Source code for pymatgen.analysis.magnetism.jahnteller

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


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__))


[docs]class JahnTellerAnalyzer: def __init__(self): """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. """ 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"}, }, }
[docs] 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
[docs] 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]
[docs] 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
[docs] 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
[docs] 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
[docs] @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"
[docs] @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