Source code for pymatgen.symmetry.maggroups

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

Magnetic space groups.

import os
from fractions import Fraction
import numpy as np
from monty.design_patterns import cached_class

import textwrap

from pymatgen.electronic_structure.core import Magmom
from pymatgen.symmetry.groups import SymmetryGroup, in_array_list
from pymatgen.symmetry.settings import JonesFaithfulTransformation
from pymatgen.core.operations import MagSymmOp
from pymatgen.util.string import transformation_to_string

import sqlite3
from array import array

__author__ = "Matthew Horton, Shyue Ping Ong"
__copyright__ = "Copyright 2017, The Materials Project"
__version__ = "0.1"
__maintainer__ = "Matthew Horton"
__email__ = ""
__status__ = "Beta"
__date__ = "Feb 2017"

MAGSYMM_DATA = os.path.join(os.path.dirname(__file__), "symm_data_magnetic.sqlite")

[docs]@cached_class class MagneticSpaceGroup(SymmetryGroup): """ Representation of a magnetic space group. """ def __init__(self, id, setting_transformation="a,b,c;0,0,0"): """ Initializes a MagneticSpaceGroup from its Belov, Neronova and Smirnova (BNS) number supplied as a list or its label supplied as a string. To create a magnetic structure in pymatgen, the Structure.from_magnetic_spacegroup() method can be used, which relies on this class. The main difference between magnetic space groups and normal crystallographic space groups is the inclusion of a time reversal operator that acts on an atom's magnetic moment. This is indicated by a prime symbol (') next to the respective symmetry operation in its label, e.g. the standard crystallographic space group Pnma has magnetic subgroups Pn'ma, Pnm'a, Pnma', Pn'm'a, Pnm'a', Pn'ma', Pn'm'a'. The magnetic space groups are classified as one of 4 types where G = magnetic space group, and F = parent crystallographic space group: 1. G=F no time reversal, i.e. the same as corresponding crystallographic group 2. G=F+F1', "grey" groups, where avg. magnetic moment is zero, e.g. a paramagnet in zero ext. mag. field 3. G=D+(F-D)1', where D is an equi-translation subgroup of F of index 2, lattice translations do not include time reversal 4. G=D+(F-D)1', where D is an equi-class subgroup of F of index 2 There are two common settings for magnetic space groups, BNS and OG. In case 4, the BNS setting != OG setting, and so a transformation to go between the two settings is required: specifically, the BNS setting is derived from D, and the OG setting is derived from F. This means that the OG setting refers to the unit cell if magnetic order is neglected, and requires multiple unit cells to reproduce the full crystal periodicity when magnetic moments are present. This does not make the OG setting, in general, useful for electronic structure calculations and the BNS setting is preferred. However, this class does contain information on the OG setting and can be initialized from OG labels or numbers if required. Conventions: ITC monoclinic unique axis b, monoclinic cell choice 1, hexagonal axis for trigonal groups, origin choice 2 for groups with more than one origin choice (ISO-MAG). Raw data comes from ISO-MAG, ISOTROPY Software Suite, with kind permission from Professor Branton Campbell, BYU Data originally compiled from: (1) Daniel B. Litvin, Magnetic Group Tables (International Union of Crystallography, 2013) (2) C. J. Bradley and A. P. Cracknell, The Mathematical Theory of Symmetry in Solids (Clarendon Press, Oxford, 1972). See for more information on magnetic symmetry. :param id: BNS number supplied as list of 2 ints or BNS label as str or index as int (1-1651) to iterate over all space groups""" self._data = {} # Datafile is stored as sqlite3 database since (a) it can be easily # queried for various different indexes (BNS/OG number/labels) and (b) # allows binary data to be stored in a compact form similar to that in # the source data file, significantly reducing file size. # Note that a human-readable JSON format was tested first but was 20x # larger and required *much* longer initial loading times. # retrieve raw data db = sqlite3.connect(MAGSYMM_DATA) c = db.cursor() if isinstance(id, str): id = "".join(id.split()) # remove any white space c.execute('SELECT * FROM space_groups WHERE BNS_label=?;', (id,)) elif isinstance(id, list): c.execute('SELECT * FROM space_groups WHERE BNS1=? AND BNS2=?;', (id[0], id[1])) elif isinstance(id, int): # OG3 index is a 'master' index, going from 1 to 1651 c.execute('SELECT * FROM space_groups WHERE OG3=?;', (id,)) raw_data = list(c.fetchone()) # Jones Faithful transformation self.jf = JonesFaithfulTransformation.from_transformation_string("a,b,c;0,0,0") if isinstance(setting_transformation, str): if setting_transformation != "a,b,c;0,0,0": self.jf = JonesFaithfulTransformation.from_transformation_string(setting_transformation) elif isinstance(setting_transformation, JonesFaithfulTransformation): if setting_transformation != self.jf: self.jf = setting_transformation self._data['magtype'] = raw_data[0] # int from 1 to 4 self._data['bns_number'] = [raw_data[1], raw_data[2]] self._data['bns_label'] = raw_data[3] self._data['og_number'] = [raw_data[4], raw_data[5], raw_data[6]] self._data['og_label'] = raw_data[7] # can differ from BNS_label def _get_point_operator(idx): """Retrieve information on point operator (rotation matrix and Seitz label).""" hex = self._data['bns_number'][0] >= 143 and self._data['bns_number'][0] <= 194 c.execute('SELECT symbol, matrix FROM point_operators WHERE idx=? AND hex=?;', (idx - 1, hex)) op = c.fetchone() op = {'symbol': op[0], 'matrix': np.array(op[1].split(','), dtype='f').reshape(3, 3)} return op def _parse_operators(b): """Parses compact binary representation into list of MagSymmOps.""" if len(b) == 0: # e.g. if magtype != 4, OG setting == BNS setting, and b == [] for OG symmops return None raw_symops = [b[i:i + 6] for i in range(0, len(b), 6)] symops = [] for r in raw_symops: point_operator = _get_point_operator(r[0]) translation_vec = [r[1] / r[4], r[2] / r[4], r[3] / r[4]] time_reversal = r[5] op = MagSymmOp.from_rotation_and_translation_and_time_reversal(rotation_matrix=point_operator['matrix'], translation_vec=translation_vec, time_reversal=time_reversal) # store string representation, e.g. (2x|1/2,1/2,1/2)' seitz = '({0}|{1},{2},{3})'.format(point_operator['symbol'], Fraction(translation_vec[0]), Fraction(translation_vec[1]), Fraction(translation_vec[2])) if time_reversal == -1: seitz += '\'' symops.append({'op': op, 'str': seitz}) return symops def _parse_wyckoff(b): """Parses compact binary representation into list of Wyckoff sites.""" if len(b) == 0: return None wyckoff_sites = [] def get_label(idx): if idx <= 25: return chr(97 + idx) # returns a-z when idx 0-25 else: return 'alpha' # when a-z labels exhausted, use alpha, only relevant for a few space groups o = 0 # offset n = 1 # nth Wyckoff site num_wyckoff = b[0] while len(wyckoff_sites) < num_wyckoff: m = b[1 + o] # multiplicity label = str(b[2 + o] * m) + get_label(num_wyckoff - n) sites = [] for j in range(m): s = b[3 + o + (j * 22):3 + o + (j * 22) + 22] # data corresponding to specific Wyckoff position translation_vec = [s[0] / s[3], s[1] / s[3], s[2] / s[3]] matrix = [[s[4], s[7], s[10]], [s[5], s[8], s[11]], [s[6], s[9], s[12]]] matrix_magmom = [[s[13], s[16], s[19]], [s[14], s[17], s[20]], [s[15], s[18], s[21]]] # store string representation, e.g. (x,y,z;mx,my,mz) wyckoff_str = "({};{})".format(transformation_to_string(matrix, translation_vec), transformation_to_string(matrix_magmom, c='m')) sites.append({'translation_vec': translation_vec, 'matrix': matrix, 'matrix_magnetic': matrix_magmom, 'str': wyckoff_str}) # only keeping string representation of Wyckoff sites for now # could do something else with these in future wyckoff_sites.append({'label': label, 'str': ' '.join([s['str'] for s in sites])}) n += 1 o += m * 22 + 2 return wyckoff_sites def _parse_lattice(b): """Parses compact binary representation into list of lattice vectors/centerings.""" if len(b) == 0: return None raw_lattice = [b[i:i + 4] for i in range(0, len(b), 4)] lattice = [] for r in raw_lattice: lattice.append({'vector': [r[0] / r[3], r[1] / r[3], r[2] / r[3]], 'str': '({0},{1},{2})+'.format(Fraction(r[0] / r[3]).limit_denominator(), Fraction(r[1] / r[3]).limit_denominator(), Fraction(r[2] / r[3]).limit_denominator())}) return lattice def _parse_transformation(b): """Parses compact binary representation into transformation between OG and BNS settings.""" if len(b) == 0: return None # capital letters used here by convention, # IUCr defines P and p specifically P = [[b[0], b[3], b[6]], [b[1], b[4], b[7]], [b[2], b[5], b[8]]] p = [b[9] / b[12], b[10] / b[12], b[11] / b[12]] P = np.array(P).transpose() P_string = transformation_to_string(P, components=('a', 'b', 'c')) p_string = "{},{},{}".format(Fraction(p[0]).limit_denominator(), Fraction(p[1]).limit_denominator(), Fraction(p[2]).limit_denominator()) return P_string + ";" + p_string for i in range(8, 15): try: raw_data[i] = array('b', raw_data[i]) # construct array from sql binary blobs except Exception: # array() behavior changed, need to explicitly convert buffer to str in earlier Python raw_data[i] = array('b', str(raw_data[i])) self._data['og_bns_transform'] = _parse_transformation(raw_data[8]) self._data['bns_operators'] = _parse_operators(raw_data[9]) self._data['bns_lattice'] = _parse_lattice(raw_data[10]) self._data['bns_wyckoff'] = _parse_wyckoff(raw_data[11]) self._data['og_operators'] = _parse_operators(raw_data[12]) self._data['og_lattice'] = _parse_lattice(raw_data[13]) self._data['og_wyckoff'] = _parse_wyckoff(raw_data[14]) db.close() @classmethod def from_og(cls, id): """ Initialize from Opechowski and Guccione (OG) label or number. :param id: OG number supplied as list of 3 ints or or OG label as str :return: """ db = sqlite3.connect(MAGSYMM_DATA) c = db.cursor() if isinstance(id, str): c.execute('SELECT BNS_label FROM space_groups WHERE OG_label=?', (id,)) elif isinstance(id, list): c.execute('SELECT BNS_label FROM space_groups WHERE OG1=? and OG2=? and OG3=?', (id[0], id[1], id[2])) bns_label = c.fetchone()[0] db.close() return cls(bns_label) def __eq__(self, other): return self._data == other._data @property def crystal_system(self): """ :return: Crystal system, e.g., cubic, hexagonal, etc. """ i = self._data["bns_number"][0] if i <= 2: return "triclinic" elif i <= 15: return "monoclinic" elif i <= 74: return "orthorhombic" elif i <= 142: return "tetragonal" elif i <= 167: return "trigonal" elif i <= 194: return "hexagonal" else: return "cubic" @property def sg_symbol(self): """ :return: Space group symbol """ return self._data["bns_label"] @property def symmetry_ops(self): """ Retrieve magnetic symmetry operations of the space group. :return: List of :class:`pymatgen.core.operations.MagSymmOp` """ ops = [op_data['op'] for op_data in self._data['bns_operators']] # add lattice centerings centered_ops = [] lattice_vectors = [l['vector'] for l in self._data['bns_lattice']] for vec in lattice_vectors: if not (np.array_equal(vec, [1, 0, 0]) or np.array_equal(vec, [0, 1, 0]) or np.array_equal(vec, [0, 0, 1])): for op in ops: new_vec = op.translation_vector + vec new_op = MagSymmOp.from_rotation_and_translation_and_time_reversal(op.rotation_matrix, translation_vec=new_vec, time_reversal=op.time_reversal) centered_ops.append(new_op) ops = ops + centered_ops # apply jones faithful transformation ops = [self.jf.transform_symmop(op) for op in ops] return ops def get_orbit(self, p, m, tol=1e-5): """ Returns the orbit for a point and its associated magnetic moment. Args: p: Point as a 3x1 array. m: A magnetic moment, compatible with :class:`pymatgen.electronic_structure.core.Magmom` tol: Tolerance for determining if sites are the same. 1e-5 should be sufficient for most purposes. Set to 0 for exact matching (and also needed for symbolic orbits). Returns: (([array], [array])) Tuple of orbit for point and magnetic moments for orbit. """ orbit = [] orbit_magmoms = [] m = Magmom(m) for o in self.symmetry_ops: pp = o.operate(p) pp = np.mod(np.round(pp, decimals=10), 1) mm = o.operate_magmom(m) if not in_array_list(orbit, pp, tol=tol): orbit.append(pp) orbit_magmoms.append(mm) return orbit, orbit_magmoms def is_compatible(self, lattice, tol=1e-5, angle_tol=5): """ Checks whether a particular lattice is compatible with the *conventional* unit cell. Args: lattice (Lattice): A Lattice. tol (float): The tolerance to check for equality of lengths. angle_tol (float): The tolerance to check for equality of angles in degrees. """ # function from pymatgen.symmetry.groups.SpaceGroup abc = lattice.lengths angles = lattice.angles crys_system = self.crystal_system def check(param, ref, tolerance): return all([abs(i - j) < tolerance for i, j in zip(param, ref) if j is not None]) if crys_system == "cubic": a = abc[0] return check(abc, [a, a, a], tol) and check(angles, [90, 90, 90], angle_tol) elif crys_system == "hexagonal" or (crys_system == "trigonal" and self.symbol.endswith("H")): a = abc[0] return check(abc, [a, a, None], tol) and check(angles, [90, 90, 120], angle_tol) elif crys_system == "trigonal": a = abc[0] return check(abc, [a, a, a], tol) elif crys_system == "tetragonal": a = abc[0] return check(abc, [a, a, None], tol) and check(angles, [90, 90, 90], angle_tol) elif crys_system == "orthorhombic": return check(angles, [90, 90, 90], angle_tol) elif crys_system == "monoclinic": return check(angles, [90, None, 90], angle_tol) return True def data_str(self, include_og=True): """ Get description of all data, including information for OG setting. :return: str """ # __str__() omits information on OG setting to reduce confusion # as to which set of symops are active, this property gives # all stored data including OG setting desc = {} # dictionary to hold description strings description = "" # parse data into strings # indicate if non-standard setting specified if self.jf != JonesFaithfulTransformation.from_transformation_string("a,b,c;0,0,0"): description += "Non-standard setting: .....\n" description += self.jf.__repr__() description += "\n\nStandard setting information: \n" desc['magtype'] = self._data['magtype'] desc['bns_number'] = ".".join(map(str, self._data["bns_number"])) desc['bns_label'] = self._data["bns_label"] desc['og_id'] = ("\t\tOG: " + ".".join(map(str, self._data["og_number"])) + " " + self._data["og_label"] if include_og else '') desc['bns_operators'] = ' '.join([op_data['str'] for op_data in self._data['bns_operators']]) desc['bns_lattice'] = (' '.join([lattice_data['str'] for lattice_data in self._data['bns_lattice'][3:]]) if len(self._data['bns_lattice']) > 3 else '') # don't show (1,0,0)+ (0,1,0)+ (0,0,1)+ desc['bns_wyckoff'] = '\n'.join([textwrap.fill(wyckoff_data['str'], initial_indent=wyckoff_data['label'] + " ", subsequent_indent=" " * len(wyckoff_data['label'] + " "), break_long_words=False, break_on_hyphens=False) for wyckoff_data in self._data['bns_wyckoff']]) desc['og_bns_transformation'] = ('OG-BNS Transform: ({})\n'.format(self._data['og_bns_transform']) if desc['magtype'] == 4 and include_og else '') bns_operators_prefix = "Operators{}: ".format(' (BNS)' if desc['magtype'] == 4 and include_og else '') bns_wyckoff_prefix = "Wyckoff Positions{}: ".format(' (BNS)' if desc['magtype'] == 4 and include_og else '') # apply textwrap on long lines desc['bns_operators'] = textwrap.fill(desc['bns_operators'], initial_indent=bns_operators_prefix, subsequent_indent=" " * len(bns_operators_prefix), break_long_words=False, break_on_hyphens=False) description += ("BNS: {d[bns_number]} {d[bns_label]}{d[og_id]}\n" "{d[og_bns_transformation]}" "{d[bns_operators]}\n" "{bns_wyckoff_prefix}{d[bns_lattice]}\n" "{d[bns_wyckoff]}").format(d=desc, bns_wyckoff_prefix=bns_wyckoff_prefix) if desc['magtype'] == 4 and include_og: desc['og_operators'] = ' '.join([op_data['str'] for op_data in self._data['og_operators']]) # include all lattice vectors because (1,0,0)+ (0,1,0)+ (0,0,1)+ # not always present in OG setting desc['og_lattice'] = ' '.join([lattice_data['str'] for lattice_data in self._data['og_lattice']]) desc['og_wyckoff'] = '\n'.join([textwrap.fill(wyckoff_data['str'], initial_indent=wyckoff_data['label'] + " ", subsequent_indent=" " * len(wyckoff_data['label'] + " "), break_long_words=False, break_on_hyphens=False) for wyckoff_data in self._data['og_wyckoff']]) og_operators_prefix = "Operators (OG): " # apply textwrap on long lines desc['og_operators'] = textwrap.fill(desc['og_operators'], initial_indent=og_operators_prefix, subsequent_indent=" " * len(og_operators_prefix), break_long_words=False, break_on_hyphens=False) description += ("\n{d[og_operators]}\n" "Wyckoff Positions (OG): {d[og_lattice]}\n" "{d[og_wyckoff]}").format(d=desc) elif desc['magtype'] == 4: description += '\nAlternative OG setting exists for this space group.' return description def __str__(self): """ String representation of the space group, specifying the setting of the space group, its magnetic symmetry operators and Wyckoff positions. :return: str """ return self.data_str(include_og=False)
def _write_all_magnetic_space_groups_to_file(filename): """ Write all magnetic space groups to a human-readable text file. Should contain same information as text files provided by ISO-MAG. :param filename: :return: """ s = ('Data parsed from raw data from:\n' 'ISO-MAG, ISOTROPY Software Suite,\n' '\n' 'Used with kind permission from Professor Branton Campbell, BYU\n\n') all_msgs = [] for i in range(1, 1652): all_msgs.append(MagneticSpaceGroup(i)) for msg in all_msgs: s += '\n{}\n\n--------\n'.format(msg.data_str()) f = open(filename, 'w') f.write(s) f.close()