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"


[docs]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)
[docs] 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__}
[docs]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
[docs] 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
[docs] 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
[docs] 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
[docs] 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}
[docs] 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}
[docs] 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
[docs] 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
[docs] 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())
[docs] 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)
[docs] 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)
[docs] 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
[docs] @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)
[docs] @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)
[docs]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
[docs] 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
[docs] 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
[docs] 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)
[docs] 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
[docs] @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)
[docs] @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)
[docs]class LobsterBandStructureSymmLine(BandStructureSymmLine): """ Lobster subclass of BandStructure with customized functions. """
[docs] 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
[docs] @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)
[docs] @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)
[docs] 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
[docs] 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
[docs]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)