pymatgen.symmetry.maggroups — pymatgen 2020.7.3 documentation

# 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__ = "mkhorton@lbl.gov"
    __status__ = "Beta"
    __date__ = "Feb 2017"

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

    @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, iso.byu.edu
            http://stokes.byu.edu/iso/magnetic_data.txt
            with kind permission from Professor Branton Campbell, BYU

            Data originally compiled from:
            (1) Daniel B. Litvin, Magnetic Group Tables (International Union
                of Crystallography, 2013) www.iucr.org/publ/978-0-9553602-2-0.
            (2) C. J. Bradley and A. P. Cracknell, The Mathematical Theory of
                Symmetry in Solids (Clarendon Press, Oxford, 1972).

            See http://stokes.byu.edu/iso/magneticspacegroupshelp.php 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, iso.byu.edu\n'
             'http://stokes.byu.edu/iso/magnetic_data.txt\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()