pymatgen.electronic_structure.bandstructure — pymatgen 2020.7.3 documentation

# Source code for pymatgen.electronic_structure.bandstructure

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

    """
    This module provides classes to define everything related to band structures.
    """

    import numpy as np
    import re
    import math
    import itertools
    import collections
    import warnings

    from monty.json import MSONable
    from pymatgen.core.periodic_table import get_el_sp, Element
    from pymatgen.core.structure import Structure
    from pymatgen.core.lattice import Lattice
    from pymatgen.electronic_structure.core import Spin, Orbital
    from pymatgen.symmetry.analyzer import SpacegroupAnalyzer
    from pymatgen.util.coord import pbc_diff

    __author__ = "Geoffroy Hautier, Shyue Ping Ong, Michael Kocher"
    __copyright__ = "Copyright 2012, The Materials Project"
    __version__ = "1.0"
    __maintainer__ = "Geoffroy Hautier"
    __email__ = "geoffroy@uclouvain.be"
    __status__ = "Development"
    __date__ = "March 14, 2012"

    class Kpoint(MSONable):
        """
        Class to store kpoint objects. A kpoint is defined with a lattice and frac
        or cartesian coordinates syntax similar than the site object in
        pymatgen.core.structure.
        """

        def __init__(self, coords, lattice, to_unit_cell=False,
                     coords_are_cartesian=False, label=None):
            """
            Args:
                coords: coordinate of the kpoint as a numpy array
                lattice: A pymatgen.core.lattice.Lattice lattice object representing
                    the reciprocal lattice of the kpoint
                to_unit_cell: Translates fractional coordinate to the basic unit
                    cell, i.e., all fractional coordinates satisfy 0 <= a < 1.
                    Defaults to False.
                coords_are_cartesian: Boolean indicating if the coordinates given are
                    in cartesian or fractional coordinates (by default fractional)
                label: the label of the kpoint if any (None by default)
            """
            self._lattice = lattice
            self._fcoords = lattice.get_fractional_coords(coords) \
                if coords_are_cartesian else coords
            self._label = label

            if to_unit_cell:
                for i in range(len(self._fcoords)):
                    self._fcoords[i] -= math.floor(self._fcoords[i])

            self._ccoords = lattice.get_cartesian_coords(self._fcoords)

        @property
        def lattice(self):
            """
            The lattice associated with the kpoint. It's a
            pymatgen.core.lattice.Lattice object
            """
            return self._lattice

        @property
        def label(self):
            """
            The label associated with the kpoint
            """
            return self._label

        @property
        def frac_coords(self):
            """
            The fractional coordinates of the kpoint as a numpy array
            """
            return np.copy(self._fcoords)

        @property
        def cart_coords(self):
            """
            The cartesian coordinates of the kpoint as a numpy array
            """
            return np.copy(self._ccoords)

        @property
        def a(self):
            """
            Fractional a coordinate of the kpoint
            """
            return self._fcoords[0]

        @property
        def b(self):
            """
            Fractional b coordinate of the kpoint
            """
            return self._fcoords[1]

        @property
        def c(self):
            """
            Fractional c coordinate of the kpoint
            """
            return self._fcoords[2]

        def __str__(self):
            """
            Returns a string with fractional, cartesian coordinates and label
            """
            return "{} {} {}".format(self.frac_coords, self.cart_coords,
                                     self.label)

        def as_dict(self):
            """
            Json-serializable dict representation of a kpoint
            """
            return {"lattice": self.lattice.as_dict(),
                    "fcoords": list(self.frac_coords),
                    "ccoords": list(self.cart_coords), "label": self.label,
                    "@module": self.__class__.__module__,
                    "@class": self.__class__.__name__}

    class BandStructure:
        """
        This is the most generic band structure data possible
        it's defined by a list of kpoints + energies for each of them

        .. attribute:: kpoints:
            the list of kpoints (as Kpoint objects) in the band structure

        .. attribute:: lattice_rec

            the reciprocal lattice of the band structure.

        .. attribute:: efermi

            the fermi energy

        .. attribute::  is_spin_polarized

            True if the band structure is spin-polarized, False otherwise

        .. attribute:: bands

            The energy eigenvalues as a {spin: ndarray}. Note that the use of an
            ndarray is necessary for computational as well as memory efficiency
            due to the large amount of numerical data. The indices of the ndarray
            are [band_index, kpoint_index].

        .. attribute:: nb_bands

            returns the number of bands in the band structure

        .. attribute:: structure

            returns the structure

        .. attribute:: projections

            The projections as a {spin: ndarray}. Note that the use of an
            ndarray is necessary for computational as well as memory efficiency
            due to the large amount of numerical data. The indices of the ndarray
            are [band_index, kpoint_index, orbital_index, ion_index].
        """

        def __init__(self, kpoints, eigenvals, lattice, efermi, labels_dict=None,
                     coords_are_cartesian=False, structure=None, projections=None):
            """
            Args:
                kpoints: list of kpoint as numpy arrays, in frac_coords of the
                    given lattice by default
                eigenvals: dict of energies for spin up and spin down
                    {Spin.up:[][],Spin.down:[][]}, the first index of the array
                    [][] refers to the band and the second to the index of the
                    kpoint. The kpoints are ordered according to the order of the
                    kpoints array. If the band structure is not spin polarized, we
                    only store one data set under Spin.up
                lattice: The reciprocal lattice as a pymatgen Lattice object.
                    Pymatgen uses the physics convention of reciprocal lattice vectors
                    WITH a 2*pi coefficient
                efermi: fermi energy
                labels_dict: (dict) of {} this links a kpoint (in frac coords or
                    cartesian coordinates depending on the coords) to a label.
                coords_are_cartesian: Whether coordinates are cartesian.
                structure: The crystal structure (as a pymatgen Structure object)
                    associated with the band structure. This is needed if we
                    provide projections to the band structure
                projections: dict of orbital projections as {spin: ndarray}. The
                    indices of the ndarrayare [band_index, kpoint_index, orbital_index,
                    ion_index].If the band structure is not spin polarized, we only
                    store one data set under Spin.up.
            """
            self.efermi = efermi
            self.lattice_rec = lattice
            self.kpoints = []
            self.labels_dict = {}
            self.structure = structure
            self.projections = projections or {}
            self.projections = {k: np.array(v) for k, v in self.projections.items()}

            if labels_dict is None:
                labels_dict = {}

            if len(self.projections) != 0 and self.structure is None:
                raise Exception("if projections are provided a structure object"
                                " needs also to be given")

            for k in kpoints:
                # let see if this kpoint has been assigned a label
                label = None
                for c in labels_dict:
                    if np.linalg.norm(k - np.array(labels_dict[c])) < 0.0001:
                        label = c
                        self.labels_dict[label] = Kpoint(
                            k, lattice, label=label,
                            coords_are_cartesian=coords_are_cartesian)
                self.kpoints.append(
                    Kpoint(k, lattice, label=label,
                           coords_are_cartesian=coords_are_cartesian))
            self.bands = {spin: np.array(v) for spin, v in eigenvals.items()}
            self.nb_bands = len(eigenvals[Spin.up])
            self.is_spin_polarized = len(self.bands) == 2

        def get_projection_on_elements(self):
            """
            Method returning a dictionary of projections on elements.

            Returns:
                a dictionary in the {Spin.up:[][{Element:values}],
                Spin.down:[][{Element:values}]} format
                if there is no projections in the band structure
                returns an empty dict
            """
            result = {}
            structure = self.structure
            for spin, v in self.projections.items():
                result[spin] = [[collections.defaultdict(float)
                                 for i in range(len(self.kpoints))]
                                for j in range(self.nb_bands)]
                for i, j, k in itertools.product(range(self.nb_bands),
                                                 range(len(self.kpoints)),
                                                 range(structure.num_sites)):
                    result[spin][i][j][str(structure[k].specie)] += np.sum(
                        v[i, j, :, k])
            return result

        def get_projections_on_elements_and_orbitals(self, el_orb_spec):
            """
            Method returning a dictionary of projections on elements and specific
            orbitals

            Args:
                el_orb_spec: A dictionary of Elements and Orbitals for which we want
                    to have projections on. It is given as: {Element:[orbitals]},
                    e.g., {'Cu':['d','s']}

            Returns:
                A dictionary of projections on elements in the
                {Spin.up:[][{Element:{orb:values}}],
                Spin.down:[][{Element:{orb:values}}]} format
                if there is no projections in the band structure returns an empty
                dict.
            """
            result = {}
            structure = self.structure
            el_orb_spec = {get_el_sp(el): orbs for el, orbs in el_orb_spec.items()}
            for spin, v in self.projections.items():
                result[spin] = [[{str(e): collections.defaultdict(float)
                                  for e in el_orb_spec}
                                 for i in range(len(self.kpoints))]
                                for j in range(self.nb_bands)]

                for i, j, k in itertools.product(
                        range(self.nb_bands), range(len(self.kpoints)),
                        range(structure.num_sites)):
                    sp = structure[k].specie
                    for orb_i in range(len(v[i][j])):
                        o = Orbital(orb_i).name[0]
                        if sp in el_orb_spec:
                            if o in el_orb_spec[sp]:
                                result[spin][i][j][str(sp)][o] += v[i][j][
                                    orb_i][k]
            return result

        def is_metal(self, efermi_tol=1e-4):
            """
            Check if the band structure indicates a metal by looking if the fermi
            level crosses a band.

            Returns:
                True if a metal, False if not
            """
            for spin, values in self.bands.items():
                for i in range(self.nb_bands):
                    if np.any(values[i, :] - self.efermi < -efermi_tol) and \
                            np.any(values[i, :] - self.efermi > efermi_tol):
                        return True
            return False

        def get_vbm(self):
            """
            Returns data about the VBM.

            Returns:
                dict as {"band_index","kpoint_index","kpoint","energy"}
                - "band_index": A dict with spin keys pointing to a list of the
                indices of the band containing the VBM (please note that you
                can have several bands sharing the VBM) {Spin.up:[],
                Spin.down:[]}
                - "kpoint_index": The list of indices in self.kpoints for the
                kpoint vbm. Please note that there can be several
                kpoint_indices relating to the same kpoint (e.g., Gamma can
                occur at different spots in the band structure line plot)
                - "kpoint": The kpoint (as a kpoint object)
                - "energy": The energy of the VBM
                - "projections": The projections along sites and orbitals of the
                VBM if any projection data is available (else it is an empty
                dictionnary). The format is similar to the projections field in
                BandStructure: {spin:{'Orbital': [proj]}} where the array
                [proj] is ordered according to the sites in structure
        """
            if self.is_metal():
                return {"band_index": [], "kpoint_index": [],
                        "kpoint": [], "energy": None, "projections": {}}
            max_tmp = -float("inf")
            index = None
            kpointvbm = None
            for spin, v in self.bands.items():
                for i, j in zip(*np.where(v < self.efermi)):
                    if v[i, j] > max_tmp:
                        max_tmp = float(v[i, j])
                        index = j
                        kpointvbm = self.kpoints[j]

            list_ind_kpts = []
            if kpointvbm.label is not None:
                for i in range(len(self.kpoints)):
                    if self.kpoints[i].label == kpointvbm.label:
                        list_ind_kpts.append(i)
            else:
                list_ind_kpts.append(index)
            # get all other bands sharing the vbm
            list_ind_band = collections.defaultdict(list)
            for spin in self.bands:
                for i in range(self.nb_bands):
                    if math.fabs(self.bands[spin][i][index] - max_tmp) < 0.001:
                        list_ind_band[spin].append(i)
            proj = {}
            for spin, v in self.projections.items():
                if len(list_ind_band[spin]) == 0:
                    continue
                proj[spin] = v[list_ind_band[spin][0]][list_ind_kpts[0]]
            return {'band_index': list_ind_band,
                    'kpoint_index': list_ind_kpts,
                    'kpoint': kpointvbm, 'energy': max_tmp,
                    'projections': proj}

        def get_cbm(self):
            """
            Returns data about the CBM.

            Returns:
                {"band_index","kpoint_index","kpoint","energy"}
                - "band_index": A dict with spin keys pointing to a list of the
                indices of the band containing the VBM (please note that you
                can have several bands sharing the VBM) {Spin.up:[],
                Spin.down:[]}
                - "kpoint_index": The list of indices in self.kpoints for the
                kpoint vbm. Please note that there can be several
                kpoint_indices relating to the same kpoint (e.g., Gamma can
                occur at different spots in the band structure line plot)
                - "kpoint": The kpoint (as a kpoint object)
                - "energy": The energy of the VBM
                - "projections": The projections along sites and orbitals of the
                VBM if any projection data is available (else it is an empty
                dictionnary). The format is similar to the projections field in
                BandStructure: {spin:{'Orbital': [proj]}} where the array
                [proj] is ordered according to the sites in structure
            """
            if self.is_metal():
                return {"band_index": [], "kpoint_index": [],
                        "kpoint": [], "energy": None, "projections": {}}
            max_tmp = float("inf")

            index = None
            kpointcbm = None
            for spin, v in self.bands.items():
                for i, j in zip(*np.where(v >= self.efermi)):
                    if v[i, j] < max_tmp:
                        max_tmp = float(v[i, j])
                        index = j
                        kpointcbm = self.kpoints[j]

            list_index_kpoints = []
            if kpointcbm.label is not None:
                for i in range(len(self.kpoints)):
                    if self.kpoints[i].label == kpointcbm.label:
                        list_index_kpoints.append(i)
            else:
                list_index_kpoints.append(index)

            # get all other bands sharing the cbm
            list_index_band = collections.defaultdict(list)
            for spin in self.bands:
                for i in range(self.nb_bands):
                    if math.fabs(self.bands[spin][i][index] - max_tmp) < 0.001:
                        list_index_band[spin].append(i)
            proj = {}
            for spin, v in self.projections.items():
                if len(list_index_band[spin]) == 0:
                    continue
                proj[spin] = v[list_index_band[spin][0]][list_index_kpoints[0]]

            return {'band_index': list_index_band,
                    'kpoint_index': list_index_kpoints,
                    'kpoint': kpointcbm, 'energy': max_tmp,
                    'projections': proj}

        def get_band_gap(self):
            r"""
            Returns band gap data.

            Returns:
                A dict {"energy","direct","transition"}:
                "energy": band gap energy
                "direct": A boolean telling if the gap is direct or not
                "transition": kpoint labels of the transition (e.g., "\\Gamma-X")
            """
            if self.is_metal():
                return {"energy": 0.0, "direct": False, "transition": None}
            cbm = self.get_cbm()
            vbm = self.get_vbm()
            result = dict(direct=False, energy=0.0, transition=None)

            result["energy"] = cbm["energy"] - vbm["energy"]

            if (cbm["kpoint"].label is not None and cbm["kpoint"].label == vbm[
                "kpoint"].label) \
                    or np.linalg.norm(cbm["kpoint"].cart_coords
                                      - vbm["kpoint"].cart_coords) < 0.01:
                result["direct"] = True

            result["transition"] = "-".join(
                [str(c.label) if c.label is not None else
                 str("(") + ",".join(["{0:.3f}".format(c.frac_coords[i])
                                      for i in range(3)])
                 + str(")") for c in [vbm["kpoint"], cbm["kpoint"]]])

            return result

        def get_direct_band_gap_dict(self):
            """
            Returns a dictionary of information about the direct
            band gap

            Returns:
                a dictionary of the band gaps indexed by spin
                along with their band indices and k-point index
            """
            if self.is_metal():
                raise ValueError("get_direct_band_gap_dict should"
                                 "only be used with non-metals")
            direct_gap_dict = {}
            for spin, v in self.bands.items():
                above = v[np.all(v > self.efermi, axis=1)]
                min_above = np.min(above, axis=0)
                below = v[np.all(v < self.efermi, axis=1)]
                max_below = np.max(below, axis=0)
                diff = min_above - max_below
                kpoint_index = np.argmin(diff)
                band_indices = [np.argmax(below[:, kpoint_index]),
                                np.argmin(above[:, kpoint_index]) + len(below)]
                direct_gap_dict[spin] = {"value": diff[kpoint_index],
                                         "kpoint_index": kpoint_index,
                                         "band_indices": band_indices}
            return direct_gap_dict

        def get_direct_band_gap(self):
            """
            Returns the direct band gap.

            Returns:
                 the value of the direct band gap
            """
            if self.is_metal():
                return 0.0
            dg = self.get_direct_band_gap_dict()
            return min(v['value'] for v in dg.values())

        def get_sym_eq_kpoints(self, kpoint, cartesian=False, tol=1e-2):
            """
            Returns a list of unique symmetrically equivalent k-points.

            Args:
                kpoint (1x3 array): coordinate of the k-point
                cartesian (bool): kpoint is in cartesian or fractional coordinates
                tol (float): tolerance below which coordinates are considered equal

            Returns:
                ([1x3 array] or None): if structure is not available returns None
            """
            if not self.structure:
                return None
            sg = SpacegroupAnalyzer(self.structure)
            symmops = sg.get_point_group_operations(cartesian=cartesian)
            points = np.dot(kpoint, [m.rotation_matrix for m in symmops])
            rm_list = []
            # identify and remove duplicates from the list of equivalent k-points:
            for i in range(len(points) - 1):
                for j in range(i + 1, len(points)):
                    if np.allclose(pbc_diff(points[i], points[j]), [0, 0, 0], tol):
                        rm_list.append(i)
                        break
            return np.delete(points, rm_list, axis=0)

        def get_kpoint_degeneracy(self, kpoint, cartesian=False, tol=1e-2):
            """
            Returns degeneracy of a given k-point based on structure symmetry
            Args:
                kpoint (1x3 array): coordinate of the k-point
                cartesian (bool): kpoint is in cartesian or fractional coordinates
                tol (float): tolerance below which coordinates are considered equal

            Returns:
                (int or None): degeneracy or None if structure is not available
            """
            all_kpts = self.get_sym_eq_kpoints(kpoint, cartesian, tol=tol)
            if all_kpts is not None:
                return len(all_kpts)

        def as_dict(self):
            """
            Json-serializable dict representation of BandStructureSymmLine.
            """
            d = {"@module": self.__class__.__module__,
                 "@class": self.__class__.__name__,
                 "lattice_rec": self.lattice_rec.as_dict(), "efermi": self.efermi,
                 "kpoints": []}
            # kpoints are not kpoint objects dicts but are frac coords (this makes
            # the dict smaller and avoids the repetition of the lattice
            for k in self.kpoints:
                d["kpoints"].append(k.as_dict()["fcoords"])
            d["bands"] = {str(int(spin)): self.bands[spin]
                          for spin in self.bands}
            d["is_metal"] = self.is_metal()
            vbm = self.get_vbm()
            d["vbm"] = {"energy": vbm["energy"],
                        "kpoint_index": vbm["kpoint_index"],
                        "band_index": {str(int(spin)): vbm["band_index"][spin]
                                       for spin in vbm["band_index"]},
                        'projections': {str(spin): v.tolist() for spin, v in vbm[
                            'projections'].items()}}
            cbm = self.get_cbm()
            d['cbm'] = {'energy': cbm['energy'],
                        'kpoint_index': cbm['kpoint_index'],
                        'band_index': {str(int(spin)): cbm['band_index'][spin]
                                       for spin in cbm['band_index']},
                        'projections': {str(spin): v.tolist() for spin, v in cbm[
                            'projections'].items()}}
            d['band_gap'] = self.get_band_gap()
            d['labels_dict'] = {}
            d['is_spin_polarized'] = self.is_spin_polarized
            for c in self.labels_dict:
                d['labels_dict'][c] = self.labels_dict[c].as_dict()['fcoords']
            d['projections'] = {}
            if len(self.projections) != 0:
                d['structure'] = self.structure.as_dict()
                d['projections'] = {str(int(spin)): np.array(v).tolist()
                                    for spin, v in self.projections.items()}
            return d

        @classmethod
        def from_dict(cls, d):
            """
            Create from dict.

            Args:
                A dict with all data for a band structure object.

            Returns:
                A BandStructure object
            """
            labels_dict = d['labels_dict']
            projections = {}
            structure = None
            if isinstance(list(d['bands'].values())[0], dict):
                eigenvals = {Spin(int(k)): np.array(d['bands'][k]['data'])
                             for k in d['bands']}
            else:
                eigenvals = {Spin(int(k)): d['bands'][k] for k in d['bands']}
            if 'structure' in d:
                structure = Structure.from_dict(d['structure'])
            if d.get('projections'):
                projections = {Spin(int(spin)): np.array(v)
                               for spin, v in d["projections"].items()}

            return BandStructure(
                d['kpoints'], eigenvals,
                Lattice(d['lattice_rec']['matrix']), d['efermi'],
                labels_dict, structure=structure, projections=projections)

        @classmethod
        def from_old_dict(cls, d):
            """
            Args:
                d (dict): A dict with all data for a band structure symm line
                    object.
            Returns:
                A BandStructureSymmLine object
            """
            # Strip the label to recover initial string (see trick used in as_dict to handle $ chars)
            labels_dict = {k.strip(): v for k, v in d['labels_dict'].items()}
            projections = {}
            structure = None
            if 'projections' in d and len(d['projections']) != 0:
                structure = Structure.from_dict(d['structure'])
                projections = {}
                for spin in d['projections']:
                    dd = []
                    for i in range(len(d['projections'][spin])):
                        ddd = []
                        for j in range(len(d['projections'][spin][i])):
                            dddd = []
                            for k in range(len(d['projections'][spin][i][j])):
                                ddddd = []
                                orb = Orbital(k).name
                                for l in range(len(d['projections'][spin][i][j][
                                                       orb])):
                                    ddddd.append(d['projections'][spin][i][j][
                                                     orb][l])
                                dddd.append(np.array(ddddd))
                            ddd.append(np.array(dddd))
                        dd.append(np.array(ddd))
                    projections[Spin(int(spin))] = np.array(dd)

            return BandStructure(
                d['kpoints'], {Spin(int(k)): d['bands'][k] for k in d['bands']},
                Lattice(d['lattice_rec']['matrix']), d['efermi'],
                labels_dict, structure=structure, projections=projections)

    class BandStructureSymmLine(BandStructure, MSONable):
        r"""
        This object stores band structures along selected (symmetry) lines in the
        Brillouin zone. We call the different symmetry lines (ex: \\Gamma to Z)
        "branches".
        """

        def __init__(self, kpoints, eigenvals, lattice, efermi, labels_dict,
                     coords_are_cartesian=False, structure=None,
                     projections=None):
            """
            Args:
                kpoints: list of kpoint as numpy arrays, in frac_coords of the
                    given lattice by default
                eigenvals: dict of energies for spin up and spin down
                    {Spin.up:[][],Spin.down:[][]}, the first index of the array
                    [][] refers to the band and the second to the index of the
                    kpoint. The kpoints are ordered according to the order of the
                    kpoints array. If the band structure is not spin polarized, we
                    only store one data set under Spin.up.
                lattice: The reciprocal lattice.
                    Pymatgen uses the physics convention of reciprocal lattice vectors
                    WITH a 2*pi coefficient
                efermi: fermi energy
                label_dict: (dict) of {} this link a kpoint (in frac coords or
                    cartesian coordinates depending on the coords).
                coords_are_cartesian: Whether coordinates are cartesian.
                structure: The crystal structure (as a pymatgen Structure object)
                    associated with the band structure. This is needed if we
                    provide projections to the band structure.
                projections: dict of orbital projections as {spin: ndarray}. The
                    indices of the ndarrayare [band_index, kpoint_index, orbital_index,
                    ion_index].If the band structure is not spin polarized, we only
                    store one data set under Spin.up.
            """
            super().__init__(
                kpoints, eigenvals, lattice, efermi, labels_dict,
                coords_are_cartesian, structure, projections)
            self.distance = []
            self.branches = []
            one_group = []
            branches_tmp = []
            # get labels and distance for each kpoint
            previous_kpoint = self.kpoints[0]
            previous_distance = 0.0

            previous_label = self.kpoints[0].label
            for i in range(len(self.kpoints)):
                label = self.kpoints[i].label
                if label is not None and previous_label is not None:
                    self.distance.append(previous_distance)
                else:
                    self.distance.append(
                        np.linalg.norm(self.kpoints[i].cart_coords -
                                       previous_kpoint.cart_coords) +
                        previous_distance)
                previous_kpoint = self.kpoints[i]
                previous_distance = self.distance[i]
                if label:
                    if previous_label:
                        if len(one_group) != 0:
                            branches_tmp.append(one_group)
                        one_group = []
                previous_label = label
                one_group.append(i)

            if len(one_group) != 0:
                branches_tmp.append(one_group)
            for b in branches_tmp:
                self.branches.append(
                    {"start_index": b[0], "end_index": b[-1],
                     "name": str(self.kpoints[b[0]].label) + "-" + str(self.kpoints[b[-1]].label)})

            self.is_spin_polarized = False
            if len(self.bands) == 2:
                self.is_spin_polarized = True

        def get_equivalent_kpoints(self, index):
            """
            Returns the list of kpoint indices equivalent (meaning they are the
            same frac coords) to the given one.

            Args:
                index: the kpoint index

            Returns:
                a list of equivalent indices

            TODO: now it uses the label we might want to use coordinates instead
            (in case there was a mislabel)
            """
            # if the kpoint has no label it can"t have a repetition along the band
            # structure line object

            if self.kpoints[index].label is None:
                return [index]

            list_index_kpoints = []
            for i in range(len(self.kpoints)):
                if self.kpoints[i].label == self.kpoints[index].label:
                    list_index_kpoints.append(i)

            return list_index_kpoints

        def get_branch(self, index):
            r"""
            Returns in what branch(es) is the kpoint. There can be several
            branches.

            Args:
                index: the kpoint index

            Returns:
                A list of dictionaries [{"name","start_index","end_index","index"}]
                indicating all branches in which the k_point is. It takes into
                account the fact that one kpoint (e.g., \\Gamma) can be in several
                branches
            """
            to_return = []
            for i in self.get_equivalent_kpoints(index):
                for b in self.branches:
                    if b["start_index"] <= i <= b["end_index"]:
                        to_return.append({"name": b["name"],
                                          "start_index": b["start_index"],
                                          "end_index": b["end_index"],
                                          "index": i})
            return to_return

        def apply_scissor(self, new_band_gap):
            """
            Apply a scissor operator (shift of the CBM) to fit the given band gap.
            If it's a metal. We look for the band crossing the fermi level
            and shift this one up. This will not work all the time for metals!

            Args:
                new_band_gap: the band gap the scissor band structure need to have.

            Returns:
                a BandStructureSymmLine object with the applied scissor shift
            """
            if self.is_metal():
                # moves then the highest index band crossing the fermi level
                # find this band...
                max_index = -1000
                # spin_index = None
                for i in range(self.nb_bands):
                    below = False
                    above = False
                    for j in range(len(self.kpoints)):
                        if self.bands[Spin.up][i][j] < self.efermi:
                            below = True
                        if self.bands[Spin.up][i][j] > self.efermi:
                            above = True
                    if above and below:
                        if i > max_index:
                            max_index = i
                            # spin_index = Spin.up
                    if self.is_spin_polarized:
                        below = False
                        above = False
                        for j in range(len(self.kpoints)):
                            if self.bands[Spin.down][i][j] < self.efermi:
                                below = True
                            if self.bands[Spin.down][i][j] > self.efermi:
                                above = True
                        if above and below:
                            if i > max_index:
                                max_index = i
                                # spin_index = Spin.down
                old_dict = self.as_dict()
                shift = new_band_gap
                for spin in old_dict['bands']:
                    for k in range(len(old_dict['bands'][spin])):
                        for v in range(len(old_dict['bands'][spin][k])):
                            if k >= max_index:
                                old_dict['bands'][spin][k][v] = \
                                    old_dict['bands'][spin][k][v] + shift
            else:

                shift = new_band_gap - self.get_band_gap()['energy']
                old_dict = self.as_dict()
                for spin in old_dict['bands']:
                    for k in range(len(old_dict['bands'][spin])):
                        for v in range(len(old_dict['bands'][spin][k])):
                            if old_dict['bands'][spin][k][v] >= \
                                    old_dict['cbm']['energy']:
                                old_dict['bands'][spin][k][v] = \
                                    old_dict['bands'][spin][k][v] + shift
                old_dict['efermi'] = old_dict['efermi'] + shift
            return self.from_dict(old_dict)

        def as_dict(self):
            """
            Json-serializable dict representation of BandStructureSymmLine.
            """

            d = {"@module": self.__class__.__module__,
                 "@class": self.__class__.__name__,
                 "lattice_rec": self.lattice_rec.as_dict(), "efermi": self.efermi,
                 "kpoints": []}
            # kpoints are not kpoint objects dicts but are frac coords (this makes
            # the dict smaller and avoids the repetition of the lattice
            for k in self.kpoints:
                d["kpoints"].append(k.as_dict()["fcoords"])
            d["branches"] = self.branches
            d["bands"] = {str(int(spin)): self.bands[spin].tolist()
                          for spin in self.bands}
            d["is_metal"] = self.is_metal()
            vbm = self.get_vbm()
            d["vbm"] = {"energy": vbm["energy"],
                        "kpoint_index": vbm["kpoint_index"],
                        "band_index": {str(int(spin)): vbm["band_index"][spin]
                                       for spin in vbm["band_index"]},
                        'projections': {str(spin): v.tolist() for spin, v in vbm[
                            'projections'].items()}}
            cbm = self.get_cbm()
            d['cbm'] = {'energy': cbm['energy'],
                        'kpoint_index': cbm['kpoint_index'],
                        'band_index': {str(int(spin)): cbm['band_index'][spin]
                                       for spin in cbm['band_index']},
                        'projections': {str(spin): v.tolist() for spin, v in cbm[
                            'projections'].items()}}
            d['band_gap'] = self.get_band_gap()
            d['labels_dict'] = {}
            d['is_spin_polarized'] = self.is_spin_polarized
            # MongoDB does not accept keys starting with $. Add a blanck space to fix the problem
            for c in self.labels_dict:
                mongo_key = c if not c.startswith("$") else " " + c
                d['labels_dict'][mongo_key] = self.labels_dict[c].as_dict()[
                    'fcoords']
            if len(self.projections) != 0:
                d['structure'] = self.structure.as_dict()
                d['projections'] = {str(int(spin)): np.array(v).tolist()
                                    for spin, v in self.projections.items()}
            return d

        @classmethod
        def from_dict(cls, d):
            """
            Args:
                d (dict): A dict with all data for a band structure symm line
                    object.

            Returns:
                A BandStructureSymmLine object
            """
            try:
                # Strip the label to recover initial string (see trick used in as_dict to handle $ chars)
                labels_dict = {k.strip(): v for k, v in d['labels_dict'].items()}
                projections = {}
                structure = None
                if d.get('projections'):
                    if isinstance(d["projections"]['1'][0][0], dict):
                        raise ValueError("Old band structure dict format detected!")
                    structure = Structure.from_dict(d['structure'])
                    projections = {Spin(int(spin)): np.array(v)
                                   for spin, v in d["projections"].items()}

                return BandStructureSymmLine(
                    d['kpoints'], {Spin(int(k)): d['bands'][k]
                                   for k in d['bands']},
                    Lattice(d['lattice_rec']['matrix']), d['efermi'],
                    labels_dict, structure=structure, projections=projections)
            except Exception:
                warnings.warn("Trying from_dict failed. Now we are trying the old "
                              "format. Please convert your BS dicts to the new "
                              "format. The old format will be retired in pymatgen "
                              "5.0.")
                return BandStructureSymmLine.from_old_dict(d)

        @classmethod
        def from_old_dict(cls, d):
            """
            Args:
                d (dict): A dict with all data for a band structure symm line
                    object.
            Returns:
                A BandStructureSymmLine object
            """
            # Strip the label to recover initial string (see trick used in as_dict to handle $ chars)
            labels_dict = {k.strip(): v for k, v in d['labels_dict'].items()}
            projections = {}
            structure = None
            if 'projections' in d and len(d['projections']) != 0:
                structure = Structure.from_dict(d['structure'])
                projections = {}
                for spin in d['projections']:
                    dd = []
                    for i in range(len(d['projections'][spin])):
                        ddd = []
                        for j in range(len(d['projections'][spin][i])):
                            dddd = []
                            for k in range(len(d['projections'][spin][i][j])):
                                ddddd = []
                                orb = Orbital(k).name
                                for l in range(len(d['projections'][spin][i][j][
                                                       orb])):
                                    ddddd.append(d['projections'][spin][i][j][
                                                     orb][l])
                                dddd.append(np.array(ddddd))
                            ddd.append(np.array(dddd))
                        dd.append(np.array(ddd))
                    projections[Spin(int(spin))] = np.array(dd)

            return BandStructureSymmLine(
                d['kpoints'], {Spin(int(k)): d['bands'][k]
                               for k in d['bands']},
                Lattice(d['lattice_rec']['matrix']), d['efermi'],
                labels_dict, structure=structure, projections=projections)

    class LobsterBandStructureSymmLine(BandStructureSymmLine):
        """
        Lobster subclass of BandStructure with customized functions.
        """

        def as_dict(self):
            """
            Json-serializable dict representation of BandStructureSymmLine.
            """

            d = {"@module": self.__class__.__module__,
                 "@class": self.__class__.__name__,
                 "lattice_rec": self.lattice_rec.as_dict(), "efermi": self.efermi,
                 "kpoints": []}
            # kpoints are not kpoint objects dicts but are frac coords (this makes
            # the dict smaller and avoids the repetition of the lattice
            for k in self.kpoints:
                d["kpoints"].append(k.as_dict()["fcoords"])
            d["branches"] = self.branches
            d["bands"] = {str(int(spin)): self.bands[spin].tolist()
                          for spin in self.bands}
            d["is_metal"] = self.is_metal()
            vbm = self.get_vbm()
            d["vbm"] = {"energy": vbm["energy"],
                        "kpoint_index": [int(x) for x in vbm["kpoint_index"]],
                        "band_index": {str(int(spin)): vbm["band_index"][spin]
                                       for spin in vbm["band_index"]},
                        'projections': {str(spin): v for spin, v in vbm[
                            'projections'].items()}}
            cbm = self.get_cbm()
            d['cbm'] = {'energy': cbm['energy'],
                        'kpoint_index': [int(x) for x in cbm["kpoint_index"]],
                        'band_index': {str(int(spin)): cbm['band_index'][spin]
                                       for spin in cbm['band_index']},
                        'projections': {str(spin): v for spin, v in cbm[
                            'projections'].items()}}
            d['band_gap'] = self.get_band_gap()
            d['labels_dict'] = {}
            d['is_spin_polarized'] = self.is_spin_polarized
            # MongoDB does not accept keys starting with $. Add a blanck space to fix the problem
            for c in self.labels_dict:
                mongo_key = c if not c.startswith("$") else " " + c
                d['labels_dict'][mongo_key] = self.labels_dict[c].as_dict()[
                    'fcoords']
            if len(self.projections) != 0:
                d['structure'] = self.structure.as_dict()
                d['projections'] = {str(int(spin)): np.array(v).tolist()
                                    for spin, v in self.projections.items()}
            return d

        @classmethod
        def from_dict(cls, d):
            """
            Args:
                d (dict): A dict with all data for a band structure symm line
                    object.

            Returns:
                A BandStructureSymmLine object
            """
            try:
                # Strip the label to recover initial string (see trick used in as_dict to handle $ chars)
                labels_dict = {k.strip(): v for k, v in d['labels_dict'].items()}
                projections = {}
                structure = None
                if d.get('projections'):
                    if isinstance(d["projections"]['1'][0][0], dict):
                        raise ValueError("Old band structure dict format detected!")
                    structure = Structure.from_dict(d['structure'])
                    projections = {Spin(int(spin)): np.array(v)
                                   for spin, v in d["projections"].items()}

                return LobsterBandStructureSymmLine(
                    d['kpoints'], {Spin(int(k)): d['bands'][k]
                                   for k in d['bands']},
                    Lattice(d['lattice_rec']['matrix']), d['efermi'],
                    labels_dict, structure=structure, projections=projections)
            except Exception:
                warnings.warn("Trying from_dict failed. Now we are trying the old "
                              "format. Please convert your BS dicts to the new "
                              "format. The old format will be retired in pymatgen "
                              "5.0.")
                return LobsterBandStructureSymmLine.from_old_dict(d)

        @classmethod
        def from_old_dict(cls, d):
            """
            Args:
                d (dict): A dict with all data for a band structure symm line
                    object.
            Returns:
                A BandStructureSymmLine object
            """
            # Strip the label to recover initial string (see trick used in as_dict to handle $ chars)
            labels_dict = {k.strip(): v for k, v in d['labels_dict'].items()}
            projections = {}
            structure = None
            if 'projections' in d and len(d['projections']) != 0:
                structure = Structure.from_dict(d['structure'])
                projections = {}
                for spin in d['projections']:
                    dd = []
                    for i in range(len(d['projections'][spin])):
                        ddd = []
                        for j in range(len(d['projections'][spin][i])):
                            ddd.append(d['projections'][spin][i][j])
                        dd.append(np.array(ddd))
                    projections[Spin(int(spin))] = np.array(dd)

            return LobsterBandStructureSymmLine(
                d['kpoints'], {Spin(int(k)): d['bands'][k]
                               for k in d['bands']},
                Lattice(d['lattice_rec']['matrix']), d['efermi'],
                labels_dict, structure=structure, projections=projections)

        def get_projection_on_elements(self):
            """
            Method returning a dictionary of projections on elements.
            It sums over all available orbitals for each element.

            Returns:
                a dictionary in the {Spin.up:[][{Element:values}],
                Spin.down:[][{Element:values}]} format
                if there is no projections in the band structure
                returns an empty dict
            """
            result = {}
            for spin, v in self.projections.items():
                result[spin] = [[collections.defaultdict(float)
                                 for i in range(len(self.kpoints))]
                                for j in range(self.nb_bands)]
                for i, j in itertools.product(range(self.nb_bands),
                                              range(len(self.kpoints))):
                    for key, item in v[i][j].items():
                        for key2, item2 in item.items():
                            specie = str(Element(re.split(r"[0-9]+", key)[0]))
                            result[spin][i][j][specie] += item2
            return result

        def get_projections_on_elements_and_orbitals(self, el_orb_spec):
            """
            Method returning a dictionary of projections on elements and specific
            orbitals

            Args:
                el_orb_spec: A dictionary of Elements and Orbitals for which we want
                    to have projections on. It is given as: {Element:[orbitals]},
                    e.g., {'Si':['3s','3p']} or {'Si':['3s','3p_x', '3p_y', '3p_z']} depending on input files

            Returns:
                A dictionary of projections on elements in the
                {Spin.up:[][{Element:{orb:values}}],
                Spin.down:[][{Element:{orb:values}}]} format
                if there is no projections in the band structure returns an empty
                dict.
            """
            result = {}
            el_orb_spec = {get_el_sp(el): orbs for el, orbs in el_orb_spec.items()}
            for spin, v in self.projections.items():
                result[spin] = [[{str(e): collections.defaultdict(float)
                                  for e in el_orb_spec}
                                 for i in range(len(self.kpoints))]
                                for j in range(self.nb_bands)]

                for i, j in itertools.product(range(self.nb_bands),
                                              range(len(self.kpoints))):
                    for key, item in v[i][j].items():
                        for key2, item2 in item.items():
                            specie = str(Element(re.split(r"[0-9]+", key)[0]))
                            if get_el_sp(str(specie)) in el_orb_spec:
                                if key2 in el_orb_spec[get_el_sp(str(specie))]:
                                    result[spin][i][j][specie][key2] += item2
            return result

    def get_reconstructed_band_structure(list_bs, efermi=None):
        """
        This method takes a list of band structures and reconstructs
        one band structure object from all of them.

        This is typically very useful when you split non self consistent
        band structure runs in several independent jobs and want to merge back
        the results

        Args:
            list_bs: A list of BandStructure or BandStructureSymmLine objects.
            efermi: The Fermi energy of the reconstructed band structure. If
                None is assigned an average of all the Fermi energy in each
                object in the list_bs is used.

        Returns:
            A BandStructure or BandStructureSymmLine object (depending on
            the type of the list_bs objects)
        """
        if efermi is None:
            efermi = sum([b.efermi for b in list_bs]) / len(list_bs)

        kpoints = []
        labels_dict = {}
        rec_lattice = list_bs[0].lattice_rec
        nb_bands = min([list_bs[i].nb_bands for i in range(len(list_bs))])

        kpoints = np.concatenate([[k.frac_coords for k in bs.kpoints]
                                  for bs in list_bs])
        dicts = [bs.labels_dict for bs in list_bs]
        labels_dict = {k: v.frac_coords for d in dicts for k, v in d.items()}

        eigenvals = {}
        eigenvals[Spin.up] = np.concatenate([bs.bands[Spin.up][:nb_bands]
                                             for bs in list_bs], axis=1)

        if list_bs[0].is_spin_polarized:
            eigenvals[Spin.down] = np.concatenate([bs.bands[Spin.down][:nb_bands]
                                                   for bs in list_bs], axis=1)

        projections = {}
        if len(list_bs[0].projections) != 0:
            projs = [bs.projections[Spin.up][:nb_bands] for bs in list_bs]
            projections[Spin.up] = np.concatenate(projs, axis=1)

            if list_bs[0].is_spin_polarized:
                projs = [bs.projections[Spin.down][:nb_bands] for bs in list_bs]
                projections[Spin.down] = np.concatenate(projs, axis=1)

        if isinstance(list_bs[0], BandStructureSymmLine):
            return BandStructureSymmLine(kpoints, eigenvals, rec_lattice,
                                         efermi, labels_dict,
                                         structure=list_bs[0].structure,
                                         projections=projections)
        else:
            return BandStructure(kpoints, eigenvals, rec_lattice, efermi,
                                 labels_dict, structure=list_bs[0].structure,
                                 projections=projections)