xref: /dports/science/py-pymatgen/pymatgen-2022.0.15/pymatgen/core/structure.py

# 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 collections
import functools
import itertools
import json
import math
import os
import random
import re
import sys
import warnings
from abc import ABCMeta, abstractmethod
from fnmatch import fnmatch
from typing import (
    Any,
    Callable,
    Dict,
    Iterable,
    Iterator,
    List,
    Optional,
    Sequence,
    Set,
    Tuple,
    Union,
)

import numpy as np
from monty.dev import deprecated
from monty.io import zopen
from monty.json import MSONable
from tabulate import tabulate

from pymatgen.core import yaml
from pymatgen.core.bonds import CovalentBond, get_bond_length
from pymatgen.core.composition import Composition
from pymatgen.core.lattice import Lattice, get_points_in_spheres
from pymatgen.core.operations import SymmOp
from pymatgen.core.periodic_table import DummySpecies, Element, Species, get_el_sp
from pymatgen.core.sites import PeriodicSite, Site
from pymatgen.core.units import Length, Mass
from pymatgen.util.coord import all_distances, get_angle, lattice_points_in_supercell
from pymatgen.util.typing import ArrayLike, CompositionLike, SpeciesLike

if sys.version_info >= (3, 8):
    from typing import Literal
else:
    from typing_extensions import Literal


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) -> np.ndarray:  # type: ignore
        """
        :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):
        """
        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:
            ([Species]) 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_species)

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

    @property
    def types_of_specie(self) -> Tuple[Union[Element, Species, DummySpecies]]:
        """
        Specie->Species rename. Maintained for backwards compatibility.
        """
        return self.types_of_species

    def group_by_types(self) -> Iterator[Union[Site, PeriodicSite]]:
        """Iterate over species grouped by type"""
        for t in self.types_of_species:
            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_species))  # 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[Species, 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: Any):
        """
        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: str):
        """
        Removes a property to a site.

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

    def replace_species(self, species_mapping: Dict[SpeciesLike, SpeciesLike]):
        """
        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.
        """

        sp_mapping = {get_el_sp(k): v for k, v in species_mapping.items()}
        sp_to_replace = set(sp_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 = sp_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[Species(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[Species(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[
                    Species(
                        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[Species(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[Species(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[ArrayLike, Lattice],
        species: Sequence[CompositionLike],
        coords: Sequence[ArrayLike],
        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 ([Species]): Sequence of species on each site. Can take in
                flexible input, including:

                i.  A sequence of element / species specified either as string
                    symbols, e.g. ["Li", "Fe2+", "P", ...] or atomic numbers,
                    e.g., (3, 56, ...) or actual Element or Species 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[PeriodicSite, ...] = 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, Species, DummySpecies, Composition]],
        coords: Sequence[Sequence[float]],
        site_properties: Dict[str, Sequence] = None,
        coords_are_cartesian: bool = False,
        tol: float = 1e-5,
    ) -> Union["IStructure", "Structure"]:
        """
        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 ([Species]): Sequence of species on each site. Can take in
                flexible input, including:

                i.  A sequence of element / species specified either as string
                    symbols, e.g. ["Li", "Fe2+", "P", ...] or atomic numbers,
                    e.g., (3, 56, ...) or actual Element or Species 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, Species, DummySpecies, 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, Species, DummySpecies, Composition]],
        coords: Sequence[Sequence[float]],
        site_properties: Dict[str, Sequence],
        coords_are_cartesian: bool = False,
        tol: float = 1e-5,
    ) -> Union["IStructure", "Structure"]:
        """
        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 ([Species]): Sequence of species on each site. Can take in
                flexible input, including:
                i.  A sequence of element / species specified either as string
                symbols, e.g. ["Li", "Fe2+", "P", ...] or atomic numbers,
                e.g., (3, 56, ...) or actual Element or Species 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, Species, DummySpecies, 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)):  # type: ignore
            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) -> float:
        """
        Overall charge of the structure
        """
        if self._charge is None:
            return super().charge
        return self._charge

    @property
    def distance_matrix(self) -> np.ndarray:
        """
        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) -> Tuple[PeriodicSite, ...]:
        """
        Returns an iterator for the sites in the Structure.
        """
        return self._sites

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

    @property
    def density(self) -> float:
        """
        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) -> Tuple[str, int]:
        """
        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: int, j: int, jimage=None) -> float:
        """
        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: ArrayLike,
        r: float,
        include_index: bool = False,
        include_image: bool = False,
    ) -> List[PeriodicNeighbor]:
        """
        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:
            [:class:`pymatgen.core.structure.PeriodicNeighbor`]
        """
        site_fcoords = np.mod(self.frac_coords, 1)
        neighbors = []  # type: List[PeriodicNeighbor]
        for fcoord, dist, i, img in self._lattice.get_points_in_sphere(site_fcoords, pt, r):
            nnsite = PeriodicNeighbor(
                self[i].species,
                fcoord,
                self._lattice,
                properties=self[i].properties,
                nn_distance=dist,
                image=img,  # type: ignore
                index=i,
            )
            neighbors.append(nnsite)
        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:
            [:class:`pymatgen.core.structure.PeriodicNeighbor`]
        """
        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:
            [:class:`pymatgen.core.structure.PeriodicNeighbor`]
        """
        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: Sequence[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_old` and 2-3x 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)  # type: ignore
        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: Sequence[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:
            [[:class:`pymatgen.core.structure.PeriodicNeighbor`], ..]
        """
        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: Sequence[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:
            [[:class:`pymatgen.core.structure.PeriodicNeighbor`],...]
        """

        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:
            [:class:`pymatgen.core.structure.PeriodicNeighbor`]
        """
        # 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 = [[] 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: ArrayLike, r: float, dr: float, include_index: bool = False, include_image: bool = False
    ) -> List[PeriodicNeighbor]:
        """
        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.nn_distance > inner]

    def get_sorted_structure(
        self, key: Optional[Callable] = None, reverse: bool = False
    ) -> Union["IStructure", "Structure"]:
        """
        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: Literal["niggli", "LLL"] = "niggli"
    ) -> Union["IStructure", "Structure"]:
        """
        Get a reduced structure.

        Args:
            reduction_algo ("niggli" | "LLL"): The lattice reduction algorithm to use.
                Defaults to "niggli".
        """
        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, v in props.items():
                site_props[p] = v[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: Union["IStructure", "Structure"],
        nimages: Union[int, Iterable] = 10,
        interpolate_lattices: bool = False,
        pbc: bool = True,
        autosort_tol: float = 0,
    ) -> List[Union["IStructure", "Structure"]]:
        """
        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: float = 0.25, use_site_props: bool = False, constrain_latt: Union[List, Dict] = 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()):  # type: ignore
                            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 get_orderings(self, mode: Literal["enum", "sqs"] = "enum", **kwargs) -> List["Structure"]:
        r"""
        Returns list of orderings for a disordered structure. If structure
        does not contain disorder, the default structure is returned.

        Args:
            mode ("enum" | "sqs"): Either "enum" or "sqs". If enum,
                the enumlib will be used to return all distinct
                orderings. If sqs, mcsqs will be used to return
                an sqs structure.
            kwargs: kwargs passed to either
                pymatgen.command_line..enumlib_caller.EnumlibAdaptor
                or pymatgen.command_line.mcsqs_caller.run_mcsqs.
                For run_mcsqs, a default cluster search of 2 cluster interactions
                with 1NN distance and 3 cluster interactions with 2NN distance
                is set.

        Returns:
            List[Structure]
        """
        if self.is_ordered:
            return [self]
        if mode.startswith("enum"):
            from pymatgen.command_line.enumlib_caller import EnumlibAdaptor

            adaptor = EnumlibAdaptor(self, **kwargs)
            adaptor.run()
            return adaptor.structures
        if mode == "sqs":
            from pymatgen.command_line.mcsqs_caller import run_mcsqs

            if "clusters" not in kwargs:
                disordered_sites = [site for site in self if not site.is_ordered]
                subset_structure = Structure.from_sites(disordered_sites)
                dist_matrix = subset_structure.distance_matrix
                dists = sorted(set(dist_matrix.ravel()))
                unique_dists = []
                for i in range(1, len(dists)):
                    if dists[i] - dists[i - 1] > 0.1:
                        unique_dists.append(dists[i])
                clusters = {(i + 2): d + 0.01 for i, d in enumerate(unique_dists) if i < 2}
                kwargs["clusters"] = clusters
            return [run_mcsqs(self, **kwargs).bestsqs]
        raise ValueError()

    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: str = None, filename=None, **kwargs) -> Optional[str]:
        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)  # type: ignore
        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*"):
            if filename:
                with zopen(filename, "wt") as f:
                    yaml.safe_dump(self.as_dict(), f)
                return None
            return yaml.safe_dump(self.as_dict())
        elif fmt == "fleur-inpgen" or fnmatch(fname, "*.in*"):
            from pymatgen.io.fleur import FleurInput

            writer = FleurInput(self, **kwargs)
        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: str,
        fmt: Literal["cif", "poscar", "cssr", "json", "yaml", "xsf", "mcsqs"],
        primitive=False,
        sort=False,
        merge_tol=0.0,
    ):
        """
        Reads a structure from a string.

        Args:
            input_string (str): String to parse.
            fmt (str): A file format specification. One of "cif", "poscar", "cssr",
                "json", "yaml", "xsf", "mcsqs".
            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
        """

        fmt_low = fmt.lower()
        if fmt_low == "cif":
            from pymatgen.io.cif import CifParser

            parser = CifParser.from_string(input_string)
            s = parser.get_structures(primitive=primitive)[0]
        elif fmt_low == "poscar":
            from pymatgen.io.vasp import Poscar

            s = Poscar.from_string(input_string, False, read_velocities=False).structure
        elif fmt_low == "cssr":
            from pymatgen.io.cssr import Cssr

            cssr = Cssr.from_string(input_string)
            s = cssr.structure
        elif fmt_low == "json":
            d = json.loads(input_string)
            s = Structure.from_dict(d)
        elif fmt_low == "yaml":
            d = yaml.safe_load(input_string)
            s = Structure.from_dict(d)
        elif fmt_low == "xsf":
            from pymatgen.io.xcrysden import XSF

            s = XSF.from_string(input_string).structure
        elif fmt_low == "mcsqs":
            from pymatgen.io.atat import Mcsqs

            s = Mcsqs.structure_from_string(input_string)
        elif fmt == "fleur-inpgen":
            from pymatgen.io.fleur import FleurInput

            s = FleurInput.from_string(input_string, inpgen_input=True).structure
        elif fmt == "fleur":
            from pymatgen.io.fleur import FleurInput

            s = FleurInput.from_string(input_string, inpgen_input=False).structure
        else:
            raise ValueError(f"Unrecognized format `{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.exciting import ExcitingInput
        from pymatgen.io.lmto import LMTOCtrl
        from pymatgen.io.vasp import Chgcar, Vasprun

        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
        elif fnmatch(fname, "inp*.xml") or fnmatch(fname, "*.in*") or fnmatch(fname, "inp_*"):
            from pymatgen.io.fleur import FleurInput

            s = FleurInput.from_file(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[CompositionLike],
        coords: Sequence[ArrayLike],
        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/Species, 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 enumerate(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, DummySpecies):
                    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) -> float:
        """
        Charge of molecule
        """
        return self._charge

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

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

    @property
    def center_of_mass(self) -> float:
        """
        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  # type: ignore

    @property
    def sites(self) -> Tuple[Site, ...]:
        """
        Returns a tuple of sites in the Molecule.
        """
        return self._sites

    @classmethod
    def from_sites(
        cls, sites: Sequence[Site], charge: float = 0, spin_multiplicity: float = None, validate_proximity: bool = False
    ) -> Union["IMolecule", "Molecule"]:
        """
        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: int, ind2: int, tol: float = 0.2) -> Tuple[Union["IMolecule", "Molecule"], ...]:
        """
        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.
        """
        clusters = [[self._sites[ind1]], [self._sites[ind2]]]

        sites = [site for i, site in enumerate(self._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 tuple(self.__class__.from_sites(cluster) for cluster in clusters)

    def get_covalent_bonds(self, tol: float = 0.2) -> List[CovalentBond]:
        """
        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) -> dict:
        """
        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: int, j: int) -> float:
        """
        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: ArrayLike, r: float) -> List[Neighbor]:
        """
        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:
            [:class:`pymatgen.core.structure.Neighbor`]
        """
        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: Site, r: float) -> List[Neighbor]:
        """
        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:
            [:class:`pymatgen.core.structure.Neighbor`]
        """
        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: ArrayLike, r: float, dr: float) -> List[Neighbor]:
        """
        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:
            [:class:`pymatgen.core.structure.Neighbor`]
        """
        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: float,
        b: float,
        c: float,
        images: ArrayLike = (1, 1, 1),
        random_rotation: bool = False,
        min_dist: float = 1.0,
        cls=None,
        offset: ArrayLike = None,
        no_cross: bool = False,
        reorder: bool = True,
    ) -> Union["IStructure", "Structure"]:
        """
        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)  # type: ignore
        nimages = images[0] * images[1] * images[2]  # type: ignore
        all_coords: List[ArrayLike] = []

        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]))  # type: ignore
        ):
            box_center = [(i + 0.5) * a, (j + 0.5) * b, (k + 0.5) * c]  # type: ignore
            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(all_coords) == 0:
                        break
                    distances = lattice.get_all_distances(
                        lattice.get_fractional_coords(new_coords),
                        lattice.get_fractional_coords(all_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.")
            all_coords.extend(new_coords)
        sprops = {k: v * nimages for k, v in self.site_properties.items()}  # type: ignore

        if cls is None:
            cls = Structure

        if reorder:
            return cls(
                lattice,
                self.species * nimages,  # type: ignore
                all_coords,
                coords_are_cartesian=True,
                site_properties=sprops,
            ).get_sorted_structure()

        return cls(
            lattice,
            self.species * nimages,  # type: ignore
            coords,
            coords_are_cartesian=True,
            site_properties=sprops,
        )

    def get_centered_molecule(self) -> Union["IMolecule", "Molecule"]:
        """
        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__(  # type: ignore
            self.species_and_occu,
            new_coords,  # type: ignore
            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.babel import BabelMolAdaptor
        from pymatgen.io.gaussian import GaussianInput
        from pymatgen.io.xyz import XYZ

        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*"):
            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: str, fmt: str):
        """
        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.gaussian import GaussianInput
        from pymatgen.io.xyz import XYZ

        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":
            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[ArrayLike, Lattice],
        species: Sequence[CompositionLike],
        coords: Sequence[ArrayLike],
        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 / species specified either as string
                    symbols, e.g. ["Li", "Fe2+", "P", ...] or atomic numbers,
                    e.g., (3, 56, ...) or actual Element or Species 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[PeriodicSite] = list(self._sites)  # type: ignore

    def __setitem__(  # type: ignore
        self, i: Union[int, slice, Sequence[int], SpeciesLike], site: Union[SpeciesLike, PeriodicSite, Sequence]
    ):
        """
        Modify a site in the structure.

        Args:
            i (int, [int], slice, Species-like): Indices to change. You can
                specify these as an int, a list of int, or a species-like
                string.
            site (PeriodicSite/Species/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, Species)):
            self.replace_species({i: site})  # type: ignore
            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  # type: ignore
            else:
                if isinstance(site, str) or (not isinstance(site, collections.abc.Sequence)):
                    self._sites[ii].species = site  # type: ignore
                else:
                    self._sites[ii].species = site[0]  # type: ignore
                    if len(site) > 1:
                        self._sites[ii].frac_coords = site[1]  # type: ignore
                    if len(site) > 2:
                        self._sites[ii].properties = site[2]  # type: ignore

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

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

    @lattice.setter
    def lattice(self, lattice: Union[ArrayLike, Lattice]):
        if not isinstance(lattice, Lattice):
            lattice = Lattice(lattice)
        self._lattice = lattice
        for site in self._sites:
            site.lattice = lattice

    def append(  # type: ignore
        self,
        species: CompositionLike,
        coords: ArrayLike,
        coords_are_cartesian: bool = False,
        validate_proximity: bool = False,
        properties: dict = 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(  # type: ignore
        self,
        i: int,
        species: CompositionLike,
        coords: ArrayLike,
        coords_are_cartesian: bool = False,
        validate_proximity: bool = False,
        properties: dict = 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: int,
        species: CompositionLike,
        coords: ArrayLike = None,
        coords_are_cartesian: bool = False,
        properties: dict = 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  # type: ignore

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

    def substitute(self, index: int, func_group: Union["IMolecule", "Molecule", str], bond_order: int = 1):
        """
        Substitute atom at index with a functional group.

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

                1. Providing an actual Molecule as the input. The first atom
                   must be a DummySpecies 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 not isinstance(func_group, Molecule):
            # Check to see whether the functional group is in database.
            if func_group not in FunctionalGroups:
                raise RuntimeError("Can't find functional group in list. " "Provide explicit coordinate instead")
            fgroup = FunctionalGroups[func_group]
        else:
            fgroup = func_group

        # 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, fgroup[1].specie, bond_order=bond_order)
        # Catches for case of incompatibility between Element(s) and Species(s)
        except TypeError:
            bl = None

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

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

        # Find angle between the attaching bond and the bond to be replaced.
        v1 = fgroup[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)
            fgroup.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(fgroup):
                fgroup[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 fgroup[1:]:
            s_new = PeriodicSite(site.species, site.coords, self.lattice, coords_are_cartesian=True)
            self._sites.append(s_new)

    def remove_species(self, species: Sequence[SpeciesLike]):
        """
        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: Sequence[int]):
        """
        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: SymmOp, fractional: bool = 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]

    def apply_strain(self, strain: ArrayLike):
        """
        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: Callable = None, reverse: bool = 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: Union[int, Sequence[int]], vector: ArrayLike, frac_coords: bool = True, to_unit_cell: bool = 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: List[int] = None,
        theta: float = 0.0,
        axis: ArrayLike = None,
        anchor: ArrayLike = None,
        to_unit_cell: bool = 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 import cross, eye
        from numpy.linalg import norm
        from scipy.linalg import expm

        if indices is None:
            indices = list(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: float, min_distance: float = 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: ArrayLike, to_unit_cell: bool = 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: float):
        """
        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: float = 0.01, mode: Literal["sum", "delete", "average"] = "sum"):
        """
        Merges sites (adding occupancies) within tol of each other.
        Removes site properties.

        Args:
            tol (float): Tolerance for distance to merge sites.
            mode ('sum' | 'delete' | 'average'): "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.

        """
        from scipy.cluster.hierarchy import fcluster, linkage
        from scipy.spatial.distance import squareform

        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.lower()[0] == "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.lower()[0] == "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 = 0.0):
        """
        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[SpeciesLike],
        coords: Sequence[ArrayLike],
        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/Species, 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[Site] = list(self._sites)  # type: ignore

    def __setitem__(  # type: ignore
        self, i: Union[int, slice, Sequence[int], SpeciesLike], site: Union[SpeciesLike, Site, Sequence]
    ):
        """
        Modify a site in the molecule.

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

        if isinstance(i, int):
            indices = [i]
        elif isinstance(i, (str, Element, Species)):
            self.replace_species({i: site})  # type: ignore
            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  # type: ignore
                else:
                    self._sites[ii].species = site[0]  # type: ignore
                    if len(site) > 1:
                        self._sites[ii].coords = site[1]  # type: ignore
                    if len(site) > 2:
                        self._sites[ii].properties = site[2]  # type: ignore

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

    def append(  # type: ignore
        self,
        species: CompositionLike,
        coords: ArrayLike,
        validate_proximity: bool = False,
        properties: dict = 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 False.
            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, DummySpecies):
                    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(  # type: ignore
        self,
        i: int,
        species: CompositionLike,
        coords: ArrayLike,
        validate_proximity: bool = False,
        properties: dict = 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: Sequence[SpeciesLike]):
        """
        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: Sequence[int]):
        """
        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: Sequence[int] = None, vector: ArrayLike = 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)  # type: ignore
            self._sites[i] = new_site

    def rotate_sites(
        self, indices: Sequence[int] = None, theta: float = 0.0, axis: ArrayLike = None, anchor: ArrayLike = 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 import cross, eye
        from numpy.linalg import norm
        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: float):
        """
        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: 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: int, func_group: Union["IMolecule", "Molecule", str], bond_order: int = 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 DummySpecies 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_group, Molecule):
            func_grp = func_group
        else:
            # Check to see whether the functional group is in database.
            if func_group not in FunctionalGroups:
                raise RuntimeError("Can't find functional group in list. " "Provide explicit coordinate instead")
            func_grp = FunctionalGroups[func_group]

        # 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()}