Source code for pymatgen.phonon.bandstructure

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

"""
This module provides classes to define a phonon band structure.
"""

import collections
import numpy as np

from pymatgen.core.structure import Structure
from pymatgen.core.lattice import Lattice
from pymatgen.electronic_structure.bandstructure import Kpoint
from monty.json import MSONable


[docs]def get_reasonable_repetitions(natoms): """ Choose the number of repetitions according to the number of atoms in the system """ if natoms < 4: return [3, 3, 3] if 4 < natoms < 15: return [2, 2, 2] if 15 < natoms < 50: return [2, 2, 1] if 50 < natoms: return [1, 1, 1]
[docs]def eigenvectors_from_displacements(disp, masses): """ Calculate the eigenvectors from the atomic displacements """ nphonons, natoms, ndirections = disp.shape sqrt_masses = np.sqrt(masses) return np.einsum("nax,a->nax", disp, sqrt_masses)
[docs]def estimate_band_connection(prev_eigvecs, eigvecs, prev_band_order): """ A function to order the phonon eigenvectors taken from phonopy """ metric = np.abs(np.dot(prev_eigvecs.conjugate().T, eigvecs)) connection_order = [] for overlaps in metric: maxval = 0 for i in reversed(range(len(metric))): val = overlaps[i] if i in connection_order: continue if val > maxval: maxval = val maxindex = i connection_order.append(maxindex) band_order = [connection_order[x] for x in prev_band_order] return band_order
[docs]class PhononBandStructure(MSONable): """ This is the most generic phonon band structure data possible it's defined by a list of qpoints + frequencies for each of them. Additional information may be given for frequencies at Gamma, where non-analytical contribution may be taken into account. """ def __init__(self, qpoints, frequencies, lattice, nac_frequencies=None, eigendisplacements=None, nac_eigendisplacements=None, labels_dict=None, coords_are_cartesian=False, structure=None): """ Args: qpoints: list of qpoint as numpy arrays, in frac_coords of the given lattice by default frequencies: list of phonon frequencies in THz as a numpy array with shape (3*len(structure), len(qpoints)). The First index of the array refers to the band and the second to the index of the qpoint. lattice: The reciprocal lattice as a pymatgen Lattice object. Pymatgen uses the physics convention of reciprocal lattice vectors WITH a 2*pi coefficient. nac_frequencies: Frequencies with non-analytical contributions at Gamma in THz. A list of tuples. The first element of each tuple should be a list defining the direction (not necessarily a versor, will be normalized internally). The second element containing the 3*len(structure) phonon frequencies with non-analytical correction for that direction. eigendisplacements: the phonon eigendisplacements associated to the frequencies in cartesian coordinates. A numpy array of complex numbers with shape (3*len(structure), len(qpoints), len(structure), 3). he First index of the array refers to the band, the second to the index of the qpoint, the third to the atom in the structure and the fourth to the cartesian coordinates. nac_eigendisplacements: the phonon eigendisplacements associated to the non-analytical frequencies in nac_frequencies in cartesian coordinates. A list of tuples. The first element of each tuple should be a list defining the direction. The second element containing a numpy array of complex numbers with shape (3*len(structure), len(structure), 3). labels_dict: (dict) of {} this links a qpoint (in frac coords or cartesian coordinates depending on the coords) to a label. coords_are_cartesian: Whether the qpoint 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 """ self.lattice_rec = lattice self.qpoints = [] self.labels_dict = {} self.structure = structure if eigendisplacements is None: eigendisplacements = np.array([]) self.eigendisplacements = eigendisplacements if labels_dict is None: labels_dict = {} for q in qpoints: # let see if this qpoint has been assigned a label label = None for c in labels_dict: if np.linalg.norm(q - np.array(labels_dict[c])) < 0.0001: label = c self.labels_dict[label] = Kpoint( q, lattice, label=label, coords_are_cartesian=coords_are_cartesian) self.qpoints.append( Kpoint(q, lattice, label=label, coords_are_cartesian=coords_are_cartesian)) self.bands = frequencies self.nb_bands = len(self.bands) self.nb_qpoints = len(self.qpoints) # normalize directions for nac_frequencies and nac_eigendisplacements self.nac_frequencies = [] self.nac_eigendisplacements = [] if nac_frequencies is not None: for t in nac_frequencies: self.nac_frequencies.append(([i / np.linalg.norm(t[0]) for i in t[0]], t[1])) if nac_eigendisplacements is not None: for t in nac_eigendisplacements: self.nac_eigendisplacements.append(([i / np.linalg.norm(t[0]) for i in t[0]], t[1]))
[docs] def min_freq(self): """ Returns the point where the minimum frequency is reached and its value """ i = np.unravel_index(np.argmin(self.bands), self.bands.shape) return self.qpoints[i[1]], self.bands[i]
[docs] def has_imaginary_freq(self, tol=1e-5): """ True if imaginary frequencies are present in the BS. """ return self.min_freq()[1] + tol < 0
@property def has_nac(self): """ True if nac_frequencies are present. """ return len(self.nac_frequencies) > 0 @property def has_eigendisplacements(self): """ True if eigendisplacements are present. """ return len(self.eigendisplacements) > 0
[docs] def get_nac_frequencies_along_dir(self, direction): """ Returns the nac_frequencies for the given direction (not necessarily a versor). None if the direction is not present or nac_frequencies has not been calculated. Args: direction: the direction as a list of 3 elements Returns: the frequencies as a numpy array o(3*len(structure), len(qpoints)). None if not found. """ versor = [i / np.linalg.norm(direction) for i in direction] for d, f in self.nac_frequencies: if np.allclose(versor, d): return f return None
[docs] def get_nac_eigendisplacements_along_dir(self, direction): """ Returns the nac_eigendisplacements for the given direction (not necessarily a versor). None if the direction is not present or nac_eigendisplacements has not been calculated. Args: direction: the direction as a list of 3 elements Returns: the eigendisplacements as a numpy array of complex numbers with shape (3*len(structure), len(structure), 3). None if not found. """ versor = [i / np.linalg.norm(direction) for i in direction] for d, e in self.nac_eigendisplacements: if np.allclose(versor, d): return e return None
[docs] def asr_breaking(self, tol_eigendisplacements=1e-5): """ Returns the breaking of the acoustic sum rule for the three acoustic modes, if Gamma is present. None otherwise. If eigendisplacements are available they are used to determine the acoustic modes: selects the bands corresponding to the eigendisplacements that represent to a translation within tol_eigendisplacements. If these are not identified or eigendisplacements are missing the first 3 modes will be used (indices [0:3]). """ for i in range(self.nb_qpoints): if np.allclose(self.qpoints[i].frac_coords, (0, 0, 0)): if self.has_eigendisplacements: acoustic_modes_index = [] for j in range(self.nb_bands): eig = self.eigendisplacements[j][i] if np.max(np.abs(eig[1:] - eig[:1])) < tol_eigendisplacements: acoustic_modes_index.append(j) # if acoustic modes are not correctly identified return use # the first three modes if len(acoustic_modes_index) != 3: acoustic_modes_index = [0, 1, 2] return self.bands[acoustic_modes_index, i] else: return self.bands[:3, i] return None
[docs] def as_dict(self): """ :return: MSONable dict """ d = {"@module": self.__class__.__module__, "@class": self.__class__.__name__, "lattice_rec": self.lattice_rec.as_dict(), "qpoints": []} # qpoints are not Kpoint objects dicts but are frac coords.Tthis makes # the dict smaller and avoids the repetition of the lattice for q in self.qpoints: d["qpoints"].append(q.as_dict()["fcoords"]) d["bands"] = self.bands.tolist() d['labels_dict'] = {} for c in self.labels_dict: d['labels_dict'][c] = self.labels_dict[c].as_dict()['fcoords'] # split the eigendisplacements to real and imaginary part for serialization d['eigendisplacements'] = dict(real=np.real(self.eigendisplacements).tolist(), imag=np.imag(self.eigendisplacements).tolist()) d['nac_eigendisplacements'] = [(direction, dict(real=np.real(e).tolist(), imag=np.imag(e).tolist())) for direction, e in self.nac_eigendisplacements] d['nac_frequencies'] = [(direction, f.tolist()) for direction, f in self.nac_frequencies] if self.structure: d['structure'] = self.structure.as_dict() return d
[docs] @classmethod def from_dict(cls, d): """ :param d: Dict representation :return: PhononBandStructure """ lattice_rec = Lattice(d['lattice_rec']['matrix']) eigendisplacements = np.array(d['eigendisplacements']['real']) + np.array(d['eigendisplacements']['imag']) * 1j nac_eigendisplacements = [(direction, np.array(e['real']) + np.array(e['imag']) * 1j) for direction, e in d['nac_eigendisplacements']] nac_frequencies = [(direction, np.array(f)) for direction, f in d['nac_frequencies']] structure = Structure.from_dict(d['structure']) if 'structure' in d else None return cls(d['qpoints'], np.array(d['bands']), lattice_rec, nac_frequencies, eigendisplacements, nac_eigendisplacements, d['labels_dict'], structure=structure)
[docs]class PhononBandStructureSymmLine(PhononBandStructure): r""" This object stores phonon band structures along selected (symmetry) lines in the Brillouin zone. We call the different symmetry lines (ex: \\Gamma to Z) "branches". """ def __init__(self, qpoints, frequencies, lattice, has_nac=False, eigendisplacements=None, labels_dict=None, coords_are_cartesian=False, structure=None): """ Args: qpoints: list of qpoints as numpy arrays, in frac_coords of the given lattice by default frequencies: list of phonon frequencies in eV as a numpy array with shape (3*len(structure), len(qpoints)) lattice: The reciprocal lattice as a pymatgen Lattice object. Pymatgen uses the physics convention of reciprocal lattice vectors WITH a 2*pi coefficient has_nac: specify if the band structure has been produced taking into account non-analytical corrections at Gamma. If True frequenciens at Gamma from diffent directions will be stored in naf. Default False. eigendisplacements: the phonon eigendisplacements associated to the frequencies in cartesian coordinates. A numpy array of complex numbers with shape (3*len(structure), len(qpoints), len(structure), 3). he First index of the array refers to the band, the second to the index of the qpoint, the third to the atom in the structure and the fourth to the cartesian coordinates. labels_dict: (dict) of {} this links a qpoint (in frac coords or cartesian coordinates depending on the coords) to a label. coords_are_cartesian: Whether the qpoint 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 """ super().__init__( qpoints, frequencies, lattice, None, eigendisplacements, None, labels_dict, coords_are_cartesian, structure) self.distance = [] self.branches = [] one_group = [] branches_tmp = [] # get labels and distance for each qpoint previous_qpoint = self.qpoints[0] previous_distance = 0.0 previous_label = self.qpoints[0].label for i in range(self.nb_qpoints): label = self.qpoints[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.qpoints[i].cart_coords - previous_qpoint.cart_coords) + previous_distance) previous_qpoint = self.qpoints[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.qpoints[b[0]].label) + "-" + str(self.qpoints[b[-1]].label)}) # extract the frequencies with non-analytical contribution at gamma if has_nac: naf = [] nac_eigendisplacements = [] for i in range(self.nb_qpoints): # get directions with nac irrespectively of the label_dict. NB: with labels # the gamma point is expected to appear twice consecutively. if np.allclose(qpoints[i], (0, 0, 0)): if i > 0 and not np.allclose(qpoints[i - 1], (0, 0, 0)): q_dir = self.qpoints[i - 1] direction = [q_dir.frac_coords / np.linalg.norm(q_dir.frac_coords)] naf.append((direction, frequencies[:, i])) nac_eigendisplacements.append((direction, eigendisplacements[:, i])) if i < len(frequencies) - 1 and not np.allclose(qpoints[i + 1], (0, 0, 0)): q_dir = self.qpoints[i + 1] direction = [q_dir.frac_coords / np.linalg.norm(q_dir.frac_coords)] naf.append((direction, frequencies[:, i])) nac_eigendisplacements.append((direction, eigendisplacements[:, i])) self.nac_frequencies = np.array(naf) self.nac_eigendisplacements = np.array(nac_eigendisplacements)
[docs] def get_equivalent_qpoints(self, index): """ Returns the list of qpoint indices equivalent (meaning they are the same frac coords) to the given one. Args: index: the qpoint 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 qpoint has no label it can"t have a repetition along the band # structure line object if self.qpoints[index].label is None: return [index] list_index_qpoints = [] for i in range(self.nb_qpoints): if self.qpoints[i].label == self.qpoints[index].label: list_index_qpoints.append(i) return list_index_qpoints
[docs] def get_branch(self, index): r""" Returns in what branch(es) is the qpoint. There can be several branches. Args: index: the qpoint index Returns: A list of dictionaries [{"name","start_index","end_index","index"}] indicating all branches in which the qpoint is. It takes into account the fact that one qpoint (e.g., \\Gamma) can be in several branches """ to_return = [] for i in self.get_equivalent_qpoints(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 write_phononwebsite(self, filename): """ Write a json file for the phononwebsite: http://henriquemiranda.github.io/phononwebsite """ import json with open(filename, 'w') as f: json.dump(self.as_phononwebsite(), f)
[docs] def as_phononwebsite(self): """ Return a dictionary with the phononwebsite format: http://henriquemiranda.github.io/phononwebsite """ d = {} # define the lattice d["lattice"] = self.structure.lattice._matrix.tolist() # define atoms atom_pos_car = [] atom_pos_red = [] atom_types = [] for site in self.structure.sites: atom_pos_car.append(site.coords.tolist()) atom_pos_red.append(site.frac_coords.tolist()) atom_types.append(site.species_string) # default for now d["repetitions"] = get_reasonable_repetitions(len(atom_pos_car)) d["natoms"] = len(atom_pos_car) d["atom_pos_car"] = atom_pos_car d["atom_pos_red"] = atom_pos_red d["atom_types"] = atom_types d["atom_numbers"] = self.structure.atomic_numbers d["formula"] = self.structure.formula d["name"] = self.structure.formula # get qpoints qpoints = [] for q in self.qpoints: qpoints.append(list(q.frac_coords)) d["qpoints"] = qpoints # get labels hsq_dict = collections.OrderedDict() for nq, q in enumerate(self.qpoints): if q.label is not None: hsq_dict[nq] = q.label # get distances dist = 0 nqstart = 0 distances = [dist] line_breaks = [] for nq in range(1, len(qpoints)): q1 = np.array(qpoints[nq]) q2 = np.array(qpoints[nq - 1]) # detect jumps if ((nq in hsq_dict) and (nq - 1 in hsq_dict)): if (hsq_dict[nq] != hsq_dict[nq - 1]): hsq_dict[nq - 1] += "|" + hsq_dict[nq] del hsq_dict[nq] line_breaks.append((nqstart, nq)) nqstart = nq else: dist += np.linalg.norm(q1 - q2) distances.append(dist) line_breaks.append((nqstart, len(qpoints))) d["distances"] = distances d["line_breaks"] = line_breaks d["highsym_qpts"] = list(hsq_dict.items()) # eigenvalues thz2cm1 = 33.35641 bands = self.bands.copy() * thz2cm1 d["eigenvalues"] = bands.T.tolist() # eigenvectors eigenvectors = self.eigendisplacements.copy() eigenvectors /= np.linalg.norm(eigenvectors[0, 0]) eigenvectors = eigenvectors.swapaxes(0, 1) eigenvectors = np.array([eigenvectors.real, eigenvectors.imag]) eigenvectors = np.rollaxis(eigenvectors, 0, 5) d["vectors"] = eigenvectors.tolist() return d
[docs] def band_reorder(self): """ Re-order the eigenvalues according to the similarity of the eigenvectors """ eiv = self.eigendisplacements eig = self.bands nphonons, nqpoints = self.bands.shape order = np.zeros([nqpoints, nphonons], dtype=int) order[0] = np.array(range(nphonons)) # get the atomic masses atomic_masses = [site.specie.atomic_mass for site in self.structure.sites] # get order for nq in range(1, nqpoints): old_eiv = eigenvectors_from_displacements(eiv[:, nq - 1], atomic_masses) new_eiv = eigenvectors_from_displacements(eiv[:, nq], atomic_masses) order[nq] = estimate_band_connection(old_eiv.reshape([nphonons, nphonons]).T, new_eiv.reshape([nphonons, nphonons]).T, order[nq - 1]) # reorder for nq in range(1, nqpoints): eivq = eiv[:, nq] eigq = eig[:, nq] eiv[:, nq] = eivq[order[nq]] eig[:, nq] = eigq[order[nq]]
[docs] def as_dict(self): """ :return: MSONable dict """ d = super().as_dict() # remove nac_frequencies and nac_eigendisplacements as they are reconstructed # in the __init__ when the dict is deserialized nac_frequencies = d.pop('nac_frequencies') d.pop('nac_eigendisplacements') d['has_nac'] = len(nac_frequencies) > 0 return d
[docs] @classmethod def from_dict(cls, d): """ :param d: Dict representation :return: PhononBandStructureSummLine """ lattice_rec = Lattice(d['lattice_rec']['matrix']) eigendisplacements = np.array(d['eigendisplacements']['real']) + np.array(d['eigendisplacements']['imag']) * 1j structure = Structure.from_dict(d['structure']) if 'structure' in d else None return cls(d['qpoints'], np.array(d['bands']), lattice_rec, d['has_nac'], eigendisplacements, d['labels_dict'], structure=structure)