pymatgen.analysis.magnetism.jahnteller — pymatgen 2020.7.3 documentation

# Source code for pymatgen.analysis.magnetism.jahnteller

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

    """
    JahnTeller distortion analysis.
    """

    import os
    import numpy as np

    from pymatgen.core.structure import Structure
    from pymatgen.analysis.local_env import (
        LocalStructOrderParams,
        get_neighbors_of_site_with_index,
    )
    from pymatgen.analysis.bond_valence import BVAnalyzer
    from pymatgen.core.periodic_table import Specie, get_el_sp
    from pymatgen.symmetry.analyzer import SpacegroupAnalyzer
    import warnings

    from typing import Dict, Tuple, Union, Optional, Any

    MODULE_DIR = os.path.dirname(os.path.abspath(__file__))

    class JahnTellerAnalyzer:
        """
        Will attempt to classify if structure *may* be Jahn-Teller active.
        Class currently uses datafile of hard-coded common Jahn-Teller
        active ions.
        If structure is annotated with magnetic moments, will estimate
        if structure may be high-spin or low-spin.
        Class aims for more false-positives than false-negatives.
        """
        def __init__(self):
            """
            Init for JahnTellerAnalyzer.
            """

            self.spin_configs = {
                "oct": {  # key is number of d electrons
                    0: {"high": {"e_g": 0, "t_2g": 0}, "default": "high"},
                    1: {"high": {"e_g": 0, "t_2g": 1}, "default": "high"},  # weak J-T
                    2: {"high": {"e_g": 0, "t_2g": 2}, "default": "high"},  # weak
                    3: {"high": {"e_g": 0, "t_2g": 3}, "default": "high"},  # no J-T
                    4: {
                        "high": {"e_g": 1, "t_2g": 3},
                        "low": {"e_g": 0, "t_2g": 4},
                        "default": "high",
                    },  # strong high, weak low
                    5: {
                        "high": {"e_g": 2, "t_2g": 3},
                        "low": {"e_g": 0, "t_2g": 5},
                        "default": "low",
                    },  # no high, weak low
                    6: {
                        "high": {"e_g": 2, "t_2g": 4},
                        "low": {"e_g": 0, "t_2g": 6},
                        "default": "high",
                    },  # weak high, no low
                    7: {
                        "high": {"e_g": 2, "t_2g": 5},
                        "low": {"e_g": 1, "t_2g": 6},
                        "default": "low",
                    },  # weak high, strong low
                    8: {"high": {"e_g": 2, "t_2g": 6}, "default": "high"},  # no
                    9: {"high": {"e_g": 3, "t_2g": 6}, "default": "high"},  # strong
                    10: {"high": {"e_g": 4, "t_2g": 6}, "default": "high"},
                },
                "tet": {  # no low spin observed experimentally in tetrahedral, all weak J-T
                    0: {"high": {"e": 0, "t_2": 0}, "default": "high"},
                    1: {"high": {"e": 1, "t_2": 0}, "default": "high"},
                    2: {"high": {"e": 2, "t_2": 0}, "default": "high"},
                    3: {"high": {"e": 2, "t_2": 1}, "default": "high"},
                    4: {"high": {"e": 2, "t_2": 2}, "default": "high"},
                    5: {"high": {"e": 2, "t_2": 3}, "default": "high"},
                    6: {"high": {"e": 3, "t_2": 3}, "default": "high"},
                    7: {"high": {"e": 4, "t_2": 3}, "default": "high"},
                    8: {"high": {"e": 4, "t_2": 4}, "default": "high"},
                    9: {"high": {"e": 4, "t_2": 5}, "default": "high"},
                    10: {"high": {"e": 4, "t_2": 6}, "default": "high"},
                },
            }

        def get_analysis_and_structure(
            self,
            structure: Structure,
            calculate_valences: bool = True,
            guesstimate_spin: bool = False,
            op_threshold: float = 0.1,
        ) -> Tuple[Dict, Structure]:
            """Obtain an analysis of a given structure and if it may be Jahn-Teller
            active or not. This is a heuristic, and may give false positives and
            false negatives (false positives are preferred).

            Args:
                structure: input structure
                calculate_valences: whether to attempt to calculate valences or not, structure
                    should have oxidation states to perform analysis (Default value = True)
                guesstimate_spin: whether to guesstimate spin state from magnetic moments
                    or not, use with caution (Default value = False)
                op_threshold: threshold for order parameter above which to consider site
                    to match an octahedral or tetrahedral motif, since Jahn-Teller structures
                    can often be
                    quite distorted, this threshold is smaller than one might expect

            Returns:
                analysis of structure, with key 'strength' which may be 'none', 'strong',
                'weak', or 'unknown' (Default value = 0.1) and decorated structure

            """

            structure = structure.get_primitive_structure()

            if calculate_valences:
                bva = BVAnalyzer()
                structure = bva.get_oxi_state_decorated_structure(structure)

            # no point testing multiple equivalent sites, doesn't make any difference to analysis
            # but makes returned
            symmetrized_structure = SpacegroupAnalyzer(
                structure
            ).get_symmetrized_structure()

            # to detect structural motifs of a given site
            op = LocalStructOrderParams(["oct", "tet"])

            # dict of site index to the Jahn-Teller analysis of that site
            jt_sites = []
            non_jt_sites = []

            for indices in symmetrized_structure.equivalent_indices:

                idx = indices[0]
                site = symmetrized_structure[idx]

                # only interested in sites with oxidation states
                if (
                    isinstance(site.specie, Specie)
                    and site.specie.element.is_transition_metal
                ):

                    # get motif around site
                    order_params = op.get_order_parameters(symmetrized_structure, idx)

                    if order_params[0] > order_params[1] and order_params[0] > op_threshold:
                        motif = "oct"
                        motif_order_parameter = order_params[0]
                    elif order_params[1] > op_threshold:
                        motif = "tet"
                        motif_order_parameter = order_params[1]
                    else:
                        motif = "unknown"
                        motif_order_parameter = None

                    if motif == "oct" or motif == "tet":

                        # guess spin of metal ion
                        if guesstimate_spin and "magmom" in site.properties:

                            # estimate if high spin or low spin
                            magmom = site.properties["magmom"]
                            spin_state = self._estimate_spin_state(
                                site.specie, motif, magmom
                            )
                        else:
                            spin_state = "unknown"

                        magnitude = self.get_magnitude_of_effect_from_species(
                            site.specie, spin_state, motif
                        )

                        if magnitude != "none":

                            ligands = get_neighbors_of_site_with_index(
                                structure, idx, approach="min_dist", delta=0.15
                            )
                            ligand_bond_lengths = [
                                ligand.distance(structure[idx]) for ligand in ligands
                            ]
                            ligands_species = list(
                                set([str(ligand.specie) for ligand in ligands])
                            )
                            ligand_bond_length_spread = max(ligand_bond_lengths) - min(
                                ligand_bond_lengths
                            )

                            def trim(f):
                                """
                                Avoid storing to unreasonable precision, hurts readability.
                                """
                                return float("{:.4f}".format(f))

                            # to be Jahn-Teller active, all ligands have to be the same
                            if len(ligands_species) == 1:
                                jt_sites.append(
                                    {
                                        "strength": magnitude,
                                        "motif": motif,
                                        "motif_order_parameter": trim(
                                            motif_order_parameter
                                        ),
                                        "spin_state": spin_state,
                                        "species": str(site.specie),
                                        "ligand": ligands_species[0],
                                        "ligand_bond_lengths": [
                                            trim(length) for length in ligand_bond_lengths
                                        ],
                                        "ligand_bond_length_spread": trim(
                                            ligand_bond_length_spread
                                        ),
                                        "site_indices": indices,
                                    }
                                )

                        # store reasons for not being J-T active
                        else:
                            non_jt_sites.append(
                                {
                                    "site_indices": indices,
                                    "strength": "none",
                                    "reason": "Not Jahn-Teller active for this "
                                    "electronic configuration.",
                                }
                            )
                    else:
                        non_jt_sites.append(
                            {
                                "site_indices": indices,
                                "strength": "none",
                                "reason": "motif is {}".format(motif),
                            }
                        )

            # perform aggregation of all sites
            if jt_sites:
                analysis = {"active": True}  # type: Dict[str, Any]
                # if any site could exhibit 'strong' Jahn-Teller effect
                # then mark whole structure as strong
                strong_magnitudes = [site["strength"] == "strong" for site in jt_sites]
                if any(strong_magnitudes):
                    analysis["strength"] = "strong"
                else:
                    analysis["strength"] = "weak"
                analysis["sites"] = jt_sites
                return analysis, structure
            else:
                return {"active": False, "sites": non_jt_sites}, structure

        def get_analysis(
            self,
            structure: Structure,
            calculate_valences: bool = True,
            guesstimate_spin: bool = False,
            op_threshold: float = 0.1,
        ) -> Dict:
            """
            Convenience method, uses get_analysis_and_structure method.

            Obtain an analysis of a given structure and if it may be Jahn-Teller
            active or not. This is a heuristic, and may give false positives and
            false negatives (false positives are preferred).

            Args:
                structure: input structure
                calculate_valences: whether to attempt to calculate valences or not, structure
                    should have oxidation states to perform analysis (Default value = True)
                guesstimate_spin: whether to guesstimate spin state from magnetic moments
                    or not, use with caution (Default value = False)
                op_threshold: threshold for order parameter above which to consider site
                    to match an octahedral or tetrahedral motif, since Jahn-Teller structures
                    can often be
                    quite distorted, this threshold is smaller than one might expect

            Returns:
                analysis of structure, with key 'strength' which may be 'none', 'strong',
                'weak', or 'unknown' (Default value = 0.1)
            """
            return self.get_analysis_and_structure(
                structure,
                calculate_valences=calculate_valences,
                guesstimate_spin=guesstimate_spin,
                op_threshold=op_threshold,
            )[0]

        def is_jahn_teller_active(
            self,
            structure: Structure,
            calculate_valences: bool = True,
            guesstimate_spin: bool = False,
            op_threshold: float = 0.1,
        ) -> bool:
            """
            Convenience method, uses get_analysis_and_structure method.
            Check if a given structure and if it may be Jahn-Teller
            active or not. This is a heuristic, and may give false positives and
            false negatives (false positives are preferred).

            Args:
                structure: input structure
                calculate_valences: whether to attempt to calculate valences or not, structure
                    should have oxidation states to perform analysis (Default value = True)
                guesstimate_spin: whether to guesstimate spin state from magnetic moments
                    or not, use with caution (Default value = False)
                op_threshold: threshold for order parameter above which to consider site
                    to match an octahedral or tetrahedral motif, since Jahn-Teller structures
                    can often be
                    quite distorted, this threshold is smaller than one might expect

            Returns:
                boolean, True if might be Jahn-Teller active, False if not
            """

            active = False

            try:
                analysis = self.get_analysis(
                    structure,
                    calculate_valences=calculate_valences,
                    guesstimate_spin=guesstimate_spin,
                    op_threshold=op_threshold,
                )
                active = analysis["active"]
            except Exception as e:
                warnings.warn(
                    "Error analyzing {}: {}".format(
                        structure.composition.reduced_formula, e
                    )
                )

            return active

        def tag_structure(
            self,
            structure: Structure,
            calculate_valences: bool = True,
            guesstimate_spin: bool = False,
            op_threshold: float = 0.1,
        ) -> Structure:
            """
            Convenience method, uses get_analysis_and_structure method.
            Add a "possible_jt_active" site property on Structure.

            Args:
                structure: input structure
                calculate_valences: whether to attempt to calculate valences or not, structure
                    should have oxidation states to perform analysis (Default value = True)
                guesstimate_spin: whether to guesstimate spin state from magnetic moments
                    or not, use with caution (Default value = False)
                op_threshold: threshold for order parameter above which to consider site
                    to match an octahedral or tetrahedral motif, since Jahn-Teller structures
                    can often be
                    quite distorted, this threshold is smaller than one might expect

            Returns:
                Decorated Structure, will be in primitive setting.

            """
            try:
                analysis, structure = self.get_analysis_and_structure(
                    structure,
                    calculate_valences=calculate_valences,
                    guesstimate_spin=guesstimate_spin,
                    op_threshold=op_threshold,
                )
                jt_sites = [False] * len(structure)
                if analysis["active"]:
                    for site in analysis["sites"]:
                        for index in site["site_indices"]:
                            jt_sites[index] = True
                            structure.add_site_property("possible_jt_active", jt_sites)
                return structure
            except Exception as e:
                warnings.warn(
                    "Error analyzing {}: {}".format(
                        structure.composition.reduced_formula, e
                    )
                )
                return structure

        @staticmethod
        def _get_number_of_d_electrons(species: Specie) -> float:
            """
            Get number of d electrons of a species.

            Args:
              species: Specie object

            Returns: Number of d electrons.
            """

            # TODO: replace with more generic Hund's rule algorithm?

            # taken from get_crystal_field_spin
            elec = species.full_electronic_structure
            if len(elec) < 4 or elec[-1][1] != "s" or elec[-2][1] != "d":
                raise AttributeError(
                    "Invalid element {} for crystal field calculation.".format(
                        species.symbol
                    )
                )
            nelectrons = int(elec[-1][2] + elec[-2][2] - species.oxi_state)
            if nelectrons < 0 or nelectrons > 10:
                raise AttributeError(
                    "Invalid oxidation state {} for element {}".format(
                        species.oxi_state, species.symbol
                    )
                )

            return nelectrons

        def get_magnitude_of_effect_from_species(
            self, species: Union[str, Specie], spin_state: str, motif: str
        ) -> str:
            """
            Get magnitude of Jahn-Teller effect from provided species, spin state and motif.

            Args:
              species: e.g. Fe2+
              spin_state: "high" or "low"
              motif: "oct" or "tet"

            Returns: "none", "weak" or "strong

            """

            magnitude = "none"

            sp = get_el_sp(species)

            # has to be Specie; we need to know the oxidation state
            if isinstance(sp, Specie) and sp.element.is_transition_metal:

                d_electrons = self._get_number_of_d_electrons(sp)

                if motif in self.spin_configs:
                    if spin_state not in self.spin_configs[motif][d_electrons]:
                        spin_state = self.spin_configs[motif][d_electrons]["default"]
                    spin_config = self.spin_configs[motif][d_electrons][spin_state]
                    magnitude = JahnTellerAnalyzer.get_magnitude_of_effect_from_spin_config(
                        motif, spin_config
                    )
            else:
                warnings.warn("No data for this species.")

            return magnitude

        @staticmethod
        def get_magnitude_of_effect_from_spin_config(
            motif: str, spin_config: Dict[str, float]
        ) -> str:
            """
            Roughly, the magnitude of Jahn-Teller distortion will be:
            * in octahedral environments, strong if e_g orbitals
            unevenly occupied but weak if t_2g orbitals unevenly
            occupied
            * in tetrahedral environments always weaker

            Args:
              motif: "oct" or "tet"
              spin_config: dict of 'e' (e_g) and 't' (t2_g)
                with number of electrons in each state

            Returns:  "none", "weak" or "strong"
            """
            magnitude = "none"
            if motif == "oct":
                e_g = spin_config["e_g"]
                t_2g = spin_config["t_2g"]
                if (e_g % 2 != 0) or (t_2g % 3 != 0):
                    magnitude = "weak"
                    if e_g % 2 == 1:
                        magnitude = "strong"
            elif motif == "tet":
                e = spin_config["e"]
                t_2 = spin_config["t_2"]
                if (e % 3 != 0) or (t_2 % 2 != 0):
                    magnitude = "weak"
            return magnitude

        @staticmethod
        def _estimate_spin_state(
            species: Union[str, Specie], motif: str, known_magmom: float
        ) -> str:
            """Simple heuristic to estimate spin state. If magnetic moment
            is sufficiently close to that predicted for a given spin state,
            we assign it that state. If we only have data for one spin
            state then that's the one we use (e.g. we assume all tetrahedral
            complexes are high-spin, since this is typically the case).

            Args:
              species: str or Species
              motif: "oct" or "tet"
              known_magmom: magnetic moment in Bohr magnetons

            Returns: "undefined" (if only one spin state possible), "low",
            "high" or "unknown"
            """
            mu_so_high = JahnTellerAnalyzer.mu_so(species, motif=motif, spin_state="high")
            mu_so_low = JahnTellerAnalyzer.mu_so(species, motif=motif, spin_state="low")
            if mu_so_high == mu_so_low:
                return "undefined"  # undefined or only one spin state possible
            elif mu_so_high is None:
                return "low"
            elif mu_so_low is None:
                return "high"
            else:
                diff = mu_so_high - mu_so_low
                # WARNING! this heuristic has not been robustly tested or benchmarked
                # using 'diff*0.25' as arbitrary measure, if known magmom is
                # too far away from expected value, we don't try to classify it
                if (
                    known_magmom > mu_so_high
                    or abs(mu_so_high - known_magmom) < diff * 0.25
                ):
                    return "high"
                elif (
                    known_magmom < mu_so_low or abs(mu_so_low - known_magmom) < diff * 0.25
                ):
                    return "low"
                else:
                    return "unknown"

        @staticmethod
        def mu_so(
            species: Union[str, Specie], motif: str, spin_state: str
        ) -> Optional[float]:
            """Calculates the spin-only magnetic moment for a
            given species. Only supports transition metals.

            Args:
              species: Species
              motif: "oct" or "tet"
              spin_state: "high" or "low"

            Returns:
              Spin-only magnetic moment in Bohr magnetons or None if
              species crystal field not defined
            """
            try:
                sp = get_el_sp(species)
                n = sp.get_crystal_field_spin(coordination=motif, spin_config=spin_state)
                # calculation spin-only magnetic moment for this number of unpaired spins
                return np.sqrt(n * (n + 2))
            except AttributeError:
                return None