pymatgen.electronic_structure.bandstructure module
This module provides classes to define everything related to band structures.
- class BandStructure(kpoints: ndarray, eigenvals: dict[pymatgen.electronic_structure.core.Spin, numpy.ndarray], lattice: Lattice, efermi: float, labels_dict=None, coords_are_cartesian: bool = False, structure: Optional[Structure] = None, projections: Optional[dict[pymatgen.electronic_structure.core.Spin, numpy.ndarray]] = None)[source]
Bases:
object
This is the most generic band structure data possible it’s defined by a list of kpoints + energies for each of them
- kpoints:
- the list of kpoints (as Kpoint objects) in the band structure
- bands[source]
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].
- projections[source]
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].
- Parameters:
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 (float) – 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.
- classmethod from_dict(d)[source]
Create from dict.
- Parameters:
object. (A dict with all data for a band structure) –
- Returns:
A BandStructure object
- classmethod from_old_dict(d)[source]
- Parameters:
d (dict) – A dict with all data for a band structure symm line object.
- Returns:
A BandStructureSymmLine object
- get_band_gap()[source]
Returns band gap data.
- Returns:
“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”)
- Return type:
A dict {“energy”,”direct”,”transition”}
- get_cbm()[source]
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 CBM (please note that you can have several bands sharing the CBM) {Spin.up:[], Spin.down:[]} - “kpoint_index”: The list of indices in self.kpoints for the kpoint CBM. 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 CBM - “projections”: The projections along sites and orbitals of the CBM if any projection data is available (else it is an empty dictionary). 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
- get_direct_band_gap()[source]
Returns the direct band gap.
- Returns:
the value of the direct band gap
- get_direct_band_gap_dict()[source]
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
- get_kpoint_degeneracy(kpoint, cartesian=False, tol: float = 0.01)[source]
Returns degeneracy of a given k-point based on structure symmetry :param kpoint: coordinate of the k-point :type kpoint: 1x3 array :param cartesian: kpoint is in Cartesian or fractional coordinates :type cartesian: bool :param tol: tolerance below which coordinates are considered equal :type tol: float
- Returns:
degeneracy or None if structure is not available
- Return type:
(int or None)
- get_projection_on_elements()[source]
Method returning a dictionary of projections on elements.
- Returns:
[][{Element:values}], Spin.down:[][{Element:values}]} format if there is no projections in the band structure returns an empty dict
- Return type:
a dictionary in the {Spin.up
- get_projections_on_elements_and_orbitals(el_orb_spec)[source]
Method returning a dictionary of projections on elements and specific orbitals
- Parameters:
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.
- get_sym_eq_kpoints(kpoint, cartesian=False, tol: float = 0.01)[source]
Returns a list of unique symmetrically equivalent k-points.
- Parameters:
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:
if structure is not available returns None
- Return type:
([1x3 array] or None)
- get_vbm()[source]
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 dictionary). 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
- class BandStructureSymmLine(kpoints, eigenvals, lattice, efermi, labels_dict, coords_are_cartesian=False, structure=None, projections=None)[source]
Bases:
BandStructure
,MSONable
This object stores band structures along selected (symmetry) lines in the Brillouin zone. We call the different symmetry lines (ex: \Gamma to Z) “branches”.
- Parameters:
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.
- apply_scissor(new_band_gap)[source]
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!
- Parameters:
new_band_gap – the band gap the scissor band structure need to have.
- Returns:
a BandStructureSymmLine object with the applied scissor shift
- get_branch(index)[source]
Returns in what branch(es) is the kpoint. There can be several branches.
- Parameters:
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
- get_equivalent_kpoints(index)[source]
Returns the list of kpoint indices equivalent (meaning they are the same frac coords) to the given one.
- Parameters:
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)
- class Kpoint(coords, lattice, to_unit_cell=False, coords_are_cartesian=False, label=None)[source]
Bases:
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.
- Parameters:
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)
- class LobsterBandStructureSymmLine(kpoints, eigenvals, lattice, efermi, labels_dict, coords_are_cartesian=False, structure=None, projections=None)[source]
Bases:
BandStructureSymmLine
Lobster subclass of BandStructure with customized functions.
- Parameters:
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.
- classmethod from_dict(d)[source]
- Parameters:
d (dict) – A dict with all data for a band structure symm line object.
- Returns:
A BandStructureSymmLine object
- classmethod from_old_dict(d)[source]
- Parameters:
d (dict) – A dict with all data for a band structure symm line object.
- Returns:
A BandStructureSymmLine object
- get_projection_on_elements()[source]
Method returning a dictionary of projections on elements. It sums over all available orbitals for each element.
- Returns:
[][{Element:values}], Spin.down:[][{Element:values}]} format if there is no projections in the band structure returns an empty dict
- Return type:
a dictionary in the {Spin.up
- get_projections_on_elements_and_orbitals(el_orb_spec)[source]
Method returning a dictionary of projections on elements and specific orbitals
- Parameters:
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.
- get_reconstructed_band_structure(list_bs, efermi=None)[source]
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
- Parameters:
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)