# Source code for pymatgen.analysis.defects.core

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

    """
    Base classes representing defects.
    """

    import logging
    import numpy as np

    from abc import ABCMeta, abstractmethod
    from monty.json import MSONable, MontyDecoder
    from functools import lru_cache

    from pymatgen.core.structure import Structure, PeriodicSite
    from pymatgen.core.composition import Composition
    from pymatgen.symmetry.analyzer import SpacegroupAnalyzer
    from pymatgen.analysis.defects.utils import kb

    __author__ = "Danny Broberg, Shyam Dwaraknath"
    __copyright__ = "Copyright 2018, The Materials Project"
    __version__ = "1.0"
    __maintainer__ = "Shyam Dwaraknath"
    __email__ = "shyamd@lbl.gov"
    __status__ = "Development"
    __date__ = "Mar 15, 2018"

    logger = logging.getLogger(__name__)

    class Defect(MSONable, metaclass=ABCMeta):
        """
        Abstract class for a single point defect
        """

        def __init__(self, structure, defect_site, charge=0., multiplicity=None):
            """
            Initializes an abstract defect

            Args:
                structure: Pymatgen Structure without any defects
                defect_site (Site): site for defect within structure
                    must have same lattice as structure
                charge: (int or float) defect charge
                    default is zero, meaning no change to NELECT after defect is created in the structure
                    (assuming use_structure_charge=True in vasp input set)
                multiplicity (int): multiplicity of defect within
                    the supercell can be supplied by user. if not
                    specified, then space group symmetry analysis is
                    used to generate multiplicity.
            """
            self._structure = structure
            self._charge = int(charge)
            self._defect_site = defect_site
            lattice_match = np.allclose(structure.lattice.matrix,
                                        defect_site.lattice.matrix,
                                        atol=1e-5)
            if not lattice_match:
                raise ValueError("defect_site lattice must be same as structure "
                                 "lattice.")
            self._multiplicity = multiplicity if multiplicity else self.get_multiplicity()

        @property
        def bulk_structure(self):
            """
            Returns the structure without any defects.
            """
            return self._structure

        @property
        def charge(self):
            """
            Returns the charge of a defect
            """
            return self._charge

        @property
        def site(self):
            """
            Returns the defect position as a site object
            """
            return self._defect_site

        @property
        def multiplicity(self):
            """
            Returns the multiplicity of a defect site within the structure (needed for concentration analysis)
            """
            return self._multiplicity

        @property  # type: ignore
        @abstractmethod
        def defect_composition(self):
            """
            Returns the defect composition as a Composition object
            """
            return

        @abstractmethod
        def generate_defect_structure(self, supercell=(1, 1, 1)):
            """
            Given structure and defect_site (and type of defect) should return a defect_structure that is charged
            Args:
                supercell (int, [3x1], or [[]] (3x3)): supercell integer, vector, or scaling matrix
            """
            return

        @property  # type: ignore
        @abstractmethod
        def name(self):
            """
            Returns a name for this defect
            """
            return

        @abstractmethod
        def get_multiplicity(self):
            """
            Method to determine multiplicity. For non-Interstitial objects, also confirms that defect_site
            is a site in bulk_structure.
            """
            return

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

            Returns:
                A copy of the Defect.
            """
            return self.from_dict(self.as_dict())

        def set_charge(self, new_charge=0.):
            """
            Sets the overall charge
            Args:
                charge (float): new charge to set
            """
            self._charge = int(new_charge)

    class Vacancy(Defect):
        """
        Subclass of Defect to capture essential information for a single Vacancy defect structure.
        """

        @property
        def defect_composition(self):
            """
            Returns: Composition of defect.
            """
            temp_comp = self.bulk_structure.composition.as_dict()
            temp_comp[str(self.site.specie)] -= 1
            return Composition(temp_comp)

        def generate_defect_structure(self, supercell=(1, 1, 1)):
            """
            Returns Defective Vacancy structure, decorated with charge
            Args:
                supercell (int, [3x1], or [[]] (3x3)): supercell integer, vector, or scaling matrix
            """
            defect_structure = self.bulk_structure.copy()
            defect_structure.make_supercell(supercell)

            # create a trivial defect structure to find where supercell transformation moves the lattice
            struct_for_defect_site = Structure(self.bulk_structure.copy().lattice,
                                               [self.site.specie],
                                               [self.site.frac_coords],
                                               to_unit_cell=True)
            struct_for_defect_site.make_supercell(supercell)
            defect_site = struct_for_defect_site[0]

            poss_deflist = sorted(
                defect_structure.get_sites_in_sphere(defect_site.coords, 0.1, include_index=True), key=lambda x: x[1])
            defindex = poss_deflist[0][2]
            defect_structure.remove_sites([defindex])
            defect_structure.set_charge(self.charge)
            return defect_structure

        def get_multiplicity(self):
            """
            Returns the multiplicity of a defect site within the structure (needed for concentration analysis)
            and confirms that defect_site is a site in bulk_structure.
            """
            sga = SpacegroupAnalyzer(self.bulk_structure)
            periodic_struc = sga.get_symmetrized_structure()
            poss_deflist = sorted(
                periodic_struc.get_sites_in_sphere(self.site.coords, 0.1, include_index=True), key=lambda x: x[1])
            if not len(poss_deflist):
                raise ValueError("Site {} is not in bulk structure! Cannot create Vacancy object.".format(self.site))
            else:
                defindex = poss_deflist[0][2]
                defect_site = self.bulk_structure[defindex]
                equivalent_sites = periodic_struc.find_equivalent_sites(defect_site)
                return len(equivalent_sites)

        @property
        def name(self):
            """
            Returns a name for this defect
            """
            return "Vac_{}_mult{}".format(self.site.specie, self.multiplicity)

    class Substitution(Defect):
        """
        Subclass of Defect to capture essential information for a single Substitution defect structure.
        """

        @property  # type: ignore
        @lru_cache(1)
        def defect_composition(self):
            """
            Returns: Composition of defect.
            """
            poss_deflist = sorted(
                self.bulk_structure.get_sites_in_sphere(self.site.coords, 0.1, include_index=True), key=lambda x: x[1])
            defindex = poss_deflist[0][2]

            temp_comp = self.bulk_structure.composition.as_dict()
            temp_comp[str(self.site.specie)] += 1
            temp_comp[str(self.bulk_structure[defindex].specie)] -= 1
            return Composition(temp_comp)

        def generate_defect_structure(self, supercell=(1, 1, 1)):
            """
            Returns Defective Substitution structure, decorated with charge.
            If bulk structure had any site properties, all of these properties are
            removed in the resulting defect structure.

            Args:
                supercell (int, [3x1], or [[]] (3x3)): supercell integer, vector, or scaling matrix
            """
            defect_structure = Structure(self.bulk_structure.copy().lattice,
                                         [site.specie for site in self.bulk_structure],
                                         [site.frac_coords for site in self.bulk_structure],
                                         to_unit_cell=True, coords_are_cartesian=False,
                                         site_properties=None)  # remove all site_properties
            defect_structure.make_supercell(supercell)

            # create a trivial defect structure to find where supercell transformation moves the defect
            struct_for_defect_site = Structure(self.bulk_structure.copy().lattice,
                                               [self.site.specie],
                                               [self.site.frac_coords],
                                               to_unit_cell=True, coords_are_cartesian=False)
            struct_for_defect_site.make_supercell(supercell)
            defect_site = struct_for_defect_site[0]

            poss_deflist = sorted(
                defect_structure.get_sites_in_sphere(defect_site.coords, 0.1, include_index=True), key=lambda x: x[1])
            defindex = poss_deflist[0][2]

            subsite = defect_structure.pop(defindex)
            defect_structure.append(self.site.specie.symbol, subsite.coords, coords_are_cartesian=True,
                                    properties=None)
            defect_structure.set_charge(self.charge)
            return defect_structure

        def get_multiplicity(self):
            """
            Returns the multiplicity of a defect site within the structure (needed for concentration analysis)
            and confirms that defect_site is a site in bulk_structure.
            """
            sga = SpacegroupAnalyzer(self.bulk_structure)
            periodic_struc = sga.get_symmetrized_structure()
            poss_deflist = sorted(
                periodic_struc.get_sites_in_sphere(self.site.coords, 0.1, include_index=True), key=lambda x: x[1])
            if not len(poss_deflist):
                raise ValueError("Site {} is not in bulk structure! Cannot create Substitution object.".format(self.site))
            else:
                defindex = poss_deflist[0][2]
                defect_site = self.bulk_structure[defindex]
                equivalent_sites = periodic_struc.find_equivalent_sites(defect_site)
                return len(equivalent_sites)

        @property  # type: ignore
        @lru_cache(1)
        def name(self):
            """
            Returns a name for this defect
            """
            poss_deflist = sorted(
                self.bulk_structure.get_sites_in_sphere(self.site.coords, 0.1, include_index=True), key=lambda x: x[1])
            defindex = poss_deflist[0][2]
            return "Sub_{}_on_{}_mult{}".format(self.site.specie, self.bulk_structure[defindex].specie, self.multiplicity)

    class Interstitial(Defect):
        """
        Subclass of Defect to capture essential information for a single Interstitial defect structure.
        """

        def __init__(self, structure, defect_site, charge=0., site_name='', multiplicity=None):
            """
            Initializes an interstial defect.
            Args:
                structure: Pymatgen Structure without any defects
                defect_site (Site): the site for the interstitial
                charge: (int or float) defect charge
                    default is zero, meaning no change to NELECT after defect is created in the structure
                    (assuming use_structure_charge=True in vasp input set)
                site_name: allows user to give a unique name to defect, since Wyckoff symbol/multiplicity
                    is sometimes insufficient to categorize the defect type.
                    default is no name beyond multiplicity.
                multiplicity (int): multiplicity of defect within
                    the supercell can be supplied by user. if not
                    specified, then space group symmetry is used
                    to generator interstitial sublattice

                    NOTE: multiplicity generation will not work for
                    interstitial complexes,
                    where multiplicity may depend on additional
                    factors (ex. orientation etc.)
                    If defect is not a complex, then this
                    process will yield the correct multiplicity,
                    provided that the defect does not undergo
                    significant relaxation.
            """
            super().__init__(structure=structure, defect_site=defect_site, charge=charge)
            self._multiplicity = multiplicity if multiplicity else self.get_multiplicity()
            self.site_name = site_name

        @property
        def defect_composition(self):
            """
            Returns: Defect composition.
            """
            temp_comp = self.bulk_structure.composition.as_dict()
            temp_comp[str(self.site.specie)] += 1
            return Composition(temp_comp)

        def generate_defect_structure(self, supercell=(1, 1, 1)):
            """
            Returns Defective Interstitial structure, decorated with charge
            If bulk structure had any site properties, all of these properties are
            removed in the resulting defect structure

            Args:
                supercell (int, [3x1], or [[]] (3x3)): supercell integer, vector, or scaling matrix
            """
            defect_structure = Structure(self.bulk_structure.copy().lattice,
                                         [site.specie for site in self.bulk_structure],
                                         [site.frac_coords for site in self.bulk_structure],
                                         to_unit_cell=True, coords_are_cartesian=False,
                                         site_properties=None)  # remove all site_properties
            defect_structure.make_supercell(supercell)

            # create a trivial defect structure to find where supercell transformation moves the defect site
            struct_for_defect_site = Structure(self.bulk_structure.copy().lattice,
                                               [self.site.specie],
                                               [self.site.frac_coords],
                                               to_unit_cell=True, coords_are_cartesian=False)
            struct_for_defect_site.make_supercell(supercell)
            defect_site = struct_for_defect_site[0]

            defect_structure.append(self.site.specie.symbol, defect_site.coords, coords_are_cartesian=True,
                                    properties=None)
            defect_structure.set_charge(self.charge)
            return defect_structure

        def get_multiplicity(self):
            """
            Returns the multiplicity of a defect site within the structure (needed for concentration analysis)
            """
            try:
                d_structure = create_saturated_interstitial_structure(self)
            except ValueError:
                logger.debug('WARNING! Multiplicity was not able to be calculated adequately '
                             'for interstitials...setting this to 1 and skipping for now...')
                return 1

            sga = SpacegroupAnalyzer(d_structure)
            periodic_struc = sga.get_symmetrized_structure()
            poss_deflist = sorted(
                periodic_struc.get_sites_in_sphere(self.site.coords, 0.1, include_index=True),
                key=lambda x: x[1])
            defindex = poss_deflist[0][2]

            equivalent_sites = periodic_struc.find_equivalent_sites(periodic_struc[defindex])
            return len(equivalent_sites)

        @property
        def name(self):
            """
            Returns a name for this defect
            """
            if self.site_name:
                return "Int_{}_{}_mult{}".format(self.site.specie, self.site_name, self.multiplicity)
            else:
                return "Int_{}_mult{}".format(self.site.specie, self.multiplicity)

    def create_saturated_interstitial_structure(interstitial_def, dist_tol=0.1):
        """
        this takes a Interstitial defect object and generates the
        sublattice for it based on the structure's space group.
        Useful for understanding multiplicity of an interstitial
        defect in thermodynamic analysis.

        NOTE: if large relaxation happens to interstitial or
            defect involves a complex then there may be additional
            degrees of freedom that need to be considered for
            the multiplicity.

        Args:
            dist_tol: changing distance tolerance of saturated structure,
                    allowing for possibly overlapping sites
                    but ensuring space group is maintained

        Returns:
            Structure object decorated with interstitial site equivalents
        """
        sga = SpacegroupAnalyzer(interstitial_def.bulk_structure.copy())
        sg_ops = sga.get_symmetry_operations(cartesian=True)

        # copy bulk structure to make saturated interstitial structure out of
        # artificially lower distance_tolerance to allow for distinct interstitials
        # with lower symmetry to be replicated - This is OK because one would never
        # actually use this structure for a practical calcualtion...
        saturated_defect_struct = interstitial_def.bulk_structure.copy()
        saturated_defect_struct.DISTANCE_TOLERANCE = dist_tol

        for sgo in sg_ops:
            new_interstit_coords = sgo.operate(interstitial_def.site.coords[:])
            poss_new_site = PeriodicSite(
                interstitial_def.site.specie,
                new_interstit_coords,
                saturated_defect_struct.lattice,
                to_unit_cell=True,
                coords_are_cartesian=True)
            try:
                # will raise value error if site already exists in structure
                saturated_defect_struct.append(
                    poss_new_site.specie, poss_new_site.coords,
                    coords_are_cartesian=True, validate_proximity=True)
            except ValueError:
                pass

        # do final space group analysis to make sure symmetry not lowered by saturating defect structure
        saturated_sga = SpacegroupAnalyzer(saturated_defect_struct)
        if saturated_sga.get_space_group_number() != sga.get_space_group_number():
            raise ValueError("Warning! Interstitial sublattice generation "
                             "has changed space group symmetry. Recommend "
                             "reducing dist_tol and trying again...")

        return saturated_defect_struct

    class DefectEntry(MSONable):
        """
        An lightweight DefectEntry object containing key computed data
        for many defect analysis.
        """

        def __init__(self, defect, uncorrected_energy, corrections=None, parameters=None, entry_id=None):
            """
            Args:
                defect:
                    A Defect object from pymatgen.analysis.defects.core
                uncorrected_energy (float): Energy of the defect entry. Usually the difference between
                    the final calculated energy for the defect supercell - the perfect
                    supercell energy
                corrections (dict):
                    Dict of corrections for defect formation energy. All values will be summed and
                    added to the defect formation energy.
                parameters (dict): An optional dict of calculation parameters and data to
                    use with correction schemes
                    (examples of parameter keys: supercell_size, axis_grid, bulk_planar_averages
                    defect_planar_averages )
                entry_id (obj): An id to uniquely identify this defect, can be any MSONable
                    type
            """
            self.defect = defect
            self.uncorrected_energy = uncorrected_energy
            self.corrections = corrections if corrections else {}
            self.entry_id = entry_id
            self.parameters = parameters if parameters else {}

        @property
        def bulk_structure(self):
            """
            Returns: Structure object of bulk.
            """
            return self.defect.bulk_structure

        def as_dict(self):
            """
            Json-serializable dict representation of DefectEntry
            """
            d = {"@module": self.__class__.__module__,
                 "@class": self.__class__.__name__,
                 "defect": self.defect.as_dict(),
                 "uncorrected_energy": self.uncorrected_energy,
                 "corrections": self.corrections,
                 "parameters": self.parameters,
                 "entry_id": self.entry_id}
            return d

        @classmethod
        def from_dict(cls, d):
            """
            Reconstitute a DefectEntry object from a dict representation created using
            as_dict().
             Args:
                d (dict): dict representation of DefectEntry.
             Returns:
                DefectEntry object
            """
            defect = MontyDecoder().process_decoded(d["defect"])
            uncorrected_energy = d["uncorrected_energy"]
            corrections = d.get("corrections", None)
            parameters = d.get("parameters", None)
            entry_id = d.get("entry_id", None)

            return cls(defect, uncorrected_energy, corrections=corrections,
                       parameters=parameters, entry_id=entry_id)

        @property
        def site(self):
            """
            Returns: Site of defect.
            """
            return self.defect.site

        @property
        def multiplicity(self):
            """
            Returns: Multiplicity of defect.
            """
            return self.defect.multiplicity

        @property
        def charge(self):
            """
            Returns: Charge of defect.
            """
            return self.defect.charge

        @property
        def energy(self):
            """
            Returns: *Corrected* energy of the entry
            """
            return self.uncorrected_energy + np.sum(list(self.corrections.values()))

        @property
        def name(self):
            """
            Returns: Defect name
            """
            return self.defect.name

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

            Returns:
                A copy of the DefectEntry.
            """
            defectentry_dict = self.as_dict()
            return DefectEntry.from_dict(defectentry_dict)

        def formation_energy(self, chemical_potentials=None, fermi_level=0):
            """
            Compute the formation energy for a defect taking into account a given chemical potential and fermi_level
             Args:
                 chemical_potentials (dict): Dictionary of elemental chemical potential values.
                    Keys are Element objects within the defect structure's composition.
                    Values are float numbers equal to the atomic chemical potential for that element.
                fermi_level (float):  Value corresponding to the electron chemical potential.
                    If "vbm" is supplied in parameters dict, then fermi_level is referenced to the VBM.
                    If "vbm" is NOT supplied in parameters dict, then fermi_level is referenced to the
                    calculation's absolute Kohn-Sham potential (and should include the vbm value provided
                    by a band structure calculation)

            Returns:
                Formation energy value (float)
            """
            chemical_potentials = chemical_potentials if chemical_potentials else {}

            chempot_correction = sum([
                chem_pot * (self.bulk_structure.composition[el] - self.defect.defect_composition[el])
                for el, chem_pot in chemical_potentials.items()
            ])

            formation_energy = self.energy + chempot_correction

            if "vbm" in self.parameters:
                formation_energy += self.charge * (self.parameters["vbm"] + fermi_level)
            else:
                formation_energy += self.charge * fermi_level

            return formation_energy

        def defect_concentration(self, chemical_potentials, temperature=300, fermi_level=0.0):
            """
            Compute the defect concentration for a temperature and Fermi level.
            Args:
                temperature:
                    the temperature in K
                fermi_level:
                    the fermi level in eV (with respect to the VBM)
            Returns:
                defects concentration in cm^-3
            """
            n = self.multiplicity * 1e24 / self.defect.bulk_structure.volume
            conc = n * np.exp(-1.0 * self.formation_energy(chemical_potentials, fermi_level=fermi_level) /
                              (kb * temperature))

            return conc

        def __repr__(self):
            """
            Human readable string representation of this entry
            """
            output = [
                "DefectEntry {} - {} - charge {}".format(self.entry_id, self.name, self.charge),
                "Energy = {:.4f}".format(self.energy),
                "Correction = {:.4f}".format(np.sum(list(self.corrections.values()))),
                "Parameters:"
            ]
            for k, v in self.parameters.items():
                output.append("\t{} = {}".format(k, v))
            return "\n".join(output)

        def __str__(self):
            return self.__repr__()

    class DefectCorrection(MSONable):
        """
        A Correction class modeled off the computed entry correction format
        """

        @abstractmethod
        def get_correction(self, entry):
            """
            Returns correction for a single entry.

            Args:
                entry: A DefectEntry object.

            Returns:
                A single dictionary with the format
                correction_name: energy_correction

            Raises:
                CompatibilityError if entry is not compatible.
            """
            return

        def correct_entry(self, entry):
            """
            Corrects a single entry.

            Args:
                entry: A DefectEntry object.

            Returns:
                An processed entry.

            Raises:
                CompatibilityError if entry is not compatible.
            """
            entry.correction.update(self.get_correction(entry))
            return entry