_image: bool = False) \
                -> List[Tuple[PeriodicSite, float, Optional[int], Optional[Tuple[int]]]]:
            """
            Find all sites within a sphere from the point, including a site (if any)
            sitting on the point itself. This includes sites in other periodic
            images.

            Algorithm:

            1. place sphere of radius r in crystal and determine minimum supercell
               (parallelpiped) which would contain a sphere of radius r. for this
               we need the projection of a_1 on a unit vector perpendicular
               to a_2 & a_3 (i.e. the unit vector in the direction b_1) to
               determine how many a_1"s it will take to contain the sphere.

               Nxmax = r * length_of_b_1 / (2 Pi)

            2. keep points falling within r.

            Args:
                pt (3x1 array): cartesian coordinates of center of sphere.
                r (float): Radius of sphere.
                include_index (bool): Whether the non-supercell site index
                    is included in the returned data
                include_image (bool): Whether to include the supercell image
                    is included in the returned data

            Returns:
                [(site, dist) ...] since most of the time, subsequent processing
                requires the distance.
            """
            site_fcoords = np.mod(self.frac_coords, 1)
            neighbors = []  # type: List[Tuple[PeriodicSite, float, Optional[int], Optional[Tuple[int]]]]
            for fcoord, dist, i, img in self._lattice.get_points_in_sphere(
                    site_fcoords, pt, r):
                nnsite = PeriodicSite(self[i].species,
                                      fcoord, self._lattice,
                                      properties=self[i].properties,
                                      skip_checks=True)

                # Get the neighbor data
                nn_data = (nnsite, dist) if not include_index else (nnsite, dist, i)  # type: ignore
                if include_image:
                    nn_data += (img, )  # type: ignore
                neighbors.append(nn_data)  # type: ignore
            return neighbors

        def get_neighbors(self, site: PeriodicSite, r: float,
                          include_index: bool = False, include_image: bool = False) \
                -> List[PeriodicNeighbor]:
            """
            Get all neighbors to a site within a sphere of radius r.  Excludes the
            site itself.

            Args:
                site (Site): Which is the center of the sphere.
                r (float): Radius of sphere.
                include_index (bool): Deprecated. Now, the non-supercell site index
                    is always included in the returned data.
                include_image (bool): Deprecated. Now the supercell image
                    is always included in the returned data.

            Returns:
                [PeriodicNeighbor] where PeriodicNeighbor is a namedtuple containing
                (site, distance, index, image).
            """
            return self.get_all_neighbors(r, include_index=include_index,
                                          include_image=include_image,
                                          sites=[site])[0]

        @deprecated(get_neighbors, "This is retained purely for checking purposes.")
        def get_neighbors_old(self, site, r, include_index=False, include_image=False):
            """
            Get all neighbors to a site within a sphere of radius r.  Excludes the
            site itself.

            Args:
                site (Site): Which is the center of the sphere.
                r (float): Radius of sphere.
                include_index (bool): Whether the non-supercell site index
                    is included in the returned data
                include_image (bool): Whether to include the supercell image
                    is included in the returned data

            Returns:
                [PeriodicNeighbor] where PeriodicNeighbor is a namedtuple containing
                (site, distance, index, image).
            """
            nn = self.get_sites_in_sphere(site.coords, r,
                                          include_index=include_index,
                                          include_image=include_image)
            return [d for d in nn if site != d[0]]

        def _get_neighbor_list_py(self, r: float,
                                  sites: List[PeriodicSite] = None,
                                  numerical_tol: float = 1e-8,
                                  exclude_self: bool = True) -> Tuple[np.ndarray, ...]:
            """
            A python version of getting neighbor_list. The returned values are a tuple of
            numpy arrays (center_indices, points_indices, offset_vectors, distances).
            Atom `center_indices[i]` has neighbor atom `points_indices[i]` that is
            translated by `offset_vectors[i]` lattice vectors, and the distance is
            `distances[i]`.

            Args:
                r (float): Radius of sphere
                sites (list of Sites or None): sites for getting all neighbors,
                    default is None, which means neighbors will be obtained for all
                    sites. This is useful in the situation where you are interested
                    only in one subspecies type, and makes it a lot faster.
                numerical_tol (float): This is a numerical tolerance for distances.
                    Sites which are < numerical_tol are determined to be conincident
                    with the site. Sites which are r + numerical_tol away is deemed
                    to be within r from the site. The default of 1e-8 should be
                    ok in most instances.
                exclude_self (bool): whether to exclude atom neighboring with itself within
                    numerical tolerance distance, default to True
            Returns: (center_indices, points_indices, offset_vectors, distances)
            """
            neighbors = self.get_all_neighbors_py(r=r, include_index=True, include_image=True,
                                                  sites=sites, numerical_tol=1e-8)
            center_indices = []
            points_indices = []
            offsets = []
            distances = []
            for i, nns in enumerate(neighbors):
                if len(nns) > 0:
                    for n in nns:
                        if exclude_self and (i == n.index) and (n.nn_distance <= numerical_tol):
                            continue
                        center_indices.append(i)
                        points_indices.append(n.index)
                        offsets.append(n.image)
                        distances.append(n.nn_distance)
            return tuple((np.array(center_indices), np.array(points_indices),
                         np.array(offsets), np.array(distances)))

        def get_neighbor_list(self, r: float,
                              sites: List[PeriodicSite] = None,
                              numerical_tol: float = 1e-8,
                              exclude_self: bool = True) -> Tuple[np.ndarray, ...]:
            """
            Get neighbor lists using numpy array representations without constructing
            Neighbor objects. If the cython extension is installed,  this method will
            be orders of magnitude faster than `get_all_neighbors`.
            The returned values are a tuple of numpy arrays
            (center_indices, points_indices, offset_vectors, distances).
            Atom `center_indices[i]` has neighbor atom `points_indices[i]` that is
            translated by `offset_vectors[i]` lattice vectors, and the distance is
            `distances[i]`.

            Args:
                r (float): Radius of sphere
                sites (list of Sites or None): sites for getting all neighbors,
                    default is None, which means neighbors will be obtained for all
                    sites. This is useful in the situation where you are interested
                    only in one subspecies type, and makes it a lot faster.
                numerical_tol (float): This is a numerical tolerance for distances.
                    Sites which are < numerical_tol are determined to be conincident
                    with the site. Sites which are r + numerical_tol away is deemed
                    to be within r from the site. The default of 1e-8 should be
                    ok in most instances.
                exclude_self (bool): whether to exclude atom neighboring with itself within
                    numerical tolerance distance, default to True
            Returns: (center_indices, points_indices, offset_vectors, distances)

            """
            try:
                from pymatgen.optimization.neighbors import find_points_in_spheres  # type: ignore
            except ImportError:
                return self._get_neighbor_list_py(r, sites, exclude_self=exclude_self)
            else:
                if sites is None:
                    sites = self.sites
                site_coords = np.array([site.coords for site in sites], dtype=float)
                cart_coords = np.ascontiguousarray(np.array(self.cart_coords), dtype=float)
                lattice_matrix = np.ascontiguousarray(np.array(self.lattice.matrix), dtype=float)
                r = float(r)
                center_indices, points_indices, images, distances = \
                    find_points_in_spheres(cart_coords, site_coords, r=r,
                                           pbc=np.array([1, 1, 1], dtype=int),
                                           lattice=lattice_matrix, tol=numerical_tol)
                cond = np.array([True] * len(center_indices))
                if exclude_self:
                    self_pair = (center_indices == points_indices) & (distances <= numerical_tol)
                    cond = ~self_pair
                return tuple((center_indices[cond], points_indices[cond],
                             images[cond], distances[cond]))

        def get_all_neighbors(self, r: float,
                              include_index: bool = False,
                              include_image: bool = False,
                              sites: List[PeriodicSite] = None,
                              numerical_tol: float = 1e-8) -> List[List[PeriodicNeighbor]]:

            """
            Get neighbors for each atom in the unit cell, out to a distance r
            Returns a list of list of neighbors for each site in structure.
            Use this method if you are planning on looping over all sites in the
            crystal. If you only want neighbors for a particular site, use the
            method get_neighbors as it may not have to build such a large supercell
            However if you are looping over all sites in the crystal, this method
            is more efficient since it only performs one pass over a large enough
            supercell to contain all possible atoms out to a distance r.
            The return type is a [(site, dist) ...] since most of the time,
            subsequent processing requires the distance.

            A note about periodic images: Before computing the neighbors, this
            operation translates all atoms to within the unit cell (having
            fractional coordinates within [0,1)). This means that the "image" of a
            site does not correspond to how much it has been translates from its
            current position, but which image of the unit cell it resides.

            Args:
                r (float): Radius of sphere.
                include_index (bool): Deprecated. Now, the non-supercell site index
                    is always included in the returned data.
                include_image (bool): Deprecated. Now the supercell image
                    is always included in the returned data.
                sites (list of Sites or None): sites for getting all neighbors,
                    default is None, which means neighbors will be obtained for all
                    sites. This is useful in the situation where you are interested
                    only in one subspecies type, and makes it a lot faster.
                numerical_tol (float): This is a numerical tolerance for distances.
                    Sites which are < numerical_tol are determined to be conincident
                    with the site. Sites which are r + numerical_tol away is deemed
                    to be within r from the site. The default of 1e-8 should be
                    ok in most instances.

            Returns:
                [PeriodicNeighbor] where PeriodicNeighbor is a namedtuple containing
                (site, distance, index, image).
            """
            if sites is None:
                sites = self.sites
            center_indices, points_indices, images, distances = \
                self.get_neighbor_list(r=r, sites=sites, numerical_tol=numerical_tol)
            if len(points_indices) < 1:
                return [[]] * len(sites)
            f_coords = self.frac_coords[points_indices] + images
            neighbor_dict: Dict[int, List] = collections.defaultdict(list)
            lattice = self.lattice
            atol = Site.position_atol
            all_sites = self.sites
            for cindex, pindex, image, f_coord, d in zip(center_indices, points_indices, images, f_coords, distances):
                psite = all_sites[pindex]
                csite = sites[cindex]
                if (d > numerical_tol or
                        # This simply compares the psite and csite. The reason why manual comparison is done is
                        # for speed. This does not check the lattice since they are always equal. Also, the or construct
                        # returns True immediately once one of the conditions are satisfied.
                        psite.species != csite.species or
                        (not np.allclose(psite.coords, csite.coords, atol=atol)) or
                        (not psite.properties == csite.properties)):
                    neighbor_dict[cindex].append(PeriodicNeighbor(
                        species=psite.species,
                        coords=f_coord,
                        lattice=lattice,
                        properties=psite.properties,
                        nn_distance=d,
                        index=pindex,
                        image=tuple(image)))

            neighbors: List[List[PeriodicNeighbor]] = []

            for i in range(len(sites)):
                neighbors.append(neighbor_dict[i])
            return neighbors

        def get_all_neighbors_py(self, r: float,
                                 include_index: bool = False,
                                 include_image: bool = False,
                                 sites: List[PeriodicSite] = None,
                                 numerical_tol: float = 1e-8) \
                -> List[List[PeriodicNeighbor]]:

            """
            Get neighbors for each atom in the unit cell, out to a distance r
            Returns a list of list of neighbors for each site in structure.
            Use this method if you are planning on looping over all sites in the
            crystal. If you only want neighbors for a particular site, use the
            method get_neighbors as it may not have to build such a large supercell
            However if you are looping over all sites in the crystal, this method
            is more efficient since it only performs one pass over a large enough
            supercell to contain all possible atoms out to a distance r.
            The return type is a [(site, dist) ...] since most of the time,
            subsequent processing requires the distance.

            A note about periodic images: Before computing the neighbors, this
            operation translates all atoms to within the unit cell (having
            fractional coordinates within [0,1)). This means that the "image" of a
            site does not correspond to how much it has been translates from its
            current position, but which image of the unit cell it resides.

            Args:
                r (float): Radius of sphere.
                include_index (bool): Deprecated. Now, the non-supercell site index
                    is always included in the returned data.
                include_image (bool): Deprecated. Now the supercell image
                    is always included in the returned data.
                sites (list of Sites or None): sites for getting all neighbors,
                    default is None, which means neighbors will be obtained for all
                    sites. This is useful in the situation where you are interested
                    only in one subspecies type, and makes it a lot faster.
                numerical_tol (float): This is a numerical tolerance for distances.
                    Sites which are < numerical_tol are determined to be conincident
                    with the site. Sites which are r + numerical_tol away is deemed
                    to be within r from the site. The default of 1e-8 should be
                    ok in most instances.

            Returns:
                [PeriodicNeighbor] where PeriodicNeighbor is a namedtuple containing
                (site, distance, index, image).
            """

            if sites is None:
                sites = self.sites
            site_coords = np.array([site.coords for site in sites])
            point_neighbors = get_points_in_spheres(self.cart_coords, site_coords, r=r, pbc=True,
                                                    numerical_tol=numerical_tol, lattice=self.lattice)
            neighbors: List[List[PeriodicNeighbor]] = []
            for point_neighbor, site in zip(point_neighbors, sites):
                nns: List[PeriodicNeighbor] = []
                if len(point_neighbor) < 1:
                    neighbors.append([])
                    continue
                for n in point_neighbor:
                    coord, d, index, image = n
                    if (d > numerical_tol) or (self[index] != site):
                        neighbor = PeriodicNeighbor(
                            species=self[index].species,
                            coords=coord,
                            lattice=self.lattice,
                            properties=self[index].properties,
                            nn_distance=d,
                            index=index,
                            image=tuple(image)
                        )
                        nns.append(neighbor)
                neighbors.append(nns)
            return neighbors

        @deprecated(get_all_neighbors, "This is retained purely for checking purposes.")
        def get_all_neighbors_old(self, r, include_index=False, include_image=False,
                                  include_site=True):
            """
            Get neighbors for each atom in the unit cell, out to a distance r
            Returns a list of list of neighbors for each site in structure.
            Use this method if you are planning on looping over all sites in the
            crystal. If you only want neighbors for a particular site, use the
            method get_neighbors as it may not have to build such a large supercell
            However if you are looping over all sites in the crystal, this method
            is more efficient since it only performs one pass over a large enough
            supercell to contain all possible atoms out to a distance r.
            The return type is a [(site, dist) ...] since most of the time,
            subsequent processing requires the distance.

            A note about periodic images: Before computing the neighbors, this
            operation translates all atoms to within the unit cell (having
            fractional coordinates within [0,1)). This means that the "image" of a
            site does not correspond to how much it has been translates from its
            current position, but which image of the unit cell it resides.

            Args:
                r (float): Radius of sphere.
                include_index (bool): Whether to include the non-supercell site
                    in the returned data
                include_image (bool): Whether to include the supercell image
                    in the returned data
                include_site (bool): Whether to include the site in the returned
                    data. Defaults to True.

            Returns:
                [Neighbor] where Neighbor is a namedtuple containing
                (site, distance, index, image).
            """
            # Use same algorithm as get_sites_in_sphere to determine supercell but
            # loop over all atoms in crystal
            recp_len = np.array(self.lattice.reciprocal_lattice.abc)
            maxr = np.ceil((r + 0.15) * recp_len / (2 * math.pi))
            nmin = np.floor(np.min(self.frac_coords, axis=0)) - maxr
            nmax = np.ceil(np.max(self.frac_coords, axis=0)) + maxr

            all_ranges = [np.arange(x, y) for x, y in zip(nmin, nmax)]
            latt = self._lattice
            matrix = latt.matrix
            neighbors = [list() for _ in range(len(self._sites))]
            all_fcoords = np.mod(self.frac_coords, 1)
            coords_in_cell = np.dot(all_fcoords, matrix)
            site_coords = self.cart_coords

            indices = np.arange(len(self))

            for image in itertools.product(*all_ranges):
                coords = np.dot(image, matrix) + coords_in_cell
                all_dists = all_distances(coords, site_coords)
                all_within_r = np.bitwise_and(all_dists <= r, all_dists > 1e-8)

                for (j, d, within_r) in zip(indices, all_dists, all_within_r):
                    if include_site:
                        nnsite = PeriodicSite(self[j].species, coords[j],
                                              latt, properties=self[j].properties,
                                              coords_are_cartesian=True,
                                              skip_checks=True)

                    for i in indices[within_r]:
                        item = []
                        if include_site:
                            item.append(nnsite)
                        item.append(d[i])
                        if include_index:
                            item.append(j)
                        # Add the image, if requested
                        if include_image:
                            item.append(image)
                        neighbors[i].append(item)
            return neighbors

        def get_neighbors_in_shell(self, origin, r, dr, include_index=False, include_image=False):
            """
            Returns all sites in a shell centered on origin (coords) between radii
            r-dr and r+dr.

            Args:
                origin (3x1 array): Cartesian coordinates of center of sphere.
                r (float): Inner radius of shell.
                dr (float): Width of shell.
                include_index (bool): Deprecated. Now, the non-supercell site index
                    is always included in the returned data.
                include_image (bool): Deprecated. Now the supercell image
                    is always included in the returned data.

            Returns:
                [NearestNeighbor] where Nearest Neighbor is a named tuple containing
                (site, distance, index, image).
            """
            outer = self.get_sites_in_sphere(origin, r + dr,
                                             include_index=include_index,
                                             include_image=include_image)
            inner = r - dr
            return [t for t in outer if t[1] > inner]

        def get_sorted_structure(self, key=None, reverse=False):
            """
            Get a sorted copy of the structure. The parameters have the same
            meaning as in list.sort. By default, sites are sorted by the
            electronegativity of the species.

            Args:
                key: Specifies a function of one argument that is used to extract
                    a comparison key from each list element: key=str.lower. The
                    default value is None (compare the elements directly).
                reverse (bool): If set to True, then the list elements are sorted
                    as if each comparison were reversed.
            """
            sites = sorted(self, key=key, reverse=reverse)
            return self.__class__.from_sites(sites, charge=self._charge)

        def get_reduced_structure(self, reduction_algo: str = "niggli"):
            """
            Get a reduced structure.

            Args:
                reduction_algo (str): The lattice reduction algorithm to use.
                    Currently supported options are "niggli" or "LLL".
            """
            if reduction_algo == "niggli":
                reduced_latt = self._lattice.get_niggli_reduced_lattice()
            elif reduction_algo == "LLL":
                reduced_latt = self._lattice.get_lll_reduced_lattice()
            else:
                raise ValueError("Invalid reduction algo : {}"
                                 .format(reduction_algo))

            if reduced_latt != self.lattice:
                return self.__class__(  # type: ignore
                    reduced_latt,
                    self.species_and_occu,
                    self.cart_coords,
                    coords_are_cartesian=True,
                    to_unit_cell=True,
                    site_properties=self.site_properties,
                    charge=self._charge)
            return self.copy()

        def copy(self, site_properties=None, sanitize=False):
            """
            Convenience method to get a copy of the structure, with options to add
            site properties.

            Args:
                site_properties (dict): Properties to add or override. The
                    properties are specified in the same way as the constructor,
                    i.e., as a dict of the form {property: [values]}. The
                    properties should be in the order of the *original* structure
                    if you are performing sanitization.
                sanitize (bool): If True, this method will return a sanitized
                    structure. Sanitization performs a few things: (i) The sites are
                    sorted by electronegativity, (ii) a LLL lattice reduction is
                    carried out to obtain a relatively orthogonalized cell,
                    (iii) all fractional coords for sites are mapped into the
                    unit cell.

            Returns:
                A copy of the Structure, with optionally new site_properties and
                optionally sanitized.
            """
            props = self.site_properties
            if site_properties:
                props.update(site_properties)
            if not sanitize:
                return self.__class__(self._lattice,
                                      self.species_and_occu,
                                      self.frac_coords,
                                      charge=self._charge,
                                      site_properties=props)
            reduced_latt = self._lattice.get_lll_reduced_lattice()
            new_sites = []
            for i, site in enumerate(self):
                frac_coords = reduced_latt.get_fractional_coords(site.coords)
                site_props = {}
                for p in props:
                    site_props[p] = props[p][i]
                new_sites.append(PeriodicSite(site.species,
                                              frac_coords, reduced_latt,
                                              to_unit_cell=True,
                                              properties=site_props,
                                              skip_checks=True))
            new_sites = sorted(new_sites)
            return self.__class__.from_sites(new_sites, charge=self._charge)

        def interpolate(self, end_structure,
                        nimages: Union[int, Iterable] = 10,
                        interpolate_lattices: bool = False,
                        pbc: bool = True,
                        autosort_tol: float = 0):
            """
            Interpolate between this structure and end_structure. Useful for
            construction of NEB inputs.

            Args:
                end_structure (Structure): structure to interpolate between this
                    structure and end.
                nimages (int,list): No. of interpolation images or a list of
                    interpolation images. Defaults to 10 images.
                interpolate_lattices (bool): Whether to interpolate the lattices.
                    Interpolates the lengths and angles (rather than the matrix)
                    so orientation may be affected.
                pbc (bool): Whether to use periodic boundary conditions to find
                    the shortest path between endpoints.
                autosort_tol (float): A distance tolerance in angstrom in
                    which to automatically sort end_structure to match to the
                    closest points in this particular structure. This is usually
                    what you want in a NEB calculation. 0 implies no sorting.
                    Otherwise, a 0.5 value usually works pretty well.

            Returns:
                List of interpolated structures. The starting and ending
                structures included as the first and last structures respectively.
                A total of (nimages + 1) structures are returned.
            """
            # Check length of structures
            if len(self) != len(end_structure):
                raise ValueError("Structures have different lengths!")

            if not (interpolate_lattices or self.lattice == end_structure.lattice):
                raise ValueError("Structures with different lattices!")

            if not isinstance(nimages, collections.abc.Iterable):
                images = np.arange(nimages + 1) / nimages
            else:
                images = nimages

            # Check that both structures have the same species
            for i, site in enumerate(self):
                if site.species != end_structure[i].species:
                    raise ValueError("Different species!\nStructure 1:\n" +
                                     str(self) + "\nStructure 2\n" +
                                     str(end_structure))

            start_coords = np.array(self.frac_coords)
            end_coords = np.array(end_structure.frac_coords)

            if autosort_tol:
                dist_matrix = self.lattice.get_all_distances(start_coords,
                                                             end_coords)
                site_mappings = collections.defaultdict(list)  # type: Dict[int, List[int]]
                unmapped_start_ind = []
                for i, row in enumerate(dist_matrix):
                    ind = np.where(row < autosort_tol)[0]
                    if len(ind) == 1:
                        site_mappings[i].append(ind[0])
                    else:
                        unmapped_start_ind.append(i)

                if len(unmapped_start_ind) > 1:
                    raise ValueError("Unable to reliably match structures "
                                     "with auto_sort_tol = %f. unmapped indices "
                                     "= %s" % (autosort_tol, unmapped_start_ind))

                sorted_end_coords = np.zeros_like(end_coords)
                matched = []
                for i, j in site_mappings.items():
                    if len(j) > 1:
                        raise ValueError("Unable to reliably match structures "
                                         "with auto_sort_tol = %f. More than one "
                                         "site match!" % autosort_tol)
                    sorted_end_coords[i] = end_coords[j[0]]
                    matched.append(j[0])

                if len(unmapped_start_ind) == 1:
                    i = unmapped_start_ind[0]
                    j = list(set(range(len(start_coords))).difference(matched))[0]  # type: ignore
                    sorted_end_coords[i] = end_coords[j]

                end_coords = sorted_end_coords

            vec = end_coords - start_coords
            if pbc:
                vec -= np.round(vec)
            sp = self.species_and_occu
            structs = []

            if interpolate_lattices:
                # interpolate lattice matrices using polar decomposition
                from scipy.linalg import polar
                # u is unitary (rotation), p is stretch
                u, p = polar(np.dot(end_structure.lattice.matrix.T,
                                    np.linalg.inv(self.lattice.matrix.T)))
                lvec = p - np.identity(3)
                lstart = self.lattice.matrix.T

            for x in images:
                if interpolate_lattices:
                    l_a = np.dot(np.identity(3) + x * lvec, lstart).T
                    lat = Lattice(l_a)
                else:
                    lat = self.lattice
                fcoords = start_coords + x * vec
                structs.append(self.__class__(lat, sp, fcoords, site_properties=self.site_properties))  # type: ignore
            return structs

        def get_miller_index_from_site_indexes(self, site_ids, round_dp=4,
                                               verbose=True):
            """
            Get the Miller index of a plane from a set of sites indexes.

            A minimum of 3 sites are required. If more than 3 sites are given
            the best plane that minimises the distance to all points will be
            calculated.

            Args:
                site_ids (list of int): A list of site indexes to consider. A
                    minimum of three site indexes are required. If more than three
                    sites are provided, the best plane that minimises the distance
                    to all sites will be calculated.
                round_dp (int, optional): The number of decimal places to round the
                    miller index to.
                verbose (bool, optional): Whether to print warnings.

            Returns:
                (tuple): The Miller index.
            """
            return self.lattice.get_miller_index_from_coords(
                self.frac_coords[site_ids], coords_are_cartesian=False,
                round_dp=round_dp, verbose=verbose)

        def get_primitive_structure(self, tolerance=0.25, use_site_props=False,
                                    constrain_latt=None):
            """
            This finds a smaller unit cell than the input. Sometimes it doesn"t
            find the smallest possible one, so this method is recursively called
            until it is unable to find a smaller cell.

            NOTE: if the tolerance is greater than 1/2 the minimum inter-site
            distance in the primitive cell, the algorithm will reject this lattice.

            Args:
                tolerance (float), Angstroms: Tolerance for each coordinate of a
                    particular site. For example, [0.1, 0, 0.1] in cartesian
                    coordinates will be considered to be on the same coordinates
                    as [0, 0, 0] for a tolerance of 0.25. Defaults to 0.25.
                use_site_props (bool): Whether to account for site properties in
                    differntiating sites.
                constrain_latt (list/dict): List of lattice parameters we want to
                    preserve, e.g. ["alpha", "c"] or dict with the lattice
                    parameter names as keys and values we want the parameters to
                    be e.g. {"alpha": 90, "c": 2.5}.

            Returns:
                The most primitive structure found.
            """
            if constrain_latt is None:
                constrain_latt = []

            def site_label(site):
                if not use_site_props:
                    return site.species_string
                d = [site.species_string]
                for k in sorted(site.properties.keys()):
                    d.append(k + "=" + str(site.properties[k]))
                return ", ".join(d)

            # group sites by species string
            sites = sorted(self._sites, key=site_label)

            grouped_sites = [
                list(a[1])
                for a in itertools.groupby(sites, key=site_label)]
            grouped_fcoords = [np.array([s.frac_coords for s in g])
                               for g in grouped_sites]

            # min_vecs are approximate periodicities of the cell. The exact
            # periodicities from the supercell matrices are checked against these
            # first
            min_fcoords = min(grouped_fcoords, key=lambda x: len(x))
            min_vecs = min_fcoords - min_fcoords[0]

            # fractional tolerance in the supercell
            super_ftol = np.divide(tolerance, self.lattice.abc)
            super_ftol_2 = super_ftol * 2

            def pbc_coord_intersection(fc1, fc2, tol):
                """
                Returns the fractional coords in fc1 that have coordinates
                within tolerance to some coordinate in fc2
                """
                d = fc1[:, None, :] - fc2[None, :, :]
                d -= np.round(d)
                np.abs(d, d)
                return fc1[np.any(np.all(d < tol, axis=-1), axis=-1)]

            # here we reduce the number of min_vecs by enforcing that every
            # vector in min_vecs approximately maps each site onto a similar site.
            # The subsequent processing is O(fu^3 * min_vecs) = O(n^4) if we do no
            # reduction.
            # This reduction is O(n^3) so usually is an improvement. Using double
            # the tolerance because both vectors are approximate
            for g in sorted(grouped_fcoords, key=lambda x: len(x)):
                for f in g:
                    min_vecs = pbc_coord_intersection(min_vecs, g - f, super_ftol_2)

            def get_hnf(fu):
                """
                Returns all possible distinct supercell matrices given a
                number of formula units in the supercell. Batches the matrices
                by the values in the diagonal (for less numpy overhead).
                Computational complexity is O(n^3), and difficult to improve.
                Might be able to do something smart with checking combinations of a
                and b first, though unlikely to reduce to O(n^2).
                """

                def factors(n):
                    for i in range(1, n + 1):
                        if n % i == 0:
                            yield i

                for det in factors(fu):
                    if det == 1:
                        continue
                    for a in factors(det):
                        for e in factors(det // a):
                            g = det // a // e
                            yield det, np.array(
                                [[[a, b, c], [0, e, f], [0, 0, g]]
                                 for b, c, f in
                                 itertools.product(range(a), range(a),
                                                   range(e))])

            # we cant let sites match to their neighbors in the supercell
            grouped_non_nbrs = []
            for gfcoords in grouped_fcoords:
                fdist = gfcoords[None, :, :] - gfcoords[:, None, :]
                fdist -= np.round(fdist)
                np.abs(fdist, fdist)
                non_nbrs = np.any(fdist > 2 * super_ftol[None, None, :], axis=-1)
                # since we want sites to match to themselves
                np.fill_diagonal(non_nbrs, True)
                grouped_non_nbrs.append(non_nbrs)

            num_fu = functools.reduce(math.gcd, map(len, grouped_sites))
            for size, ms in get_hnf(num_fu):
                inv_ms = np.linalg.inv(ms)

                # find sets of lattice vectors that are are present in min_vecs
                dist = inv_ms[:, :, None, :] - min_vecs[None, None, :, :]
                dist -= np.round(dist)
                np.abs(dist, dist)
                is_close = np.all(dist < super_ftol, axis=-1)
                any_close = np.any(is_close, axis=-1)
                inds = np.all(any_close, axis=-1)

                for inv_m, m in zip(inv_ms[inds], ms[inds]):
                    new_m = np.dot(inv_m, self.lattice.matrix)
                    ftol = np.divide(tolerance, np.sqrt(np.sum(new_m ** 2, axis=1)))

                    valid = True
                    new_coords = []
                    new_sp = []
                    new_props = collections.defaultdict(list)
                    for gsites, gfcoords, non_nbrs in zip(grouped_sites,
                                                          grouped_fcoords,
                                                          grouped_non_nbrs):
                        all_frac = np.dot(gfcoords, m)

                        # calculate grouping of equivalent sites, represented by
                        # adjacency matrix
                        fdist = all_frac[None, :, :] - all_frac[:, None, :]
                        fdist = np.abs(fdist - np.round(fdist))
                        close_in_prim = np.all(fdist < ftol[None, None, :], axis=-1)
                        groups = np.logical_and(close_in_prim, non_nbrs)

                        # check that groups are correct
                        if not np.all(np.sum(groups, axis=0) == size):
                            valid = False
                            break

                        # check that groups are all cliques
                        for g in groups:
                            if not np.all(groups[g][:, g]):
                                valid = False
                                break
                        if not valid:
                            break

                        # add the new sites, averaging positions
                        added = np.zeros(len(gsites))
                        new_fcoords = all_frac % 1
                        for i, group in enumerate(groups):
                            if not added[i]:
                                added[group] = True
                                inds = np.where(group)[0]
                                coords = new_fcoords[inds[0]]
                                for n, j in enumerate(inds[1:]):
                                    offset = new_fcoords[j] - coords
                                    coords += (offset - np.round(offset)) / (n + 2)
                                new_sp.append(gsites[inds[0]].species)
                                for k in gsites[inds[0]].properties:
                                    new_props[k].append(gsites[inds[0]].properties[k])
                                new_coords.append(coords)

                    if valid:
                        inv_m = np.linalg.inv(m)
                        new_l = Lattice(np.dot(inv_m, self.lattice.matrix))
                        s = Structure(new_l, new_sp, new_coords,
                                      site_properties=new_props,
                                      coords_are_cartesian=False)

                        # Default behavior
                        p = s.get_primitive_structure(
                            tolerance=tolerance, use_site_props=use_site_props,
                            constrain_latt=constrain_latt
                        ).get_reduced_structure()
                        if not constrain_latt:
                            return p

                        # Only return primitive structures that
                        # satisfy the restriction condition
                        p_latt, s_latt = p.lattice, self.lattice
                        if type(constrain_latt).__name__ == "list":
                            if all([getattr(p_latt, p) == getattr(s_latt, p) for p in constrain_latt]):
                                return p
                        elif type(constrain_latt).__name__ == "dict":
                            if all([getattr(p_latt, p) == constrain_latt[p] for p in constrain_latt.keys()]):
                                return p

            return self.copy()

        def __repr__(self):
            outs = ["Structure Summary", repr(self.lattice)]
            if self._charge:
                if self._charge >= 0:
                    outs.append("Overall Charge: +{}".format(self._charge))
                else:
                    outs.append("Overall Charge: -{}".format(self._charge))
            for s in self:
                outs.append(repr(s))
            return "\n".join(outs)

        def __str__(self):
            outs = ["Full Formula ({s})".format(s=self.composition.formula),
                    "Reduced Formula: {}".format(self.composition.reduced_formula)]

            def to_s(x):
                return "%0.6f" % x
            outs.append("abc   : " + " ".join([to_s(i).rjust(10)
                                               for i in self.lattice.abc]))
            outs.append("angles: " + " ".join([to_s(i).rjust(10)
                                               for i in self.lattice.angles]))
            if self._charge:
                if self._charge >= 0:
                    outs.append("Overall Charge: +{}".format(self._charge))
                else:
                    outs.append("Overall Charge: -{}".format(self._charge))
            outs.append("Sites ({i})".format(i=len(self)))
            data = []
            props = self.site_properties
            keys = sorted(props.keys())
            for i, site in enumerate(self):
                row = [str(i), site.species_string]
                row.extend([to_s(j) for j in site.frac_coords])
                for k in keys:
                    row.append(props[k][i])
                data.append(row)
            outs.append(tabulate(data, headers=["#", "SP", "a", "b", "c"] + keys,
                                 ))
            return "\n".join(outs)

        def as_dict(self, verbosity=1, fmt=None, **kwargs):
            """
            Dict representation of Structure.

            Args:
                verbosity (int): Verbosity level. Default of 1 includes both
                    direct and cartesian coordinates for all sites, lattice
                    parameters, etc. Useful for reading and for insertion into a
                    database. Set to 0 for an extremely lightweight version
                    that only includes sufficient information to reconstruct the
                    object.
                fmt (str): Specifies a format for the dict. Defaults to None,
                    which is the default format used in pymatgen. Other options
                    include "abivars".
                **kwargs: Allow passing of other kwargs needed for certain
                formats, e.g., "abivars".

            Returns:
                JSON serializable dict representation.
            """
            if fmt == "abivars":
                """Returns a dictionary with the ABINIT variables."""
                from pymatgen.io.abinit.abiobjects import structure_to_abivars
                return structure_to_abivars(self, **kwargs)

            latt_dict = self._lattice.as_dict(verbosity=verbosity)
            del latt_dict["@module"]
            del latt_dict["@class"]

            d = {"@module": self.__class__.__module__,
                 "@class": self.__class__.__name__,
                 "charge": self._charge,
                 "lattice": latt_dict, "sites": []}
            for site in self:
                site_dict = site.as_dict(verbosity=verbosity)
                del site_dict["lattice"]
                del site_dict["@module"]
                del site_dict["@class"]
                d["sites"].append(site_dict)
            return d

        def as_dataframe(self):
            """
            Returns a Pandas dataframe of the sites. Structure level attributes are stored in DataFrame.attrs. Example:

            Species    a    b             c    x             y             z  magmom
            0    (Si)  0.0  0.0  0.000000e+00  0.0  0.000000e+00  0.000000e+00       5
            1    (Si)  0.0  0.0  1.000000e-07  0.0 -2.217138e-07  3.135509e-07      -5
            """
            data = []
            site_properties = self.site_properties
            prop_keys = list(site_properties.keys())
            for site in self:
                row = [site.species] + list(site.frac_coords) + list(site.coords)
                for k in prop_keys:
                    row.append(site.properties.get(k))
                data.append(row)
            import pandas as pd
            df = pd.DataFrame(data, columns=["Species", "a", "b", "c", "x", "y", "z"] + prop_keys)
            df.attrs["Reduced Formula"] = self.composition.reduced_formula
            df.attrs["Lattice"] = self.lattice
            return df

        @classmethod
        def from_dict(cls, d, fmt=None):
            """
            Reconstitute a Structure object from a dict representation of Structure
            created using as_dict().

            Args:
                d (dict): Dict representation of structure.

            Returns:
                Structure object
            """
            if fmt == "abivars":
                from pymatgen.io.abinit.abiobjects import structure_from_abivars
                return structure_from_abivars(cls=cls, **d)

            lattice = Lattice.from_dict(d["lattice"])
            sites = [PeriodicSite.from_dict(sd, lattice) for sd in d["sites"]]
            charge = d.get("charge", None)
            return cls.from_sites(sites, charge=charge)

        def to(self, fmt=None, filename=None, **kwargs):
            r"""
            Outputs the structure to a file or string.

            Args:
                fmt (str): Format to output to. Defaults to JSON unless filename
                    is provided. If fmt is specifies, it overrides whatever the
                    filename is. Options include "cif", "poscar", "cssr", "json".
                    Non-case sensitive.
                filename (str): If provided, output will be written to a file. If
                    fmt is not specified, the format is determined from the
                    filename. Defaults is None, i.e. string output.
                **kwargs: Kwargs passthru to relevant methods. E.g., This allows
                    the passing of parameters like symprec to the
                    CifWriter.__init__ method for generation of symmetric cifs.

            Returns:
                (str) if filename is None. None otherwise.
            """
            filename = filename or ""
            fmt = "" if fmt is None else fmt.lower()
            fname = os.path.basename(filename)

            if fmt == "cif" or fnmatch(fname.lower(), "*.cif*"):
                from pymatgen.io.cif import CifWriter
                writer = CifWriter(self, **kwargs)
            elif fmt == "mcif" or fnmatch(fname.lower(), "*.mcif*"):
                from pymatgen.io.cif import CifWriter
                writer = CifWriter(self, write_magmoms=True, **kwargs)
            elif fmt == "poscar" or fnmatch(fname, "*POSCAR*"):
                from pymatgen.io.vasp import Poscar
                writer = Poscar(self, **kwargs)
            elif fmt == "cssr" or fnmatch(fname.lower(), "*.cssr*"):
                from pymatgen.io.cssr import Cssr
                writer = Cssr(self, **kwargs)
            elif fmt == "json" or fnmatch(fname.lower(), "*.json"):
                s = json.dumps(self.as_dict())
                if filename:
                    with zopen(filename, "wt") as f:
                        f.write("%s" % s)
                return s
            elif fmt == "xsf" or fnmatch(fname.lower(), "*.xsf*"):
                from pymatgen.io.xcrysden import XSF
                s = XSF(self).to_string()
                if filename:
                    with zopen(fname, "wt", encoding='utf8') as f:
                        f.write(s)
                return s
            elif fmt == 'mcsqs' or fnmatch(fname, "*rndstr.in*") \
                    or fnmatch(fname, "*lat.in*") \
                    or fnmatch(fname, "*bestsqs*"):
                from pymatgen.io.atat import Mcsqs
                s = Mcsqs(self).to_string()
                if filename:
                    with zopen(fname, "wt", encoding='ascii') as f:
                        f.write(s)
                return s
            elif fmt == 'prismatic' or fnmatch(fname, "*prismatic*"):
                from pymatgen.io.prismatic import Prismatic
                s = Prismatic(self).to_string()
                return s
            elif fmt == "yaml" or fnmatch(fname, "*.yaml*") or fnmatch(fname, "*.yml*"):
                import ruamel.yaml as yaml
                if filename:
                    with zopen(filename, "wt") as f:
                        yaml.safe_dump(self.as_dict(), f)
                    return None
                return yaml.safe_dump(self.as_dict())
            else:
                raise ValueError("Invalid format: `%s`" % str(fmt))

            if filename:
                writer.write_file(filename)
                return None
            return writer.__str__()

        @classmethod
        def from_str(cls, input_string, fmt, primitive=False, sort=False,
                     merge_tol=0.0):
            """
            Reads a structure from a string.

            Args:
                input_string (str): String to parse.
                fmt (str): A format specification.
                primitive (bool): Whether to find a primitive cell. Defaults to
                    False.
                sort (bool): Whether to sort the sites in accordance to the default
                    ordering criteria, i.e., electronegativity.
                merge_tol (float): If this is some positive number, sites that
                    are within merge_tol from each other will be merged. Usually
                    0.01 should be enough to deal with common numerical issues.

            Returns:
                IStructure / Structure
            """
            from pymatgen.io.cif import CifParser
            from pymatgen.io.vasp import Poscar
            from pymatgen.io.cssr import Cssr
            from pymatgen.io.xcrysden import XSF
            from pymatgen.io.atat import Mcsqs
            fmt = fmt.lower()
            if fmt == "cif":
                parser = CifParser.from_string(input_string)
                s = parser.get_structures(primitive=primitive)[0]
            elif fmt == "poscar":
                s = Poscar.from_string(input_string, False,
                                       read_velocities=False).structure
            elif fmt == "cssr":
                cssr = Cssr.from_string(input_string)
                s = cssr.structure
            elif fmt == "json":
                d = json.loads(input_string)
                s = Structure.from_dict(d)
            elif fmt == "yaml":
                import ruamel.yaml as yaml
                d = yaml.safe_load(input_string)
                s = Structure.from_dict(d)
            elif fmt == "xsf":
                s = XSF.from_string(input_string).structure
            elif fmt == "mcsqs":
                s = Mcsqs.structure_from_string(input_string)
            else:
                raise ValueError("Unrecognized format `%s`!" % fmt)

            if sort:
                s = s.get_sorted_structure()
            if merge_tol:
                s.merge_sites(merge_tol)
            return cls.from_sites(s)

        @classmethod
        def from_file(cls, filename, primitive=False, sort=False, merge_tol=0.0):
            """
            Reads a structure from a file. For example, anything ending in
            a "cif" is assumed to be a Crystallographic Information Format file.
            Supported formats include CIF, POSCAR/CONTCAR, CHGCAR, LOCPOT,
            vasprun.xml, CSSR, Netcdf and pymatgen's JSON serialized structures.

            Args:
                filename (str): The filename to read from.
                primitive (bool): Whether to convert to a primitive cell
                    Only available for cifs. Defaults to False.
                sort (bool): Whether to sort sites. Default to False.
                merge_tol (float): If this is some positive number, sites that
                    are within merge_tol from each other will be merged. Usually
                    0.01 should be enough to deal with common numerical issues.

            Returns:
                Structure.
            """
            filename = str(filename)
            if filename.endswith(".nc"):
                # Read Structure from a netcdf file.
                from pymatgen.io.abinit.netcdf import structure_from_ncdata
                s = structure_from_ncdata(filename, cls=cls)
                if sort:
                    s = s.get_sorted_structure()
                return s

            from pymatgen.io.lmto import LMTOCtrl
            from pymatgen.io.vasp import Vasprun, Chgcar
            from pymatgen.io.exciting import ExcitingInput
            fname = os.path.basename(filename)
            with zopen(filename, "rt") as f:
                contents = f.read()
            if fnmatch(fname.lower(), "*.cif*") or fnmatch(fname.lower(), "*.mcif*"):
                return cls.from_str(contents, fmt="cif",
                                    primitive=primitive, sort=sort,
                                    merge_tol=merge_tol)
            if fnmatch(fname, "*POSCAR*") or fnmatch(fname, "*CONTCAR*") or fnmatch(fname, "*.vasp"):
                s = cls.from_str(contents, fmt="poscar",
                                 primitive=primitive, sort=sort,
                                 merge_tol=merge_tol)

            elif fnmatch(fname, "CHGCAR*") or fnmatch(fname, "LOCPOT*"):
                s = Chgcar.from_file(filename).structure
            elif fnmatch(fname, "vasprun*.xml*"):
                s = Vasprun(filename).final_structure
            elif fnmatch(fname.lower(), "*.cssr*"):
                return cls.from_str(contents, fmt="cssr",
                                    primitive=primitive, sort=sort,
                                    merge_tol=merge_tol)
            elif fnmatch(fname, "*.json*") or fnmatch(fname, "*.mson*"):
                return cls.from_str(contents, fmt="json",
                                    primitive=primitive, sort=sort,
                                    merge_tol=merge_tol)
            elif fnmatch(fname, "*.yaml*"):
                return cls.from_str(contents, fmt="yaml",
                                    primitive=primitive, sort=sort,
                                    merge_tol=merge_tol)
            elif fnmatch(fname, "*.xsf"):
                return cls.from_str(contents, fmt="xsf",
                                    primitive=primitive, sort=sort,
                                    merge_tol=merge_tol)
            elif fnmatch(fname, "input*.xml"):
                return ExcitingInput.from_file(fname).structure
            elif fnmatch(fname, "*rndstr.in*") \
                    or fnmatch(fname, "*lat.in*") \
                    or fnmatch(fname, "*bestsqs*"):
                return cls.from_str(contents, fmt="mcsqs",
                                    primitive=primitive, sort=sort,
                                    merge_tol=merge_tol)
            elif fnmatch(fname, "CTRL*"):
                return LMTOCtrl.from_file(filename=filename).structure
            else:
                raise ValueError("Unrecognized file extension!")
            if sort:
                s = s.get_sorted_structure()
            if merge_tol:
                s.merge_sites(merge_tol)

            s.__class__ = cls
            return s

    class IMolecule(SiteCollection, MSONable):
        """
        Basic immutable Molecule object without periodicity. Essentially a
        sequence of sites. IMolecule is made to be immutable so that they can
        function as keys in a dict. For a mutable molecule,
        use the :class:Molecule.

        Molecule extends Sequence and Hashable, which means that in many cases,
        it can be used like any Python sequence. Iterating through a molecule is
        equivalent to going through the sites in sequence.
        """

        def __init__(self,
                     species: Sequence[Union[str, Element, Specie, DummySpecie, Composition]],
                     coords: Sequence[Sequence[float]],
                     charge: float = 0.0,
                     spin_multiplicity: float = None,
                     validate_proximity: bool = False,
                     site_properties: dict = None):
            """
            Creates a Molecule.

            Args:
                species: list of atomic species. Possible kinds of input include a
                    list of dict of elements/species and occupancies, a List of
                    elements/specie specified as actual Element/Specie, Strings
                    ("Fe", "Fe2+") or atomic numbers (1,56).
                coords (3x1 array): list of cartesian coordinates of each species.
                charge (float): Charge for the molecule. Defaults to 0.
                spin_multiplicity (int): Spin multiplicity for molecule.
                    Defaults to None, which means that the spin multiplicity is
                    set to 1 if the molecule has no unpaired electrons and to 2
                    if there are unpaired electrons.
                validate_proximity (bool): Whether to check if there are sites
                    that are less than 1 Ang apart. Defaults to False.
                site_properties (dict): Properties associated with the sites as
                    a dict of sequences, e.g., {"magmom":[5,5,5,5]}. The
                    sequences have to be the same length as the atomic species
                    and fractional_coords. Defaults to None for no properties.
            """
            if len(species) != len(coords):
                raise StructureError(("The list of atomic species must be of the",
                                      " same length as the list of fractional ",
                                      "coordinates."))

            sites = []
            for i in range(len(species)):
                prop = None
                if site_properties:
                    prop = {k: v[i] for k, v in site_properties.items()}
                sites.append(Site(species[i], coords[i], properties=prop))

            self._sites = tuple(sites)
            if validate_proximity and not self.is_valid():
                raise StructureError(("Molecule contains sites that are ",
                                      "less than 0.01 Angstrom apart!"))

            self._charge = charge
            nelectrons = 0.0
            for site in sites:
                for sp, amt in site.species.items():
                    if not isinstance(sp, DummySpecie):
                        nelectrons += sp.Z * amt  # type: ignore
            nelectrons -= charge
            self._nelectrons = nelectrons
            if spin_multiplicity:
                if (nelectrons + spin_multiplicity) % 2 != 1:
                    raise ValueError(
                        "Charge of %d and spin multiplicity of %d is"
                        " not possible for this molecule" %
                        (self._charge, spin_multiplicity))
                self._spin_multiplicity = spin_multiplicity
            else:
                self._spin_multiplicity = 1 if nelectrons % 2 == 0 else 2

        @property
        def charge(self):
            """
            Charge of molecule
            """
            return self._charge

        @property
        def spin_multiplicity(self):
            """
            Spin multiplicity of molecule.
            """
            return self._spin_multiplicity

        @property
        def nelectrons(self):
            """
            Number of electrons in the molecule.
            """
            return self._nelectrons

        @property
        def center_of_mass(self):
            """
            Center of mass of molecule.
            """
            center = np.zeros(3)
            total_weight = 0
            for site in self:
                wt = site.species.weight
                center += site.coords * wt
                total_weight += wt
            return center / total_weight

        @property
        def sites(self):
            """
            Returns a tuple of sites in the Molecule.
            """
            return self._sites

        @classmethod
        def from_sites(cls, sites, charge=0, spin_multiplicity=None,
                       validate_proximity=False):
            """
            Convenience constructor to make a Molecule from a list of sites.

            Args:
                sites ([Site]): Sequence of Sites.
                charge (int): Charge of molecule. Defaults to 0.
                spin_multiplicity (int): Spin multicipity. Defaults to None,
                    in which it is determined automatically.
                validate_proximity (bool): Whether to check that atoms are too
                    close.
            """
            props = collections.defaultdict(list)
            for site in sites:
                for k, v in site.properties.items():
                    props[k].append(v)
            return cls([site.species for site in sites],
                       [site.coords for site in sites],
                       charge=charge, spin_multiplicity=spin_multiplicity,
                       validate_proximity=validate_proximity,
                       site_properties=props)

        def break_bond(self, ind1, ind2, tol=0.2):
            """
            Returns two molecules based on breaking the bond between atoms at index
            ind1 and ind2.

            Args:
                ind1 (int): Index of first site.
                ind2 (int): Index of second site.
                tol (float): Relative tolerance to test. Basically, the code
                    checks if the distance between the sites is less than (1 +
                    tol) * typical bond distances. Defaults to 0.2, i.e.,
                    20% longer.

            Returns:
                Two Molecule objects representing the two clusters formed from
                breaking the bond.
            """
            sites = self._sites
            clusters = [[sites[ind1]], [sites[ind2]]]

            sites = [site for i, site in enumerate(sites) if i not in (ind1, ind2)]

            def belongs_to_cluster(site, cluster):
                for test_site in cluster:
                    if CovalentBond.is_bonded(site, test_site, tol=tol):
                        return True
                return False

            while len(sites) > 0:
                unmatched = []
                for site in sites:
                    for cluster in clusters:
                        if belongs_to_cluster(site, cluster):
                            cluster.append(site)
                            break
                    else:
                        unmatched.append(site)

                if len(unmatched) == len(sites):
                    raise ValueError("Not all sites are matched!")
                sites = unmatched

            return (self.__class__.from_sites(cluster)
                    for cluster in clusters)

        def get_covalent_bonds(self, tol=0.2):
            """
            Determines the covalent bonds in a molecule.

            Args:
                tol (float): The tol to determine bonds in a structure. See
                    CovalentBond.is_bonded.

            Returns:
                List of bonds
            """
            bonds = []
            for site1, site2 in itertools.combinations(self._sites, 2):
                if CovalentBond.is_bonded(site1, site2, tol):
                    bonds.append(CovalentBond(site1, site2))
            return bonds

        def __eq__(self, other):
            if other is None:
                return False
            if len(self) != len(other):
                return False
            if self.charge != other.charge:
                return False
            if self.spin_multiplicity != other.spin_multiplicity:
                return False
            for site in self:
                if site not in other:
                    return False
            return True

        def __ne__(self, other):
            return not self.__eq__(other)

        def __hash__(self):
            # For now, just use the composition hash code.
            return self.composition.__hash__()

        def __repr__(self):
            outs = ["Molecule Summary"]
            for s in self:
                outs.append(s.__repr__())
            return "\n".join(outs)

        def __str__(self):
            outs = ["Full Formula (%s)" % self.composition.formula,
                    "Reduced Formula: " + self.composition.reduced_formula,
                    "Charge = %s, Spin Mult = %s" % (
                        self._charge, self._spin_multiplicity),
                    "Sites (%d)" % len(self)]
            for i, site in enumerate(self):
                outs.append(" ".join([str(i), site.species_string,
                                      " ".join([("%0.6f" % j).rjust(12)
                                                for j in site.coords])]))
            return "\n".join(outs)

        def as_dict(self):
            """
            Json-serializable dict representation of Molecule
            """
            d = {"@module": self.__class__.__module__,
                 "@class": self.__class__.__name__,
                 "charge": self._charge,
                 "spin_multiplicity": self._spin_multiplicity,
                 "sites": []}
            for site in self:
                site_dict = site.as_dict()
                del site_dict["@module"]
                del site_dict["@class"]
                d["sites"].append(site_dict)
            return d

        @classmethod
        def from_dict(cls, d):
            """
            Reconstitute a Molecule object from a dict representation created using
            as_dict().

            Args:
                d (dict): dict representation of Molecule.

            Returns:
                Molecule object
            """
            sites = [Site.from_dict(sd) for sd in d["sites"]]
            charge = d.get("charge", 0)
            spin_multiplicity = d.get("spin_multiplicity")
            return cls.from_sites(sites, charge=charge, spin_multiplicity=spin_multiplicity)

        def get_distance(self, i, j):
            """
            Get distance between site i and j.

            Args:
                i (int): Index of first site
                j (int): Index of second site

            Returns:
                Distance between the two sites.
            """
            return self[i].distance(self[j])

        def get_sites_in_sphere(self, pt, r):
            """
            Find all sites within a sphere from a point.

            Args:
                pt (3x1 array): Cartesian coordinates of center of sphere
                r (float): Radius of sphere.

            Returns:
                [Neighbor] since most of the time, subsequent processing
                requires the distance.
            """
            neighbors = []
            for i, site in enumerate(self._sites):
                dist = site.distance_from_point(pt)
                if dist <= r:
                    neighbors.append(Neighbor(site.species, site.coords,
                                              site.properties, dist, i))
            return neighbors

        def get_neighbors(self, site, r):
            """
            Get all neighbors to a site within a sphere of radius r.  Excludes the
            site itself.

            Args:
                site (Site): Site at the center of the sphere.
                r (float): Radius of sphere.

            Returns:
                [(site, dist) ...] since most of the time, subsequent processing
                requires the distance.
            """
            nns = self.get_sites_in_sphere(site.coords, r)
            return [nn for nn in nns if nn != site]

        def get_neighbors_in_shell(self, origin, r, dr):
            """
            Returns all sites in a shell centered on origin (coords) between radii
            r-dr and r+dr.

            Args:
                origin (3x1 array): Cartesian coordinates of center of sphere.
                r (float): Inner radius of shell.
                dr (float): Width of shell.

            Returns:
                [(site, dist) ...] since most of the time, subsequent processing
                requires the distance.
            """
            outer = self.get_sites_in_sphere(origin, r + dr)
            inner = r - dr
            return [nn for nn in outer if nn.nn_distance > inner]

        def get_boxed_structure(self, a, b, c, images=(1, 1, 1),
                                random_rotation=False, min_dist=1, cls=None,
                                offset=None, no_cross=False, reorder=True):
            """
            Creates a Structure from a Molecule by putting the Molecule in the
            center of a orthorhombic box. Useful for creating Structure for
            calculating molecules using periodic codes.

            Args:
                a (float): a-lattice parameter.
                b (float): b-lattice parameter.
                c (float): c-lattice parameter.
                images: No. of boxed images in each direction. Defaults to
                    (1, 1, 1), meaning single molecule with 1 lattice parameter
                    in each direction.
                random_rotation (bool): Whether to apply a random rotation to
                    each molecule. This jumbles all the molecules so that they
                    are not exact images of each other.
                min_dist (float): The minimum distance that atoms should be from
                    each other. This is only used if random_rotation is True.
                    The randomized rotations are searched such that no two atoms
                    are less than min_dist from each other.
                cls: The Structure class to instantiate (defaults to pymatgen
                    structure)
                offset: Translation to offset molecule from center of mass coords
                no_cross: Whether to forbid molecule coords from extending beyond
                    boundary of box.
                reorder: Whether to reorder the sites to be in electronegativity
                    order.

            Returns:
                Structure containing molecule in a box.
            """
            if offset is None:
                offset = np.array([0, 0, 0])

            coords = np.array(self.cart_coords)
            x_range = max(coords[:, 0]) - min(coords[:, 0])
            y_range = max(coords[:, 1]) - min(coords[:, 1])
            z_range = max(coords[:, 2]) - min(coords[:, 2])

            if a <= x_range or b <= y_range or c <= z_range:
                raise ValueError("Box is not big enough to contain Molecule.")
            lattice = Lattice.from_parameters(a * images[0], b * images[1],
                                              c * images[2],
                                              90, 90, 90)
            nimages = images[0] * images[1] * images[2]
            coords = []

            centered_coords = self.cart_coords - self.center_of_mass + offset

            for i, j, k in itertools.product(list(range(images[0])),
                                             list(range(images[1])),
                                             list(range(images[2]))):
                box_center = [(i + 0.5) * a, (j + 0.5) * b, (k + 0.5) * c]
                if random_rotation:
                    while True:
                        op = SymmOp.from_origin_axis_angle(
                            (0, 0, 0), axis=np.random.rand(3),
                            angle=random.uniform(-180, 180))
                        m = op.rotation_matrix
                        new_coords = np.dot(m, centered_coords.T).T + box_center
                        if no_cross:
                            x_max, x_min = max(new_coords[:, 0]), min(new_coords[:, 0])
                            y_max, y_min = max(new_coords[:, 1]), min(new_coords[:, 1])
                            z_max, z_min = max(new_coords[:, 2]), min(new_coords[:, 2])
                            if x_max > a or x_min < 0 or y_max > b or y_min < 0 or z_max > c or z_min < 0:
                                raise ValueError("Molecule crosses boundary of box.")
                        if len(coords) == 0:
                            break
                        distances = lattice.get_all_distances(
                            lattice.get_fractional_coords(new_coords),
                            lattice.get_fractional_coords(coords))
                        if np.amin(distances) > min_dist:
                            break
                else:
                    new_coords = centered_coords + box_center
                    if no_cross:
                        x_max, x_min = max(new_coords[:, 0]), min(new_coords[:, 0])
                        y_max, y_min = max(new_coords[:, 1]), min(new_coords[:, 1])
                        z_max, z_min = max(new_coords[:, 2]), min(new_coords[:, 2])
                        if x_max > a or x_min < 0 or y_max > b or y_min < 0 or z_max > c or z_min < 0:
                            raise ValueError("Molecule crosses boundary of box.")
                coords.extend(new_coords)
            sprops = {k: v * nimages for k, v in self.site_properties.items()}

            if cls is None:
                cls = Structure

            if reorder:
                return cls(lattice, self.species * nimages, coords,
                           coords_are_cartesian=True,
                           site_properties=sprops).get_sorted_structure()
            else:
                return cls(lattice, self.species * nimages, coords,
                           coords_are_cartesian=True,
                           site_properties=sprops)

        def get_centered_molecule(self):
            """
            Returns a Molecule centered at the center of mass.

            Returns:
                Molecule centered with center of mass at origin.
            """
            center = self.center_of_mass
            new_coords = np.array(self.cart_coords) - center
            return self.__class__(self.species_and_occu, new_coords,
                                  charge=self._charge,
                                  spin_multiplicity=self._spin_multiplicity,
                                  site_properties=self.site_properties)

        def to(self, fmt=None, filename=None):
            """
            Outputs the molecule to a file or string.

            Args:
                fmt (str): Format to output to. Defaults to JSON unless filename
                    is provided. If fmt is specifies, it overrides whatever the
                    filename is. Options include "xyz", "gjf", "g03", "json". If
                    you have OpenBabel installed, any of the formats supported by
                    OpenBabel. Non-case sensitive.
                filename (str): If provided, output will be written to a file. If
                    fmt is not specified, the format is determined from the
                    filename. Defaults is None, i.e. string output.

            Returns:
                (str) if filename is None. None otherwise.
            """
            from pymatgen.io.xyz import XYZ
            from pymatgen.io.gaussian import GaussianInput
            from pymatgen.io.babel import BabelMolAdaptor

            fmt = "" if fmt is None else fmt.lower()
            fname = os.path.basename(filename or "")
            if fmt == "xyz" or fnmatch(fname.lower(), "*.xyz*"):
                writer = XYZ(self)
            elif any([fmt == r or fnmatch(fname.lower(), "*.{}*".format(r))
                      for r in ["gjf", "g03", "g09", "com", "inp"]]):
                writer = GaussianInput(self)
            elif fmt == "json" or fnmatch(fname, "*.json*") or fnmatch(fname,
                                                                       "*.mson*"):
                if filename:
                    with zopen(filename, "wt", encoding='utf8') as f:
                        return json.dump(self.as_dict(), f)
                else:
                    return json.dumps(self.as_dict())
            elif fmt == "yaml" or fnmatch(fname, "*.yaml*"):
                import ruamel.yaml as yaml

                if filename:
                    with zopen(fname, "wt", encoding='utf8') as f:
                        return yaml.safe_dump(self.as_dict(), f)
                else:
                    return yaml.safe_dump(self.as_dict())

            else:
                m = re.search(r"\.(pdb|mol|mdl|sdf|sd|ml2|sy2|mol2|cml|mrv)",
                              fname.lower())
                if (not fmt) and m:
                    fmt = m.group(1)
                writer = BabelMolAdaptor(self)
                return writer.write_file(filename, file_format=fmt)

            if filename:
                writer.write_file(filename)
            return str(writer)

        @classmethod
        def from_str(cls, input_string, fmt):
            """
            Reads the molecule from a string.

            Args:
                input_string (str): String to parse.
                fmt (str): Format to output to. Defaults to JSON unless filename
                    is provided. If fmt is specifies, it overrides whatever the
                    filename is. Options include "xyz", "gjf", "g03", "json". If
                    you have OpenBabel installed, any of the formats supported by
                    OpenBabel. Non-case sensitive.

            Returns:
                IMolecule or Molecule.
            """
            from pymatgen.io.xyz import XYZ
            from pymatgen.io.gaussian import GaussianInput
            if fmt.lower() == "xyz":
                m = XYZ.from_string(input_string).molecule
            elif fmt in ["gjf", "g03", "g09", "com", "inp"]:
                m = GaussianInput.from_string(input_string).molecule
            elif fmt == "json":
                d = json.loads(input_string)
                return cls.from_dict(d)
            elif fmt == "yaml":
                import ruamel.yaml as yaml
                d = yaml.safe_load(input_string)
                return cls.from_dict(d)
            else:
                from pymatgen.io.babel import BabelMolAdaptor
                m = BabelMolAdaptor.from_string(input_string,
                                                file_format=fmt).pymatgen_mol
            return cls.from_sites(m)

        @classmethod
        def from_file(cls, filename):
            """
            Reads a molecule from a file. Supported formats include xyz,
            gaussian input (gjf|g03|g09|com|inp), Gaussian output (.out|and
            pymatgen's JSON serialized molecules. Using openbabel,
            many more extensions are supported but requires openbabel to be
            installed.

            Args:
                filename (str): The filename to read from.

            Returns:
                Molecule
            """
            filename = str(filename)
            from pymatgen.io.gaussian import GaussianOutput
            with zopen(filename) as f:
                contents = f.read()
            fname = filename.lower()
            if fnmatch(fname, "*.xyz*"):
                return cls.from_str(contents, fmt="xyz")
            if any([fnmatch(fname.lower(), "*.{}*".format(r))
                    for r in ["gjf", "g03", "g09", "com", "inp"]]):
                return cls.from_str(contents, fmt="g09")
            if any([fnmatch(fname.lower(), "*.{}*".format(r))
                    for r in ["out", "lis", "log"]]):
                return GaussianOutput(filename).final_structure
            if fnmatch(fname, "*.json*") or fnmatch(fname, "*.mson*"):
                return cls.from_str(contents, fmt="json")
            if fnmatch(fname, "*.yaml*"):
                return cls.from_str(contents, fmt="yaml")
            from pymatgen.io.babel import BabelMolAdaptor
            m = re.search(r"\.(pdb|mol|mdl|sdf|sd|ml2|sy2|mol2|cml|mrv)",
                          filename.lower())
            if m:
                new = BabelMolAdaptor.from_file(filename,
                                                m.group(1)).pymatgen_mol
                new.__class__ = cls
                return new
            raise ValueError("Cannot determine file type.")

    class Structure(IStructure, collections.abc.MutableSequence):
        """
        Mutable version of structure.
        """
        __hash__ = None  # type: ignore

        def __init__(self,
                     lattice: Union[List, np.ndarray, Lattice],
                     species: Sequence[Union[str, Element, Specie, DummySpecie, Composition]],
                     coords: Sequence[Sequence[float]],
                     charge: float = None,
                     validate_proximity: bool = False,
                     to_unit_cell: bool = False,
                     coords_are_cartesian: bool = False,
                     site_properties: dict = None):
            """
            Create a periodic structure.

            Args:
                lattice: The lattice, either as a pymatgen.core.lattice.Lattice or
                    simply as any 2D array. Each row should correspond to a lattice
                    vector. E.g., [[10,0,0], [20,10,0], [0,0,30]] specifies a
                    lattice with lattice vectors [10,0,0], [20,10,0] and [0,0,30].
                species: List of species on each site. Can take in flexible input,
                    including:

                    i.  A sequence of element / specie specified either as string
                        symbols, e.g. ["Li", "Fe2+", "P", ...] or atomic numbers,
                        e.g., (3, 56, ...) or actual Element or Specie objects.

                    ii. List of dict of elements/species and occupancies, e.g.,
                        [{"Fe" : 0.5, "Mn":0.5}, ...]. This allows the setup of
                        disordered structures.
                coords (Nx3 array): list of fractional/cartesian coordinates of
                    each species.
                charge (int): overall charge of the structure. Defaults to behavior
                    in SiteCollection where total charge is the sum of the oxidation
                    states.
                validate_proximity (bool): Whether to check if there are sites
                    that are less than 0.01 Ang apart. Defaults to False.
                to_unit_cell (bool): Whether to map all sites into the unit cell,
                    i.e., fractional coords between 0 and 1. Defaults to False.
                coords_are_cartesian (bool): Set to True if you are providing
                    coordinates in cartesian coordinates. Defaults to False.
                site_properties (dict): Properties associated with the sites as a
                    dict of sequences, e.g., {"magmom":[5,5,5,5]}. The sequences
                    have to be the same length as the atomic species and
                    fractional_coords. Defaults to None for no properties.
            """
            super().__init__(
                lattice, species, coords, charge=charge,
                validate_proximity=validate_proximity, to_unit_cell=to_unit_cell,
                coords_are_cartesian=coords_are_cartesian,
                site_properties=site_properties)

            self._sites = list(self._sites)  # type: ignore

        def __setitem__(self, i, site):
            """
            Modify a site in the structure.

            Args:
                i (int, [int], slice, Specie-like): Indices to change. You can
                    specify these as an int, a list of int, or a species-like
                    string.
                site (PeriodicSite/Specie/Sequence): Three options exist. You
                    can provide a PeriodicSite directly (lattice will be
                    checked). Or more conveniently, you can provide a
                    specie-like object or a tuple of up to length 3.

                Examples:
                    s[0] = "Fe"
                    s[0] = Element("Fe")
                    both replaces the species only.
                    s[0] = "Fe", [0.5, 0.5, 0.5]
                    Replaces site and *fractional* coordinates. Any properties
                    are inherited from current site.
                    s[0] = "Fe", [0.5, 0.5, 0.5], {"spin": 2}
                    Replaces site and *fractional* coordinates and properties.

                    s[(0, 2, 3)] = "Fe"
                    Replaces sites 0, 2 and 3 with Fe.

                    s[0::2] = "Fe"
                    Replaces all even index sites with Fe.

                    s["Mn"] = "Fe"
                    Replaces all Mn in the structure with Fe. This is
                    a short form for the more complex replace_species.

                    s["Mn"] = "Fe0.5Co0.5"
                    Replaces all Mn in the structure with Fe: 0.5, Co: 0.5, i.e.,
                    creates a disordered structure!
            """

            if isinstance(i, int):
                indices = [i]
            elif isinstance(i, (str, Element, Specie)):
                self.replace_species({i: site})
                return
            elif isinstance(i, slice):
                to_mod = self[i]
                indices = [ii for ii, s in enumerate(self._sites)
                           if s in to_mod]
            else:
                indices = list(i)

            for ii in indices:
                if isinstance(site, PeriodicSite):
                    if site.lattice != self._lattice:
                        raise ValueError("PeriodicSite added must have same lattice "
                                         "as Structure!")
                    if len(indices) != 1:
                        raise ValueError("Site assignments makes sense only for "
                                         "single int indices!")
                    self._sites[ii] = site
                else:
                    if isinstance(site, str) or (
                            not isinstance(site, collections.abc.Sequence)):
                        self._sites[ii].species = site
                    else:
                        self._sites[ii].species = site[0]
                        if len(site) > 1:
                            self._sites[ii].frac_coords = site[1]
                        if len(site) > 2:
                            self._sites[ii].properties = site[2]

        def __delitem__(self, i):
            """
            Deletes a site from the Structure.
            """
            self._sites.__delitem__(i)

        @property
        def lattice(self):
            """
            :return: Lattice assciated with structure.
            """
            return self._lattice

        @lattice.setter
        def lattice(self, lattice):
            self._lattice = lattice
            for site in self._sites:
                site.lattice = lattice

        def append(self, species, coords, coords_are_cartesian=False,
                   validate_proximity=False, properties=None):
            """
            Append a site to the structure.

            Args:
                species: Species of inserted site
                coords (3x1 array): Coordinates of inserted site
                coords_are_cartesian (bool): Whether coordinates are cartesian.
                    Defaults to False.
                validate_proximity (bool): Whether to check if inserted site is
                    too close to an existing site. Defaults to False.
                properties (dict): Properties of the site.

            Returns:
                New structure with inserted site.
            """
            return self.insert(len(self), species, coords,
                               coords_are_cartesian=coords_are_cartesian,
                               validate_proximity=validate_proximity,
                               properties=properties)

        def insert(self, i, species, coords, coords_are_cartesian=False,
                   validate_proximity=False, properties=None):
            """
            Insert a site to the structure.

            Args:
                i (int): Index to insert site
                species (species-like): Species of inserted site
                coords (3x1 array): Coordinates of inserted site
                coords_are_cartesian (bool): Whether coordinates are cartesian.
                    Defaults to False.
                validate_proximity (bool): Whether to check if inserted site is
                    too close to an existing site. Defaults to False.
                properties (dict): Properties associated with the site.

            Returns:
                New structure with inserted site.
            """
            if not coords_are_cartesian:
                new_site = PeriodicSite(species, coords, self._lattice,
                                        properties=properties)
            else:
                frac_coords = self._lattice.get_fractional_coords(coords)
                new_site = PeriodicSite(species, frac_coords, self._lattice,
                                        properties=properties)

            if validate_proximity:
                for site in self:
                    if site.distance(new_site) < self.DISTANCE_TOLERANCE:
                        raise ValueError("New site is too close to an existing "
                                         "site!")

            self._sites.insert(i, new_site)

        def replace(self, i, species, coords=None, coords_are_cartesian=False,
                    properties=None):
            """
            Replace a single site. Takes either a species or a dict of species and
            occupations.

            Args:
                i (int): Index of the site in the _sites list.
                species (species-like): Species of replacement site
                coords (3x1 array): Coordinates of replacement site. If None,
                    the current coordinates are assumed.
                coords_are_cartesian (bool): Whether coordinates are cartesian.
                    Defaults to False.
                properties (dict): Properties associated with the site.
            """
            if coords is None:
                frac_coords = self[i].frac_coords
            elif coords_are_cartesian:
                frac_coords = self._lattice.get_fractional_coords(coords)
            else:
                frac_coords = coords

            new_site = PeriodicSite(species, frac_coords, self._lattice,
                                    properties=properties)
            self._sites[i] = new_site

        def substitute(self, index, func_grp, bond_order=1):
            """
            Substitute atom at index with a functional group.

            Args:
                index (int): Index of atom to substitute.
                func_grp: Substituent molecule. There are two options:

                    1. Providing an actual Molecule as the input. The first atom
                       must be a DummySpecie X, indicating the position of
                       nearest neighbor. The second atom must be the next
                       nearest atom. For example, for a methyl group
                       substitution, func_grp should be X-CH3, where X is the
                       first site and C is the second site. What the code will
                       do is to remove the index site, and connect the nearest
                       neighbor to the C atom in CH3. The X-C bond indicates the
                       directionality to connect the atoms.
                    2. A string name. The molecule will be obtained from the
                       relevant template in func_groups.json.
                bond_order (int): A specified bond order to calculate the bond
                    length between the attached functional group and the nearest
                    neighbor site. Defaults to 1.
            """

            # Find the nearest neighbor that is not a terminal atom.
            all_non_terminal_nn = []
            for nn, dist, _, _ in self.get_neighbors(self[index], 3):
                # Check that the nn has neighbors within a sensible distance but
                # is not the site being substituted.
                for inn, dist2, _, _ in self.get_neighbors(nn, 3):
                    if inn != self[index] and \
                            dist2 < 1.2 * get_bond_length(nn.specie, inn.specie):
                        all_non_terminal_nn.append((nn, dist))
                        break

            if len(all_non_terminal_nn) == 0:
                raise RuntimeError("Can't find a non-terminal neighbor to attach"
                                   " functional group to.")

            non_terminal_nn = min(all_non_terminal_nn, key=lambda d: d[1])[0]

            # Set the origin point to be the coordinates of the nearest
            # non-terminal neighbor.
            origin = non_terminal_nn.coords

            # Pass value of functional group--either from user-defined or from
            # functional.json
            if isinstance(func_grp, Molecule):
                func_grp = func_grp
            else:
                # Check to see whether the functional group is in database.
                if func_grp not in FunctionalGroups:
                    raise RuntimeError("Can't find functional group in list. "
                                       "Provide explicit coordinate instead")
                func_grp = FunctionalGroups[func_grp]

            # If a bond length can be found, modify func_grp so that the X-group
            # bond length is equal to the bond length.
            try:
                bl = get_bond_length(non_terminal_nn.specie, func_grp[1].specie,
                                     bond_order=bond_order)
            # Catches for case of incompatibility between Element(s) and Specie(s)
            except TypeError:
                bl = None

            if bl is not None:
                func_grp = func_grp.copy()
                vec = func_grp[0].coords - func_grp[1].coords
                vec /= np.linalg.norm(vec)
                func_grp[0] = "X", func_grp[1].coords + float(bl) * vec

            # Align X to the origin.
            x = func_grp[0]
            func_grp.translate_sites(list(range(len(func_grp))), origin - x.coords)

            # Find angle between the attaching bond and the bond to be replaced.
            v1 = func_grp[1].coords - origin
            v2 = self[index].coords - origin
            angle = get_angle(v1, v2)

            if 1 < abs(angle % 180) < 179:
                # For angles which are not 0 or 180, we perform a rotation about
                # the origin along an axis perpendicular to both bonds to align
                # bonds.
                axis = np.cross(v1, v2)
                op = SymmOp.from_origin_axis_angle(origin, axis, angle)
                func_grp.apply_operation(op)
            elif abs(abs(angle) - 180) < 1:
                # We have a 180 degree angle. Simply do an inversion about the
                # origin
                for i, fg in enumerate(func_grp):
                    func_grp[i] = (fg.species, origin - (fg.coords - origin))

            # Remove the atom to be replaced, and add the rest of the functional
            # group.
            del self[index]
            for site in func_grp[1:]:
                s_new = PeriodicSite(site.species, site.coords,
                                     self.lattice, coords_are_cartesian=True)
                self._sites.append(s_new)

        def remove_species(self, species):
            """
            Remove all occurrences of several species from a structure.

            Args:
                species: Sequence of species to remove, e.g., ["Li", "Na"].
            """
            new_sites = []
            species = [get_el_sp(s) for s in species]

            for site in self._sites:
                new_sp_occu = {sp: amt for sp, amt in site.species.items()
                               if sp not in species}
                if len(new_sp_occu) > 0:
                    new_sites.append(PeriodicSite(
                        new_sp_occu, site.frac_coords, self._lattice,
                        properties=site.properties))
            self._sites = new_sites

        def remove_sites(self, indices):
            """
            Delete sites with at indices.

            Args:
                indices: Sequence of indices of sites to delete.
            """
            self._sites = [s for i, s in enumerate(self._sites)
                           if i not in indices]

        def apply_operation(self, symmop, fractional=False):
            """
            Apply a symmetry operation to the structure and return the new
            structure. The lattice is operated by the rotation matrix only.
            Coords are operated in full and then transformed to the new lattice.

            Args:
                symmop (SymmOp): Symmetry operation to apply.
                fractional (bool): Whether the symmetry operation is applied in
                    fractional space. Defaults to False, i.e., symmetry operation
                    is applied in cartesian coordinates.
            """
            if not fractional:
                self._lattice = Lattice([symmop.apply_rotation_only(row)
                                         for row in self._lattice.matrix])

                def operate_site(site):
                    new_cart = symmop.operate(site.coords)
                    new_frac = self._lattice.get_fractional_coords(new_cart)
                    return PeriodicSite(site.species, new_frac,
                                        self._lattice,
                                        properties=site.properties,
                                        skip_checks=True)

            else:
                new_latt = np.dot(symmop.rotation_matrix, self._lattice.matrix)
                self._lattice = Lattice(new_latt)

                def operate_site(site):
                    return PeriodicSite(site.species,
                                        symmop.operate(site.frac_coords),
                                        self._lattice,
                                        properties=site.properties,
                                        skip_checks=True)

            self._sites = [operate_site(s) for s in self._sites]

        @deprecated(message="Simply set using Structure.lattice = lattice. This will be removed in pymatgen v2020.")
        def modify_lattice(self, new_lattice):
            """
            Modify the lattice of the structure.  Mainly used for changing the
            basis.

            Args:
                new_lattice (Lattice): New lattice
            """
            self._lattice = new_lattice
            for site in self._sites:
                site.lattice = new_lattice

        def apply_strain(self, strain):
            """
            Apply a strain to the lattice.

            Args:
                strain (float or list): Amount of strain to apply. Can be a float,
                    or a sequence of 3 numbers. E.g., 0.01 means all lattice
                    vectors are increased by 1%. This is equivalent to calling
                    modify_lattice with a lattice with lattice parameters that
                    are 1% larger.
            """
            s = (1 + np.array(strain)) * np.eye(3)
            self.lattice = Lattice(np.dot(self._lattice.matrix.T, s).T)

        def sort(self, key=None, reverse=False):
            """
            Sort a structure in place. The parameters have the same meaning as in
            list.sort. By default, sites are sorted by the electronegativity of
            the species. The difference between this method and
            get_sorted_structure (which also works in IStructure) is that the
            latter returns a new Structure, while this just sorts the Structure
            in place.

            Args:
                key: Specifies a function of one argument that is used to extract
                    a comparison key from each list element: key=str.lower. The
                    default value is None (compare the elements directly).
                reverse (bool): If set to True, then the list elements are sorted
                    as if each comparison were reversed.
            """
            self._sites.sort(key=key, reverse=reverse)

        def translate_sites(self, indices, vector, frac_coords=True,
                            to_unit_cell=True):
            """
            Translate specific sites by some vector, keeping the sites within the
            unit cell.

            Args:
                indices: Integer or List of site indices on which to perform the
                    translation.
                vector: Translation vector for sites.
                frac_coords (bool): Whether the vector corresponds to fractional or
                    cartesian coordinates.
                to_unit_cell (bool): Whether new sites are transformed to unit
                    cell
            """
            if not isinstance(indices, collections.abc.Iterable):
                indices = [indices]

            for i in indices:
                site = self._sites[i]
                if frac_coords:
                    fcoords = site.frac_coords + vector
                else:
                    fcoords = self._lattice.get_fractional_coords(
                        site.coords + vector)
                if to_unit_cell:
                    fcoords = np.mod(fcoords, 1)
                self._sites[i].frac_coords = fcoords

        def rotate_sites(self, indices=None, theta=0, axis=None, anchor=None,
                         to_unit_cell=True):
            """
            Rotate specific sites by some angle around vector at anchor.

            Args:
                indices (list): List of site indices on which to perform the
                    translation.
                theta (float): Angle in radians
                axis (3x1 array): Rotation axis vector.
                anchor (3x1 array): Point of rotation.
                to_unit_cell (bool): Whether new sites are transformed to unit
                    cell
            """

            from numpy.linalg import norm
            from numpy import cross, eye
            from scipy.linalg import expm

            if indices is None:
                indices = range(len(self))

            if axis is None:
                axis = [0, 0, 1]

            if anchor is None:
                anchor = [0, 0, 0]

            anchor = np.array(anchor)
            axis = np.array(axis)

            theta %= 2 * np.pi

            rm = expm(cross(eye(3), axis / norm(axis)) * theta)
            for i in indices:
                site = self._sites[i]
                coords = ((np.dot(rm, np.array(site.coords - anchor).T)).T + anchor).ravel()
                new_site = PeriodicSite(
                    site.species, coords, self._lattice,
                    to_unit_cell=to_unit_cell, coords_are_cartesian=True,
                    properties=site.properties,
                    skip_checks=True)
                self._sites[i] = new_site

        def perturb(self, distance, min_distance=None):
            """
            Performs a random perturbation of the sites in a structure to break
            symmetries.

            Args:
                distance (float): Distance in angstroms by which to perturb each
                    site.
                min_distance (None, int, or float): if None, all displacements will
                    be equal amplitude. If int or float, perturb each site a
                    distance drawn from the uniform distribution between
                    'min_distance' and 'distance'.

            """

            def get_rand_vec():
                # deals with zero vectors.
                vector = np.random.randn(3)
                vnorm = np.linalg.norm(vector)
                dist = distance
                if isinstance(min_distance, (float, int)):
                    dist = np.random.uniform(min_distance, dist)
                return vector / vnorm * dist if vnorm != 0 else get_rand_vec()

            for i in range(len(self._sites)):
                self.translate_sites([i], get_rand_vec(), frac_coords=False)

        def make_supercell(self, scaling_matrix, to_unit_cell=True):
            """
            Create a supercell.

            Args:
                scaling_matrix: A scaling matrix for transforming the lattice
                    vectors. Has to be all integers. Several options are possible:

                    a. A full 3x3 scaling matrix defining the linear combination
                       the old lattice vectors. E.g., [[2,1,0],[0,3,0],[0,0,
                       1]] generates a new structure with lattice vectors a' =
                       2a + b, b' = 3b, c' = c where a, b, and c are the lattice
                       vectors of the original structure.
                    b. An sequence of three scaling factors. E.g., [2, 1, 1]
                       specifies that the supercell should have dimensions 2a x b x
                       c.
                    c. A number, which simply scales all lattice vectors by the
                       same factor.
                to_unit_cell: Whether or not to fall back sites into the unit cell
            """
            s = self * scaling_matrix
            if to_unit_cell:
                for site in s:
                    site.to_unit_cell(in_place=True)
            self._sites = s.sites
            self._lattice = s.lattice

        def scale_lattice(self, volume):
            """
            Performs a scaling of the lattice vectors so that length proportions
            and angles are preserved.

            Args:
                volume (float): New volume of the unit cell in A^3.
            """
            self.lattice = self._lattice.scale(volume)

        def merge_sites(self, tol=0.01, mode="sum"):
            """
            Merges sites (adding occupancies) within tol of each other.
            Removes site properties.

            Args:
                tol (float): Tolerance for distance to merge sites.
                mode (str): Three modes supported. "delete" means duplicate sites are
                    deleted. "sum" means the occupancies are summed for the sites.
                    "average" means that the site is deleted but the properties are averaged
                    Only first letter is considered.

            """
            mode = mode.lower()[0]
            from scipy.spatial.distance import squareform
            from scipy.cluster.hierarchy import fcluster, linkage

            d = self.distance_matrix
            np.fill_diagonal(d, 0)
            clusters = fcluster(linkage(squareform((d + d.T) / 2)),
                                tol, 'distance')
            sites = []
            for c in np.unique(clusters):
                inds = np.where(clusters == c)[0]
                species = self[inds[0]].species
                coords = self[inds[0]].frac_coords
                props = self[inds[0]].properties
                for n, i in enumerate(inds[1:]):
                    sp = self[i].species
                    if mode == "s":
                        species += sp
                    offset = self[i].frac_coords - coords
                    coords = coords + ((offset - np.round(offset)) / (n + 2)).astype(
                        coords.dtype)
                    for key in props.keys():
                        if props[key] is not None and self[i].properties[key] != props[key]:
                            if mode == 'a' and isinstance(props[key], float):
                                # update a running total
                                props[key] = props[key] * (n + 1) / (n + 2) + self[i].properties[key] / (n + 2)
                            else:
                                props[key] = None
                                warnings.warn("Sites with different site property %s are merged. "
                                              "So property is set to none" % key)
                sites.append(PeriodicSite(species, coords, self.lattice, properties=props))

            self._sites = sites

        def set_charge(self, new_charge: float = 0.):
            """
            Sets the overall structure charge

            Args:
                new_charge (float): new charge to set
            """
            self._charge = new_charge

    class Molecule(IMolecule, collections.abc.MutableSequence):
        """
        Mutable Molecule. It has all the methods in IMolecule, but in addition,
        it allows a user to perform edits on the molecule.
        """
        __hash__ = None  # type: ignore

        def __init__(self,
                     species: Sequence[Union[str, Element, Specie, DummySpecie, Composition]],
                     coords: Sequence[Sequence[float]],
                     charge: float = 0.0,
                     spin_multiplicity: float = None,
                     validate_proximity: bool = False,
                     site_properties: dict = None):
            """
            Creates a MutableMolecule.

            Args:
                species: list of atomic species. Possible kinds of input include a
                    list of dict of elements/species and occupancies, a List of
                    elements/specie specified as actual Element/Specie, Strings
                    ("Fe", "Fe2+") or atomic numbers (1,56).
                coords (3x1 array): list of cartesian coordinates of each species.
                charge (float): Charge for the molecule. Defaults to 0.
                spin_multiplicity (int): Spin multiplicity for molecule.
                    Defaults to None, which means that the spin multiplicity is
                    set to 1 if the molecule has no unpaired electrons and to 2
                    if there are unpaired electrons.
                validate_proximity (bool): Whether to check if there are sites
                    that are less than 1 Ang apart. Defaults to False.
                site_properties (dict): Properties associated with the sites as
                    a dict of sequences, e.g., {"magmom":[5,5,5,5]}. The
                    sequences have to be the same length as the atomic species
                    and fractional_coords. Defaults to None for no properties.
            """
            super().__init__(species, coords, charge=charge,
                             spin_multiplicity=spin_multiplicity,
                             validate_proximity=validate_proximity,
                             site_properties=site_properties)
            self._sites = list(self._sites)  # type: ignore

        def __setitem__(self, i, site):
            """
            Modify a site in the molecule.

            Args:
                i (int, [int], slice, Specie-like): Indices to change. You can
                    specify these as an int, a list of int, or a species-like
                    string.
                site (PeriodicSite/Specie/Sequence): Three options exist. You can
                    provide a Site directly, or for convenience, you can provide
                    simply a Specie-like string/object, or finally a (Specie,
                    coords) sequence, e.g., ("Fe", [0.5, 0.5, 0.5]).
            """

            if isinstance(i, int):
                indices = [i]
            elif isinstance(i, (str, Element, Specie)):
                self.replace_species({i: site})
                return
            elif isinstance(i, slice):
                to_mod = self[i]
                indices = [ii for ii, s in enumerate(self._sites)
                           if s in to_mod]
            else:
                indices = list(i)

            for ii in indices:
                if isinstance(site, Site):
                    self._sites[ii] = site
                else:
                    if isinstance(site, str) or (
                            not isinstance(site, collections.abc.Sequence)):
                        self._sites[ii].species = site
                    else:
                        self._sites[ii].species = site[0]
                        if len(site) > 1:
                            self._sites[ii].coords = site[1]
                        if len(site) > 2:
                            self._sites[ii].properties = site[2]

        def __delitem__(self, i):
            """
            Deletes a site from the Structure.
            """
            self._sites.__delitem__(i)

        def append(self, species, coords, validate_proximity=True, properties=None):
            """
            Appends a site to the molecule.

            Args:
                species: Species of inserted site
                coords: Coordinates of inserted site
                validate_proximity (bool): Whether to check if inserted site is
                    too close to an existing site. Defaults to True.
                properties (dict): A dict of properties for the Site.

            Returns:
                New molecule with inserted site.
            """
            return self.insert(len(self), species, coords,
                               validate_proximity=validate_proximity,
                               properties=properties)

        def set_charge_and_spin(self, charge: float, spin_multiplicity: Optional[float] = None):
            """
            Set the charge and spin multiplicity.

            Args:
                charge (int): Charge for the molecule. Defaults to 0.
                spin_multiplicity (int): Spin multiplicity for molecule.
                    Defaults to None, which means that the spin multiplicity is
                    set to 1 if the molecule has no unpaired electrons and to 2
                    if there are unpaired electrons.
            """
            self._charge = charge
            nelectrons = 0.0
            for site in self._sites:
                for sp, amt in site.species.items():
                    if not isinstance(sp, DummySpecie):
                        nelectrons += sp.Z * amt
            nelectrons -= charge
            self._nelectrons = nelectrons
            if spin_multiplicity:
                if (nelectrons + spin_multiplicity) % 2 != 1:
                    raise ValueError(
                        "Charge of {} and spin multiplicity of {} is"
                        " not possible for this molecule".format(
                            self._charge, spin_multiplicity))
                self._spin_multiplicity = spin_multiplicity
            else:
                self._spin_multiplicity = 1 if nelectrons % 2 == 0 else 2

        def insert(self, i, species, coords, validate_proximity=False,
                   properties=None):
            """
            Insert a site to the molecule.

            Args:
                i (int): Index to insert site
                species: species of inserted site
                coords (3x1 array): coordinates of inserted site
                validate_proximity (bool): Whether to check if inserted site is
                    too close to an existing site. Defaults to True.
                properties (dict): Dict of properties for the Site.

            Returns:
                New molecule with inserted site.
            """
            new_site = Site(species, coords, properties=properties)
            if validate_proximity:
                for site in self:
                    if site.distance(new_site) < self.DISTANCE_TOLERANCE:
                        raise ValueError("New site is too close to an existing "
                                         "site!")
            self._sites.insert(i, new_site)

        def remove_species(self, species):
            """
            Remove all occurrences of a species from a molecule.

            Args:
                species: Species to remove.
            """
            new_sites = []
            species = [get_el_sp(sp) for sp in species]
            for site in self._sites:
                new_sp_occu = {sp: amt for sp, amt in site.species.items()
                               if sp not in species}
                if len(new_sp_occu) > 0:
                    new_sites.append(Site(new_sp_occu, site.coords,
                                          properties=site.properties))
            self._sites = new_sites

        def remove_sites(self, indices):
            """
            Delete sites with at indices.

            Args:
                indices: Sequence of indices of sites to delete.
            """
            self._sites = [self._sites[i] for i in range(len(self._sites))
                           if i not in indices]

        def translate_sites(self, indices=None, vector=None):
            """
            Translate specific sites by some vector, keeping the sites within the
            unit cell.

            Args:
                indices (list): List of site indices on which to perform the
                    translation.
                vector (3x1 array): Translation vector for sites.
            """
            if indices is None:
                indices = range(len(self))
            if vector is None:
                vector == [0, 0, 0]
            for i in indices:
                site = self._sites[i]
                new_site = Site(site.species, site.coords + vector,
                                properties=site.properties)
                self._sites[i] = new_site

        def rotate_sites(self, indices=None, theta=0, axis=None, anchor=None):
            """
            Rotate specific sites by some angle around vector at anchor.

            Args:
                indices (list): List of site indices on which to perform the
                    translation.
                theta (float): Angle in radians
                axis (3x1 array): Rotation axis vector.
                anchor (3x1 array): Point of rotation.
            """

            from numpy.linalg import norm
            from numpy import cross, eye
            from scipy.linalg import expm

            if indices is None:
                indices = range(len(self))

            if axis is None:
                axis = [0, 0, 1]

            if anchor is None:
                anchor = [0, 0, 0]

            anchor = np.array(anchor)
            axis = np.array(axis)

            theta %= 2 * np.pi

            rm = expm(cross(eye(3), axis / norm(axis)) * theta)

            for i in indices:
                site = self._sites[i]
                s = ((np.dot(rm, (site.coords - anchor).T)).T + anchor).ravel()
                new_site = Site(site.species, s,
                                properties=site.properties)
                self._sites[i] = new_site

        def perturb(self, distance):
            """
            Performs a random perturbation of the sites in a structure to break
            symmetries.

            Args:
                distance (float): Distance in angstroms by which to perturb each
                    site.
            """

            def get_rand_vec():
                # deals with zero vectors.
                vector = np.random.randn(3)
                vnorm = np.linalg.norm(vector)
                return vector / vnorm * distance if vnorm != 0 else get_rand_vec()

            for i in range(len(self._sites)):
                self.translate_sites([i], get_rand_vec())

        def apply_operation(self, symmop):
            """
            Apply a symmetry operation to the molecule.

            Args:
                symmop (SymmOp): Symmetry operation to apply.
            """

            def operate_site(site):
                new_cart = symmop.operate(site.coords)
                return Site(site.species, new_cart,
                            properties=site.properties)

            self._sites = [operate_site(s) for s in self._sites]

        def copy(self):
            """
            Convenience method to get a copy of the molecule.

            Returns:
                A copy of the Molecule.
            """
            return self.__class__.from_sites(self)

        def substitute(self, index, func_grp, bond_order=1):
            """
            Substitute atom at index with a functional group.

            Args:
                index (int): Index of atom to substitute.
                func_grp: Substituent molecule. There are two options:

                    1. Providing an actual molecule as the input. The first atom
                       must be a DummySpecie X, indicating the position of
                       nearest neighbor. The second atom must be the next
                       nearest atom. For example, for a methyl group
                       substitution, func_grp should be X-CH3, where X is the
                       first site and C is the second site. What the code will
                       do is to remove the index site, and connect the nearest
                       neighbor to the C atom in CH3. The X-C bond indicates the
                       directionality to connect the atoms.
                    2. A string name. The molecule will be obtained from the
                       relevant template in func_groups.json.
                bond_order (int): A specified bond order to calculate the bond
                    length between the attached functional group and the nearest
                    neighbor site. Defaults to 1.
            """

            # Find the nearest neighbor that is not a terminal atom.
            all_non_terminal_nn = []
            for nn in self.get_neighbors(self[index], 3):
                # Check that the nn has neighbors within a sensible distance but
                # is not the site being substituted.
                for nn2 in self.get_neighbors(nn, 3):
                    if nn2 != self[index] and nn2.nn_distance < 1.2 * get_bond_length(nn.specie, nn2.specie):
                        all_non_terminal_nn.append(nn)
                        break

            if len(all_non_terminal_nn) == 0:
                raise RuntimeError("Can't find a non-terminal neighbor to attach"
                                   " functional group to.")

            non_terminal_nn = min(all_non_terminal_nn, key=lambda nn: nn.nn_distance)

            # Set the origin point to be the coordinates of the nearest
            # non-terminal neighbor.
            origin = non_terminal_nn.coords

            # Pass value of functional group--either from user-defined or from
            # functional.json
            if isinstance(func_grp, Molecule):
                func_grp = func_grp
            else:
                # Check to see whether the functional group is in database.
                if func_grp not in FunctionalGroups:
                    raise RuntimeError("Can't find functional group in list. "
                                       "Provide explicit coordinate instead")
                func_grp = FunctionalGroups[func_grp]

            # If a bond length can be found, modify func_grp so that the X-group
            # bond length is equal to the bond length.
            bl = get_bond_length(non_terminal_nn.specie, func_grp[1].specie,
                                 bond_order=bond_order)
            if bl is not None:
                func_grp = func_grp.copy()
                vec = func_grp[0].coords - func_grp[1].coords
                vec /= np.linalg.norm(vec)
                func_grp[0] = "X", func_grp[1].coords + float(bl) * vec

            # Align X to the origin.
            x = func_grp[0]
            func_grp.translate_sites(list(range(len(func_grp))), origin - x.coords)

            # Find angle between the attaching bond and the bond to be replaced.
            v1 = func_grp[1].coords - origin
            v2 = self[index].coords - origin
            angle = get_angle(v1, v2)

            if 1 < abs(angle % 180) < 179:
                # For angles which are not 0 or 180, we perform a rotation about
                # the origin along an axis perpendicular to both bonds to align
                # bonds.
                axis = np.cross(v1, v2)
                op = SymmOp.from_origin_axis_angle(origin, axis, angle)
                func_grp.apply_operation(op)
            elif abs(abs(angle) - 180) < 1:
                # We have a 180 degree angle. Simply do an inversion about the
                # origin
                for i, fg in enumerate(func_grp):
                    func_grp[i] = (fg.species, origin - (fg.coords - origin))

            # Remove the atom to be replaced, and add the rest of the functional
            # group.
            del self[index]
            for site in func_grp[1:]:
                self._sites.append(site)

    class StructureError(Exception):
        """
        Exception class for Structure.
        Raised when the structure has problems, e.g., atoms that are too close.
        """
        pass

    with open(os.path.join(os.path.dirname(__file__),
                           "func_groups.json"), "rt") as f:
        FunctionalGroups = {k: Molecule(v["species"], v["coords"])
                            for k, v in json.load(f).items()}