# 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 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)