pymatgen.analysis namespace — pymatgen 2026.3.9 documentation

# pymatgen.analysis namespace

## Subpackages

- pymatgen.analysis.chemenv package
  - Subpackages
    - pymatgen.analysis.chemenv.connectivity package
      - Submodules
      - pymatgen.analysis.chemenv.connectivity.connected_components module
        - `ConnectedComponent`
          - `ConnectedComponent.as_dict()`
          - `ConnectedComponent.compute_periodicity()`
          - `ConnectedComponent.compute_periodicity_all_simple_paths_algorithm()`
          - `ConnectedComponent.compute_periodicity_cycle_basis()`
          - `ConnectedComponent.coordination_sequence()`
          - `ConnectedComponent.description()`
          - `ConnectedComponent.elastic_centered_graph()`
          - `ConnectedComponent.from_dict()`
          - `ConnectedComponent.from_graph()`
          - `ConnectedComponent.graph`
          - `ConnectedComponent.is_0d`
          - `ConnectedComponent.is_1d`
          - `ConnectedComponent.is_2d`
          - `ConnectedComponent.is_3d`
          - `ConnectedComponent.is_periodic`
          - `ConnectedComponent.make_supergraph()`
          - `ConnectedComponent.periodicity`
          - `ConnectedComponent.periodicity_vectors`
          - `ConnectedComponent.show_graph()`
        - `draw_network()`
        - `make_supergraph()`
      - pymatgen.analysis.chemenv.connectivity.connectivity_finder module
        - `ConnectivityFinder`
          - `ConnectivityFinder.get_structure_connectivity()`
          - `ConnectivityFinder.setup_parameters()`
      - pymatgen.analysis.chemenv.connectivity.environment_nodes module
        - `AbstractEnvironmentNode`
          - `AbstractEnvironmentNode.ATOM`
          - `AbstractEnvironmentNode.CE_NNBCES_NBCES_LIGANDS`
          - `AbstractEnvironmentNode.COORDINATION_ENVIRONMENT`
          - `AbstractEnvironmentNode.DEFAULT_EXTENSIONS`
          - `AbstractEnvironmentNode.LIGANDS_ARRANGEMENT`
          - `AbstractEnvironmentNode.NEIGHBORING_CES`
          - `AbstractEnvironmentNode.NEIGHBORING_COORDINATION_ENVIRONMENTS`
          - `AbstractEnvironmentNode.NEIGHBORS_LIGANDS_ARRANGEMENT`
          - `AbstractEnvironmentNode.NUMBER_OF_LIGANDS_FOR_EACH_NEIGHBORING_CE`
          - `AbstractEnvironmentNode.NUMBER_OF_LIGANDS_FOR_EACH_NEIGHBORING_COORDINATION_ENVIRONMENT`
          - `AbstractEnvironmentNode.NUMBER_OF_NEIGHBORING_CES`
          - `AbstractEnvironmentNode.NUMBER_OF_NEIGHBORING_COORDINATION_ENVIRONMENTS`
          - `AbstractEnvironmentNode.atom_symbol`
          - `AbstractEnvironmentNode.ce`
          - `AbstractEnvironmentNode.ce_symbol`
          - `AbstractEnvironmentNode.coordination_environment`
          - `AbstractEnvironmentNode.everything_equal()`
          - `AbstractEnvironmentNode.isite`
          - `AbstractEnvironmentNode.mp_symbol`
        - `EnvironmentNode`
          - `EnvironmentNode.coordination_environment`
          - `EnvironmentNode.everything_equal()`
        - `get_environment_node()`
      - pymatgen.analysis.chemenv.connectivity.structure_connectivity module
        - `StructureConnectivity`
          - `StructureConnectivity.add_bonds()`
          - `StructureConnectivity.add_sites()`
          - `StructureConnectivity.as_dict()`
          - `StructureConnectivity.environment_subgraph()`
          - `StructureConnectivity.from_dict()`
          - `StructureConnectivity.get_connected_components()`
          - `StructureConnectivity.print_links()`
          - `StructureConnectivity.setup_atom_environment_subgraph()`
          - `StructureConnectivity.setup_atom_environments_subgraph()`
          - `StructureConnectivity.setup_connectivity_description()`
          - `StructureConnectivity.setup_environment_subgraph()`
          - `StructureConnectivity.setup_environments_subgraph()`
        - `get_delta_image()`
    - pymatgen.analysis.chemenv.coordination_environments package
      - Subpackages
        - pymatgen.analysis.chemenv.coordination_environments.coordination_geometries_files package
      - Submodules
      - pymatgen.analysis.chemenv.coordination_environments.chemenv_strategies module
        - `AbstractChemenvStrategy`
          - `AbstractChemenvStrategy.AC`
          - `AbstractChemenvStrategy.DEFAULT_SYMMETRY_MEASURE_TYPE`
          - `AbstractChemenvStrategy.STRATEGY_DESCRIPTION`
          - `AbstractChemenvStrategy.STRATEGY_INFO_FIELDS`
          - `AbstractChemenvStrategy.STRATEGY_OPTIONS`
          - `AbstractChemenvStrategy.as_dict()`
          - `AbstractChemenvStrategy.equivalent_site_index_and_transform()`
          - `AbstractChemenvStrategy.from_dict()`
          - `AbstractChemenvStrategy.get_site_ce_fractions_and_neighbors()`
          - `AbstractChemenvStrategy.get_site_coordination_environment()`
          - `AbstractChemenvStrategy.get_site_coordination_environments()`
          - `AbstractChemenvStrategy.get_site_coordination_environments_fractions()`
          - `AbstractChemenvStrategy.get_site_neighbors()`
          - `AbstractChemenvStrategy.prepare_symmetries()`
          - `AbstractChemenvStrategy.set_option()`
          - `AbstractChemenvStrategy.set_structure_environments()`
          - `AbstractChemenvStrategy.setup_options()`
          - `AbstractChemenvStrategy.symmetry_measure_type`
          - `AbstractChemenvStrategy.uniquely_determines_coordination_environments`
        - `AdditionalConditionInt`
          - `AdditionalConditionInt.allowed_values`
          - `AdditionalConditionInt.as_dict()`
          - `AdditionalConditionInt.description`
          - `AdditionalConditionInt.from_dict()`
          - `AdditionalConditionInt.integer`
        - `AngleCutoffFloat`
          - `AngleCutoffFloat.allowed_values`
          - `AngleCutoffFloat.as_dict()`
          - `AngleCutoffFloat.from_dict()`
        - `AngleNbSetWeight`
          - `AngleNbSetWeight.SHORT_NAME`
          - `AngleNbSetWeight.angle_sum()`
          - `AngleNbSetWeight.angle_sumn()`
          - `AngleNbSetWeight.as_dict()`
          - `AngleNbSetWeight.from_dict()`
          - `AngleNbSetWeight.weight()`
        - `AnglePlateauNbSetWeight`
          - `AnglePlateauNbSetWeight.SHORT_NAME`
          - `AnglePlateauNbSetWeight.as_dict()`
          - `AnglePlateauNbSetWeight.from_dict()`
          - `AnglePlateauNbSetWeight.weight()`
        - `CNBiasNbSetWeight`
          - `CNBiasNbSetWeight.SHORT_NAME`
          - `CNBiasNbSetWeight.as_dict()`
          - `CNBiasNbSetWeight.explicit()`
          - `CNBiasNbSetWeight.from_description()`
          - `CNBiasNbSetWeight.from_dict()`
          - `CNBiasNbSetWeight.geometrically_equidistant()`
          - `CNBiasNbSetWeight.linearly_equidistant()`
          - `CNBiasNbSetWeight.weight()`
        - `CSMFloat`
          - `CSMFloat.allowed_values`
          - `CSMFloat.as_dict()`
          - `CSMFloat.from_dict()`
        - `DeltaCSMNbSetWeight`
          - `DeltaCSMNbSetWeight.DEFAULT_EFFECTIVE_CSM_ESTIMATOR`
          - `DeltaCSMNbSetWeight.DEFAULT_SYMMETRY_MEASURE_TYPE`
          - `DeltaCSMNbSetWeight.DEFAULT_WEIGHT_ESTIMATOR`
          - `DeltaCSMNbSetWeight.SHORT_NAME`
          - `DeltaCSMNbSetWeight.as_dict()`
          - `DeltaCSMNbSetWeight.delta_cn_specifics()`
          - `DeltaCSMNbSetWeight.from_dict()`
          - `DeltaCSMNbSetWeight.weight()`
        - `DeltaDistanceNbSetWeight`
          - `DeltaDistanceNbSetWeight.SHORT_NAME`
          - `DeltaDistanceNbSetWeight.as_dict()`
          - `DeltaDistanceNbSetWeight.from_dict()`
          - `DeltaDistanceNbSetWeight.weight()`
        - `DistanceAngleAreaNbSetWeight`
          - `DistanceAngleAreaNbSetWeight.AC`
          - `DistanceAngleAreaNbSetWeight.DEFAULT_SURFACE_DEFINITION`
          - `DistanceAngleAreaNbSetWeight.SHORT_NAME`
          - `DistanceAngleAreaNbSetWeight.as_dict()`
          - `DistanceAngleAreaNbSetWeight.from_dict()`
          - `DistanceAngleAreaNbSetWeight.rectangle_crosses_area()`
          - `DistanceAngleAreaNbSetWeight.w_area_has_intersection()`
          - `DistanceAngleAreaNbSetWeight.w_area_intersection_nbsfh_fbs_onb0()`
          - `DistanceAngleAreaNbSetWeight.weight()`
        - `DistanceCutoffFloat`
          - `DistanceCutoffFloat.allowed_values`
          - `DistanceCutoffFloat.as_dict()`
          - `DistanceCutoffFloat.from_dict()`
        - `DistanceNbSetWeight`
          - `DistanceNbSetWeight.SHORT_NAME`
          - `DistanceNbSetWeight.as_dict()`
          - `DistanceNbSetWeight.from_dict()`
          - `DistanceNbSetWeight.weight()`
        - `DistancePlateauNbSetWeight`
          - `DistancePlateauNbSetWeight.SHORT_NAME`
          - `DistancePlateauNbSetWeight.as_dict()`
          - `DistancePlateauNbSetWeight.from_dict()`
          - `DistancePlateauNbSetWeight.weight()`
        - `MultiWeightsChemenvStrategy`
          - `MultiWeightsChemenvStrategy.DEFAULT_CE_ESTIMATOR`
          - `MultiWeightsChemenvStrategy.STRATEGY_DESCRIPTION`
          - `MultiWeightsChemenvStrategy.as_dict()`
          - `MultiWeightsChemenvStrategy.from_dict()`
          - `MultiWeightsChemenvStrategy.stats_article_weights_parameters()`
          - `MultiWeightsChemenvStrategy.uniquely_determines_coordination_environments`
        - `NbSetWeight`
          - `NbSetWeight.as_dict()`
          - `NbSetWeight.weight()`
        - `NormalizedAngleDistanceNbSetWeight`
          - `NormalizedAngleDistanceNbSetWeight.SHORT_NAME`
          - `NormalizedAngleDistanceNbSetWeight.ang()`
          - `NormalizedAngleDistanceNbSetWeight.anginvdist()`
          - `NormalizedAngleDistanceNbSetWeight.anginvndist()`
          - `NormalizedAngleDistanceNbSetWeight.angn()`
          - `NormalizedAngleDistanceNbSetWeight.angninvdist()`
          - `NormalizedAngleDistanceNbSetWeight.angninvndist()`
          - `NormalizedAngleDistanceNbSetWeight.as_dict()`
          - `NormalizedAngleDistanceNbSetWeight.aweight()`
          - `NormalizedAngleDistanceNbSetWeight.from_dict()`
          - `NormalizedAngleDistanceNbSetWeight.gweight()`
          - `NormalizedAngleDistanceNbSetWeight.invdist()`
          - `NormalizedAngleDistanceNbSetWeight.invndist()`
          - `NormalizedAngleDistanceNbSetWeight.weight()`
        - `SelfCSMNbSetWeight`
          - `SelfCSMNbSetWeight.DEFAULT_EFFECTIVE_CSM_ESTIMATOR`
          - `SelfCSMNbSetWeight.DEFAULT_SYMMETRY_MEASURE_TYPE`
          - `SelfCSMNbSetWeight.DEFAULT_WEIGHT_ESTIMATOR`
          - `SelfCSMNbSetWeight.SHORT_NAME`
          - `SelfCSMNbSetWeight.as_dict()`
          - `SelfCSMNbSetWeight.from_dict()`
          - `SelfCSMNbSetWeight.weight()`
        - `SimpleAbundanceChemenvStrategy`
          - `SimpleAbundanceChemenvStrategy.DEFAULT_ADDITIONAL_CONDITION`
          - `SimpleAbundanceChemenvStrategy.DEFAULT_MAX_DIST`
          - `SimpleAbundanceChemenvStrategy.STRATEGY_DESCRIPTION`
          - `SimpleAbundanceChemenvStrategy.STRATEGY_OPTIONS`
          - `SimpleAbundanceChemenvStrategy.as_dict()`
          - `SimpleAbundanceChemenvStrategy.from_dict()`
          - `SimpleAbundanceChemenvStrategy.get_site_coordination_environment()`
          - `SimpleAbundanceChemenvStrategy.get_site_coordination_environments()`
          - `SimpleAbundanceChemenvStrategy.get_site_neighbors()`
          - `SimpleAbundanceChemenvStrategy.uniquely_determines_coordination_environments`
        - `SimplestChemenvStrategy`
          - `SimplestChemenvStrategy.DEFAULT_ADDITIONAL_CONDITION`
          - `SimplestChemenvStrategy.DEFAULT_ANGLE_CUTOFF`
          - `SimplestChemenvStrategy.DEFAULT_CONTINUOUS_SYMMETRY_MEASURE_CUTOFF`
          - `SimplestChemenvStrategy.DEFAULT_DISTANCE_CUTOFF`
          - `SimplestChemenvStrategy.STRATEGY_DESCRIPTION`
          - `SimplestChemenvStrategy.STRATEGY_OPTIONS`
          - `SimplestChemenvStrategy.add_strategy_visualization_to_subplot()`
          - `SimplestChemenvStrategy.additional_condition`
          - `SimplestChemenvStrategy.angle_cutoff`
          - `SimplestChemenvStrategy.as_dict()`
          - `SimplestChemenvStrategy.continuous_symmetry_measure_cutoff`
          - `SimplestChemenvStrategy.distance_cutoff`
          - `SimplestChemenvStrategy.from_dict()`
          - `SimplestChemenvStrategy.get_site_coordination_environment()`
          - `SimplestChemenvStrategy.get_site_coordination_environments()`
          - `SimplestChemenvStrategy.get_site_coordination_environments_fractions()`
          - `SimplestChemenvStrategy.get_site_neighbors()`
          - `SimplestChemenvStrategy.uniquely_determines_coordination_environments`
        - `StrategyOption`
          - `StrategyOption.allowed_values`
          - `StrategyOption.as_dict()`
        - `TargetedPenaltiedAbundanceChemenvStrategy`
          - `TargetedPenaltiedAbundanceChemenvStrategy.DEFAULT_TARGET_ENVIRONMENTS`
          - `TargetedPenaltiedAbundanceChemenvStrategy.as_dict()`
          - `TargetedPenaltiedAbundanceChemenvStrategy.from_dict()`
          - `TargetedPenaltiedAbundanceChemenvStrategy.get_site_coordination_environment()`
          - `TargetedPenaltiedAbundanceChemenvStrategy.uniquely_determines_coordination_environments`
        - `WeightedNbSetChemenvStrategy`
          - `WeightedNbSetChemenvStrategy.DEFAULT_CE_ESTIMATOR`
          - `WeightedNbSetChemenvStrategy.STRATEGY_DESCRIPTION`
          - `WeightedNbSetChemenvStrategy.as_dict()`
          - `WeightedNbSetChemenvStrategy.from_dict()`
          - `WeightedNbSetChemenvStrategy.get_site_coordination_environment()`
          - `WeightedNbSetChemenvStrategy.get_site_coordination_environments()`
          - `WeightedNbSetChemenvStrategy.get_site_coordination_environments_fractions()`
          - `WeightedNbSetChemenvStrategy.get_site_neighbors()`
          - `WeightedNbSetChemenvStrategy.uniquely_determines_coordination_environments`
        - `get_effective_csm()`
        - `set_info()`
      - pymatgen.analysis.chemenv.coordination_environments.coordination_geometries module
        - `AbstractChemenvAlgorithm`
          - `AbstractChemenvAlgorithm.algorithm_type`
          - `AbstractChemenvAlgorithm.as_dict()`
        - `AllCoordinationGeometries`
          - `AllCoordinationGeometries.get_geometries()`
          - `AllCoordinationGeometries.get_geometry_from_IUCr_symbol()`
          - `AllCoordinationGeometries.get_geometry_from_IUPAC_symbol()`
          - `AllCoordinationGeometries.get_geometry_from_mp_symbol()`
          - `AllCoordinationGeometries.get_geometry_from_name()`
          - `AllCoordinationGeometries.get_implemented_geometries()`
          - `AllCoordinationGeometries.get_not_implemented_geometries()`
          - `AllCoordinationGeometries.get_symbol_cn_mapping()`
          - `AllCoordinationGeometries.get_symbol_name_mapping()`
          - `AllCoordinationGeometries.is_a_valid_coordination_geometry()`
          - `AllCoordinationGeometries.pretty_print()`
        - `CoordinationGeometry`
          - `CoordinationGeometry.CSM_SKIP_SEPARATION_PLANE_ALGO`
          - `CoordinationGeometry.IUCr_symbol`
          - `CoordinationGeometry.IUCr_symbol_str`
          - `CoordinationGeometry.IUPAC_symbol`
          - `CoordinationGeometry.IUPAC_symbol_str`
          - `CoordinationGeometry.NeighborsSetsHints`
            - `CoordinationGeometry.NeighborsSetsHints.ALLOWED_HINTS_TYPES`
            - `CoordinationGeometry.NeighborsSetsHints.as_dict()`
            - `CoordinationGeometry.NeighborsSetsHints.double_cap_hints()`
            - `CoordinationGeometry.NeighborsSetsHints.from_dict()`
            - `CoordinationGeometry.NeighborsSetsHints.hints()`
            - `CoordinationGeometry.NeighborsSetsHints.single_cap_hints()`
            - `CoordinationGeometry.NeighborsSetsHints.triple_cap_hints()`
          - `CoordinationGeometry.algorithms`
          - `CoordinationGeometry.as_dict()`
          - `CoordinationGeometry.ce_symbol`
          - `CoordinationGeometry.coordination_number`
          - `CoordinationGeometry.distfactor_max`
          - `CoordinationGeometry.edges()`
          - `CoordinationGeometry.faces()`
          - `CoordinationGeometry.from_dict()`
          - `CoordinationGeometry.get_central_site()`
          - `CoordinationGeometry.get_coordination_number()`
          - `CoordinationGeometry.get_name()`
          - `CoordinationGeometry.get_pmeshes()`
          - `CoordinationGeometry.is_implemented()`
          - `CoordinationGeometry.mp_symbol`
          - `CoordinationGeometry.number_of_permutations`
          - `CoordinationGeometry.pauling_stability_ratio`
          - `CoordinationGeometry.ref_permutation()`
          - `CoordinationGeometry.solid_angles()`
        - `ExplicitPermutationsAlgorithm`
          - `ExplicitPermutationsAlgorithm.as_dict()`
          - `ExplicitPermutationsAlgorithm.from_dict()`
          - `ExplicitPermutationsAlgorithm.permutations`
        - `SeparationPlane`
          - `SeparationPlane.argsorted_ref_separation_perm`
          - `SeparationPlane.as_dict()`
          - `SeparationPlane.from_dict()`
          - `SeparationPlane.permutations`
          - `SeparationPlane.ref_separation_perm`
          - `SeparationPlane.safe_separation_permutations()`
      - pymatgen.analysis.chemenv.coordination_environments.coordination_geometry_finder module
        - `AbstractGeometry`
          - `AbstractGeometry.cn`
          - `AbstractGeometry.coordination_number`
          - `AbstractGeometry.from_cg()`
          - `AbstractGeometry.points_wcs_csc()`
          - `AbstractGeometry.points_wcs_ctwcc()`
          - `AbstractGeometry.points_wcs_ctwocc()`
          - `AbstractGeometry.points_wocs_csc()`
          - `AbstractGeometry.points_wocs_ctwcc()`
          - `AbstractGeometry.points_wocs_ctwocc()`
        - `LocalGeometryFinder`
          - `LocalGeometryFinder.BVA_DISTANCE_SCALE_FACTORS`
          - `LocalGeometryFinder.DEFAULT_BVA_DISTANCE_SCALE_FACTOR`
          - `LocalGeometryFinder.DEFAULT_SPG_ANALYZER_OPTIONS`
          - `LocalGeometryFinder.DEFAULT_STRATEGY`
          - `LocalGeometryFinder.PRESETS`
          - `LocalGeometryFinder.STRUCTURE_REFINEMENT_NONE`
          - `LocalGeometryFinder.STRUCTURE_REFINEMENT_REFINED`
          - `LocalGeometryFinder.STRUCTURE_REFINEMENT_SYMMETRIZED`
          - `LocalGeometryFinder.compute_coordination_environments()`
          - `LocalGeometryFinder.compute_structure_environments()`
          - `LocalGeometryFinder.coordination_geometry_symmetry_measures()`
          - `LocalGeometryFinder.coordination_geometry_symmetry_measures_fallback_random()`
          - `LocalGeometryFinder.coordination_geometry_symmetry_measures_separation_plane()`
          - `LocalGeometryFinder.coordination_geometry_symmetry_measures_separation_plane_optim()`
          - `LocalGeometryFinder.coordination_geometry_symmetry_measures_sepplane_optim()`
          - `LocalGeometryFinder.coordination_geometry_symmetry_measures_standard()`
          - `LocalGeometryFinder.get_coordination_symmetry_measures()`
          - `LocalGeometryFinder.get_coordination_symmetry_measures_optim()`
          - `LocalGeometryFinder.get_structure()`
          - `LocalGeometryFinder.set_structure()`
          - `LocalGeometryFinder.setup_explicit_indices_local_geometry()`
          - `LocalGeometryFinder.setup_local_geometry()`
          - `LocalGeometryFinder.setup_ordered_indices_local_geometry()`
          - `LocalGeometryFinder.setup_parameter()`
          - `LocalGeometryFinder.setup_parameters()`
          - `LocalGeometryFinder.setup_random_indices_local_geometry()`
          - `LocalGeometryFinder.setup_random_structure()`
          - `LocalGeometryFinder.setup_structure()`
          - `LocalGeometryFinder.setup_test_perfect_environment()`
          - `LocalGeometryFinder.update_nb_set_environments()`
        - `find_rotation()`
        - `find_scaling_factor()`
        - `symmetry_measure()`
      - pymatgen.analysis.chemenv.coordination_environments.structure_environments module
        - `ChemicalEnvironments`
          - `ChemicalEnvironments.add_coord_geom()`
          - `ChemicalEnvironments.as_dict()`
          - `ChemicalEnvironments.from_dict()`
          - `ChemicalEnvironments.is_close_to()`
          - `ChemicalEnvironments.minimum_geometries()`
          - `ChemicalEnvironments.minimum_geometry()`
        - `LightStructureEnvironments`
          - `LightStructureEnvironments.DEFAULT_STATISTICS_FIELDS`
          - `LightStructureEnvironments.DELTA_MAX_OXIDATION_STATE`
          - `LightStructureEnvironments.NeighborsSet`
            - `LightStructureEnvironments.NeighborsSet.as_dict()`
            - `LightStructureEnvironments.NeighborsSet.from_dict()`
            - `LightStructureEnvironments.NeighborsSet.neighb_coords`
            - `LightStructureEnvironments.NeighborsSet.neighb_indices_and_images`
            - `LightStructureEnvironments.NeighborsSet.neighb_sites`
            - `LightStructureEnvironments.NeighborsSet.neighb_sites_and_indices`
          - `LightStructureEnvironments.as_dict()`
          - `LightStructureEnvironments.clear_environments()`
          - `LightStructureEnvironments.contains_only_one_anion()`
          - `LightStructureEnvironments.contains_only_one_anion_atom()`
          - `LightStructureEnvironments.environments_identified()`
          - `LightStructureEnvironments.from_dict()`
          - `LightStructureEnvironments.from_structure_environments()`
          - `LightStructureEnvironments.get_site_info_for_specie_allces()`
          - `LightStructureEnvironments.get_site_info_for_specie_ce()`
          - `LightStructureEnvironments.get_statistics()`
          - `LightStructureEnvironments.setup_statistic_lists()`
          - `LightStructureEnvironments.site_contains_environment()`
          - `LightStructureEnvironments.site_has_clear_environment()`
          - `LightStructureEnvironments.structure_contains_atom_environment()`
          - `LightStructureEnvironments.structure_has_clear_environments()`
          - `LightStructureEnvironments.uniquely_determines_coordination_environments`
        - `StructureEnvironments`
          - `StructureEnvironments.AC`
          - `StructureEnvironments.NeighborsSet`
            - `StructureEnvironments.NeighborsSet.add_source()`
            - `StructureEnvironments.NeighborsSet.angle_plateau()`
            - `StructureEnvironments.NeighborsSet.angles`
            - `StructureEnvironments.NeighborsSet.as_dict()`
            - `StructureEnvironments.NeighborsSet.coords`
            - `StructureEnvironments.NeighborsSet.detailed_voronoi`
            - `StructureEnvironments.NeighborsSet.distance_plateau()`
            - `StructureEnvironments.NeighborsSet.distances`
            - `StructureEnvironments.NeighborsSet.from_dict()`
            - `StructureEnvironments.NeighborsSet.get_neighb_voronoi_indices()`
            - `StructureEnvironments.NeighborsSet.info`
            - `StructureEnvironments.NeighborsSet.isite`
            - `StructureEnvironments.NeighborsSet.local_planes`
            - `StructureEnvironments.NeighborsSet.neighb_coords`
            - `StructureEnvironments.NeighborsSet.neighb_coordsOpt`
            - `StructureEnvironments.NeighborsSet.neighb_sites`
            - `StructureEnvironments.NeighborsSet.neighb_sites_and_indices`
            - `StructureEnvironments.NeighborsSet.normalized_angles`
            - `StructureEnvironments.NeighborsSet.normalized_distances`
            - `StructureEnvironments.NeighborsSet.separations`
            - `StructureEnvironments.NeighborsSet.site_voronoi_indices`
            - `StructureEnvironments.NeighborsSet.source`
            - `StructureEnvironments.NeighborsSet.sources`
            - `StructureEnvironments.NeighborsSet.structure`
            - `StructureEnvironments.NeighborsSet.voronoi`
            - `StructureEnvironments.NeighborsSet.voronoi_grid_surface_points()`
          - `StructureEnvironments.add_neighbors_set()`
          - `StructureEnvironments.as_dict()`
          - `StructureEnvironments.differences_wrt()`
          - `StructureEnvironments.from_dict()`
          - `StructureEnvironments.get_coordination_environments()`
          - `StructureEnvironments.get_csm()`
          - `StructureEnvironments.get_csm_and_maps()`
          - `StructureEnvironments.get_csms()`
          - `StructureEnvironments.get_environments_figure()`
          - `StructureEnvironments.init_neighbors_sets()`
          - `StructureEnvironments.plot_csm_and_maps()`
          - `StructureEnvironments.plot_environments()`
          - `StructureEnvironments.save_environments_figure()`
          - `StructureEnvironments.update_coordination_environments()`
          - `StructureEnvironments.update_site_info()`
      - pymatgen.analysis.chemenv.coordination_environments.voronoi module
        - `DetailedVoronoiContainer`
          - `DetailedVoronoiContainer.AC`
          - `DetailedVoronoiContainer.as_dict()`
          - `DetailedVoronoiContainer.default_normalized_angle_tolerance`
          - `DetailedVoronoiContainer.default_normalized_distance_tolerance`
          - `DetailedVoronoiContainer.default_voronoi_cutoff`
          - `DetailedVoronoiContainer.from_dict()`
          - `DetailedVoronoiContainer.get_rdf_figure()`
          - `DetailedVoronoiContainer.get_sadf_figure()`
          - `DetailedVoronoiContainer.is_close_to()`
          - `DetailedVoronoiContainer.maps_and_surfaces()`
          - `DetailedVoronoiContainer.maps_and_surfaces_bounded()`
          - `DetailedVoronoiContainer.neighbors()`
          - `DetailedVoronoiContainer.neighbors_surfaces()`
          - `DetailedVoronoiContainer.neighbors_surfaces_bounded()`
          - `DetailedVoronoiContainer.setup_neighbors_distances_and_angles()`
          - `DetailedVoronoiContainer.setup_voronoi_list()`
          - `DetailedVoronoiContainer.to_bson_voronoi_list2()`
          - `DetailedVoronoiContainer.voronoi_parameters_bounds_and_limits()`
        - `from_bson_voronoi_list2()`
    - pymatgen.analysis.chemenv.utils package
      - Submodules
      - pymatgen.analysis.chemenv.utils.chemenv_config module
        - `ChemEnvConfig`
          - `ChemEnvConfig.DEFAULT_PACKAGE_OPTIONS`
          - `ChemEnvConfig.auto_load()`
          - `ChemEnvConfig.has_materials_project_access`
          - `ChemEnvConfig.package_options_description()`
          - `ChemEnvConfig.save()`
          - `ChemEnvConfig.setup()`
          - `ChemEnvConfig.setup_package_options()`
      - pymatgen.analysis.chemenv.utils.chemenv_errors module
        - `AbstractChemenvError`
        - `ChemenvError`
        - `EquivalentSiteSearchError`
        - `NeighborsNotComputedChemenvError`
        - `SolidAngleError`
      - pymatgen.analysis.chemenv.utils.coordination_geometry_utils module
        - `Plane`
          - `Plane.TEST_2D_POINTS`
          - `Plane.a`
          - `Plane.abcd`
          - `Plane.b`
          - `Plane.c`
          - `Plane.coefficients`
          - `Plane.crosses_origin`
          - `Plane.d`
          - `Plane.distance_to_origin`
          - `Plane.distance_to_point()`
          - `Plane.distances()`
          - `Plane.distances_indices_groups()`
          - `Plane.distances_indices_sorted()`
          - `Plane.fit_error()`
          - `Plane.fit_least_square_distance_error()`
          - `Plane.fit_maximum_distance_error()`
          - `Plane.from_2points_and_origin()`
          - `Plane.from_3points()`
          - `Plane.from_coefficients()`
          - `Plane.from_npoints()`
          - `Plane.from_npoints_least_square_distance()`
          - `Plane.from_npoints_maximum_distance()`
          - `Plane.indices_separate()`
          - `Plane.init_3points()`
          - `Plane.is_in_list()`
          - `Plane.is_in_plane()`
          - `Plane.is_same_plane_as()`
          - `Plane.orthonormal_vectors()`
          - `Plane.perpendicular_bisector()`
          - `Plane.project_and_to2dim()`
          - `Plane.project_and_to2dim_ordered_indices()`
          - `Plane.projectionpoints()`
        - `anticlockwise_sort()`
        - `anticlockwise_sort_indices()`
        - `changebasis()`
        - `collinear()`
        - `diamond_functions()`
        - `function_comparison()`
        - `get_lower_and_upper_f()`
        - `is_anion_cation_bond()`
        - `matrixTimesVector()`
        - `quarter_ellipsis_functions()`
        - `rectangle_surface_intersection()`
        - `rotateCoords()`
        - `rotateCoordsOpt()`
        - `separation_in_list()`
        - `solid_angle()`
        - `sort_separation()`
        - `sort_separation_tuple()`
        - `spline_functions()`
        - `vectorsToMatrix()`
      - pymatgen.analysis.chemenv.utils.defs_utils module
        - `AdditionalConditions`
          - `AdditionalConditions.ALL`
          - `AdditionalConditions.CONDITION_DESCRIPTION`
          - `AdditionalConditions.NONE`
          - `AdditionalConditions.NO_AC`
          - `AdditionalConditions.NO_ADDITIONAL_CONDITION`
          - `AdditionalConditions.NO_E2SEB`
          - `AdditionalConditions.NO_ELEMENT_TO_SAME_ELEMENT_BONDS`
          - `AdditionalConditions.ONLY_ACB`
          - `AdditionalConditions.ONLY_ACB_AND_NO_E2SEB`
          - `AdditionalConditions.ONLY_ANION_CATION_BONDS`
          - `AdditionalConditions.ONLY_ANION_CATION_BONDS_AND_NO_ELEMENT_TO_SAME_ELEMENT_BONDS`
          - `AdditionalConditions.ONLY_E2OB`
          - `AdditionalConditions.ONLY_ELEMENT_TO_OXYGEN_BONDS`
          - `AdditionalConditions.check_condition()`
      - pymatgen.analysis.chemenv.utils.func_utils module
        - `AbstractRatioFunction`
          - `AbstractRatioFunction.ALLOWED_FUNCTIONS`
          - `AbstractRatioFunction.evaluate()`
          - `AbstractRatioFunction.from_dict()`
          - `AbstractRatioFunction.setup_parameters()`
        - `CSMFiniteRatioFunction`
          - `CSMFiniteRatioFunction.ALLOWED_FUNCTIONS`
          - `CSMFiniteRatioFunction.fractions()`
          - `CSMFiniteRatioFunction.mean_estimator()`
          - `CSMFiniteRatioFunction.power2_decreasing_exp()`
          - `CSMFiniteRatioFunction.ratios()`
          - `CSMFiniteRatioFunction.smootherstep()`
          - `CSMFiniteRatioFunction.smoothstep()`
        - `CSMInfiniteRatioFunction`
          - `CSMInfiniteRatioFunction.ALLOWED_FUNCTIONS`
          - `CSMInfiniteRatioFunction.fractions()`
          - `CSMInfiniteRatioFunction.mean_estimator()`
          - `CSMInfiniteRatioFunction.power2_inverse_decreasing()`
          - `CSMInfiniteRatioFunction.power2_inverse_power2_decreasing()`
          - `CSMInfiniteRatioFunction.ratios()`
        - `DeltaCSMRatioFunction`
          - `DeltaCSMRatioFunction.ALLOWED_FUNCTIONS`
          - `DeltaCSMRatioFunction.smootherstep()`
        - `RatioFunction`
          - `RatioFunction.ALLOWED_FUNCTIONS`
          - `RatioFunction.inverse_smootherstep()`
          - `RatioFunction.inverse_smoothstep()`
          - `RatioFunction.power2_decreasing_exp()`
          - `RatioFunction.power2_inverse_decreasing()`
          - `RatioFunction.power2_inverse_power2_decreasing()`
          - `RatioFunction.smootherstep()`
          - `RatioFunction.smoothstep()`
      - pymatgen.analysis.chemenv.utils.graph_utils module
        - `MultiGraphCycle`
          - `MultiGraphCycle.order()`
          - `MultiGraphCycle.validate()`
        - `SimpleGraphCycle`
          - `SimpleGraphCycle.as_dict()`
          - `SimpleGraphCycle.from_dict()`
          - `SimpleGraphCycle.from_edges()`
          - `SimpleGraphCycle.order()`
          - `SimpleGraphCycle.validate()`
        - `get_all_elementary_cycles()`
        - `get_all_simple_paths_edges()`
        - `get_delta()`
      - pymatgen.analysis.chemenv.utils.math_utils module
        - `cosinus_step()`
        - `divisors()`
        - `get_center_of_arc()`
        - `get_linearly_independent_vectors()`
        - `normal_cdf_step()`
        - `power2_decreasing_exp()`
        - `power2_inverse_decreasing()`
        - `power2_inverse_power2_decreasing()`
        - `power2_inverse_powern_decreasing()`
        - `power2_tangent_decreasing()`
        - `power3_step()`
        - `powern_decreasing()`
        - `powern_parts_step()`
        - `prime_factors()`
        - `scale_and_clamp()`
        - `smootherstep()`
        - `smoothstep()`
      - pymatgen.analysis.chemenv.utils.scripts_utils module
        - `compute_environments()`
        - `draw_cg()`
        - `visualize()`
- pymatgen.analysis.compatibility package
  - `AnionCorrection`
    - `AnionCorrection.get_correction()`
  - `AqueousCorrection`
    - `AqueousCorrection.get_correction()`
  - `Compatibility`
    - `Compatibility.explain()`
    - `Compatibility.get_adjustments()`
    - `Compatibility.process_entries()`
    - `Compatibility.process_entry()`
  - `CompatibilityError`
  - `Correction`
    - `Correction.correct_entry()`
    - `Correction.get_correction()`
  - `CorrectionsList`
    - `CorrectionsList.explain()`
    - `CorrectionsList.get_adjustments()`
    - `CorrectionsList.get_corrections_dict()`
    - `CorrectionsList.get_explanation_dict()`
  - `GasCorrection`
    - `GasCorrection.get_correction()`
  - `MITAqueousCompatibility`
  - `MITCompatibility`
  - `MaterialsProject2020Compatibility`
    - `MaterialsProject2020Compatibility.DEFAULT_CONFIG_FILE`
    - `MaterialsProject2020Compatibility.get_adjustments()`
  - `MaterialsProjectAqueousCompatibility`
    - `MaterialsProjectAqueousCompatibility.get_adjustments()`
    - `MaterialsProjectAqueousCompatibility.process_entries()`
  - `MaterialsProjectCompatibility`
  - `PotcarCorrection`
    - `PotcarCorrection.get_correction()`
  - `SmoothPESCompatibility`
    - `SmoothPESCompatibility.DEFAULT_CONFIG_FILE`
  - `UCorrection`
    - `UCorrection.common_peroxides`
    - `UCorrection.common_superoxides`
    - `UCorrection.get_correction()`
    - `UCorrection.ozonides`
  - `needs_u_correction()`
  - Submodules
  - pymatgen.analysis.compatibility.compatibility module
  - pymatgen.analysis.compatibility.computed_entries module
    - `GibbsComputedStructureEntry`
      - `GibbsComputedStructureEntry.as_dict()`
      - `GibbsComputedStructureEntry.from_dict()`
      - `GibbsComputedStructureEntry.from_entries()`
      - `GibbsComputedStructureEntry.from_pd()`
      - `GibbsComputedStructureEntry.gf_sisso()`
  - pymatgen.analysis.compatibility.correction_calculator module
    - `CorrectionCalculator`
      - `CorrectionCalculator.species`
      - `CorrectionCalculator.exp_compounds`
      - `CorrectionCalculator.calc_compounds`
      - `CorrectionCalculator.corrections`
      - `CorrectionCalculator.corrections_std_error`
      - `CorrectionCalculator.corrections_dict`
      - `CorrectionCalculator.compute_corrections()`
      - `CorrectionCalculator.compute_from_files()`
      - `CorrectionCalculator.graph_residual_error()`
      - `CorrectionCalculator.graph_residual_error_per_species()`
      - `CorrectionCalculator.make_yaml()`
  - pymatgen.analysis.compatibility.entry_tools module
    - `EntrySet`
      - `EntrySet.add()`
      - `EntrySet.as_dict()`
      - `EntrySet.chemsys`
      - `EntrySet.discard()`
      - `EntrySet.from_csv()`
      - `EntrySet.get_subset_in_chemsys()`
      - `EntrySet.ground_states`
      - `EntrySet.is_ground_state()`
      - `EntrySet.remove_non_ground_states()`
      - `EntrySet.to_csv()`
    - `group_entries_by_composition()`
    - `group_entries_by_structure()`
  - pymatgen.analysis.compatibility.exp_entries module
    - `ExpEntry`
      - `ExpEntry.as_dict()`
      - `ExpEntry.from_dict()`
  - pymatgen.analysis.compatibility.mixing_scheme module
    - `MaterialsProjectDFTMixingScheme`
      - `MaterialsProjectDFTMixingScheme.display_entries()`
      - `MaterialsProjectDFTMixingScheme.get_adjustments()`
      - `MaterialsProjectDFTMixingScheme.get_mixing_state_data()`
      - `MaterialsProjectDFTMixingScheme.process_entries()`
      - `MaterialsProjectDFTMixingScheme.run_type_2`
- pymatgen.analysis.diffraction package
  - Submodules
  - pymatgen.analysis.diffraction.core module
    - `AbstractDiffractionPatternCalculator`
      - `AbstractDiffractionPatternCalculator.SCALED_INTENSITY_TOL`
      - `AbstractDiffractionPatternCalculator.TWO_THETA_TOL`
      - `AbstractDiffractionPatternCalculator.get_pattern()`
      - `AbstractDiffractionPatternCalculator.get_plot()`
      - `AbstractDiffractionPatternCalculator.plot_structures()`
      - `AbstractDiffractionPatternCalculator.show_plot()`
    - `DiffractionPattern`
      - `DiffractionPattern.XLABEL`
      - `DiffractionPattern.YLABEL`
    - `get_unique_families()`
  - pymatgen.analysis.diffraction.neutron module
    - `NDCalculator`
      - `NDCalculator.get_pattern()`
  - pymatgen.analysis.diffraction.tem module
    - `TEMCalculator`
      - `TEMCalculator.bragg_angles()`
      - `TEMCalculator.cell_intensity()`
      - `TEMCalculator.cell_scattering_factors()`
      - `TEMCalculator.electron_scattering_factors()`
      - `TEMCalculator.generate_points()`
      - `TEMCalculator.get_first_point()`
      - `TEMCalculator.get_interplanar_angle()`
      - `TEMCalculator.get_interplanar_spacings()`
      - `TEMCalculator.get_pattern()`
      - `TEMCalculator.get_plot_2d()`
      - `TEMCalculator.get_plot_2d_concise()`
      - `TEMCalculator.get_plot_coeffs()`
      - `TEMCalculator.get_positions()`
      - `TEMCalculator.get_s2()`
      - `TEMCalculator.is_parallel()`
      - `TEMCalculator.normalized_cell_intensity()`
      - `TEMCalculator.tem_dots()`
      - `TEMCalculator.wavelength_rel()`
      - `TEMCalculator.x_ray_factors()`
      - `TEMCalculator.zone_axis_filter()`
  - pymatgen.analysis.diffraction.xrd module
    - `XRDCalculator`
      - `XRDCalculator.AVAILABLE_RADIATION`
      - `XRDCalculator.get_pattern()`
- pymatgen.analysis.elasticity package
  - Submodules
  - pymatgen.analysis.elasticity.elastic module
  - pymatgen.analysis.elasticity.strain module
  - pymatgen.analysis.elasticity.stress module
- pymatgen.analysis.ferroelectricity package
  - Submodules
  - pymatgen.analysis.ferroelectricity.polarization module
    - `EnergyTrend`
      - `EnergyTrend.endpoints_minima()`
      - `EnergyTrend.max_spline_jump()`
      - `EnergyTrend.smoothness()`
      - `EnergyTrend.spline()`
    - `Polarization`
      - `Polarization.from_outcars_and_structures()`
      - `Polarization.get_lattice_quanta()`
      - `Polarization.get_pelecs_and_pions()`
      - `Polarization.get_polarization_change()`
      - `Polarization.get_polarization_change_norm()`
      - `Polarization.get_same_branch_polarization_data()`
      - `Polarization.max_spline_jumps()`
      - `Polarization.same_branch_splines()`
      - `Polarization.smoothness()`
    - `calc_ionic()`
    - `get_nearest_site()`
    - `get_total_ionic_dipole()`
    - `zval_dict_from_potcar()`
- pymatgen.analysis.interfaces package
  - Submodules
  - pymatgen.analysis.interfaces.coherent_interfaces module
    - `CoherentInterfaceBuilder`
      - `CoherentInterfaceBuilder.get_interfaces()`
    - `from_2d_to_3d()`
    - `get_2d_transform()`
    - `get_rot_3d_for_2d()`
  - pymatgen.analysis.interfaces.substrate_analyzer module
    - `SubstrateAnalyzer`
      - `SubstrateAnalyzer.calculate()`
      - `SubstrateAnalyzer.generate_surface_vectors()`
    - `SubstrateMatch`
      - `SubstrateMatch.elastic_energy`
      - `SubstrateMatch.film_miller`
      - `SubstrateMatch.from_zsl()`
      - `SubstrateMatch.ground_state_energy`
      - `SubstrateMatch.strain`
      - `SubstrateMatch.substrate_miller`
      - `SubstrateMatch.total_energy`
      - `SubstrateMatch.von_mises_strain`
  - pymatgen.analysis.interfaces.zsl module
    - `ZSLGenerator`
      - `ZSLGenerator.generate_sl_transformation_sets()`
      - `ZSLGenerator.get_equiv_transformations()`
    - `ZSLMatch`
      - `ZSLMatch.film_sl_vectors`
      - `ZSLMatch.film_transformation`
      - `ZSLMatch.film_vectors`
      - `ZSLMatch.match_area`
      - `ZSLMatch.match_transformation`
      - `ZSLMatch.substrate_sl_vectors`
      - `ZSLMatch.substrate_transformation`
      - `ZSLMatch.substrate_vectors`
    - `fast_norm()`
    - `gen_sl_transform_matrices()`
    - `get_factors()`
    - `is_same_vectors()`
    - `reduce_vectors()`
    - `rel_angle()`
    - `rel_strain()`
    - `vec_angle()`
    - `vec_area()`
- pymatgen.analysis.magnetism package
  - Submodules
  - pymatgen.analysis.magnetism.analyzer module
    - `CollinearMagneticStructureAnalyzer`
      - `CollinearMagneticStructureAnalyzer.get_exchange_group_info()`
      - `CollinearMagneticStructureAnalyzer.get_ferromagnetic_structure()`
      - `CollinearMagneticStructureAnalyzer.get_nonmagnetic_structure()`
      - `CollinearMagneticStructureAnalyzer.get_structure_with_only_magnetic_atoms()`
      - `CollinearMagneticStructureAnalyzer.get_structure_with_spin()`
      - `CollinearMagneticStructureAnalyzer.is_magnetic`
      - `CollinearMagneticStructureAnalyzer.magmoms`
      - `CollinearMagneticStructureAnalyzer.magnetic_species_and_magmoms`
      - `CollinearMagneticStructureAnalyzer.matches_ordering()`
      - `CollinearMagneticStructureAnalyzer.number_of_magnetic_sites`
      - `CollinearMagneticStructureAnalyzer.number_of_unique_magnetic_sites()`
      - `CollinearMagneticStructureAnalyzer.ordering`
      - `CollinearMagneticStructureAnalyzer.types_of_magnetic_specie`
      - `CollinearMagneticStructureAnalyzer.types_of_magnetic_species`
    - `MagneticDeformation`
      - `MagneticDeformation.deformation`
      - `MagneticDeformation.type`
    - `MagneticStructureEnumerator`
      - `MagneticStructureEnumerator.available_strategies`
      - `MagneticStructureEnumerator.ordered_structure_origins`
      - `MagneticStructureEnumerator.ordered_structures`
    - `Ordering`
      - `Ordering.AFM`
      - `Ordering.FM`
      - `Ordering.FiM`
      - `Ordering.NM`
      - `Ordering.Unknown`
    - `OverwriteMagmomMode`
      - `OverwriteMagmomMode.none`
      - `OverwriteMagmomMode.normalize`
      - `OverwriteMagmomMode.replace_all`
      - `OverwriteMagmomMode.replace_all_if_undefined`
      - `OverwriteMagmomMode.respect_sign`
      - `OverwriteMagmomMode.respect_zeros`
    - `magnetic_deformation()`
  - pymatgen.analysis.magnetism.heisenberg module
    - `HeisenbergMapper`
      - `HeisenbergMapper.strategy`
      - `HeisenbergMapper.sgraphs`
      - `HeisenbergMapper.unique_site_ids`
      - `HeisenbergMapper.wyckoff_ids`
      - `HeisenbergMapper.nn_interactions`
      - `HeisenbergMapper.dists`
      - `HeisenbergMapper.ex_mat`
      - `HeisenbergMapper.ex_params`
      - `HeisenbergMapper.estimate_exchange()`
      - `HeisenbergMapper.get_exchange()`
      - `HeisenbergMapper.get_heisenberg_model()`
      - `HeisenbergMapper.get_interaction_graph()`
      - `HeisenbergMapper.get_low_energy_orderings()`
      - `HeisenbergMapper.get_mft_temperature()`
    - `HeisenbergModel`
      - `HeisenbergModel.as_dict()`
      - `HeisenbergModel.from_dict()`
    - `HeisenbergScreener`
      - `HeisenbergScreener.screened_structures`
      - `HeisenbergScreener.screened_energies`
  - pymatgen.analysis.magnetism.jahnteller module
    - `JahnTellerAnalyzer`
      - `JahnTellerAnalyzer.get_analysis()`
      - `JahnTellerAnalyzer.get_analysis_and_structure()`
      - `JahnTellerAnalyzer.get_magnitude_of_effect_from_species()`
      - `JahnTellerAnalyzer.get_magnitude_of_effect_from_spin_config()`
      - `JahnTellerAnalyzer.is_jahn_teller_active()`
      - `JahnTellerAnalyzer.mu_so()`
      - `JahnTellerAnalyzer.tag_structure()`
- pymatgen.analysis.prototypes package
  - `AflowPrototypeMatcher`
    - `AflowPrototypeMatcher.get_prototypes()`
  - `canonicalize_element_wyckoffs()`
  - `count_crystal_dof()`
  - `count_crystal_sites()`
  - `count_distinct_wyckoff_letters()`
  - `count_values_for_wyckoff()`
  - `count_wyckoff_positions()`
  - `get_anonymous_formula_from_prototype_formula()`
  - `get_formula_from_protostructure_label()`
  - `get_protostructure_label()`
  - `get_protostructure_label_from_aflow()`
  - `get_protostructure_label_from_moyopy()`
  - `get_protostructure_label_from_spg_analyzer()`
  - `get_protostructure_label_from_spglib()`
  - `get_protostructures_from_aflow_label_and_composition()`
  - `get_prototype_formula_from_composition()`
  - `get_prototype_from_protostructure()`
  - `get_random_structure_for_protostructure()`
  - `sort_and_score_element_wyckoffs()`
  - `split_alpha_numeric()`
- pymatgen.analysis.solar package
  - Submodules
  - pymatgen.analysis.solar.slme module
    - `absorption_coefficient()`
    - `get_dir_indir_gap()`
    - `optics()`
    - `parse_dielectric_data()`
    - `slme()`
    - `to_matrix()`
- pymatgen.analysis.structure_prediction package
  - Submodules
  - pymatgen.analysis.structure_prediction.dopant_predictor module
  - pymatgen.analysis.structure_prediction.substitution_probability module
  - pymatgen.analysis.structure_prediction.substitutor module
  - pymatgen.analysis.structure_prediction.volume_predictor module
- pymatgen.analysis.topological package
  - Submodules
  - pymatgen.analysis.topological.spillage module
    - `SOCSpillage`
      - `SOCSpillage.isclose()`
      - `SOCSpillage.orth()`
      - `SOCSpillage.overlap_so_spinpol()`
- pymatgen.analysis.xas package
  - Submodules
  - pymatgen.analysis.xas.spectrum module
    - `XAS`
      - `XAS.x`
      - `XAS.y`
      - `XAS.absorbing_element`
      - `XAS.edge`
      - `XAS.spectrum_type`
      - `XAS.absorbing_index`
      - `XAS.zero_negative_intensity`
      - `XAS.XLABEL`
      - `XAS.YLABEL`
      - `XAS.stitch()`
    - `site_weighted_spectrum()`

## Submodules

## pymatgen.analysis.adsorption module

This module provides classes used to enumerate surface sites and to find adsorption sites on slabs.

## pymatgen.analysis.bond_dissociation module

Module for BondDissociationEnergies.

class BondDissociationEnergies(molecule_entry: dict[str, str | dict[str, str | int]], fragment_entries: list[dict[str, str | dict[str, str | int]]], allow_additional_charge_separation: bool = False, multibreak: bool = False)

  Bases: `MSONable`

  Standard constructor for bond dissociation energies. All bonds in the principle molecule are looped through and their dissociation energies are calculated given the energies of the resulting fragments, or, in the case of a ring bond, from the energy of the molecule obtained from breaking the bond and opening the ring. This class should only be called after the energies of the optimized principle molecule and all relevant optimized fragments have been determined, either from quantum chemistry or elsewhere. It was written to provide the analysis after running an atomate fragmentation workflow.

  The provided entries must have the following keys: formula_pretty, initial_molecule, final_molecule. If a PCM is present, all entries should also have a pcm_dielectric key.

  Parameters:

    - molecule_entry (dict) – Entry for the principle molecule. Should have the keys mentioned above.

    - fragment_entries (list[dict]) – Fragment entries. Each should have the keys mentioned above.

    - allow_additional_charge_separation (bool) – If True, consider larger than normal charge separation among fragments. Defaults to False. See the definition of self.expected_charges below for more specific information.

    - multibreak (bool) – If True, additionally attempt to break pairs of bonds. Defaults to False.

  build_new_entry(frags: list, bonds: list) → list

    Build a new entry for bond dissociation that will be returned to the user.

    Parameters:

      - frags (list) – Fragments involved in the bond dissociation.

      - bonds (list) – Bonds broken in the dissociation process.

    Returns:

      Formatted bond dissociation entries.

    Return type:

      list

  filter_fragment_entries(fragment_entries: list) → None

    Filter the fragment entries.

    Parameters:

      fragment_entries (List) – Fragment entries to be filtered.

  fragment_and_process(bonds)

    Fragment and process bonds.

    Parameters:

      bonds (list) – bonds to process.

  search_fragment_entries(frag) → list

    Search all fragment entries for those isomorphic to the given fragment. We distinguish between entries where both initial and final MoleculeGraphs are isomorphic to the given fragment (entries) vs those where only the initial MoleculeGraph is isomorphic to the given fragment (initial_entries) vs those where only the final MoleculeGraph is isomorphic (final_entries).

    Parameters:

      frag – Fragment

## pymatgen.analysis.bond_valence module

This module implements classes to perform bond valence analyses.

## pymatgen.analysis.chempot_diagram module

This module implements the construction and plotting of chemical potential diagrams from a list of entries within a chemical system containing 2 or more elements. The chemical potential diagram is the mathematical dual to the traditional compositional phase diagram.

For more information, please cite/reference the paper below:

> Todd, P. K., McDermott, M. J., Rom, C. L., Corrao, A. A., Denney, J. J., Dwaraknath, S. S., Khalifah, P. G., Persson, K. A., & Neilson, J. R. (2021). Selectivity in Yttrium Manganese Oxide Synthesis via Local Chemical Potentials in Hyperdimensional Phase Space. Journal of the American Chemical Society, 143(37), 15185-15194. https://doi.org/10.1021/jacs.1c06229

Please also consider referencing the original 1999 paper by H. Yokokawa, who outlined many of its possible uses:

> Yokokawa, H. “Generalized chemical potential diagram and its applications to chemical reactions at interfaces between dissimilar materials.” JPE 20, 258 (1999). https://doi.org/10.1361/105497199770335794

class ChemicalPotentialDiagram(entries: list[PDEntry], limits: dict[Element, tuple[float, float]] | None = None, default_min_limit: float = -50.0, formal_chempots: bool = True)

  Bases: `MSONable`

  The chemical potential diagram is the mathematical dual to the compositional phase diagram. To create the diagram, convex minimization is performed in energy (E) vs. chemical potential (μ) space by taking the lower convex envelope of hyperplanes. Accordingly, “points” on the compositional phase diagram become N-dimensional convex polytopes (domains) in chemical potential space.

  For more information on this specific implementation of the algorithm, please cite/reference the paper below:

  > Todd, P. K., McDermott, M. J., Rom, C. L., Corrao, A. A., Denney, J. J., Dwaraknath, S. S., Khalifah, P. G., Persson, K. A., & Neilson, J. R. (2021). Selectivity in Yttrium Manganese Oxide Synthesis via Local Chemical Potentials in Hyperdimensional Phase Space. Journal of the American Chemical Society, 143(37), 15185-15194. https://doi.org/10.1021/jacs.1c06229

  Parameters:

    - entries (list[PDEntry]) – PDEntry-like objects containing a composition and energy. Must contain elemental references and be suitable for typical phase diagram construction. Entries must be within a chemical system of with 2+ elements.

    - limits (dict[Element, float] | None) – Bounds of elemental chemical potentials (min, max), which are used to construct the border hyperplanes used in the HalfSpaceIntersection algorithm; these constrain the space over which the domains are calculated and also determine the size of the plotted diagram. Any elemental limits not specified are covered in the default_min_limit argument. e.g. {Element(“Li”): [-12.0, 0.0], …}

    - default_min_limit (float) – Default minimum chemical potential limit (i.e., lower bound) for unspecified elements within the “limits” argument.

    - formal_chempots (bool) – Whether to plot the formal (‘reference’) chemical potentials (i.e. μ_X - μ_X^0) or the absolute DFT reference energies (i.e. μ_X(DFT)). Default is True (i.e. plot formal chemical potentials).

  property border_hyperplanes: ndarray

    Bordering hyperplanes.

  property chemical_system: str

    The chemical system (A-B-C-…) of diagram object.

  property domains: dict[str, ndarray]

    Mapping of formulas to array of domain boundary points.

  property el_refs: dict[Element, PDEntry]

    A dictionary of elements and reference entries.

  property entry_dict: dict[str, ComputedEntry]

    Mapping between reduced formula and ComputedEntry.

  get_plot(elements: list[Element | str] | None = None, label_stable: bool | None = True, formulas_to_draw: list[str] | None = None, draw_formula_meshes: bool | None = True, draw_formula_lines: bool | None = True, formula_colors: list[str] = ['rgb(27,158,119)', 'rgb(217,95,2)', 'rgb(117,112,179)', 'rgb(231,41,138)', 'rgb(102,166,30)', 'rgb(230,171,2)', 'rgb(166,118,29)', 'rgb(102,102,102)'], element_padding: float | None = 1.0) → Figure

    Plot the 2-dimensional or 3-dimensional chemical potential diagram using an interactive Plotly interface.

    Elemental axes can be specified; if none provided, will automatically default to first 2-3 elements within the “elements” attribute.

    In 3D, this method also allows for plotting of lower-dimensional “slices” of hyperdimensional polytopes (e.g., the LiMnO2 domain within a Y-Mn-O diagram). This allows for visualization of some of the phase boundaries that can only be seen fully in high dimensional space; see the “formulas_to_draw” argument.

    Parameters:

      - elements – list of elements to use as axes in the diagram. If None, automatically defaults to the first 2 or elements within the object’s “elements” attribute.

      - label_stable – whether to label stable phases by their reduced formulas. Defaults to True.

      - formulas_to_draw – for 3-dimensional diagrams, an optional list of formulas to plot on the diagram; if these are from a different chemical system a 3-d polyhedron “slice” will be plotted. Defaults to None.

      - draw_formula_meshes – whether to draw a colored mesh for the optionally specified formulas_to_draw. Defaults to True.

      - draw_formula_lines – whether to draw bounding lines for the optionally specified formulas_to_draw. Defaults to True.

      - formula_colors – a list of colors to use in the plotting of the optionally specified formulas_to-draw. Defaults to the Plotly Dark2 color scheme.

      - element_padding – if provided, automatically adjusts chemical potential axis limits of the plot such that elemental domains have the specified padding (in eV/atom), helping provide visual clarity. Defaults to 1.0.

    Returns:

      plotly.graph_objects.Figure

  property hyperplane_entries: list[PDEntry]

    List of entries corresponding to hyperplanes.

  property hyperplanes: ndarray

    Array of hyperplane data.

  property lims: ndarray

    Array of limits used in constructing hyperplanes.

get_2d_orthonormal_vector(line_pts: ndarray) → ndarray

  Calculates a vector that is orthonormal to a line given by a set of points. Used for determining the location of an annotation on a 2-d chemical potential diagram.

  Parameters:

    line_pts – a 2x2 array in the form of [[x0, y0], [x1, y1]] giving the coordinates of a line

  Returns:

    A length-2 vector that is orthonormal to the line.

  Return type:

    np.ndarray

get_centroid_2d(vertices: ndarray) → ndarray

  A bare-bones implementation of the formula for calculating the centroid of a 2D polygon. Useful for calculating the location of an annotation on a chemical potential domain within a 3D chemical potential diagram.

  NOTE vertices must be ordered circumferentially!

  Parameters:

    vertices – array of 2-d coordinates corresponding to a polygon, ordered circumferentially

  Returns:

    Giving 2-d centroid coordinates.

  Return type:

    np.ndarray

simple_pca(data: ndarray, k: int = 2) → tuple[ndarray, ndarray, ndarray]

  A bare-bones implementation of principal component analysis (PCA) used in the ChemicalPotentialDiagram class for plotting.

  Parameters:

    - data – array of observations

    - k – Number of principal components returned

  Returns:

    projected data, eigenvalues, eigenvectors

  Return type:

    tuple

## pymatgen.analysis.cost module

This module is used to estimate the cost of various compounds. Costs are taken from the a CostDB instance, for example a CSV file via CostDBCSV. For compounds with no cost listed, a Phase Diagram style convex hull optimization is performed to determine a set of compositions that can be mixed to give the desired compound with lowest total cost.

class CostAnalyzer(costdb: CostDB)

  Bases: `object`

  Given a CostDB, figures out the minimum cost solutions via convex hull.

  Parameters:

    costdb (CostDB) – Cost database to use.

  get_cost_per_kg(comp)

    Get best estimate of minimum cost/kg based on known data.

    Parameters:

      comp (CompositionLike) – chemical formula

    Returns:

      energy cost/kg

    Return type:

      float

  get_cost_per_mol(comp: CompositionLike) → float

    Get best estimate of minimum cost/mol based on known data.

    Parameters:

      comp (CompositionLike) – chemical formula

    Returns:

      energy cost/mol

    Return type:

      float

  get_lowest_decomposition(composition)

    Get the decomposition leading to lowest cost.

    Parameters:

      composition – Composition as a pymatgen.core.structure.Composition

    Returns:

      amount}

    Return type:

      Decomposition as a dict of {Entry

class CostDB

  Bases: `ABC`

  Abstract class for representing a Cost database. Can be extended, e.g. for file-based or REST-based databases.

  abstractmethod get_entries(chemsys)

    For a given chemical system, return an array of CostEntries.

    Parameters:

      chemsys (list[SpeciesLike]) – Elements defining the chemical system.

    Returns:

      list[CostEntries]

class CostDBCSV(filename)

  Bases: `CostDB`

  Read a CSV file to get costs. Format is formula,cost_per_kg,name,BibTeX.

  Parameters:

    filename (str) – Filename of cost database.

  get_entries(chemsys)

    For a given chemical system, return an array of CostEntries.

    Parameters:

      chemsys (list[Element]) – Elements defining the chemical system.

    Returns:

      array of CostEntries

class CostEntry(composition, cost, name, reference)

  Bases: `PDEntry`

  Extends PDEntry to include a BibTeX reference and include language about cost.

  Parameters:

    - composition (Composition) – chemical composition of the entry

    - cost (float) – per mol, NOT per kg of the full Composition

    - name (str) – Optional parameter to name the entry. Defaults to the reduced chemical formula as in PDEntry.

    - reference (str) – Reference data as BiBTeX string.

## pymatgen.analysis.dimensionality module

This module provides functions to get the dimensionality of a structure.

A number of different algorithms are implemented. These are based on the following publications:

get_dimensionality_larsen:

  - P. M. Larsen, M. Pandey, M. Strange, K. W. Jacobsen. Definition of a scoring parameter to identify low-dimensional materials components. Phys. Rev. Materials 3, 034003 (2019).

get_dimensionality_cheon:

  - Cheon, G.; Duerloo, K.-A. N.; Sendek, A. D.; Porter, C.; Chen, Y.; Reed, E. J. Data Mining for New Two- and One-Dimensional Weakly Bonded Solids and Lattice-Commensurate Heterostructures. Nano Lett. 2017.

get_dimensionality_gorai:

  - Gorai, P., Toberer, E. & Stevanovic, V. Computational Identification of Promising Thermoelectric Materials Among Known Quasi-2D Binary Compounds. J. Mater. Chem. A 2, 4136 (2016).

calculate_dimensionality_of_site(bonded_structure, site_index, inc_vertices=False)

  Calculate the dimensionality of the component containing the given site.

  Implements directly the modified breadth-first-search algorithm described in Algorithm 1 of:

  P. M. Larsen, M. Pandey, M. Strange, K. W. Jacobsen. Definition of a scoring parameter to identify low-dimensional materials components. Phys. Rev. Materials 3, 034003 (2019).

  Parameters:

    - bonded_structure (StructureGraph) – A structure with bonds, represented as a pymatgen structure graph. For example, generated using the CrystalNN.get_bonded_structure() method.

    - site_index (int) – The index of a site in the component of interest.

    - inc_vertices (bool, optional) – Whether to return the vertices (site images) of the component.

  Returns:

    If inc_vertices is False, the dimensionality of the

      component will be returned as an int. If inc_vertices is true, the function will return a tuple of (dimensionality, vertices), where vertices is a list of tuples. E.g. [(0, 0, 0), (1, 1, 1)].

  Return type:

    int | tuple

find_clusters(struct, connected_matrix)

  Find bonded clusters of atoms in the structure with periodic boundary conditions.

  If there are atoms that are not bonded to anything, returns [0,1,0]. (For faster computation time)

  Author: Gowoon Cheon Email: gcheon@stanford.edu

  Parameters:

    - struct (Structure) – Input structure

    - connected_matrix – Must be made from the same structure with find_connected_atoms() function.

  Returns:

    the size of the largest cluster in the crystal structure min_cluster: the size of the smallest cluster in the crystal structure clusters: list of bonded clusters found here, clusters are formatted as sets of indices of atoms

  Return type:

    max_cluster

find_connected_atoms(struct, tolerance=0.45, ldict=None)

  Find bonded atoms and returns a adjacency matrix of bonded atoms.

  Author: “Gowoon Cheon” Email: “gcheon@stanford.edu”

  Parameters:

    - struct (Structure) – Input structure

    - tolerance – length in angstroms used in finding bonded atoms. Two atoms are considered bonded if (radius of atom 1) + (radius of atom 2) + (tolerance) < (distance between atoms 1 and 2). Default value = 0.45, the value used by JMol and Cheon et al.

    - ldict – dictionary of bond lengths used in finding bonded atoms. Values from JMol are used as default

  Returns:

    A numpy array of shape (number of atoms, number of atoms);

      If any image of atom j is bonded to atom i with periodic boundary conditions, the matrix element [atom i, atom j] is 1.

  Return type:

    np.ndarray

get_dimensionality_cheon(structure_raw, tolerance=0.45, ldict=None, standardize=True, larger_cell=False)

  Algorithm for finding the dimensions of connected subunits in a structure. This method finds the dimensionality of the material even when the material is not layered along low-index planes, or does not have flat layers/molecular wires.

  Author: “Gowoon Cheon” Email: “gcheon@stanford.edu”

  See details at :

  Cheon, G.; Duerloo, K.-A. N.; Sendek, A. D.; Porter, C.; Chen, Y.; Reed, E. J. Data Mining for New Two- and One-Dimensional Weakly Bonded Solids and Lattice-Commensurate Heterostructures. Nano Lett. 2017.

  Parameters:

    - structure_raw (Structure) – A pymatgen Structure object.

    - tolerance (float) – length in angstroms used in finding bonded atoms. Two atoms are considered bonded if (radius of atom 1) + (radius of atom 2) + (tolerance) < (distance between atoms 1 and 2). Default value = 0.45, the value used by JMol and Cheon et al.

    - ldict (dict) – dictionary of bond lengths used in finding bonded atoms. Values from JMol are used as default

    - standardize – works with conventional standard structures if True. It is recommended to keep this as True.

    - larger_cell –

      tests with 3x3x3 supercell instead of 2x2x2. Testing with 2x2x2 supercell is faster but misclassifies rare interpenetrated 3D

      > structures. Testing with a larger cell circumvents this problem

  Returns:

    dimension of the largest cluster as a string. If there are ions

      or molecules it returns ‘intercalated ion/molecule’

  Return type:

    str

get_dimensionality_gorai(structure, max_hkl=2, el_radius_updates=None, min_slab_size=5, min_vacuum_size=5, standardize=True, bonds=None)

  This method returns whether a structure is 3D, 2D (layered), or 1D (linear chains or molecules) according to the algorithm published in Gorai, P., Toberer, E. & Stevanovic, V. Computational Identification of Promising Thermoelectric Materials Among Known Quasi-2D Binary Compounds. J. Mater. Chem. A 2, 4136 (2016).

  Note that a 1D structure detection might indicate problems in the bonding algorithm, particularly for ionic crystals (e.g., NaCl)

  Users can change the behavior of bonds detection by passing either el_radius_updates to update atomic radii for auto-detection of max bond distances, or bonds to explicitly specify max bond distances for atom pairs. Note that if you pass both, el_radius_updates are ignored.

  Parameters:

    - structure (Structure) – structure to analyze dimensionality for

    - max_hkl (int) – max index of planes to look for layers

    - el_radius_updates (dict) – symbol->float to update atomic radii

    - min_slab_size (float) – internal surface construction parameter

    - min_vacuum_size (float) – internal surface construction parameter

    - standardize (bool) – whether to standardize the structure before analysis. Set to False only if you already have the structure in a convention where layers / chains will be along low <hkl> indexes.

    - bonds (dict[tuple, float]) – bonds are specified as a dict of 2-tuples of Species mapped to floats, the max bonding distance. For example, PO4 groups may be defined as {(“P”, “O”): 3}.

  Returns:

    the dimensionality of the structure - 1 (molecules/chains),

      2 (layered), or 3 (3D)

  Return type:

    int

get_dimensionality_larsen(bonded_structure)

  Gets the dimensionality of a bonded structure.

  The dimensionality of the structure is the highest dimensionality of all structure components. This method is very robust and can handle many tricky structures, regardless of structure type or improper connections due to periodic boundary conditions.

  Requires a StructureGraph object as input. This can be generated using one of the NearNeighbor classes. For example, using the CrystalNN class:

  > bonded_structure = CrystalNN().get_bonded_structure(structure)

  Based on the modified breadth-first-search algorithm described in:

  P. M. Larsen, M. Pandey, M. Strange, K. W. Jacobsen. Definition of a scoring parameter to identify low-dimensional materials components. Phys. Rev. Materials 3, 034003 (2019).

  Parameters:

    bonded_structure (StructureGraph) – A structure with bonds, represented as a pymatgen structure graph. For example, generated using the CrystalNN.get_bonded_structure() method.

  Returns:

    The dimensionality of the structure.

  Return type:

    int

get_structure_components(bonded_structure, inc_orientation=False, inc_site_ids=False, inc_molecule_graph=False)

  Gets information on the components in a bonded structure.

  Correctly determines the dimensionality of all structures, regardless of structure type or improper connections due to periodic boundary conditions.

  Requires a StructureGraph object as input. This can be generated using one of the NearNeighbor classes. For example, using the CrystalNN class:

  > bonded_structure = CrystalNN().get_bonded_structure(structure)

  Based on the modified breadth-first-search algorithm described in:

  P. M. Larsen, M. Pandey, M. Strange, K. W. Jacobsen. Definition of a scoring parameter to identify low-dimensional materials components. Phys. Rev. Materials 3, 034003 (2019).

  Parameters:

    - bonded_structure (StructureGraph) – A structure with bonds, represented as a pymatgen structure graph. For example, generated using the CrystalNN.get_bonded_structure() method.

    - inc_orientation (bool, optional) – Whether to include the orientation of the structure component. For surfaces, the miller index is given, for one-dimensional structures, the direction of the chain is given.

    - inc_site_ids (bool, optional) – Whether to include the site indices of the sites in the structure component.

    - inc_molecule_graph (bool, optional) – Whether to include MoleculeGraph objects for zero-dimensional components.

  Returns:

    Information on the components in a structure as a list

      of dictionaries with the keys:

      - ”structure_graph”: A pymatgen StructureGraph object for the

          component.

      - ”dimensionality”: The dimensionality of the structure component as an

          int.

      - ”orientation”: If inc_orientation is True, the orientation of the

          component as a tuple. E.g. (1, 1, 1)

      - ”site_ids”: If inc_site_ids is True, the site indices of the

          sites in the component as a tuple.

      - ”molecule_graph”: If inc_molecule_graph is True, the site a

          MoleculeGraph object for zero-dimensional components.

  Return type:

    list[dict]

zero_d_graph_to_molecule_graph(bonded_structure, graph)

  Converts a zero-dimensional networkx Graph object into a MoleculeGraph.

  Implements a similar breadth-first search to that in calculate_dimensionality_of_site().

  Parameters:

    - bonded_structure (StructureGraph) – A structure with bonds, represented as a pymatgen structure graph. For example, generated using the CrystalNN.get_bonded_structure() method.

    - graph (nx.Graph) – A networkx Graph object for the component of interest.

  Returns:

    A MoleculeGraph object of the component.

  Return type:

    MoleculeGraph

## pymatgen.analysis.disorder module

This module provides various methods to analyze order/disorder in materials.

get_warren_cowley_parameters(structure: Structure, r: float, dr: float) → dict[tuple, float]

  Warren-Crowley parameters.

  Parameters:

    - structure – Pymatgen Structure.

    - r – Radius

    - dr – Shell width

  Returns:

    -1.0, …}

  Return type:

    Warren-Crowley parameters in the form of a dict, e.g. {(Element Mo, Element W)

## pymatgen.analysis.energy_models module

This module implements a EnergyModel abstract class and some basic implementations. Basically, an EnergyModel is any model that returns an “energy” for any given structure.

## pymatgen.analysis.eos module

This module implements various equation of states.

Note: Most of the code were initially adapted from ASE and deltafactor by @gmatteo but has since undergone major refactoring.

class Birch(volumes: Sequence[float], energies: Sequence[float])

  Bases: `EOSBase`

  Birch EOS.

  Parameters:

    - volumes (Sequence[float]) – in Ang^3.

    - energies (Sequence[float]) – in eV.

class BirchMurnaghan(volumes: Sequence[float], energies: Sequence[float])

  Bases: `EOSBase`

  BirchMurnaghan EOS.

  Parameters:

    - volumes (Sequence[float]) – in Ang^3.

    - energies (Sequence[float]) – in eV.

class DeltaFactor(volumes: Sequence[float], energies: Sequence[float])

  Bases: `PolynomialEOS`

  Fitting a polynomial EOS using delta factor.

  Parameters:

    - volumes (Sequence[float]) – in Ang^3.

    - energies (Sequence[float]) – in eV.

  fit(order: int = 3) → None

    Overridden since this eos works with volume**(2/3) instead of volume.

class EOS(eos_name: str = 'murnaghan')

  Bases: `object`

  Convenient wrapper. Retained in its original state to ensure backward compatibility.

  Fit equation of state for bulk systems.

  The following equations are supported:

  > murnaghan: PRB 28, 5480 (1983)

  > birch: Intermetallic compounds: Principles and Practice, Vol I:

  >   Principles. pages 195-210

  > birch_murnaghan: PRB 70, 224107

  > pourier_tarantola: PRB 70, 224107

  > vinet: PRB 70, 224107

  > deltafactor

  > numerical_eos: 10.1103/PhysRevB.90.174107.

  Usage:

  > eos = EOS(eos_name=’murnaghan’) eos_fit = eos.fit(volumes, energies) eos_fit.plot()

  Parameters:

    eos_name (str) – Type of EOS to fit.

  MODELS: ClassVar[dict[str, Any]] = {'birch': <class 'pymatgen.analysis.eos.Birch'>, 'birch_murnaghan': <class 'pymatgen.analysis.eos.BirchMurnaghan'>, 'deltafactor': <class 'pymatgen.analysis.eos.DeltaFactor'>, 'murnaghan': <class 'pymatgen.analysis.eos.Murnaghan'>, 'numerical_eos': <class 'pymatgen.analysis.eos.NumericalEOS'>, 'pourier_tarantola': <class 'pymatgen.analysis.eos.PourierTarantola'>, 'vinet': <class 'pymatgen.analysis.eos.Vinet'>}
  fit(volumes: Sequence[float], energies: Sequence[float]) → EOSBase

    Fit energies as function of volumes.

    Parameters:

      - volumes (Sequence[float]) – in Ang^3

      - energies (Sequence[float]) – in eV

    Returns:

      EOSBase object

    Return type:

      EOSBase

class EOSBase(volumes: Sequence[float], energies: Sequence[float])

  Bases: `ABC`

  Abstract class that must be subclassed by all equation of state implementations.

  Parameters:

    - volumes (Sequence[float]) – in Ang^3.

    - energies (Sequence[float]) – in eV.

  property b0: float

    The bulk modulus in units of energy/unit of volume^3.

  property b0_GPa: FloatWithUnit

    The bulk modulus in GPa. This assumes the energy and volumes are in eV and Ang^3.

  property b1

    The derivative of bulk modulus w.r.t. pressure(dimensionless).

  property e0: float

    The min energy.

  eos_params: Sequence | None
  fit() → None

    Do the fitting. Does least square fitting. If you want to use custom fitting, must override this.

  func(volume)

    The equation of state function with the parameters other than volume set to the ones obtained from fitting.

    Parameters:

      volume (float | list[float]) – volumes in Ang^3

    Returns:

      numpy.array

  plot(width: float = 8, height: float | None = None, ax: Axes = None, dpi: float | None = None, **kwargs) → Axes

    Plot the equation of state.

    Parameters:

      - width (float) – Width of plot in inches. Defaults to 8in.

      - height (float) – Height of plot in inches. Defaults to width * golden ratio.

      - ax (plt.Axes) – If supplied, changes will be made to the existing Axes. Otherwise, new Axes will be created.

      - dpi (float) – DPI.

      - kwargs (dict) – additional args fed to pyplot.plot. supported keys: style, color, text, label

    Returns:

      The matplotlib axes.

    Return type:

      plt.Axes

  plot_ax(ax: Axes | None = None, fontsize: float = 12, **kwargs) → plt.Figure

    Plot the equation of state on axis ax.

    Parameters:

      - ax – matplotlib Axes or None if a new figure should be created.

      - fontsize – Legend fontsize.

    Returns:

      matplotlib figure.

    Return type:

      plt.Figure

    Keyword arguments controlling the display of the figure:

    kwargs | Meaning
    --- | ---
    title | Title of the plot (Default: None).
    show | True to show the figure (default: True).
    savefig | “abc.png” or “abc.eps” to save the figure to a file.
    size_kwargs | Dictionary with options passed to fig.set_size_inches e.g. size_kwargs=dict(w=3, h=4)
    tight_layout | True to call fig.tight_layout (default: False)
    ax_grid | True (False) to add (remove) grid from all axes in fig. Default: None i.e. fig is left unchanged.
    ax_annotate | Add labels to subplots e.g. (a), (b). Default: False
    fig_close | Close figure. Default: False.

  property results: dict[str, Any]

    A summary dict.

  property v0

    The minimum or the reference volume in Ang^3.

exception EOSError

  Bases: `Exception`

  Error class for EOS fitting.

class Murnaghan(volumes: Sequence[float], energies: Sequence[float])

  Bases: `EOSBase`

  Murnaghan EOS.

  Parameters:

    - volumes (Sequence[float]) – in Ang^3.

    - energies (Sequence[float]) – in eV.

class NumericalEOS(volumes: Sequence[float], energies: Sequence[float])

  Bases: `PolynomialEOS`

  A numerical EOS.

  Parameters:

    - volumes (Sequence[float]) – in Ang^3.

    - energies (Sequence[float]) – in eV.

  fit(min_ndata_factor: int = 3, max_poly_order_factor: int = 5, min_poly_order: int = 2) → None

    Fit the input data to the ‘numerical eos’, the equation of state employed in the quasiharmonic Debye model described in the paper: 10.1103/PhysRevB.90.174107.

    credits: Cormac Toher

    Parameters:

      - min_ndata_factor (int) – parameter that controls the minimum number of data points that will be used for fitting. minimum number of data points = total data points-2*min_ndata_factor

      - max_poly_order_factor (int) – parameter that limits the max order of the polynomial used for fitting. max_poly_order = number of data points used for fitting - max_poly_order_factor

      - min_poly_order (int) – minimum order of the polynomial to be considered for fitting.

class PolynomialEOS(volumes: Sequence[float], energies: Sequence[float])

  Bases: `EOSBase`

  Derives from EOSBase. Polynomial based equations of states must subclass this.

  Parameters:

    - volumes (Sequence[float]) – in Ang^3.

    - energies (Sequence[float]) – in eV.

  fit(order: int) → None

    Do polynomial fitting and set the parameters. Uses numpy polyfit.

    Parameters:

      order (int) – order of the fit polynomial

class PourierTarantola(volumes: Sequence[float], energies: Sequence[float])

  Bases: `EOSBase`

  Pourier-Tarantola EOS.

  Parameters:

    - volumes (Sequence[float]) – in Ang^3.

    - energies (Sequence[float]) – in eV.

class Vinet(volumes: Sequence[float], energies: Sequence[float])

  Bases: `EOSBase`

  Vinet EOS.

  Parameters:

    - volumes (Sequence[float]) – in Ang^3.

    - energies (Sequence[float]) – in eV.

## pymatgen.analysis.ewald module

This module provides classes for calculating the Ewald sum of a structure.

## pymatgen.analysis.excitation module

This module defines an excitation spectrum class.

class ExcitationSpectrum(x, y)

  Bases: `Spectrum`

  Basic excitation spectrum object.

  x

    The sequence of energies.

    Type:

      Sequence[float]

  y

    The sequence of mu(E).

    Type:

      Sequence[float]

  Parameters:

    - x – A sequence of x-ray energies in eV

    - y – A sequence of intensity values.

  XLABEL = 'Energy (eV)'
  YLABEL = 'Intensity'

## pymatgen.analysis.fragmenter module

Perform fragmentation of molecules.

class Fragmenter(molecule: Molecule, edges: list | None = None, depth: int = 1, open_rings: bool = False, use_metal_edge_extender: bool = False, opt_steps: int = 10000, prev_unique_frag_dict: dict | None = None, assume_previous_thoroughness: bool = True)

  Bases: `MSONable`

  Molecule fragmenter class.

  Standard constructor for molecule fragmentation.

  Parameters:

    - molecule (Molecule) – The molecule to fragment.

    - edges (list) – List of index pairs that define graph edges, aka molecule bonds. If not set, edges will be determined with OpenBabel. Defaults to None.

    - depth (int) – The number of levels of iterative fragmentation to perform, where each level will include fragments obtained by breaking one bond of a fragment one level up. Defaults to 1. However, if set to 0, instead all possible fragments are generated using an alternative, non-iterative scheme.

    - open_rings (bool) – Whether or not to open any rings encountered during fragmentation. Defaults to False. If true, any bond that fails to yield disconnected graphs when broken is instead removed and the entire structure is optimized with OpenBabel in order to obtain a good initial guess for an opened geometry that can then be put back into QChem to be optimized without the ring just reforming.

    - use_metal_edge_extender (bool) – Whether or not to attempt to add additional edges from O, N, F, or Cl to any Li or Mg atoms present that OpenBabel may have missed. Defaults to False. Most important for ionic bonding. Note that additional metal edges may yield new “rings” (e.g. -C-O-Li-O- in LiEC) that will not play nicely with ring opening.

    - opt_steps (int) – Number of optimization steps when opening rings. Defaults to 10000.

    - prev_unique_frag_dict (dict) – A dictionary of previously identified unique fragments. Defaults to None. Typically only used when trying to find the set of unique fragments that come from multiple molecules.

    - assume_previous_thoroughness (bool) – Whether or not to assume that a molecule / fragment provided in prev_unique_frag_dict has all of its unique subfragments also provided in prev_unique_frag_dict. Defaults to True. This is an essential optimization when trying to find the set of unique fragments that come from multiple molecules if all of those molecules are being fully iteratively fragmented. However, if you’re passing a prev_unique_frag_dict which includes a molecule and its fragments that were generated at insufficient depth to find all possible subfragments to a fragmentation calculation of a different molecule that you aim to find all possible subfragments of and which has common subfragments with the previous molecule, this optimization will cause you to miss some unique subfragments.

open_ring(mol_graph: MoleculeGraph, bond: list, opt_steps: int) → MoleculeGraph

  Open a ring using OpenBabel’s local opt. Given a molecule graph and a bond, convert the molecule graph into an OpenBabel molecule, remove the given bond, perform the local opt with the number of steps determined by self.steps, and then convert the resulting structure back into a molecule graph to be returned.

## pymatgen.analysis.functional_groups module

Determine functional groups present in a Molecule.

class FunctionalGroupExtractor(molecule, optimize=False)

  Bases: `object`

  This class is used to algorithmically parse a molecule (represented by an instance of pymatgen.analysis.graphs.MoleculeGraph) and determine arbitrary functional groups.

  Instantiation method for FunctionalGroupExtractor.

  Parameters:

    - molecule – Either a filename, a pymatgen.core.structure.Molecule object, or a pymatgen.analysis.graphs.MoleculeGraph object.

    - optimize – Default False. If True, then the input molecule will be modified, adding Hydrogens, performing a simple conformer search, etc.

  categorize_functional_groups(groups)

    Determine classes of functional groups present in a set.

    Parameters:

      groups – Set of functional groups.

    Returns:

      dict containing representations of the groups, the indices of where the group occurs in the MoleculeGraph, and how many of each type of group there is.

  get_all_functional_groups(elements=None, func_groups=None, catch_basic=True)

    Identify all functional groups (or all within a certain subset) in the molecule, combining the methods described above.

    Parameters:

      - elements – List of elements that will qualify a carbon as special (if only certain functional groups are of interest). Default None.

      - func_groups – List of strs representing the functional groups of interest. Default to None, meaning that all of the functional groups defined in this function will be sought.

      - catch_basic – bool. If True, use get_basic_functional_groups and other methods

    Returns:

      list of sets of ints, representing groups of connected atoms

  get_basic_functional_groups(func_groups=None)

    Identify functional groups that cannot be identified by the Ertl method of get_special_carbon and get_heteroatoms, such as benzene rings, methyl groups, and ethyl groups.

    TODO: Think of other functional groups that are important enough to be added (ex: do we need ethyl, butyl, propyl?)

    Parameters:

      func_groups – List of strs representing the functional groups of interest. Default to None, meaning that all of the functional groups defined in this function will be sought.

    Returns:

      list of sets of ints, representing groups of connected atoms

  get_heteroatoms(elements=None)

    Identify non-H, non-C atoms in the MoleculeGraph, returning a list of their node indices.

    Parameters:

      - elements – List of elements to identify (if only certain

      - interest). (functional groups are of)

    Returns:

      set of ints representing node indices

  get_special_carbon(elements=None)

    Identify Carbon atoms in the MoleculeGraph that fit the characteristics defined Ertl (2017), returning a list of their node indices.

    The conditions for marking carbon atoms are (quoted from Ertl):

      “- atoms connected by non-aromatic double or triple bond to any heteroatom - atoms in nonaromatic carbon-carbon double or triple bonds - acetal carbons, i.e. sp3 carbons connected to two or more oxygens, nitrogens or sulfurs; these O, N or S atoms must have only single bonds - all atoms in oxirane, aziridine and thiirane rings”

    Parameters:

      elements – List of elements that will qualify a carbon as special (if only certain functional groups are of interest). Default None.

    Returns:

      set of ints representing node indices

  link_marked_atoms(atoms)

    Take a list of marked “interesting” atoms (heteroatoms, special carbons) and attempt to connect them, returning a list of disjoint groups of special atoms (and their connected hydrogens).

    Parameters:

      atoms – set of marked “interesting” atoms, presumably identified using other functions in this class.

    Returns:

      list of sets of ints, representing groups of connected atoms

## pymatgen.analysis.graphs module

Module for graph representations of crystals and molecules.

## pymatgen.analysis.hhi module

This module is used to estimate the Herfindahl-Hirschman Index, or HHI, of chemical compounds. The HHI is a measure of how geographically confined or dispersed the elements comprising a compound are. A low HHI is desirable because it means the component elements are geographically dispersed.

Data/strategy from “Data-Driven Review of Thermoelectric Materials: Performance and Resource Considerations” by Gaultois et al., published in Chemistry of Materials (2013).

## pymatgen.analysis.interface_reactions module

This module provides a class to predict and analyze interfacial reactions between two solids, with or without an open element (e.g., flowing O2).

class GrandPotentialInterfacialReactivity(c1: Composition, c2: Composition, grand_pd: GrandPotentialPhaseDiagram, pd_non_grand: PhaseDiagram, include_no_mixing_energy: bool = False, norm: bool = True, use_hull_energy: bool = True)

  Bases: `InterfacialReactivity`

  Extends upon InterfacialReactivity to allow for modelling possible reactions at the interface between two solids in the presence of an open element. The thermodynamics of the open system are provided by the user via the GrandPotentialPhaseDiagram class.

  Parameters:

    - c1 – Reactant 1 composition

    - c2 – Reactant 2 composition

    - grand_pd – Grand potential phase diagram object built from all elements in composition c1 and c2.

    - include_no_mixing_energy – No_mixing_energy for a reactant is the opposite number of its energy above grand potential convex hull. In cases where reactions involve elements reservoir, this param determines whether no_mixing_energy of reactants will be included in the final reaction energy calculation. By definition, if pd is not a GrandPotentialPhaseDiagram object, this param is False.

    - pd_non_grand – PhaseDiagram object but not GrandPotentialPhaseDiagram object built from elements in c1 and c2.

    - norm – Whether or not the total number of atoms in composition of reactant will be normalized to 1.

    - use_hull_energy – Whether or not use the convex hull energy for a given composition for reaction energy calculation. If false, the energy of ground state structure will be used instead. Note that in case when ground state can not be found for a composition, convex hull energy will be used associated with a warning message.

  get_no_mixing_energy()

    Generate the opposite number of energy above grand potential convex hull for both reactants.

    Returns:

      [(reactant1, no_mixing_energy1),(reactant2,no_mixing_energy2)].

class InterfacialReactivity(c1: Composition, c2: Composition, pd: PhaseDiagram, norm: bool = True, use_hull_energy: bool = False, **kwargs)

  Bases: `MSONable`

  Model an interface between two solids and its possible reactions. The two reactants are provided as Composition objects (c1 and c2), along with the relevant compositional PhaseDiagram object. Possible reactions are calculated by finding all points along a tie-line between c1 and c2 where there is a “kink” in the phase diagram; i.e. a point or facet of the phase diagram.

  Please consider citing one or both of the following papers if you use this code in your own work.

  References

  Richards, W. D., Miara, L. J., Wang, Y., Kim, J. C., &amp; Ceder, G. (2015). Interface stability in solid-state batteries. Chemistry of Materials, 28(1), 266-273. https://doi.org/10.1021/acs.chemmater.5b04082

  Xiao, Y., Wang, Y., Bo, S.-H., Kim, J. C., Miara, L. J., &amp; Ceder, G. (2019). Understanding interface stability in solid-state batteries. Nature Reviews Materials, 5(2), 105-126. https://doi.org/10.1038/s41578-019-0157-5

  Parameters:

    - c1 – Reactant 1 composition

    - c2 – Reactant 2 composition

    - pd – Phase diagram object built from all elements in composition c1 and c2.

    - norm – Whether or not the total number of atoms in composition of reactant will be normalized to 1.

    - use_hull_energy – Whether or not use the convex hull energy for a given composition for reaction energy calculation. If false, the energy of ground state structure will be used instead. Note that in case when ground state can not be found for a composition, convex hull energy will be used associated with a warning message.

  EV_TO_KJ_PER_MOL = 96.4853
  classmethod get_chempot_correction(element: str, temp: float, pres: float)

    Get the normalized correction term Δμ for chemical potential of a gas phase consisting of element at given temperature and pressure, referenced to that in the standard state (T_std = 298.15 K, T_std = 1 bar). The gas phase is limited to be one of O2, N2, Cl2, F2, H2. Calculation formula can be found in the documentation of Materials Project website.

    Parameters:

      - element – The string representing the element.

      - temp – The temperature of the gas phase in Kelvin.

      - pres – The pressure of the gas phase in Pa. # codespell:ignore pres

    Returns:

      The correction of chemical potential in eV/atom of the gas phase at given temperature and pressure.

  get_critical_original_kink_ratio()

    Get a list of molar mixing ratio for each kink between ORIGINAL (instead of processed) reactant compositions. This is the same list as mixing ratio obtained from get_kinks method if self.norm = False.

    Returns:

      A list of floats representing molar mixing ratios between the original reactant compositions for each kink.

  get_dataframe() → DataFrame

    Get a pandas DataFrame representation of the data produced by the get_kinks() method.

  get_kinks() → list[tuple[int, float, float, Reaction, float]]

    Find all the kinks in mixing ratio where reaction products changes along the tie-line of composition self.c1 and composition self.c2.

    Returns:

      (index, mixing ratio, reaction energy in eV/atom, Reaction object, reaction energy per mol of formula in kJ/mol).

    Return type:

      List object of tuples, each of which contains 5 elements

  property labels

    A dictionary containing kink information: {index: ‘x= mixing_ratio energy= reaction_energy reaction_equation’}. e.g. {1: ‘x= 0 energy = 0 Mn -> Mn’,

    > 2: ‘x= 0.5 energy = -15 O2 + Mn -> MnO2’, 3: ‘x= 1 energy = 0 O2 -> O2’}.

  property minimum

    The minimum reaction energy E_min and corresponding mixing ratio x_min as tuple[float, float]: (x_min, E_min).

  plot(backend: Literal['plotly', 'matplotlib'] = 'plotly') → Figure | plt.Figure

    Plots reaction energy as a function of mixing ratio x in self.c1 - self.c2 tie line.

    Parameters:

      backend ("plotly" | "matplotlib") – Plotting library used to create the plot. Defaults to “plotly” but can also be “matplotlib”.

    Returns:

      Plot of reaction energies as a function of mixing ratio

  property products

    List of formulas of potential products. e.g. [‘Li’,’O2’,’Mn’].

## pymatgen.analysis.lobster_env module

This module provides classes to perform analyses of the local environments (e.g., finding near neighbors) of single sites in molecules and structures based on bonding analysis with LOBSTER.

If you use this module, please cite: J. George, G. Petretto, A. Naik, M. Esters, A. J. Jackson, R. Nelson, R. Dronskowski, G.-M. Rignanese, G. Hautier, “Automated Bonding Analysis with Crystal Orbital Hamilton Populations”, ChemPlusChem 2022, e202200123, DOI: 10.1002/cplu.202200123.

class ICOHPNeighborsInfo(total_icohp: float, list_icohps: list[float], n_bonds: int, labels: list[str], atoms: list[list[str]], central_isites: list[int] | None)

  Bases: `NamedTuple`

  Tuple to record information on relevant bonds.

  Parameters:

    - total_icohp (float) – Sum of ICOHP values of neighbors to the selected sites (given by the index in structure).

    - list_icohps (list) – Summed ICOHP values for all identified interactions with neighbors.

    - n_bonds (int) – Number of identified bonds to the selected sites.

    - labels (list[str]) – Labels (from ICOHPLIST) for all identified bonds.

    - atoms (list[list[str]]) – Lists describing the species present (from ICOHPLIST) in the identified interactions , e.g. [“Ag3”, “O5”].

    - central_isites (list[int]) – The central site indexes for each identified interaction.

  Create new instance of ICOHPNeighborsInfo(total_icohp, list_icohps, n_bonds, labels, atoms, central_isites)

  atoms: list[list[str]]

    Alias for field number 4

  central_isites: list[int] | None

    Alias for field number 5

  labels: list[str]

    Alias for field number 3

  list_icohps: list[float]

    Alias for field number 1

  n_bonds: int

    Alias for field number 2

  total_icohp: float

    Alias for field number 0

class LobsterLightStructureEnvironments(strategy, coordination_environments=None, all_nbs_sites=None, neighbors_sets=None, structure=None, valences=None, valences_origin=None)

  Bases: `LightStructureEnvironments`

  Store LightStructureEnvironments based on LOBSTER outputs.

  Constructor for the LightStructureEnvironments object.

  Parameters:

    - strategy – ChemEnv strategy used to get the environments.

    - coordination_environments – The coordination environments identified.

    - all_nbs_sites – All the possible neighbors for each site in the structure.

    - neighbors_sets – The neighbors sets of each site in the structure.

    - structure – The structure.

    - valences – The valences used to get the environments (if needed).

    - valences_origin – How the valences were obtained (e.g. from the Bond-valence analysis or from the original structure).

  as_dict() → dict[str, Any]

    Bson-serializable dict representation of the object.

    Returns:

      Bson-serializable dict representation.

  classmethod from_Lobster(list_ce_symbol: list[str | None], list_csm: list[float | None], list_permutation: list, list_neighsite: list[PeriodicSite], list_neighisite: list[list[int]], structure: Structure | IStructure, valences: list[float] | None = None) → Self

    Set up a LightStructureEnvironments from LOBSTER.

    Parameters:

      - list_ce_symbol (list[str]) – Coordination environments symbols.

      - list_csm (list[float]) – Continuous symmetry measures.

      - list_permutation (list) – Permutations.

      - list_neighsite (list[PeriodicSite]) – Neighboring sites.

      - list_neighisite (list[list[int]]) – Neighboring sites indexes.

      - structure (Structure) – Structure object.

      - valences (list[float]) – Valences.

    Returns:

      LobsterLightStructureEnvironments

  property uniquely_determines_coordination_environments: Literal[True]

    Whether the coordination environments are uniquely determined.

class LobsterNeighbors(structure: Structure | IStructure, filename_icohp: PathLike | None = 'ICOHPLIST.lobster', obj_icohp: Icohplist | None = None, are_coops: bool = False, are_cobis: bool = False, valences: list[float] | None = None, limits: tuple[float, float] | None = None, additional_condition: Literal[0, 1, 2, 3, 4, 5, 6] = 0, only_bonds_to: list[str] | None = None, perc_strength_icohp: float = 0.15, noise_cutoff: float = 0.1, valences_from_charges: bool = False, filename_charge: PathLike | None = None, obj_charge: Charge | None = None, which_charge: Literal['Mulliken', 'Loewdin'] = 'Mulliken', adapt_extremum_to_add_cond: bool = False, add_additional_data_sg: bool = False, filename_blist_sg1: PathLike | None = None, filename_blist_sg2: PathLike | None = None, id_blist_sg1: Literal['icoop', 'icobi'] = 'icoop', id_blist_sg2: Literal['icoop', 'icobi'] = 'icobi', backward_compatibility: bool = False)

  Bases: `NearNeighbors`

  This class combines capabilities from LocalEnv and ChemEnv to determine coordination environments based on bonding analysis.

  Parameters:

    - filename_icohp (PathLike) – Path to ICOHPLIST.lobster or ICOOPLIST.lobster or ICOBILIST.lobster.

    - obj_icohp (Icohplist) – Icohplist object.

    - structure (Structure) – Typically constructed by Structure.from_file(“POSCAR”).

    - are_coops (bool) – Whether the file is a ICOOPLIST.lobster (True) or a ICOHPLIST.lobster (False). Only tested for ICOHPLIST.lobster so far.

    - are_cobis (bool) – Whether the file is a ICOBILIST.lobster (True) or a ICOHPLIST.lobster (False).

    - valences (list[float]) – Valence/charge for each element.

    - limits (tuple[float, float]) – Range to decide which ICOHPs (ICOOP or ICOBI) should be considered.

    - additional_condition (int) –

      Additional condition that decides which kind of bonds will be considered:

      > 0 - NO_ADDITIONAL_CONDITION 1 - ONLY_ANION_CATION_BONDS 2 - NO_ELEMENT_TO_SAME_ELEMENT_BONDS 3 - ONLY_ANION_CATION_BONDS_AND_NO_ELEMENT_TO_SAME_ELEMENT_BONDS 4 - ONLY_ELEMENT_TO_OXYGEN_BONDS 5 - DO_NOT_CONSIDER_ANION_CATION_BONDS 6 - ONLY_CATION_CATION_BONDS

    - only_bonds_to (list[str]) – Only consider bonds to certain elements (e.g. [“O”] for oxygen).

    - perc_strength_icohp (float) – If no “limits” are given, this will decide which ICOHPs will be considered (relative to the strongest ICOHP/ICOOP/ICOBI).

    - noise_cutoff (float) – The lower limit of ICOHPs considered.

    - valences_from_charges (bool) – If True and path to CHARGE.lobster is provided, will use LOBSTER charges (Mulliken) instead of valences.

    - filename_charge (PathLike) – Path to Charge.lobster.

    - obj_charge (Charge) – Charge object.

    - which_charge ("Mulliken" | "Loewdin") – Source of charge.

    - adapt_extremum_to_add_cond (bool) – Whether to adapt the limits to only focus on the bonds determined by the additional condition.

    - add_additional_data_sg (bool) – Add the information from filename_add_bondinglist_sg1.

    - filename_blist_sg1 (PathLike) – Path to additional ICOOP, ICOBI data for structure graphs.

    - filename_blist_sg2 (PathLike) – Path to additional ICOOP, ICOBI data for structure graphs.

    - id_blist_sg1 ("icoop" | "icobi") – Identity of data in filename_blist_sg1.

    - id_blist_sg2 ("icoop" | "icobi") – Identity of data in filename_blist_sg2.

    - backward_compatibility (bool) – compatibility with neighbor detection prior 2025 (less strict).

  property anion_types: set[Element]

    The set of anion types in crystal structure.

    Returns:

      Anions in the crystal structure.

    Return type:

      set[Element]

  classmethod from_files(structure_path: PathLike = 'CONTCAR', icoxxlist_path: PathLike = 'ICOHPLIST.lobster', are_coops: bool = False, are_cobis: bool = False, charge_path: PathLike | None = None, blist_sg1_path: PathLike | None = None, blist_sg2_path: PathLike | None = None, id_blist_sg1: Literal['icoop', 'icobi'] = 'icoop', id_blist_sg2: Literal['icoop', 'icobi'] = 'icobi', **kwargs)

    Instanitate LobsterNeighbors using file paths.

    Parameters:

      - structure_path (PathLike) – Path to structure file, typically CONTCAR

      - icoxxlist_path (PathLike) – Path to ICOHPLIST.lobster or ICOOPLIST.lobster or ICOBILIST.lobster.

      - are_coops (bool) – Whether the file is a ICOOPLIST.lobster (True) or a ICOHPLIST.lobster (False). Only tested for ICOHPLIST.lobster so far.

      - are_cobis (bool) – Whether the file is a ICOBILIST.lobster (True) or a ICOHPLIST.lobster (False).

      - charge_path (PathLike) – Path to Charge.lobster.

      - blist_sg1_path (PathLike) – Path to additional ICOOP, ICOBI data for structure graphs.

      - blist_sg2_path (PathLike) – Path to additional ICOOP, ICOBI data for structure graphs.

      - id_blist_sg1 ("icoop" | "icobi") – Population type in blist_sg1_path.

      - id_blist_sg2 ("icoop" | "icobi") – Population type in in blist_sg2_path.

  get_anion_types() → set[Element]
  get_info_cohps_to_neighbors(path_to_cohpcar: PathLike | None = 'COHPCAR.lobster', coxxcar_obj: CompleteCohp | None = None, isites: list[int] | None = None, only_bonds_to: list[str] | None = None, onlycation_isites: bool = True, per_bond: bool = True, summed_spin_channels: bool = False) → tuple[str | None, CompleteCohp | None]

    Get the COHPs (COOPs or COBIs) as a summed Cohp object and a label from all sites mentioned in isites with neighbors.

    Parameters:

      - path_to_cohpcar (PathLike) – Path to COHPCAR/COOPCAR/COBICAR.

      - coxxcar_obj (CompleteCohp | None) – CompleteCohp object.

      - isites (list[int]) – The indexes of the sites.

      - only_bonds_to (list[str]) – Only show COHPs to selected element, e.g. [“O”].

      - onlycation_isites (bool) – If isites is None, only cation sites will be returned.

      - per_bond (bool) – Whether to normalize per bond.

      - summed_spin_channels (bool) – Whether to sum both spin channels.

    Returns:

      Label for COHP. CompleteCohp: Describe all COHPs/COOPs/COBIs of the sites

      > as given by isites and the other arguments.

    Return type:

      str

  get_info_icohps_between_neighbors(isites: list[int] | None = None, onlycation_isites: bool = True) → ICOHPNeighborsInfo

    Get interactions between neighbors of certain sites.

    Parameters:

      - isites (list[int]) – Site IDs. If is None, all sites will be used.

      - onlycation_isites (bool) – Only use cations, if isite is None.

    Returns:

      ICOHPNeighborsInfo

  get_info_icohps_to_neighbors(isites: list[int] | None = None, onlycation_isites: bool = True) → ICOHPNeighborsInfo

    Get information on the ICOHPs of neighbors for certain sites as identified by their site id.

    This is useful for plotting the COHPs (ICOOPLIST.lobster/ ICOHPLIST.lobster/ICOBILIST.lobster) of a site in the structure.

    Parameters:

      - isites (list[int]) – Site IDs. If is None, all isites will be used to add the ICOHPs of the neighbors.

      - onlycation_isites (bool) – If True and if isite is None, will only analyse the cations sites.

    Returns:

      ICOHPNeighborsInfo

  get_light_structure_environment(only_cation_environments: bool = False, only_indices: list[int] | None = None, on_error: Literal['raise', 'warn', 'ignore'] = 'raise') → LobsterLightStructureEnvironments

    Get a LobsterLightStructureEnvironments object if the structure only contains coordination environments smaller 13.

    Parameters:

      - only_cation_environments (bool) – Only return data for cations.

      - only_indices (list[int]) – Only evaluate indexes in this list.

      - on_error ("raise" | "warn" | "ignore") – Whether to raise an error, warn or ignore if the environment of a site cannot be determined.

    Returns:

      LobsterLightStructureEnvironments

  get_nn_info(structure: Structure | IStructure, n: int, use_weights: bool = False) → dict[str, Any]

    Get coordination number (CN) of site by index.

    Parameters:

      - structure (Structure) – Input structure.

      - n (int) – Index of site for which to determine CN.

      - use_weights (bool) – Whether to use weights for computing the CN (True), or each coordinated site has equal weight (False). The former is not implemented yet.

    Raises:

      ValueError – If use_weights is True, or if arg “structure” and structure used to initialize LobsterNeighbors have different lengths.

    Returns:

      coordination number and a list of nearest neighbors.

    Return type:

      dict[str, Any]

  property molecules_allowed: Literal[False]

    Whether this LobsterNeighbors class can be used with Molecule objects.

  plot_cohps_of_neighbors(path_to_cohpcar: PathLike | None = 'COHPCAR.lobster', coxxcar_obj: CompleteCohp | None = None, isites: list[int] | None = None, onlycation_isites: bool = True, only_bonds_to: list[str] | None = None, per_bond: bool = False, summed_spin_channels: bool = False, xlim: tuple[float, float] | None = None, ylim: tuple[float, float] = (-10, 6), integrated: bool = False) → mpl.axes.Axes

    Plot summed COHPs or COBIs or COOPs.

    Please be careful in the spin polarized case (plots might overlap).

    Parameters:

      - path_to_cohpcar (PathLike) – Path to COHPCAR or COOPCAR or COBICAR.

      - coxxcar_obj (CompleteCohp | None) – CompleteCohp object

      - isites (list[int]) – Site IDs. If empty, all sites will be used to add the ICOHPs of the neighbors.

      - onlycation_isites (bool) – Only use cations, if isite is empty.

      - only_bonds_to (list[str]) – Only anions in this list will be considered.

      - per_bond (bool) – Whether to plot a normalization of the plotted COHP per number of bond (True), or the sum (False).

      - xlim (tuple[float, float]) – Limits of x values.

      - ylim (tuple[float, float]) – Limits of y values.

      - integrated (bool) – Whether to show integrated COHP instead of COHP.

    Returns:

      plt of the COHPs or COBIs or COOPs.

  property structures_allowed: Literal[True]

    Whether this LobsterNeighbors class can be used with Structure objects.

  valences: list[float] | None

check_ICOHPs(lengths_from_ICOHPs, selected_ICOHPs, translation, length_threshold=0.01, energy_threshold=0.1)

## pymatgen.analysis.local_env module

This module provides classes to perform analyses of the local environments (e.g., finding near neighbors) of single sites in molecules and structures.

## pymatgen.analysis.molecule_matcher module

This module provides classes to perform fitting of molecule with arbitrary atom orders. This module is supposed to perform exact comparisons without the atom order correspondence prerequisite, while molecule_structure_comparator is supposed to do rough comparisons with the atom order correspondence prerequisite.

The implementation is based on an excellent python package called rmsd that you can find at https://github.com/charnley/rmsd.

## pymatgen.analysis.molecule_structure_comparator module

This module provides classes to comparison the structures of the two molecule. As long as the two molecule have the same bond connection tables, the molecules are deemed to be same. The atom in the two molecule must be paired accordingly. This module is supposed to perform rough comparisons with the atom order correspondence prerequisite, while molecule_matcher is supposed to do exact comparisons without the atom order correspondence prerequisite.

## pymatgen.analysis.nmr module

A module for NMR analysis.

class ChemicalShielding(cs_matrix, vscale=None)

  Bases: `SquareTensor`

  This class extends the SquareTensor to perform extra analysis unique to NMR Chemical shielding tensors.

  Three notations to describe chemical shielding tensor (RK Harris; Magn. Resonance Chem. 2008, 46, 582-598; DOI: 10.1002/mrc.2225) are supported.

  Authors: Shyam Dwaraknath, Xiaohui Qu

  Create a Chemical Shielding tensor. Note that the constructor uses __new__ rather than __init__ according to the standard method of subclassing numpy ndarrays.

  Parameters:

    - cs_matrix (1x3 or 3x3 array-like) – the 3x3 array-like representing the chemical shielding tensor or a 1x3 array of the primary sigma values corresponding to the principal axis system

    - vscale (6x1 array-like) – 6x1 array-like scaling the Voigt notation vector with the tensor entries

  class HaeberlenNotation(sigma_iso, delta_sigma_iso, zeta, eta)

    Bases: `NamedTuple`

    Create new instance of HaeberlenNotation(sigma_iso, delta_sigma_iso, zeta, eta)

    delta_sigma_iso: Any

      Alias for field number 1

    eta: Any

      Alias for field number 3

    sigma_iso: Any

      Alias for field number 0

    zeta: Any

      Alias for field number 2

  class MarylandNotation(sigma_iso, omega, kappa)

    Bases: `NamedTuple`

    Create new instance of MarylandNotation(sigma_iso, omega, kappa)

    kappa: Any

      Alias for field number 2

    omega: Any

      Alias for field number 1

    sigma_iso: Any

      Alias for field number 0

  class MehringNotation(sigma_iso, sigma_11, sigma_22, sigma_33)

    Bases: `NamedTuple`

    Create new instance of MehringNotation(sigma_iso, sigma_11, sigma_22, sigma_33)

    sigma_11: Any

      Alias for field number 1

    sigma_22: Any

      Alias for field number 2

    sigma_33: Any

      Alias for field number 3

    sigma_iso: Any

      Alias for field number 0

  classmethod from_maryland_notation(sigma_iso, omega, kappa) → Self

    Initialize from Maryland notation.

    Parameters:

      - sigma_iso (float) – isotropic chemical shielding

      - omega (float) – anisotropy

      - kappa (float) – asymmetry parameter

    Returns:

      ChemicalShielding

  property haeberlen_values

    The Chemical shielding tensor in Haeberlen Notation.

  property maryland_values

    The Chemical shielding tensor in Maryland Notation.

  property mehring_values

    The Chemical shielding tensor in Mehring Notation.

  property principal_axis_system

    A chemical shielding tensor aligned to the principle axis system so that only the 3 diagonal components are non-zero.

class ElectricFieldGradient(efg_matrix, vscale=None)

  Bases: `SquareTensor`

  This class extends the SquareTensor to perform extra analysis unique to NMR Electric Field Gradient tensors in units of V/Angstrom^2.

  Authors: Shyam Dwaraknath, Xiaohui Qu

  Create a Chemical Shielding tensor. Note that the constructor uses __new__ rather than __init__ according to the standard method of subclassing numpy ndarrays.

  Parameters:

    - efg_matrix (1x3 or 3x3 array-like) – the 3x3 array-like representing the electric field tensor or a 1x3 array of the primary values corresponding to the principal axis system

    - vscale (6x1 array-like) – 6x1 array-like scaling the Voigt notation vector with the tensor entries

  property V_xx

    First diagonal element.

  property V_yy

    Second diagonal element.

  property V_zz

    Third diagonal element.

  property asymmetry

    Asymmetry of the electric field tensor defined as (V_yy - V_xx)/V_zz.

  coupling_constant(specie)

    Compute the coupling constant C_q as defined in:

    > Wasylishen R E, Ashbrook S E, Wimperis S. NMR of quadrupolar nuclei in solid materials[M]. John Wiley & Sons, 2012. (Chapter 3.2).

    C_q for a specific atom type for this electric field tensor:

      > C_q=e*Q*V_zz/h

      h: Planck’s constant Q: nuclear electric quadrupole moment in mb (millibarn e: elementary proton charge

    Parameters:

      specie – flexible input to specify the species at this site. Can take a isotope or element string, Species object, or Site object

    Returns:

      the coupling constant as a FloatWithUnit in MHz

  property principal_axis_system

    An electric field gradient tensor aligned to the principle axis system so that only the 3 diagonal components are non-zero.

## pymatgen.analysis.optics module

Perform optical property calculations.

class DielectricAnalysis(energies: list[float], eps_real: list[list[float]], eps_imag: list[list[float]])

  Bases: `object`

  Class to compute optical properties of materials based on provided energy levels, real and imaginary components of the dielectric function. The resulting properties include wavelength, refractive index (n), extinction coefficient (k), reflectivity (R), absorptivity (L), and transmittance (T) for up to six configurations.

  This class provides capabilities to compute these properties from supplied dielectric data or parsed data from VASP calculation results.

  energies

    Array of energy levels in electron volts (eV).

    Type:

      numpy.ndarray

  eps_real

    Array of real parts of the dielectric function for different configurations. The structure aligns with the input list provided at initialization.

    Type:

      numpy.ndarray

  eps_imag

    Array of imaginary parts of the dielectric function matching the structure of eps_real.

    Type:

      numpy.ndarray

  wavelengths

    Array of wavelengths (in nanometers) corresponding to the energy levels. Computed using Planck’s constant and the speed of light.

    Type:

      numpy.ndarray

  n

    Array of refractive indices for each energy level and corresponding configuration.

    Type:

      numpy.ndarray

  k

    Array of extinction coefficients for each energy level and corresponding configuration.

    Type:

      numpy.ndarray

  R

    Array of reflectivity values for each energy level and corresponding configuration.

    Type:

      numpy.ndarray

  L

    Array of absorptivity values for each energy level and corresponding configuration.

    Type:

      numpy.ndarray

  T

    Array of transmittance values for each energy level and corresponding configuration.

    Type:

      numpy.ndarray

  Class to compute optical properties of materials based on provided energy levels, real and imaginary components of the dielectric function. The resulting properties include wavelength, refractive index (n), extinction coefficient (k), reflectivity (R), absorptivity (L), and transmittance (T).

  Parameters:

    - energies (list[float]) – List of energy levels in electron volts (eV).

    - eps_real (list[list[float]]) – 2D list of real parts of the dielectric function for different configurations. The outer list corresponds to different energy levels, and the inner list corresponds to configurations.

    - eps_imag (list[list[float]]) – 2D list of imaginary parts of the dielectric function matching the structure of eps_real.

  classmethod from_vasprun(vasprun: Vasprun) → DielectricAnalysis

    Creates an instance of the DielectricAnalysis class using the dielectric data extracted from a VASP calculation parsed by the vasprun object. The dielectric data typically includes the energies, real part of the dielectric tensor, and imaginary part of the dielectric tensor.

    Parameters:

      - vasprun (Vasprun) – Object containing parsed VASP calculation results, specifically

      - calculation. (the dielectric data extracted from the)

    Returns:

      An instance of the DielectricAnalysis class initialized with the dielectric data (energies, real dielectric tensor, and imaginary dielectric tensor).

    Return type:

      DielectricAnalysis

## pymatgen.analysis.phase_diagram module

This module defines tools to generate and analyze phase diagrams.

class CompoundPhaseDiagram(entries: Sequence[Entry], terminal_compositions: Sequence[Composition], normalize_terminal_compositions: bool = True)

  Bases: `PhaseDiagram`

  Generates phase diagrams from compounds as terminations instead of elements.

  Initialize a CompoundPhaseDiagram.

  Parameters:

    - entries ([PDEntry]) – Sequence of input entries. For example, if you want a Li2O-P2O5 phase diagram, you might have all Li-P-O entries as an input.

    - terminal_compositions (list[Composition]) – Terminal compositions of phase space. In the Li2O-P2O5 example, these will be the Li2O and P2O5 compositions.

    - normalize_terminal_compositions (bool) – Whether to normalize the terminal compositions to a per atom basis. If normalized, the energy above hulls will be consistent for comparison across systems. Non-normalized terminals are more intuitive in terms of compositional breakdowns.

  amount_tol: ClassVar[float] = 1e-05
  as_dict()

    Get MSONable dict representation of CompoundPhaseDiagram.

  classmethod from_dict(dct: dict) → Self
    Parameters:

      dct (dict) – dictionary representation of CompoundPhaseDiagram.

    Returns:

      CompoundPhaseDiagram

  static num2str(num)

    Convert number to a list of letter(s). First letter must be f.

    Parameters:

      int (num) – Number to convert

    Return type:

      str

    :return Converted string

  transform_entries(entries: Sequence[Entry], terminal_compositions: Sequence[Composition]) → tuple[list[TransformedPDEntry], dict[Composition, DummySpecies]]

    Method to transform all entries to the composition coordinate in the terminal compositions. If the entry does not fall within the space defined by the terminal compositions, they are excluded. For example, Li3PO4 is mapped into a Li2O:1.5, P2O5:0.5 composition. The terminal compositions are represented by DummySpecies.

    TODO: update serialization here.

    Parameters:

      - entries – Sequence of all input entries

      - terminal_compositions – Terminal compositions of phase space.

    Returns:

      Sequence of TransformedPDEntries falling within the phase space.

class GrandPotPDEntry(entry: PDEntry, chempots: dict[Element, float], name: str | None = None)

  Bases: `PDEntry`

  A grand potential pd entry object encompassing all relevant data for phase diagrams. Chemical potentials are given as a element-chemical potential dict.

  Parameters:

    - entry – A PDEntry-like object.

    - chempots – Chemical potential specification as {Element: float}.

    - name – Optional parameter to name the entry. Defaults to the reduced chemical formula of the original entry.

  as_dict() → dict[str, Any]

    Get MSONable dict representation of GrandPotPDEntry.

  property chemical_energy: float

    The chemical energy term mu*N in the grand potential.

    Returns:

      The chemical energy term mu*N in the grand potential

  property composition: Composition

    The composition after removing free species.

    Returns:

      Composition

  property energy: float

    Grand potential energy.

  classmethod from_dict(dct: dict) → Self
    Parameters:

      dct (dict) – dictionary representation of GrandPotPDEntry.

    Returns:

      GrandPotPDEntry

class GrandPotentialPhaseDiagram(entries: Collection[Entry], chempots: dict[Element, float], elements: Collection[Element] | None = None, *, computed_data: dict[str, Any] | None = None)

  Bases: `PhaseDiagram`

  A class representing a Grand potential phase diagram. Grand potential phase diagrams are essentially phase diagrams that are open to one or more components. To construct such phase diagrams, the relevant free energy is the grand potential, which can be written as the Legendre transform of the Gibbs free energy as follows.

  Grand potential = G - u_X N_X

  The algorithm is based on the work in the following papers:

  1. S. P. Ong, L. Wang, B. Kang, and G. Ceder, Li-Fe-P-O2 Phase Diagram from First Principles Calculations. Chem. Mater., 2008, 20(5), 1798-1807. doi:10.1021/cm702327g

  2. S. P. Ong, A. Jain, G. Hautier, B. Kang, G. Ceder, Thermal stabilities of delithiated olivine MPO4 (M=Fe, Mn) cathodes investigated using first principles calculations. Electrochem. Comm., 2010, 12(3), 427-430. doi:10.1016/j.elecom.2010.01.010

  Standard constructor for grand potential phase diagram.

  TODO: update serialization here.

  Parameters:

    - entries (Sequence[Entry]) – A list of Entry objects having an energy, energy_per_atom and composition.

    - chempots (dict[Element, float]) – Specify the chemical potentials of the open elements.

    - elements (Sequence[Element]) – Optional list of elements in the phase diagram. If set to None, the elements are determined from the entries themselves.

    - computed_data (dict[str, Any]) – A dict containing pre-computed data. This allows PhaseDiagram object to be reconstituted without performing the expensive convex hull computation. The dict is the output from the PhaseDiagram._compute() method and is stored in PhaseDiagram.computed_data when generated for the first time.

  as_dict()

    Get MSONable dict representation of GrandPotentialPhaseDiagram.

  classmethod from_dict(dct: dict) → Self
    Parameters:

      dct (dict) – dictionary representation of GrandPotentialPhaseDiagram.

    Returns:

      GrandPotentialPhaseDiagram

class PDEntry(composition: CompositionLike, energy: float, name: str | None = None, attribute: object = None)

  Bases: `Entry`

  An object encompassing all relevant data for phase diagrams.

  composition

    The composition associated with the PDEntry.

    Type:

      Composition

  energy

    The energy associated with the entry.

    Type:

      float

  name

    A name for the entry. This is the string shown in the phase diagrams. By default, this is the reduced formula for the composition, but can be set to some other string for display purposes.

    Type:

      str

  attribute

    A arbitrary attribute. Can be used to specify that the entry is a newly found compound, or to specify a particular label for the entry, etc. An attribute can be anything but must be MSONable.

    Type:

      MSONable

  Parameters:

    - composition (CompositionLike) – Composition

    - energy (float) – Energy for composition.

    - name (str) – Optional parameter to name the entry. Defaults to the reduced chemical formula.

    - attribute – Optional attribute of the entry. Must be MSONable.

  as_dict() → dict[str, Any]

    Get MSONable dict representation of PDEntry.

  property energy: float

    The entry’s energy.

  classmethod from_dict(dct: dict[str, Any]) → Self
    Parameters:

      dct (dict) – dictionary representation of PDEntry.

    Returns:

      PDEntry

class PDPlotter(phasediagram: PhaseDiagram, show_unstable: float = 0.2, backend: Literal['plotly', 'matplotlib'] = 'plotly', ternary_style: Literal['2d', '3d'] = '2d', **plotkwargs)

  Bases: `object`

  A plotting class for compositional phase diagrams.

  To use, initialize this class with a PhaseDiagram object containing 1-4 components and call get_plot() or show().

  Parameters:

    - phasediagram (PhaseDiagram) – PhaseDiagram object (must be 1-4 components).

    - show_unstable (float) – Whether unstable (above the hull) phases will be plotted. If a number > 0 is entered, all phases with e_hull < show_unstable (eV/atom) will be shown.

    - backend ("plotly" | "matplotlib") – Python package to use for plotting. Defaults to “plotly”.

    - ternary_style ("2d" | "3d") – Ternary phase diagrams are typically plotted in two-dimensions (2d), but can be plotted in three dimensions (3d) to visualize the depth of the hull. This argument only applies when backend=”plotly”. Defaults to “2d”.

    - **plotkwargs (dict) –

      Keyword args passed to matplotlib.pyplot.plot (only applies when backend=”matplotlib”). Can be used to customize markers etc. If not set, the default is:

      > {

      >   “markerfacecolor”: “#4daf4a”, “markersize”: 10, “linewidth”: 3

      > }.

  get_chempot_range_map_plot(elements: Sequence[Element], referenced: bool = True) → plt.Axes

    Get a plot of the chemical potential range _map. Currently works only for 3-component PDs.

    Note: this functionality is now included in the ChemicalPotentialDiagram class (pymatgen.analysis.chempot_diagram).

    Parameters:

      - elements – Sequence of elements to be considered as independent variables. e.g. if you want to show the stability ranges of all Li-Co-O phases w.r.t. to uLi and uO, you will supply [Element(“Li”), Element(“O”)]

      - referenced – if True, gives the results with a reference being the energy of the elemental phase. If False, gives absolute values.

    Returns:

      matplotlib axes object.

    Return type:

      plt.Axes

  get_contour_pd_plot() → Axes

    Plot a contour phase diagram plot, where phase triangles are colored according to degree of instability by interpolation. Currently only works for 3-component phase diagrams.

    Returns:

      A matplotlib plot object.

  get_plot(label_stable: bool = True, label_unstable: bool = True, ordering: Sequence[Literal['Up', 'Left', 'Right']] | None = None, energy_colormap: str | Colormap | None = None, process_attributes: bool = False, ax: plt.Axes | None = None, label_uncertainties: bool = False, fill: bool = True, highlight_entries: Collection[PDEntry] | None = None) → go.Figure | plt.Axes | None
    Parameters:

      - label_stable – Whether to label stable compounds.

      - label_unstable – Whether to label unstable compounds.

      - ordering – Ordering of vertices, given as a list [“Up”, “Left”, “Right”] (matplotlib only).

      - energy_colormap – Colormap for coloring energy (matplotlib only).

      - process_attributes – Whether to process the attributes (matplotlib only).

      - ax – Existing matplotlib Axes object if plotting multiple phase diagrams (matplotlib only).

      - label_uncertainties – Whether to add error bars to the hull. For binaries, this also shades the hull with the uncertainty window. (plotly only).

      - fill – Whether to shade the hull. For ternary_2d and quaternary plots, this colors facets arbitrarily for visual clarity. For ternary_3d plots, this shades the hull by formation energy (plotly only).

      - highlight_entries – Entries to highlight in the plot (plotly only). This will create a new marker trace that is separate from the other entries.

    Returns:

      Plotly figure or matplotlib axes object depending on backend.

    Return type:

      go.Figure | plt.Axes

  property pd_plot_data: tuple[list, dict, dict]

    Plotting data for phase diagram. Cached for repetitive calls.

    2-comp - Full hull with energies 3/4-comp - Projection into 2D or 3D Gibbs triangles

    Returns:

      - lines: a list of list of coordinates for lines in the PD.

      - stable_entries: a dict of {coordinates: entry} for each stable node

          in the phase diagram. (Each coordinate can only have one stable phase)

      - unstable_entries: a dict of {entry: coordinates} for all unstable

          nodes in the phase diagram.

    Return type:

      A tuple containing three objects (lines, stable_entries, unstable_entries)

  plot_chempot_range_map(elements: Sequence[Element], referenced: bool = True) → None

    Plot the chemical potential range _map using matplotlib. Currently works only for 3-component PDs. This shows the plot but does not return it.

    Note: this functionality is now included in the ChemicalPotentialDiagram class (pymatgen.analysis.chempot_diagram).

    Parameters:

      - elements – Sequence of elements to be considered as independent variables. e.g. if you want to show the stability ranges of all Li-Co-O phases w.r.t. to uLi and uO, you will supply [Element(“Li”), Element(“O”)]

      - referenced – if True, gives the results with a reference being the energy of the elemental phase. If False, gives absolute values.

  plot_element_profile(element: Element, comp: Composition, show_label_index: list[int] | None = None, xlim: float = 5) → Axes

    Draw the element profile plot for a composition varying different chemical potential of an element.

    X value is the negative value of the chemical potential reference to elemental chemical potential. For example, if choose Element(“Li”), X= -(μLi-μLi0), which corresponds to the voltage versus metal anode. Y values represent for the number of element uptake in this composition (unit: per atom). All reactions are printed to help choosing the profile steps you want to show label in the plot.

    Parameters:

      - element (Element) – An element of which the chemical potential is considered. It also must be in the phase diagram.

      - comp (Composition) – A composition.

      - show_label_index (list of integers) – The labels for reaction products you want to show in the plot. Default to None (not showing any annotation for reaction products). For the profile steps you want to show the labels, just add it to the show_label_index. The profile step counts from zero. For example, you can set show_label_index=[0, 2, 5] to label profile step 0,2,5.

      - xlim (float) – The max x value. x value is from 0 to xlim. Default to 5 eV.

    Returns:

      Plot of element profile evolution by varying the chemical potential of an element.

  show(*args, **kwargs) → None

    Draw the phase diagram with the provided arguments and display it. This shows the figure but does not return it.

    Parameters:

      - *args – Passed to get_plot.

      - **kwargs – Passed to get_plot.

  write_image(stream: str | StringIO, image_format: str = 'svg', **kwargs) → None

    Directly save the plot to a file. This is a wrapper for calling plt.savefig() or fig.write_image(), depending on the backend. For more customization, it is recommended to call those methods directly.

    Parameters:

      - stream (str | StringIO) – Filename or StringIO stream.

      - image_format (str) – Can be any supported image format for the plotting backend. Defaults to ‘svg’ (vector graphics).

      - **kwargs – Optinoal kwargs passed to the get_plot function.

class PatchedPhaseDiagram(entries: Sequence[Entry] | set[Entry], elements: Sequence[Element] | None = None, keep_all_spaces: bool = False, verbose: bool = False, *, computed_data: dict[str, Any] | None = None)

  Bases: `PhaseDiagram`

  Computing the Convex Hull of a large set of data in multiple dimensions is highly expensive. This class acts to breakdown large chemical spaces into smaller chemical spaces which can be computed much more quickly due to having both reduced dimensionality and data set sizes.

  subspaces ({str

    {Element, }}): Dictionary of the sets of elements for each of the PhaseDiagrams within the PatchedPhaseDiagram.

  pds ({str

    PhaseDiagram}): Dictionary of PhaseDiagrams within the PatchedPhaseDiagram.

  all_entries

    All entries provided for Phase Diagram construction. Note that this does not mean that all these entries are actually used in the phase diagram. For example, this includes the positive formation energy entries that are filtered out before Phase Diagram construction.

    Type:

      list[PDEntry]

  min_entries

    List of the lowest energy entries for each composition in the data provided for Phase Diagram construction.

    Type:

      list[PDEntry]

  el_refs

    List of elemental references for the phase diagrams. These are entries corresponding to the lowest energy element entries for simple compositional phase diagrams.

    Type:

      list[PDEntry]

  elements

    List of elements in the phase diagram.

    Type:

      list[Element]

  NOTE following methods are inherited unchanged from PhaseDiagram:

    - __repr__

    - all_entries_hulldata

    - unstable_entries

    - stable_entries

    - get_form_energy

    - get_form_energy_per_atom

    - get_hull_energy

    - get_e_above_hull

    - get_decomp_and_e_above_hull

    - get_decomp_and_phase_separation_energy

    - get_phase_separation_energ

  Parameters:

    - entries (Sequence[Entry] | set[Entry]) – A list of Entry objects having an energy, energy_per_atom and composition.

    - elements (Sequence[Element], optional) – Optional list of elements in the phase diagram. If set to None, the elements are determined from the entries themselves and are sorted alphabetically. If specified, element ordering (e.g. for pd coordinates) is preserved.

    - keep_all_spaces (bool) – Pass True to keep chemical spaces that are subspaces of other spaces.

    - verbose (bool) – Whether to show progress bar during convex hull construction.

    - computed_data (dict) – A dict containing pre-computed data. This allows PatchedPhaseDiagram object to be reconstituted without performing the expensive convex hull computation. The dict is the output from the PatchedPhaseDiagram._compute() method.

  as_dict() → dict[str, Any]

    Write the entries and elements used to construct the PatchedPhaseDiagram to a dictionary.

  classmethod from_dict(dct: dict) → Self

    Reconstruct PatchedPhaseDiagram from dictionary serialization.

    Parameters:

      dct (dict) – dictionary representation of PatchedPhaseDiagram.

    Returns:

      PatchedPhaseDiagram

  get_all_chempots()

    Not Implemented - See PhaseDiagram.

  get_chempot_range_map()

    Not Implemented - See PhaseDiagram.

  get_chempot_range_stability_phase()

    Not Implemented - See PhaseDiagram.

  get_composition_chempots()

    Not Implemented - See PhaseDiagram.

  get_critical_compositions()

    Not Implemented - See PhaseDiagram.

  get_decomp_and_e_above_hull(entry: PDEntry, allow_negative: bool = False, check_stable: bool = False, on_error: Literal['raise', 'warn', 'ignore'] = 'raise') → tuple[dict[PDEntry, float], float] | tuple[None, None]

    Same as method on parent class PhaseDiagram except check_stable defaults to False for speed. See https://github.com/materialsproject/pymatgen/issues/2840 for details.

  get_decomposition(comp: Composition) → dict[PDEntry, float]

    See PhaseDiagram.

    Parameters:

      comp (Composition) – A composition

    Returns:

      amount} where amount is the amount of the fractional composition.

    Return type:

      Decomposition as a dict of {PDEntry

  get_element_profile()

    Not Implemented - See PhaseDiagram.

  get_equilibrium_reaction_energy(entry: Entry) → float

    See PhaseDiagram.

    NOTE this is only approximately the same as the what we would get from PhaseDiagram as we make use of the slsqp approach inside get_phase_separation_energy().

    Parameters:

      entry (PDEntry) – A PDEntry like object

    Returns:

      Equilibrium reaction energy of entry. Stable entries should have equilibrium reaction energy <= 0. The energy is given per atom.

  get_pd_for_entry(entry: Entry | Composition) → PhaseDiagram

    Get the possible phase diagrams for an entry.

    Parameters:

      entry (PDEntry | Composition) – A PDEntry or Composition-like object

    Returns:

      phase diagram that the entry is part of

    Return type:

      PhaseDiagram

    Raises:

      ValueError – If no suitable PhaseDiagram is found for the entry.

  get_transition_chempots()

    Not Implemented - See PhaseDiagram.

  getmu_vertices_stability_phase()

    Not Implemented - See PhaseDiagram.

  static remove_redundant_spaces(spaces: set[frozenset[Element]], keep_all_spaces: bool = False) → set[frozenset[Element]]

class PhaseDiagram(entries: Collection[Entry], elements: Collection[Element] | None = None, *, computed_data: dict[str, Any] | None = None)

  Bases: `MSONable`

  Simple phase diagram class taking in elements and entries as inputs. The algorithm is based on the work in the following papers:

  1. 19. 16. Ong, L. Wang, B. Kang, and G. Ceder, Li-Fe-P-O2 Phase Diagram from

     > First Principles Calculations. Chem. Mater., 2008, 20(5), 1798-1807. doi:10.1021/cm702327g

  2. 19. 16. Ong, A. Jain, G. Hautier, B. Kang, G. Ceder, Thermal stabilities

     > of delithiated olivine MPO4 (M=Fe, Mn) cathodes investigated using first principles calculations. Electrochem. Comm., 2010, 12(3), 427-430. doi:10.1016/j.elecom.2010.01.010

  dim

    The dimensionality of the phase diagram.

    Type:

      int

  elements

    Elements in the phase diagram.

  el_refs

    List of elemental references for the phase diagrams. These are entries corresponding to the lowest energy element entries for simple compositional phase diagrams.

  all_entries

    All entries provided for Phase Diagram construction. Note that this does not mean that all these entries are actually used in the phase diagram. For example, this includes the positive formation energy entries that are filtered out before Phase Diagram construction.

  qhull_entries

    Actual entries used in convex hull. Excludes all positive formation energy entries.

  qhull_data

    Data used in the convex hull operation. This is essentially a matrix of composition data and energy per atom values created from qhull_entries.

  facets

    Facets of the phase diagram in the form of [[1,2,3],[4,5,6]…]. For a ternary, it is the indices (references to qhull_entries and qhull_data) for the vertices of the phase triangles. Similarly extended to higher D simplices for higher dimensions.

  simplices

    The simplices of the phase diagram as a list of np.ndarray, i.e., the list of stable compositional coordinates in the phase diagram.

  Parameters:

    - entries (list[PDEntry]) – A list of PDEntry-like objects having an energy, energy_per_atom and composition.

    - elements (list[Element]) – Optional list of elements in the phase diagram. If set to None, the elements are determined from the entries themselves and are sorted alphabetically. If specified, element ordering (e.g. for pd coordinates) is preserved.

    - computed_data (dict) – A dict containing pre-computed data. This allows PhaseDiagram object to be reconstituted without performing the expensive convex hull computation. The dict is the output from the PhaseDiagram._compute() method and is stored in PhaseDiagram.computed_data when generated for the first time.

  property all_entries_hulldata: ndarray

    The ndarray used to construct the convex hull.

  as_dict() → dict[str, Any]

    Get MSONable dict representation of PhaseDiagram.

  property dim: int

    The dimensionality of the phase diagram.

  formation_energy_tol: ClassVar[float] = 1e-11
  classmethod from_dict(dct: dict[str, Any]) → Self
    Parameters:

      dct (dict) – dictionary representation of PhaseDiagram.

    Returns:

      PhaseDiagram

  get_all_chempots(comp: Composition) → dict[str, dict[Element, float]]

    Get chemical potentials at a given composition.

    Parameters:

      comp (Composition) – Composition

    Returns:

      Chemical potentials.

  get_chempot_range_map(elements: Sequence[Element], referenced: bool = True, joggle: bool = True) → dict[Element, list[Simplex]]

    Get a chemical potential range map for each stable entry.

    Parameters:

      - elements – Sequence of elements to be considered as independent variables. e.g. if you want to show the stability ranges of all Li-Co-O phases with respect to mu_Li and mu_O, you will supply [Element(“Li”), Element(“O”)]

      - referenced – If True, gives the results with a reference being the energy of the elemental phase. If False, gives absolute values.

      - joggle (bool) – Whether to joggle the input to avoid precision errors.

    Returns:

      [simplices]}. The list of simplices are the sides of the N-1 dim polytope bounding the allowable chemical potential range of each entry.

    Return type:

      Returns a dict of the form {entry

  get_chempot_range_stability_phase(target_comp: Composition, open_elt: Element) → dict[Element, tuple[float, float]]

    Get a set of chemical potentials corresponding to the max and min chemical potential of the open element for a given composition. It is quite common to have for instance a ternary oxide (e.g., ABO3) for which you want to know what are the A and B chemical potential leading to the highest and lowest oxygen chemical potential (reducing and oxidizing conditions). This is useful for defect computations.

    Parameters:

      - target_comp – A Composition object

      - open_elt – Element that you want to constrain to be max or min

    Returns:

      A dictionary of the form {Element: (min_mu, max_mu)} where min_mu and max_mu are the minimum and maximum chemical potentials for the given element (as “absolute” values, i.e. not referenced to 0).

    Return type:

      dict[Element, (float, float)]

  get_composition_chempots(comp: Composition) → dict[Element, float]

    Get the chemical potentials for all elements at a given composition.

    Parameters:

      comp (Composition) – Composition

    Returns:

      Dictionary of chemical potentials.

  get_critical_compositions(comp1: Composition, comp2: Composition) → list[Composition]

    Get the critical compositions along the tieline between two compositions. I.e. where the decomposition products change. The endpoints are also returned.

    Parameters:

      - comp1 (Composition) – First composition to define the tieline

      - comp2 (Composition) – Second composition to define the tieline

    Returns:

      list of critical compositions. All are of

        the form x * comp1 + (1-x) * comp2

    Return type:

      [(Composition)]

  get_decomp_and_e_above_hull(entry: PDEntry, allow_negative: bool = False, check_stable: bool = True, on_error: Literal['raise', 'warn', 'ignore'] = 'raise') → tuple[dict[PDEntry, float], float] | tuple[None, None]

    Provides the decomposition and energy above convex hull for an entry. Due to caching, can be much faster if entries with the same composition are processed together.

    Parameters:

      - entry (PDEntry) – A PDEntry like object

      - allow_negative (bool) – Whether to allow negative e_above_hulls. Used to calculate equilibrium reaction energies. Defaults to False.

      - check_stable (bool) – Whether to first check whether an entry is stable. In normal circumstances, this is the faster option since checking for stable entries is relatively fast. However, if you have a huge proportion of unstable entries, then this check can slow things down. You should then set this to False.

      - on_error ('raise' | 'warn' | 'ignore') – What to do if no valid decomposition was found. ‘raise’ will throw ValueError. ‘warn’ will print return (None, None). ‘ignore’ just returns (None, None). Defaults to ‘raise’.

    Raises:

      ValueError – If on_error is ‘raise’ and no valid decomposition exists in this phase diagram for given entry.

    Returns:

      The decomposition is provided

        as a dict of {PDEntry: amount} where amount is the amount of the fractional composition. Stable entries should have energy above convex hull of 0. The energy is given per atom.

    Return type:

      tuple[decomp, energy_above_hull]

  get_decomp_and_hull_energy_per_atom(comp: Composition) → tuple[dict[PDEntry, float], float]
    Parameters:

      comp (Composition) – Input composition.

    Returns:

      Energy of lowest energy equilibrium at desired composition per atom

  get_decomp_and_phase_separation_energy(entry: PDEntry, space_limit: int = 200, stable_only: bool = False, tols: Sequence[float] = (1e-08,), maxiter: int = 1000, **kwargs: Any) → tuple[dict[PDEntry, float], float] | tuple[None, None]

    Provides the combination of entries in the PhaseDiagram that gives the lowest formation enthalpy with the same composition as the given entry excluding entries with the same composition and the energy difference per atom between the given entry and the energy of the combination found.

    For unstable entries that are not polymorphs of stable entries (or completely novel entries) this is simply the energy above (or below) the convex hull.

    For entries with the same composition as one of the stable entries in the phase diagram setting stable_only to False (Default) allows for entries not previously on the convex hull to be considered in the combination. In this case the energy returned is what is referred to as the decomposition enthalpy in:

    1. Bartel, C., Trewartha, A., Wang, Q., Dunn, A., Jain, A., Ceder, G.,

         A critical examination of compound stability predictions from machine-learned formation energies, npj Computational Materials 6, 97 (2020)

    For stable entries setting stable_only to True returns the same energy as get_equilibrium_reaction_energy. This function is based on a constrained optimization rather than recalculation of the convex hull making it algorithmically cheaper. However, if tol is too loose there is potential for this algorithm to converge to a different solution.

    Parameters:

      - entry (PDEntry) – A PDEntry like object.

      - space_limit (int) – The maximum number of competing entries to consider before calculating a second convex hull to reducing the complexity of the optimization.

      - stable_only (bool) – Only use stable materials as competing entries.

      - tols (list[float]) – Tolerances for convergence of the SLSQP optimization when finding the equilibrium reaction. Tighter tolerances tested first.

      - maxiter (int) – The maximum number of iterations of the SLSQP optimizer when finding the equilibrium reaction.

      - **kwargs – Passed to get_decomp_and_e_above_hull.

    Returns:

      The decomposition is given as a dict of {PDEntry, amount}

        for all entries in the decomp reaction where amount is the amount of the fractional composition. The phase separation energy is given per atom.

    Return type:

      tuple[decomp, energy]

  get_decomposition(comp: Composition) → dict[PDEntry, float]

    Provides the decomposition at a particular composition.

    Parameters:

      comp (Composition) – A composition

    Returns:

      amount} where amount is the amount of the fractional composition.

    Return type:

      Decomposition as a dict of {PDEntry

  get_e_above_hull(entry: PDEntry, **kwargs: Any) → float | None

    Provides the energy above convex hull for an entry.

    Parameters:

      - entry (PDEntry) – A PDEntry like object.

      - **kwargs – Passed to get_decomp_and_e_above_hull().

    Returns:

      Energy above convex hull of entry. Stable entries should have

        energy above hull of 0. The energy is given per atom.

    Return type:

      float | None

  get_element_profile(element: Element, comp: Composition, comp_tol: float = 1e-05) → list[dict[str, Any]]

    Provides the element evolution data for a composition. For example, can be used to analyze Li conversion voltages by varying mu_Li and looking at the phases formed. Also can be used to analyze O2 evolution by varying mu_O2.

    Parameters:

      - element – An element. Must be in the phase diagram.

      - comp – A Composition

      - comp_tol – The tolerance to use when calculating decompositions. Phases with amounts less than this tolerance are excluded. Defaults to 1e-5.

    Returns:

      [ {‘chempot’: -10.487582, ‘evolution’: -2.0, ‘reaction’: Reaction Object], …]

    Return type:

      Evolution data as a list of dictionaries of the following format

  get_equilibrium_reaction_energy(entry: PDEntry) → float | None

    Provides the reaction energy of a stable entry from the neighboring equilibrium stable entries (also known as the inverse distance to hull).

    Parameters:

      entry (PDEntry) – A PDEntry like object

    Returns:

      Equilibrium reaction energy of entry. Stable entries should have

        equilibrium reaction energy <= 0. The energy is given per atom.

    Return type:

      float | None

  get_form_energy(entry: PDEntry) → float

    Get the formation energy for an entry (NOT normalized) from the elemental references.

    Parameters:

      entry (PDEntry) – A PDEntry-like object.

    Returns:

      Formation energy from the elemental references.

    Return type:

      float

  get_form_energy_per_atom(entry: PDEntry) → float

    Get the formation energy per atom for an entry from the elemental references.

    Parameters:

      entry (PDEntry) – An PDEntry-like object

    Returns:

      Formation energy per atom from the elemental references.

  get_hull_energy(comp: Composition) → float
    Parameters:

      comp (Composition) – Input composition.

    Returns:

      Energy of lowest energy equilibrium at desired composition. Not

        normalized by atoms, i.e. E(Li4O2) = 2 * E(Li2O)

  get_hull_energy_per_atom(comp: Composition, **kwargs) → float
    Parameters:

      comp (Composition) – Input composition.

    Returns:

      Energy of lowest energy equilibrium at desired composition.

  get_phase_separation_energy(entry: PDEntry, **kwargs)

    Provides the energy to the convex hull for the given entry. For stable entries already in the phase diagram the algorithm provides the phase separation energy which is referred to as the decomposition enthalpy in:

    1. Bartel, C., Trewartha, A., Wang, Q., Dunn, A., Jain, A., Ceder, G.,

         A critical examination of compound stability predictions from machine-learned formation energies, npj Computational Materials 6, 97 (2020)

    Parameters:

      - entry (PDEntry) – A PDEntry like object

      - **kwargs –

        Keyword args passed to get_decomp_and_decomp_energy space_limit (int): The maximum number of competing entries to consider. stable_only (bool): Only use stable materials as competing entries tol (float): The tolerance for convergence of the SLSQP optimization

        > when finding the equilibrium reaction.

        maxiter (int): The maximum number of iterations of the SLSQP optimizer

          when finding the equilibrium reaction.

    Returns:

      phase separation energy per atom of entry. Stable entries should have energies <= 0, Stable elemental entries should have energies = 0 and unstable entries should have energies > 0. Entries that have the same composition as a stable energy may have positive or negative phase separation energies depending on their own energy.

  get_plot(show_unstable: float = 0.2, backend: Literal['plotly', 'matplotlib'] = 'plotly', ternary_style: Literal['2d', '3d'] = '2d', label_stable: bool = True, label_unstable: bool = True, ordering: Sequence[Literal['Up', 'Left', 'Right']] | None = None, energy_colormap: str | Colormap | None = None, process_attributes: bool = False, ax: plt.Axes | None = None, label_uncertainties: bool = False, fill: bool = True, **kwargs) → go.Figure | plt.Axes

    Convenient wrapper for PDPlotter. Initializes a PDPlotter object and calls get_plot() with provided combined arguments.

    Plotting is only supported for phase diagrams with <=4 elements (unary, binary, ternary, or quaternary systems).

    Parameters:

      - show_unstable (float) – Whether unstable (above the hull) phases will be plotted. If a number > 0 is entered, all phases with e_hull < show_unstable (eV/atom) will be shown.

      - backend ("plotly" | "matplotlib") – Python package to use for plotting. Defaults to “plotly”.

      - ternary_style ("2d" | "3d") – Ternary phase diagrams are typically plotted in two-dimensions (2d), but can be plotted in three dimensions (3d) to visualize the depth of the hull. This argument only applies when backend=”plotly”. Defaults to “2d”.

      - label_stable – Whether to label stable compounds.

      - label_unstable – Whether to label unstable compounds.

      - ordering – Ordering of vertices (matplotlib backend only).

      - energy_colormap – Colormap for coloring energy (matplotlib backend only).

      - process_attributes – Whether to process the attributes (matplotlib backend only).

      - ax – Existing Axes object if plotting multiple phase diagrams (matplotlib backend only).

      - label_uncertainties – Whether to add error bars to the hull (plotly backend only). For binaries, this also shades the hull with the uncertainty window.

      - fill – Whether to shade the hull. For ternary_2d and quaternary plots, this colors facets arbitrarily for visual clarity. For ternary_3d plots, this shades the hull by formation energy (plotly backend only).

      - **kwargs (dict) – Keyword args passed to PDPlotter.get_plot(). Can be used to customize markers etc. If not set, the default is { “markerfacecolor”: “#4daf4a”, “markersize”: 10, “linewidth”: 3 }

  get_reference_energy(comp: Composition) → float

    Sum of elemental reference energies over all elements in a composition.

    Parameters:

      comp (Composition) – Input composition.

    Returns:

      Reference energy

    Return type:

      float

  get_reference_energy_per_atom(comp: Composition) → float

    Sum of elemental reference energies over all elements in a composition.

    Parameters:

      comp (Composition) – Input composition.

    Returns:

      Reference energy per atom

    Return type:

      float

  get_transition_chempots(element: Element) → tuple[float, ...]

    Get the critical chemical potentials for an element in the Phase Diagram.

    Parameters:

      element – An element. Has to be in the PD in the first place.

    Returns:

      A sorted sequence of critical chemical potentials, from less negative to more negative.

  getmu_vertices_stability_phase(target_comp: Composition, dep_elt: Element, tol_en: float = 0.01) → list[dict[Element, float]] | None

    Get a set of chemical potentials corresponding to the vertices of the simplex in the chemical potential phase diagram. The simplex is built using all elements in the target_composition except dep_elt. The chemical potential of dep_elt is computed from the target composition energy. This method is useful to get the limiting conditions for defects computations for instance.

    Parameters:

      - target_comp – A Composition object

      - dep_elt – the element for which the chemical potential is computed from the energy of the stable phase at the target composition

      - tol_en – a tolerance on the energy to set

    Returns:

      mu}]: An array of conditions on simplex vertices for which each element has a chemical potential set to a given value. “absolute” values (i.e., not referenced to element energies)

    Return type:

      [{Element

  numerical_tol: ClassVar[float] = 1e-08
  pd_coords(comp: Composition) → ndarray

    The phase diagram is generated in a reduced dimensional space (n_elements - 1). This function returns the coordinates in that space. These coordinates are compatible with the stored simplex objects.

    Parameters:

      comp (Composition) – A composition

    Returns:

      The coordinates for a given composition in the PhaseDiagram’s basis

  property stable_entries: set[Entry]

    Returns: set[Entry]: of stable entries in the phase diagram.

  property unstable_entries: set[Entry]

    Returns: set[Entry]: unstable entries in the phase diagram. Includes positive formation energy entries.

exception PhaseDiagramError

  Bases: `Exception`

  An exception class for Phase Diagram generation.

class ReactionDiagram(entry1: ComputedEntry, entry2: ComputedEntry, all_entries: list[ComputedEntry], tol: float = 0.0001, float_fmt: str = '%.4f')

  Bases: `object`

  Analyzes the possible reactions between a pair of compounds, e.g. an electrolyte and an electrode.

  Parameters:

    - entry1 (ComputedEntry) – Entry for 1st component. Note that corrections, if any, must already be pre-applied. This is to give flexibility for different kinds of corrections, e.g. if a particular entry is fitted to an experimental data (such as EC molecule).

    - entry2 (ComputedEntry) – Entry for 2nd component. Note that corrections must already be pre-applied. This is to give flexibility for different kinds of corrections, e.g. if a particular entry is fitted to an experimental data (such as EC molecule).

    - all_entries ([ComputedEntry]) – All other entries to be considered in the analysis. Note that corrections, if any, must already be pre-applied.

    - tol (float) – Tolerance to be used to determine validity of reaction. Defaults to 1e-4.

    - float_fmt (str) – Formatting string to be applied to all floats. Determines number of decimal places in reaction string. Defaults to “%.4f”.

  get_compound_pd() → CompoundPhaseDiagram

    Get the CompoundPhaseDiagram object, which can then be used for plotting.

    Returns:

      CompoundPhaseDiagram

class TransformedPDEntry(entry, sp_mapping, name=None)

  Bases: `PDEntry`

  This class represents a TransformedPDEntry, which allows for a PDEntry to be transformed to a different composition coordinate space. It is used in the construction of phase diagrams that do not have elements as the terminal compositions.

  Parameters:

    - entry (PDEntry) – Original entry to be transformed.

    - ({Composition (sp_mapping) – DummySpecies}): dictionary mapping Terminal Compositions to Dummy Species.

  amount_tol: ClassVar[float] = 1e-05
  as_dict()

    Get MSONable dict representation of TransformedPDEntry.

  property composition: Composition

    The composition in the dummy species space.

    Returns:

      Composition

  classmethod from_dict(dct: dict) → Self
    Parameters:

      dct (dict) – dictionary representation of TransformedPDEntry.

    Returns:

      TransformedPDEntry

exception TransformedPDEntryError

  Bases: `Exception`

  An exception class for TransformedPDEntry.

get_facets(qhull_data: ArrayLike, joggle: bool = False) → ConvexHull

  Get the simplex facets for the Convex hull.

  Parameters:

    - qhull_data (np.ndarray) – The data from which to construct the convex hull as a Nxd array (N being number of data points and d being the dimension)

    - joggle (bool) – Whether to joggle the input to avoid precision errors.

  Returns:

    with list of simplices of the convex hull.

  Return type:

    scipy.spatial.ConvexHull

order_phase_diagram(lines: list, stable_entries: dict[Any, PDEntry], unstable_entries: dict[PDEntry, Any], ordering: Sequence[Literal['Up', 'Left', 'Right']]) → tuple[list, dict[Any, PDEntry], dict[PDEntry, Any]]

  Orders the entries (their coordinates) in a phase diagram plot according to the user specified ordering. Ordering should be given as [‘Up’, ‘Left’, ‘Right’], where Up, Left and Right are the names of the entries in the upper, left and right corners of the triangle respectively.

  Parameters:

    - lines – list of list of coordinates for lines in the PD.

    - stable_entries – {coordinate : entry} for each stable node in the phase diagram. (Each coordinate can only have one stable phase)

    - unstable_entries – {entry: coordinates} for all unstable nodes in the phase diagram.

    - ordering – Ordering of the phase diagram, given as a list [‘Up’, ‘Left’,’Right’]

  Returns:

    - a list of list of coordinates for lines in the PD.

    - a {coordinate: entry} for each stable node

    in the phase diagram. (Each coordinate can only have one stable phase) - a {entry: coordinates} for all unstable nodes in the phase diagram.

  Return type:

    tuple[list, dict, dict]

tet_coord(coord: ArrayLike) → np.ndarray

  Convert a 3D coordinate into a tetrahedron based coordinate system for a prettier phase diagram.

  Parameters:

    coord – coordinate used in the convex hull computation.

  Returns:

    coordinates in a tetrahedron-based coordinate system.

triangular_coord(coord: ArrayLike) → np.ndarray

  Convert a 2D coordinate into a triangle-based coordinate system for a prettier phase diagram.

  Parameters:

    coord – coordinate used in the convex hull computation.

  Returns:

    coordinates in a triangular-based coordinate system.

uniquelines(q: list[NDArray[int]]) → set[tuple[int, int]]

  Given all the facets, convert it into a set of unique lines. Specifically used for converting convex hull facets into line pairs of coordinates.

  Parameters:

    q – A 2-dim sequence, where each row represents a facet. e.g. [[1, 2, 3], [3, 6, 7], …]

  Returns:

    A set of tuple of lines. e.g. ((1, 2), (1, 3), …)

  Return type:

    setoflines

## pymatgen.analysis.piezo module

This module provides classes for the Piezoelectric tensor.

class PiezoTensor(input_array: ArrayLike, tol: float = 0.001)

  Bases: `Tensor`

  This class describes the 3x6 piezo tensor in Voigt notation.

  Create an PiezoTensor object. The constructor throws an error if the shape of the input_matrix argument is not 3x3x3, i.e. in true tensor notation. Note that the constructor uses __new__ rather than __init__ according to the standard method of subclassing numpy ndarrays.

  Parameters:

    input_matrix (3x3x3 array-like) – the 3x6 array-like representing the piezo tensor

  classmethod from_vasp_voigt(input_vasp_array: ArrayLike) → Self
    Parameters:

      input_vasp_array (ArrayLike) – Voigt form of tensor.

    Returns:

      PiezoTensor

## pymatgen.analysis.piezo_sensitivity module

Piezo sensitivity analysis module.

class BornEffectiveCharge(structure: Structure, bec, pointops, tol: float = 0.001)

  Bases: `object`

  This class describes the Nx3x3 born effective charge tensor.

  Create an BornEffectiveChargeTensor object defined by a structure, point operations of the structure’s atomic sites. Note that the constructor uses __new__ rather than __init__ according to the standard method of subclassing numpy ndarrays.

  Parameters:

    input_matrix (Nx3x3 array-like) – the Nx3x3 array-like representing the born effective charge tensor

  get_BEC_operations(eigtol=1e-05, opstol=0.001)

    Get the symmetry operations which maps the tensors belonging to equivalent sites onto each other in the form [site index 1, site index 2, [Symmops mapping from site index 1 to site index 2]].

    Parameters:

      - eigtol (float) – tolerance for determining if two sites are

      - symmetry (related by)

      - opstol (float) – tolerance for determining if a symmetry

      - sites (operation relates two)

    Returns:

      list of symmetry operations mapping equivalent sites and the indexes of those sites.

  get_rand_BEC(max_charge=1)

    Generate a random born effective charge tensor which obeys a structure’s symmetry and the acoustic sum rule.

    Parameters:

      max_charge (float) – maximum born effective charge value

    Returns:

      np.array Born effective charge tensor

class ForceConstantMatrix(structure: Structure, fcm, pointops, sharedops, tol: float = 0.001)

  Bases: `object`

  This class describes the NxNx3x3 force constant matrix defined by a structure, point operations of the structure’s atomic sites, and the shared symmetry operations between pairs of atomic sites.

  Create an ForceConstantMatrix object.

  Parameters:

    input_matrix (NxNx3x3 array-like) – the NxNx3x3 array-like representing the force constant matrix

  get_FCM_operations(eigtol=1e-05, opstol=1e-05)

    Get the symmetry operations which maps the tensors belonging to equivalent sites onto each other in the form [site index 1a, site index 1b, site index 2a, site index 2b, [Symmops mapping from site index 1a, 1b to site index 2a, 2b]].

    Parameters:

      - eigtol (float) – tolerance for determining if two sites are

      - symmetry (related by)

      - opstol (float) – tolerance for determining if a symmetry

      - sites (operation relates two)

    Returns:

      list of symmetry operations mapping equivalent sites and the indexes of those sites.

  get_asum_FCM(fcm: ndarray, numiter: int = 15)

    Generate a symmetrized force constant matrix that obeys the objects symmetry constraints and obeys the acoustic sum rule through an iterative procedure.

    Parameters:

      - fcm (numpy array) – 3Nx3N unsymmetrized force constant matrix

      - numiter (int) – number of iterations to attempt to obey the acoustic sum rule

    Returns:

      numpy array representing the force constant matrix

  get_rand_FCM(asum=15, force=10)

    Generate a symmetrized force constant matrix from an unsymmetrized matrix that has no unstable modes and also obeys the acoustic sum rule through an iterative procedure.

    Parameters:

      - force (float) – maximum force constant

      - asum (int) – number of iterations to attempt to obey the acoustic sum rule

    Returns:

      NxNx3x3 np.array representing the force constant matrix

  get_stable_FCM(fcm, fcmasum=10)

    Generate a symmetrized force constant matrix that obeys the objects symmetry constraints, has no unstable modes and also obeys the acoustic sum rule through an iterative procedure.

    Parameters:

      - fcm (numpy array) – unsymmetrized force constant matrix

      - fcmasum (int) – number of iterations to attempt to obey the acoustic sum rule

    Returns:

      3Nx3N numpy array representing the force constant matrix

  get_symmetrized_FCM(unsymmetrized_fcm, max_force=1)

    Generate a symmetrized force constant matrix from an unsymmetrized matrix.

    Parameters:

      - unsymmetrized_fcm (numpy array) – unsymmetrized force constant matrix

      - max_charge (float) – maximum born effective charge value

    Returns:

      3Nx3N numpy array representing the force constant matrix

  get_unstable_FCM(max_force=1)

    Generate an unsymmetrized force constant matrix.

    Parameters:

      max_charge (float) – maximum born effective charge value

    Returns:

      numpy array representing the force constant matrix

class InternalStrainTensor(structure: Structure, ist, pointops, tol: float = 0.001)

  Bases: `object`

  This class describes the Nx3x3x3 internal tensor defined by a structure, point operations of the structure’s atomic sites.

  Create an InternalStrainTensor object.

  Parameters:

    input_matrix (Nx3x3x3 array-like) – the Nx3x3x3 array-like representing the internal strain tensor

  get_IST_operations(opstol=0.001) → list[list[list]]

    Get the symmetry operations which maps the tensors belonging to equivalent sites onto each other in the form [site index 1, site index 2, [SymmOps mapping from site index 1 to site index 2]].

    Parameters:

      - opstol (float) – tolerance for determining if a symmetry

      - sites (operation relates two)

    Returns:

      symmetry operations mapping equivalent sites and the indexes of those sites.

    Return type:

      list[list[list]]

  get_rand_IST(max_force=1)

    Generate a random internal strain tensor which obeys a structure’s symmetry and the acoustic sum rule.

    Parameters:

      max_force (float) – maximum born effective charge value

    Returns:

      InternalStrainTensor

get_piezo(BEC, IST, FCM, rcond=0.0001)

  Generate a random piezoelectric tensor based on a structure and corresponding symmetry.

  Parameters:

    - BEC (numpy array) – Nx3x3 array representing the born effective charge tensor

    - IST (numpy array) – Nx3x3x3 array representing the internal strain tensor

    - FCM (numpy array) – NxNx3x3 array representing the born effective charge tensor

    - rcondy (float) – condition for excluding eigenvalues in the pseudoinverse

  Returns:

    3x3x3 calculated Piezo tensor

rand_piezo(struct, pointops, sharedops, BEC, IST, FCM, anumiter=10)

  Generate a random piezoelectric tensor based on a structure and corresponding symmetry.

  Parameters:

    - struct (pymatgen structure) – structure whose symmetry operations the piezo tensor must obey

    - pointops – list of point operations obeyed by a single atomic site

    - sharedops – list of point operations shared by a pair of atomic sites

    - BEC (numpy array) – Nx3x3 array representing the born effective charge tensor

    - IST (numpy array) – Nx3x3x3 array representing the internal strain tensor

    - FCM (numpy array) – NxNx3x3 array representing the born effective charge tensor

    - anumiter (int) – number of iterations for acoustic sum rule convergence

  Returns:

    list in the form of [Nx3x3 random born effective charge tenosr, Nx3x3x3 random internal strain tensor, NxNx3x3 random force constant matrix, 3x3x3 piezo tensor]

## pymatgen.analysis.pourbaix_diagram module

This module is intended to be used to compute Pourbaix diagrams of arbitrary compositions and formation energies.

class IonEntry(ion: Ion, energy: float, name: str | None = None, attribute=None)

  Bases: `PDEntry`

  Object similar to PDEntry, but contains an Ion object instead of a Composition object.

  name

    A name for the entry. This is the string shown in the phase diagrams. By default, this is the reduced formula for the composition, but can be set to some other string for display purposes.

    Type:

      str

  Parameters:

    - ion – Ion object

    - energy – Energy for composition.

    - name – Optional parameter to name the entry. Defaults to the chemical formula.

    - attribute – Optional attribute of the entry, e.g. band gap.

  as_dict() → dict[Literal['ion', 'energy', 'name'], Any]

    Create a dict of composition, energy, and ion name.

  classmethod from_dict(dct: dict) → Self

    Get an IonEntry object from a dict.

class MultiEntry(entry_list: Sequence[PourbaixEntry], weights: list[float] | None = None)

  Bases: `PourbaixEntry`

  PourbaixEntry-like object for constructing multi-elemental Pourbaix diagrams.

  Initialize a MultiEntry.

  Parameters:

    - entry_list (Sequence[PourbaixEntry]) – Component PourbaixEntries.

    - weights (list[float]) – Weights associated with each entry. Default is None

  as_dict() → dict[str, Any]

    Get MSONable dict.

  classmethod from_dict(dct: dict) → Self
    Parameters:

      dct (dict) – Dict representation.

    Returns:

      MultiEntry

  property name: str

    MultiEntry name, i.e. the name of each entry joined by ‘ + ‘.

class PourbaixDiagram(entries: list[PourbaixEntry] | list[MultiEntry], comp_dict: dict[str, float] | None = None, conc_dict: dict[str, float] | None = None, filter_solids: bool = True, nproc: int | None = None)

  Bases: `MSONable`

  Create a Pourbaix diagram from entries.

  Parameters:

    - entries ([PourbaixEntry] or [MultiEntry]) – Entries list containing Solids and Ions or a list of MultiEntries

    - comp_dict (dict[str, float]) – Dictionary of compositions, defaults to equal parts of each elements

    - conc_dict (dict[str, float]) – Dictionary of ion concentrations, defaults to 1e-6 for each element

    - filter_solids (bool) – applying this filter to a Pourbaix diagram ensures all included solid phases are filtered by stability on the compositional phase diagram. Defaults to True. The practical consequence of this is that highly oxidized or reduced phases that might show up in experiments due to kinetic limitations on oxygen/hydrogen evolution won’t appear in the diagram, but they are not actually “stable” (and are frequently overstabilized from DFT errors). Hence, including only the stable solid phases generally leads to the most accurate Pourbaix diagrams.

    - nproc (int) – number of processes to generate multi-entries with in parallel. Defaults to None (serial processing).

  property all_entries: list

    All entries used to generate the Pourbaix diagram.

  as_dict() → dict[str, Any]

    Get MSONable dict.

  elements_ho: ClassVar[set[Element]] = {Element H, Element O}
  find_stable_entry(pH: float, V: float) → PourbaixEntry

    Find stable entry at a pH,V condition.

    Parameters:

      - pH (float) – pH to find stable entry

      - V (float) – V to find stable entry.

    Returns:

      stable entry at pH, V

    Return type:

      PourbaixEntry

  classmethod from_dict(dct: dict) → Self
    Parameters:

      dct (dict) – Dict representation.

    Returns:

      PourbaixDiagram

  get_decomposition_energy(entry: PourbaixEntry, pH: float, V: float) → NDArray

    Find decomposition to most stable entries in eV/atom, supports vectorized inputs for pH and V.

    Parameters:

      - entry (PourbaixEntry) – PourbaixEntry corresponding to compound to find the decomposition for

      - pH (float) – pH at which to find the decomposition

      - V (float) – voltage at which to find the decomposition

    Returns:

      Decomposition energy for the entry, i.e. the energy above

        the “Pourbaix hull” in eV/atom at the given conditions

  get_hull_energy(pH: float | list[float], V: float | list[float]) → NDArray

    Get the minimum energy of the Pourbaix “basin” that is formed from the stable Pourbaix planes. Vectorized.

    Parameters:

      - pH (float | list[float]) – pH at which to find the hull energy

      - V (float | list[float]) – V at which to find the hull energy

    Returns:

      minimum Pourbaix energy at conditions

    Return type:

      np.array

  static get_pourbaix_domains(pourbaix_entries: list[PourbaixEntry], limits: list[list[float]] | None = None) → tuple[dict, dict]

    Get a set of Pourbaix stable domains (i.e. polygons) in pH-V space from a list of pourbaix_entries.

    This function works by using scipy’s HalfspaceIntersection function to construct all of the 2-D polygons that form the boundaries of the planes corresponding to individual entry gibbs free energies as a function of pH and V. Hyperplanes of the form a*pH + b*V + 1 - g(0, 0) are constructed and supplied to HalfspaceIntersection, which then finds the boundaries of each Pourbaix region using the intersection points.

    Parameters:

      - pourbaix_entries (list[PourbaixEntry]) – Pourbaix entries with which to construct stable Pourbaix domains

      - limits (list[list[float]]) – limits in which to do the pourbaix analysis

    Returns:

      The first dict is of form: {entry: [boundary_points]}. The list of boundary points are the sides of the N-1 dim polytope bounding the allowable ph-V range of each entry.

    Return type:

      tuple[dict[PourbaixEntry, list], dict[PourbaixEntry, NDArray]

  get_stable_entry(pH: float, V: float) → PourbaixEntry | MultiEntry

    Get the stable entry at a given pH, V condition.

    Parameters:

      - pH (float) – pH at a given condition

      - V (float) – V at a given condition

    Returns:

      Pourbaix or multi-entry

        corresponding to the minimum energy entry at a given pH, V condition

    Return type:

      PourbaixEntry | MultiEntry

  static process_multientry(entry_list: Sequence, prod_comp: Composition, coeff_threshold: float = 0.0001) → MultiEntry | None

    Static method for finding a multientry based on a list of entries and a product composition. Essentially checks to see if a valid aqueous reaction exists between the entries and the product composition and returns a MultiEntry with weights according to the coefficients if so.

    Parameters:

      - entry_list (Sequence[Entry]) – Entries from which to create a MultiEntry

      - prod_comp (Composition) – composition constraint for setting weights of MultiEntry

      - coeff_threshold (float) – threshold of stoichiometric coefficients to filter, if weights are lower than this value, the entry is not returned

  property stable_entries: list

    The stable entries in the Pourbaix diagram.

  property unprocessed_entries: list

    Unprocessed entries.

  property unstable_entries: list

    All unstable entries in the Pourbaix diagram.

class PourbaixEntry(entry: ComputedEntry | ComputedStructureEntry, entry_id: str | None = None, concentration: float = 1e-06)

  Bases: `MSONable`, `Stringify`

  An object encompassing all data relevant to a solid or ion in a Pourbaix diagram. Each bulk solid/ion has an energy g of the form: e = e0 + 0.0591 log10(conc) - nO mu_H2O + (nH - 2nO) pH + phi (-nH + 2nO + q).

  Note that the energies corresponding to the input entries should be formation energies with respect to hydrogen and oxygen gas in order for the Pourbaix diagram formalism to work. This may be changed to be more flexible in the future.

  Parameters:

    - entry (ComputedEntry | ComputedStructureEntry | PDEntry | IonEntry) – An entry object

    - entry_id (str) – A string id for the entry

    - concentration (float) – Concentration of the entry in M. Defaults to 1e-6.

  as_dict()

    Get dict which contains Pourbaix Entry data. Note that the pH, voltage, H2O factors are always calculated when constructing a PourbaixEntry object.

  property composition: Composition

    Composition.

  property conc_term: float

    The concentration contribution to the free energy. Should only be present when there are ions in the entry.

  property elements: list[Element | Species | DummySpecies]

    Elements in the entry.

  property energy: float

    Total energy of the Pourbaix entry (at pH, V = 0 vs. SHE).

  energy_at_conditions(pH: float, V: float) → float

    Get free energy for a given pH and V.

    Parameters:

      - pH (float) – pH at which to evaluate free energy

      - V (float) – voltage at which to evaluate free energy

    Returns:

      free energy at conditions

  property energy_per_atom: float

    Energy per atom of the Pourbaix entry.

  entry_id: str | None
  classmethod from_dict(dct: dict) → Self

    Invokes a PourbaixEntry from a dictionary.

  get_element_fraction(element: Element | str) → float

    Get the elemental fraction of a given non-OH element.

    Parameters:

      element (Element or str) – string or element corresponding to element to get from composition

    Returns:

      fraction of element / sum(all non-OH elements)

  property nH2O: float

    The number of H2O.

  property nPhi: float

    The number of electrons.

  property name: str

    The entry’s name.

  property normalization_factor: float

    Sum of number of atoms minus the number of H and O in composition.

  property normalized_energy: float

    Energy normalized by number of non H or O atoms, e.g. for Zn2O6, energy / 2 or for AgTe3(OH)3, energy / 4.

  normalized_energy_at_conditions(pH: float, V: float) → float

    Energy at an electrochemical condition, compatible with numpy arrays for pH/V input.

    Parameters:

      - pH (float) – pH at condition

      - V (float) – applied potential at condition

    Returns:

      energy normalized by number of non-O/H atoms at condition

  property npH: float

    The number of H.

  property num_atoms: float

    Number of atoms in current formula. Useful for normalization.

  to_pretty_string() → str

    A pretty string representation.

class PourbaixPlotter(pourbaix_diagram: PourbaixDiagram)

  Bases: `object`

  A plotter class for phase diagrams.

  Parameters:

    pourbaix_diagram (PourbaixDiagram) – A PourbaixDiagram object.

  domain_vertices(entry) → list

    Get the vertices of the Pourbaix domain.

    Parameters:

      entry – Entry for which domain vertices are desired

    Returns:

      list of vertices

  get_pourbaix_plot(limits: tuple[tuple[float, float], tuple[float, float]] | None = None, title: str = '', label_domains: bool = True, label_fontsize: int = 20, show_water_lines: bool = True, show_neutral_axes: bool = True, ax: plt.Axes = None) → plt.Axes

    Plot Pourbaix diagram.

    Parameters:

      - limits – tuple containing limits of the Pourbaix diagram of the form ((xlo, xhi), (ylo, yhi)).

      - title (str) – Title to display on plot

      - label_domains (bool) – whether to label Pourbaix domains

      - label_fontsize – font size for domain labels

      - show_water_lines – whether to show dashed lines indicating the region of water stability.

      - lines (show_neutral_axes; whether to show dashed horizontal and vertical) – at 0 V and pH 7, respectively.

      - ax (Axes) – Matplotlib Axes instance for plotting

    Returns:

      matplotlib Axes object with Pourbaix diagram

    Return type:

      Axes

  plot_entry_stability(entry: Any, pH_range: tuple[float, float] = (-2, 16), pH_resolution: int = 100, V_range: tuple[float, float] = (-3, 3), V_resolution: int = 100, e_hull_max: float = 1, cmap: str = 'RdYlBu_r', ax: plt.Axes | None = None, **kwargs: Any) → plt.Axes

    Plots the stability of an entry in the Pourbaix diagram.

    Parameters:

      - entry (Any) – The entry to plot stability for.

      - pH_range (tuple[float, float]) – pH range for the plot. Defaults to (-2, 16).

      - pH_resolution (int) – pH resolution. Defaults to 100.

      - V_range (tuple[float, float]) – Voltage range for the plot. Defaults to (-3, 3).

      - V_resolution (int) – Voltage resolution. Defaults to 100.

      - e_hull_max (float) – Maximum energy above the hull. Defaults to 1.

      - cmap (str) – Colormap for the plot. Defaults to “RdYlBu_r”.

      - ax (Axes, optional) – Existing matplotlib Axes object for plotting. Defaults to None.

      - **kwargs (Any) – Additional keyword arguments passed to get_pourbaix_plot.

    Returns:

      Matplotlib Axes object with the plotted stability.

    Return type:

      plt.Axes

  show(*args, **kwargs) → None

    Show the Pourbaix plot.

    Parameters:

      - *args – args to get_pourbaix_plot

      - **kwargs – kwargs to get_pourbaix_plot

ion_or_solid_comp_object(formula: str) → Composition | Ion

  Get an Ion or Composition from a formula.

  Parameters:

    formula (str) – Formula. E.g. of ion: NaOH(aq), Na[+], Na+; E.g. of solid: Fe2O3(s), Fe(s), Na2O.

  Returns:

    Composition/Ion object.

## pymatgen.analysis.quasiharmonic module

This module implements the Quasi-harmonic Debye approximation that can be used to compute thermal properties.

See the following papers for more info:

> https://doi.org/10.1016/j.comphy.2003.12.001 (2004) https://doi.org/10.1103/PhysRevB.90.174107 (2014)

class QuasiHarmonicDebyeApprox(energies, volumes, structure, t_min=300.0, t_step=100, t_max=300.0, eos='vinet', pressure=0.0, poisson=0.25, use_mie_gruneisen=False, anharmonic_contribution=False)

  Bases: `object`

  Quasi-harmonic approximation.

  Parameters:

    - energies (list) – list of DFT energies in eV

    - volumes (list) – list of volumes in Ang^3

    - structure (Structure) – pymatgen structure object

    - t_min (float) – min temperature

    - t_step (float) – temperature step

    - t_max (float) – max temperature

    - eos (str) –

      equation of state used for fitting the energies and the volumes. options supported by pymatgen: “quadratic”, “murnaghan”, “birch”,

      > ”birch_murnaghan”, “pourier_tarantola”, “vinet”, “deltafactor”, “numerical_eos”

    - pressure (float) – in GPa, optional.

    - poisson (float) – poisson ratio.

    - use_mie_gruneisen (bool) – whether or not to use the mie-gruneisen formulation to compute the gruneisen parameter. The default is the slater-gamma formulation.

    - anharmonic_contribution (bool) – whether or not to consider the anharmonic contribution to the Debye temperature. Cannot be used with use_mie_gruneisen. Defaults to False.

  static debye_integral(y)

    Debye integral. Eq(5) in doi.org/10.1016/j.comphy.2003.12.001.

    Parameters:

      y (float) – Debye temperature / T, upper limit

    Returns:

      unitless

    Return type:

      float

  debye_temperature(volume: float) → float

    Calculates the Debye temperature. Eq(6) in doi.org/10.1016/j.comphy.2003.12.001. Thanks to Joey.

    Eq(6) above is equivalent to Eq(3) in doi.org/10.1103/PhysRevB.37.790 which does not consider anharmonic effects. Eq(20) in the same paper and Eq(18) in doi.org/10.1016/j.commatsci.2009.12.006 both consider anharmonic contributions to the Debye temperature through the Gruneisen parameter at 0K (Gruneisen constant).

    The anharmonic contribution is toggled by setting the anharmonic_contribution to True or False in the QuasiHarmonicDebyeApprox constructor.

    Parameters:

      volume (float) – in Ang^3

    Returns:

      Debye temperature in K

    Return type:

      float

  get_summary_dict()

    Get a dict with a summary of the computed properties.

  gruneisen_parameter(temperature, volume)
    Slater-gamma formulation(the default):
      gruneisen parameter = - d log(theta)/ d log(V) = - (1/6 + 0.5 d log(B)/ d log(V))

        = - (1/6 + 0.5 V/B dB/dV), where dB/dV = d^2E/dV^2 + V * d^3E/dV^3.

    Mie-gruneisen formulation:

      Eq(31) in doi.org/10.1016/j.comphy.2003.12.001 Eq(7) in Blanco et. al. Journal of Molecular Structure (Theochem)

      > 368 (1996) 245-255

      Also see J.P. Poirier, Introduction to the Physics of the Earth’s

        Interior, 2nd ed. (Cambridge University Press, Cambridge, 2000) Eq(3.53)

    Parameters:

      - temperature (float) – temperature in K

      - volume (float) – in Ang^3

    Returns:

      unitless

    Return type:

      float

  optimize_gibbs_free_energy()

    Evaluate the Gibbs free energy as a function of V, T and P i.e G(V, T, P), minimize G(V, T, P) w.r.t. V for each T and store the optimum values.

    Note: The data points for which the equation of state fitting fails

      are skipped.

  optimizer(temperature)

    Evaluate G(V, T, P) at the given temperature(and pressure) and minimize it w.r.t. V.

    1. Compute the vibrational Helmholtz free energy, A_vib.

    2. Compute the Gibbs free energy as a function of volume, temperature

         and pressure, G(V,T,P).

    3. Perform an equation of state fit to get the functional form of

         Gibbs free energy:G(V, T, P).

    4. Finally G(V, P, T) is minimized with respect to V.

    Parameters:

      temperature (float) – temperature in K

    Returns:

      G_opt(V_opt, T, P) in eV and V_opt in Ang^3.

    Return type:

      float, float

  thermal_conductivity(temperature: float, volume: float) → float

    Eq(17) in 10.1103/PhysRevB.90.174107.

    Parameters:

      - temperature (float) – temperature in K

      - volume (float) – in Ang^3

    Returns:

      thermal conductivity in W/K/m

    Return type:

      float

  vibrational_free_energy(temperature, volume)

    Vibrational Helmholtz free energy, A_vib(V, T). Eq(4) in doi.org/10.1016/j.comphy.2003.12.001.

    Parameters:

      - temperature (float) – temperature in K

      - volume (float)

    Returns:

      vibrational free energy in eV

    Return type:

      float

  vibrational_internal_energy(temperature, volume)

    Vibrational internal energy, U_vib(V, T). Eq(4) in doi.org/10.1016/j.comphy.2003.12.001.

    Parameters:

      - temperature (float) – temperature in K

      - volume (float) – in Ang^3

    Returns:

      vibrational internal energy in eV

    Return type:

      float

class QuasiharmonicDebyeApprox(energies, volumes, structure, t_min=300.0, t_step=100, t_max=300.0, eos='vinet', pressure=0.0, poisson=0.25, use_mie_gruneisen=False, anharmonic_contribution=False)

  Bases: `QuasiHarmonicDebyeApprox`

  Parameters:

    - energies (list) – list of DFT energies in eV

    - volumes (list) – list of volumes in Ang^3

    - structure (Structure) – pymatgen structure object

    - t_min (float) – min temperature

    - t_step (float) – temperature step

    - t_max (float) – max temperature

    - eos (str) –

      equation of state used for fitting the energies and the volumes. options supported by pymatgen: “quadratic”, “murnaghan”, “birch”,

      > ”birch_murnaghan”, “pourier_tarantola”, “vinet”, “deltafactor”, “numerical_eos”

    - pressure (float) – in GPa, optional.

    - poisson (float) – poisson ratio.

    - use_mie_gruneisen (bool) – whether or not to use the mie-gruneisen formulation to compute the gruneisen parameter. The default is the slater-gamma formulation.

    - anharmonic_contribution (bool) – whether or not to consider the anharmonic contribution to the Debye temperature. Cannot be used with use_mie_gruneisen. Defaults to False.

## pymatgen.analysis.quasirrho module

A module to calculate free energies using the Quasi-Rigid Rotor Harmonic Oscillator approximation. Modified from a script by Steven Wheeler. See: Grimme, S. Chem. Eur. J. 2012, 18, 9955.

class QuasiRRHO(mol: Molecule, frequencies: list[float], energy: float, mult: int, sigma_r: float = 1, temp: float = 298.15, press: float = 101317, v0: float = 100)

  Bases: `object`

  Calculate thermochemistry using Grimme’s Quasi-RRHO approximation. All outputs are in atomic units, e.g. energy outputs are in Hartrees. Citation: Grimme, S. Chemistry - A European Journal 18, 9955-9964 (2012).

  temp

    Temperature [K]

    Type:

      float

  press

    Pressure [Pa]

    Type:

      float

  v0

    Cutoff frequency for Quasi-RRHO method [1/cm]

    Type:

      float

  entropy_quasiRRHO

    Quasi-RRHO entropy [Ha/K]

    Type:

      float

  entropy_ho

    Total entropy calculated with a harmonic oscillator approximation for the vibrational entropy [Ha/K]

    Type:

      float

  h_corrected

    Thermal correction to the enthalpy [Ha]

    Type:

      float

  free_energy_quasiRRHO

    Quasi-RRHO free energy [Ha]

    Type:

      float

  free_energy_ho

    Free energy calculated without the Quasi-RRHO method, i.e. with a harmonic oscillator approximation for the vibrational entropy [Ha]

    Type:

      float

  Parameters:

    - mol (Molecule) – Pymatgen molecule

    - frequencies (list) – List of frequencies (float) [cm^-1]

    - energy (float) – Electronic energy [Ha]

    - mult (int) – Spin multiplicity

    - sigma_r (int) – Rotational symmetry number. Defaults to 1.

    - temp (float) – Temperature [K]. Defaults to 298.15.

    - press (float) – Pressure [Pa]. Defaults to 101_317.

    - v0 (float) – Cutoff frequency for Quasi-RRHO method [cm^-1]. Defaults to 100.

  classmethod from_gaussian_output(output: GaussianOutput, **kwargs) → Self
    Parameters:

      output (GaussianOutput) – Pymatgen GaussianOutput object.

    Returns:

      QuasiRRHO class instantiated from a Gaussian Output

    Return type:

      QuasiRRHO

  classmethod from_qc_output(output: QCOutput, **kwargs) → Self
    Parameters:

      output (QCOutput) – Pymatgen QCOutput object.

    Returns:

      QuasiRRHO class instantiated from a QChem Output

    Return type:

      QuasiRRHO

get_avg_mom_inertia(mol)

  Calculate the average moment of inertia of a molecule.

  Parameters:

    mol (Molecule) – Pymatgen Molecule

  Returns:

    average moment of inertia, eigenvalues of the inertia tensor

  Return type:

    int, list

## pymatgen.analysis.reaction_calculator module

This module provides classes that define a chemical reaction.

class BalancedReaction(reactants_coeffs: Mapping[CompositionLike, float], products_coeffs: Mapping[CompositionLike, float])

  Bases: `MSONable`

  Represent a complete chemical reaction.

  Reactants and products to be specified as dict of {Composition: coeff}.

  Parameters:

    - reactants_coeffs (dict[Composition, float]) – Reactants as dict of {Composition: amt}.

    - products_coeffs (dict[Composition, float]) – Products as dict of {Composition: amt}.

  TOLERANCE: float = 1e-06
  property all_comp: list[Composition]

    List of all compositions in the reaction.

  as_dict() → dict
    Returns:

      A dictionary representation of BalancedReaction.

  as_entry(energies) → ComputedEntry

    Get a ComputedEntry representation of the reaction.

  calculate_energy(energies: dict[Composition, ufloat]) → AffineScalarFunc
  calculate_energy(energies: dict[Composition, float]) → float

    Calculates the energy of the reaction.

    Parameters:

      ({Composition (energies) – float}): Energy for each composition. E.g ., {comp1: energy1, comp2: energy2}.

    Returns:

      reaction energy as a float.

  property coeffs: list[float]

    Final coefficients of the calculated reaction.

  property elements: list[Element | Species]

    List of elements in the reaction.

  classmethod from_dict(dct: dict) → Self
    Parameters:

      dct (dict) – from as_dict().

    Returns:

      BalancedReaction

  classmethod from_str(rxn_str: str) → Self

    Generate a balanced reaction from a string. The reaction must already be balanced.

    Parameters:

      rxn_string (str) – The reaction string. For example, “4 Li + O2 -> 2Li2O”

    Returns:

      BalancedReaction

  get_coeff(comp: Composition) → float

    Get coefficient for a particular composition.

  get_el_amount(element: Element | Species) → float

    Get the amount of the element in the reaction.

    Parameters:

      element (SpeciesLike) – Element in the reaction

    Returns:

      Amount of that element in the reaction.

  normalize_to(comp: Composition, factor: float = 1) → None

    Normalizes the reaction to one of the compositions. By default, normalizes such that the composition given has a coefficient of 1. Another factor can be specified.

    Parameters:

      - comp (Composition) – Composition to normalize to

      - factor (float) – Factor to normalize to. Defaults to 1.

  normalize_to_element(element: Species | Element, factor: float = 1) → None

    Normalizes the reaction to one of the elements. By default, normalizes such that the amount of the element is 1. Another factor can be specified.

    Parameters:

      - element (SpeciesLike) – Element to normalize to.

      - factor (float) – Factor to normalize to. Defaults to 1.

  property normalized_repr: str

    A normalized representation of the reaction. All factors are converted to lowest common factors.

  normalized_repr_and_factor() → tuple[str, float]

    Normalized representation for a reaction For example, `4 Li + 2 O -> 2Li2O` becomes `2 Li + O -> Li2O`.

  property products: list[Composition]

    List of products.

  property reactants: list[Composition]

    List of reactants.

class ComputedReaction(reactant_entries: list[ComputedEntry], product_entries: list[ComputedEntry])

  Bases: `Reaction`

  Convenience class to generate a reaction from ComputedEntry objects, with some additional attributes, such as a reaction energy based on computed energies.

  Parameters:

    - reactant_entries ([ComputedEntry]) – List of reactant_entries.

    - product_entries ([ComputedEntry]) – List of product_entries.

  property all_entries

    Equivalent of all_comp but returns entries, in the same order as the coefficients.

  as_dict() → dict
    Returns:

      A dictionary representation of ComputedReaction.

  property calculated_reaction_energy: float

    Returns: float: The calculated reaction energy.

  property calculated_reaction_energy_uncertainty: float

    Calculates the uncertainty in the reaction energy based on the uncertainty in the energies of the products and reactants.

  classmethod from_dict(dct: dict) → Self
    Parameters:

      dct (dict) – from as_dict().

    Returns:

      A ComputedReaction object.

class Reaction(reactants: list[Composition], products: list[Composition])

  Bases: `BalancedReaction`

  A more flexible class representing a Reaction. The reaction amounts will be automatically balanced. Reactants and products can swap sides so that all coefficients are positive, however this class will find the solution with the minimum number of swaps and coefficients of 0. Normalizes so that the FIRST product (or products, if underdetermined) has a coefficient of one.

  Reactants and products to be specified as list of pymatgen.core.structure.Composition. e.g. [comp1, comp2].

  Parameters:

    - reactants ([Composition]) – List of reactants.

    - products ([Composition]) – List of products.

  as_dict() → dict
    Returns:

      A dictionary representation of Reaction.

  copy() → Self

    Get a copy of the Reaction object.

  classmethod from_dict(dct: dict) → Self
    Parameters:

      dct (dict) – from as_dict().

    Returns:

      Reaction

exception ReactionError(msg: str)

  Bases: `Exception`

  Exception class for Reactions. Allows more information in exception messages to cover situations not covered by standard exception classes.

  Create a ReactionError.

  Parameters:

    msg (str) – More information about the ReactionError.

## pymatgen.analysis.structure_analyzer module

This module provides classes to perform topological analyses of structures.

## pymatgen.analysis.structure_matcher module

This module provides classes to perform fitting of structures.

## pymatgen.analysis.surface_analysis module

This module defines tools to analyze surface and adsorption related quantities as well as related plots. If you use this module, please consider citing the following works:

> 18. Tran, Z. Xu, B. Radhakrishnan, D. Winston, W. Sun, K. A. Persson,

> S. P. Ong, “Surface Energies of Elemental Crystals”, Scientific Data, 2016, 3:160080, doi: 10.1038/sdata.2016.80.

> and

> Kang, S., Mo, Y., Ong, S. P., & Ceder, G. (2014). Nanoscale stabilization of sodium oxides: Implications for Na-O2 batteries. Nano Letters, 14(2), 1016-1020. https://doi.org/10.1021/nl404557w

> and

> Montoya, J. H., & Persson, K. A. (2017). A high-throughput framework

>   for determining adsorption energies on solid surfaces. Npj Computational Materials, 3(1), 14. https://doi.org/10.1038/s41524-017-0017-z

Todo: - Still assumes individual elements have their own chempots

> in a molecular adsorbate instead of considering a single chempot for a single molecular adsorbate. E.g. for an OH adsorbate, the surface energy is a function of delu_O and delu_H instead of delu_OH

- Need a method to automatically get chempot range when

    dealing with non-stoichiometric slabs

- Simplify the input for SurfaceEnergyPlotter such that the

    user does not need to generate a dict

class NanoscaleStability(se_analyzers, symprec=1e-05)

  Bases: `object`

  A class for analyzing the stability of nanoparticles of different polymorphs with respect to size. The Wulff shape will be the model for the nanoparticle. Stability will be determined by an energetic competition between the weighted surface energy (surface energy of the Wulff shape) and the bulk energy. A future release will include a 2D phase diagram (e.g. w.r.t. size vs chempot for adsorbed or non-stoichiometric surfaces). Based on the following work:

  Kang, S., Mo, Y., Ong, S. P., & Ceder, G. (2014). Nanoscale

    stabilization of sodium oxides: Implications for Na-O2 batteries. Nano Letters, 14(2), 1016-1020. https://doi.org/10.1021/nl404557w

  se_analyzers

    Each item corresponds to a different polymorph.

    Type:

      list[SurfaceEnergyPlotter]

  symprec

    Tolerance for symmetry finding. See WulffShape.

    Type:

      float

  Analyzes the nanoscale stability of different polymorphs.

  static bulk_gform(bulk_entry)

    Get the formation energy of the bulk.

    Parameters:

      bulk_entry (ComputedStructureEntry) – Entry of the corresponding bulk.

    Returns:

      bulk formation energy (in eV)

    Return type:

      float

  plot_all_stability_map(max_r, increments=50, delu_dict=None, delu_default=0, ax=None, labels=None, from_sphere_area=False, e_units='keV', r_units='nanometers', normalize=False, scale_per_atom=False)
    Get the plot of the formation energy of a particles

      of different polymorphs against its effect radius.

    Parameters:

      - max_r (float) – The maximum radius of the particle to plot up to.

      - increments (int) – Number of plot points

      - delu_dict (dict) – Dictionary of the chemical potentials to be set as constant. Note the key should be a sympy Symbol object of the format: Symbol(“delu_el”) where el is the name of the element.

      - delu_default (float) – Default value for all unset chemical potentials

      - plt (pyplot) – Plot

      - labels (list) – List of labels for each plot, corresponds to the list of se_analyzers

      - from_sphere_area (bool) – There are two ways to calculate the bulk formation energy. Either by treating the volume and thus surface area of the particle as a perfect sphere, or as a Wulff shape.

    Returns:

      matplotlib Axes object

    Return type:

      plt.Axes

  plot_one_stability_map(analyzer, max_r, delu_dict=None, label='', increments=50, delu_default=0, ax=None, from_sphere_area=False, e_units='keV', r_units='nanometers', normalize=False, scale_per_atom=False)
    Get the plot of the formation energy of a particle against its

      effect radius.

    Parameters:

      - analyzer (SurfaceEnergyPlotter) – Analyzer associated with the first polymorph

      - max_r (float) – The maximum radius of the particle to plot up to.

      - delu_dict (dict) – Dictionary of the chemical potentials to be set as constant. Note the key should be a sympy Symbol object of the format: Symbol(“delu_el”) where el is the name of the element.

      - label (str) – Label of the plot for legend

      - increments (int) – Number of plot points

      - delu_default (float) – Default value for all unset chemical potentials

      - plt (pyplot) – Plot

      - from_sphere_area (bool) – There are two ways to calculate the bulk formation energy. Either by treating the volume and thus surface area of the particle as a perfect sphere, or as a Wulff shape.

      - r_units (str) – Can be nanometers or Angstrom

      - e_units (str) – Can be keV or eV

      - normalize (str) – Whether or not to normalize energy by volume

    Returns:

      matplotlib Axes object

    Return type:

      plt.Axes

  scaled_wulff(wulff_shape, r)
    Scales the Wulff shape with an effective radius r. Note that the resulting

      Wulff does not necessarily have the same effective radius as the one provided. The Wulff shape is scaled by its surface energies where first the surface energies are scale by the minimum surface energy and then multiplied by the given effective radius.

    Parameters:

      - wulff_shape (WulffShape) – Initial, unscaled WulffShape

      - r (float) – Arbitrary effective radius of the WulffShape

    Returns:

      WulffShape (scaled by r)

  solve_equilibrium_point(analyzer1, analyzer2, delu_dict=None, delu_default=0, units='nanometers')

    Get the radial size of two particles where equilibrium is reached between both particles. NOTE: the solution here is not the same as the solution visualized in the plot because solving for r requires that both the total surface area and volume of the particles are functions of r.

    Parameters:

      - analyzer1 (SurfaceEnergyPlotter) – Analyzer associated with the first polymorph

      - analyzer2 (SurfaceEnergyPlotter) – Analyzer associated with the second polymorph

      - delu_dict (dict) – Dictionary of the chemical potentials to be set as constant. Note the key should be a sympy Symbol object of the format: Symbol(“delu_el”) where el is the name of the element.

      - delu_default (float) – Default value for all unset chemical potentials

      - units (str) – Can be nanometers or Angstrom

    Returns:

      Particle radius in nm or Angstrom

    Return type:

      float

  wulff_gform_and_r(wulff_shape, bulk_entry, r, from_sphere_area=False, r_units='nanometers', e_units='keV', normalize=False, scale_per_atom=False)

    Calculates the formation energy of the particle with arbitrary radius r.

    Parameters:

      - wulff_shape (WulffShape) – Initial unscaled WulffShape

      - bulk_entry (ComputedStructureEntry) – Entry of the corresponding bulk.

      - r (float (Ang)) – Arbitrary effective radius of the WulffShape

      - from_sphere_area (bool) – There are two ways to calculate the bulk formation energy. Either by treating the volume and thus surface area of the particle as a perfect sphere, or as a Wulff shape.

      - r_units (str) – Can be nanometers or Angstrom

      - e_units (str) – Can be keV or eV

      - normalize (bool) – Whether or not to normalize energy by volume

      - scale_per_atom (True) – Whether or not to normalize by number of atoms in the particle

    Returns:

      particle formation energy (float in keV), effective radius

class SlabEntry(structure, energy, miller_index, correction=0.0, parameters=None, data=None, entry_id=None, label=None, adsorbates=None, clean_entry=None, marker=None, color=None)

  Bases: `ComputedStructureEntry`

  A ComputedStructureEntry object encompassing all data relevant to a

    slab for analyzing surface thermodynamics.

  miller_index

    Miller index of plane parallel to surface.

    Type:

      tuple

  label

    Brief description for this slab.

    Type:

      str

  adsorbates

    List of ComputedStructureEntry for the types of adsorbates.

    Type:

      list

  clean_entry

    SlabEntry for the corresponding clean slab for an adsorbed slab.

    Type:

      SlabEntry

  ads_entries_dict

    Dictionary where the key is the reduced composition of the adsorbate entry and value is the entry itself.

    Type:

      dict

  Make a SlabEntry containing all relevant surface thermodynamics data.

  Parameters:

    - structure (Slab) – The primary slab associated with this entry.

    - energy (float) – Energy from total energy calculation

    - miller_index (tuple(h, k, l)) – Miller index of plane parallel to surface

    - correction (float) – See ComputedSlabEntry

    - parameters (dict) – See ComputedSlabEntry

    - data (dict) – See ComputedSlabEntry

    - entry_id (str) – See ComputedSlabEntry

    - data – See ComputedSlabEntry

    - entry_id – See ComputedSlabEntry

    - label (str) – Any particular label for this slab, e.g. “Tasker 2”, “non-stoichiometric”, “reconstructed”

    - adsorbates ([ComputedStructureEntry]) – List of reference entries for the adsorbates on the slab, can be an isolated molecule (e.g. O2 for O or O2 adsorption), a bulk structure (eg. fcc Cu for Cu adsorption) or anything.

    - clean_entry (ComputedStructureEntry) – If the SlabEntry is for an adsorbed slab, this is the corresponding SlabEntry for the clean slab

    - marker (str) – Custom marker for gamma plots (”–” and “-” are typical)

    - color (str or rgba) – Custom color for gamma plots

  property Nads_in_slab

    The TOTAL number of adsorbates in the slab on BOTH sides.

  property Nsurfs_ads_in_slab

    The TOTAL number of adsorbed surfaces in the slab.

  as_dict()

    Get dict which contains Slab Entry data.

  property cleaned_up_slab

    A slab with the adsorbates removed.

  property create_slab_label

    A label (str) for this particular slab based on composition, coverage and Miller index.

  classmethod from_computed_structure_entry(entry, miller_index, label=None, adsorbates=None, clean_entry=None, **kwargs) → Self

    Get SlabEntry from a ComputedStructureEntry.

  classmethod from_dict(dct: dict) → Self

    Get a SlabEntry by reading in an dictionary.

  property get_monolayer

    The primitive unit surface area density of the adsorbate.

  property get_unit_primitive_area

    The surface area of the adsorbed system per unit area of the primitive slab system.

  gibbs_binding_energy(eads=False)

    Get the adsorption energy or Gibbs binding energy of an adsorbate on a surface.

    Parameters:

      eads (bool) – Whether to calculate the adsorption energy (True) or the binding energy (False) which is just adsorption energy normalized by number of adsorbates.

  property surface_area

    Calculate the surface area of the slab.

  surface_energy(ucell_entry, ref_entries=None)

    Calculates the surface energy of this SlabEntry.

    Parameters:

      - ucell_entry (entry) – An entry object for the bulk

      - (list (ref_entries) – [entry]): A list of entries for each type of element to be used as a reservoir for non-stoichiometric systems. The length of this list MUST be n-1 where n is the number of different elements in the bulk entry. The chempot of the element ref_entry that is not in the list will be treated as a variable.

    Returns:

      The surface energy of the slab.

    Return type:

      float

class SurfaceEnergyPlotter(all_slab_entries, ucell_entry, ref_entries=None)

  Bases: `object`

  A class used for generating plots to analyze the thermodynamics of surfaces of a material. Produces stability maps of different slab configurations, phases diagrams of two parameters to determine stability of configurations (future release), and Wulff shapes.

  all_slab_entries

    Either a list of SlabEntry objects (note for a list, the SlabEntry must have the adsorbates and clean_entry parameter plugged in) or a Nested dictionary containing a list of entries for slab calculations as items and the corresponding Miller index of the slab as the key. To account for adsorption, each value is a sub-dictionary with the entry of a clean slab calculation as the sub-key and a list of entries for adsorption calculations as the sub-value. The sub-value can contain different adsorption configurations such as a different site or a different coverage, however, ordinarily only the most stable configuration for a particular coverage will be considered as the function of the adsorbed surface energy has an intercept dependent on the adsorption energy (ie an adsorption site with a higher adsorption energy will always provide a higher surface energy than a site with a lower adsorption energy). An example parameter is provided: {(h1,k1,l1): {clean_entry1: [ads_entry1, ads_entry2, …], clean_entry2: […], …}, (h2,k2,l2): {…}} where clean_entry1 can be a pristine surface and clean_entry2 can be a reconstructed surface while ads_entry1 can be adsorption at site 1 with a 2x2 coverage while ads_entry2 can have a 3x3 coverage. If adsorption entries are present (i.e. if all_slab_entries[(h,k,l)][clean_entry1]), we consider adsorption in all plots and analysis for this particular facet.

    Type:

      dict | list

  color_dict

    Dictionary of colors (r,g,b,a) when plotting surface energy stability. The keys are individual surface entries where clean surfaces have a solid color while the corresponding adsorbed surface will be transparent.

    Type:

      dict

  ucell_entry

    ComputedStructureEntry of the bulk reference for this particular material.

    Type:

      ComputedStructureEntry

  ref_entries

    List of ComputedStructureEntries to be used for calculating chemical potential.

    Type:

      list

  facet_color_dict

    Randomly generated dictionary of colors associated with each facet.

    Type:

      dict

  Object for plotting surface energy in different ways for clean and

    adsorbed surfaces.

  Parameters:

    - all_slab_entries (dict or list) – Dictionary or list containing all entries for slab calculations. See attributes.

    - ucell_entry (ComputedStructureEntry) – ComputedStructureEntry of the bulk reference for this particular material.

    - ref_entries ([ComputedStructureEntries]) – A list of entries for each type of element to be used as a reservoir for non-stoichiometric systems. The length of this list MUST be n-1 where n is the number of different elements in the bulk entry. The bulk energy term in the grand surface potential can be defined by a summation of the chemical potentials for each element in the system. As the bulk energy is already provided, one can solve for one of the chemical potentials as a function of the other chemical potentials and bulk energy. i.e. there are n-1 variables (chempots). e.g. if your ucell_entry is for LiFePO4 than your ref_entries should have an entry for Li, Fe, and P if you want to use the chempot of O as the variable.

  BE_vs_clean_SE(delu_dict, delu_default=0, plot_eads=False, annotate_monolayer=True, JPERM2=False)
    For each facet, plot the clean surface energy against the most

      stable binding energy.

    Parameters:

      - delu_dict (dict) – Dictionary of the chemical potentials to be set as constant. Note the key should be a sympy Symbol object of the format: Symbol(“delu_el”) where el is the name of the element.

      - delu_default (float) – Default value for all unset chemical potentials

      - plot_eads (bool) – Option to plot the adsorption energy (binding energy multiplied by number of adsorbates) instead.

      - annotate_monolayer (bool) – Whether or not to label each data point with its monolayer (adsorbate density per unit primiitve area)

      - JPERM2 (bool) – Whether to plot surface energy in /m^2 (True) or eV/A^2 (False)

    Returns:

      Plot of clean surface energy vs binding energy for

        all facets.

    Return type:

      Plot

  area_frac_vs_chempot_plot(ref_delu: Symbol, chempot_range: list[float], delu_dict: dict[Symbol, float] | None = None, delu_default: float = 0, increments: int = 10, no_clean: bool = False, no_doped: bool = False) → Axes

    1D plot. Plots the change in the area contribution of each facet as a function of chemical potential.

    Parameters:

      - ref_delu (Symbol) – The free variable chempot with the format: Symbol(“delu_el”) where el is the name of the element.

      - chempot_range (list[float]) – Min/max range of chemical potential to plot along.

      - delu_dict (dict[Symbol, float]) – Dictionary of the chemical potentials to be set as constant. Note the key should be a sympy Symbol object of the format: Symbol(“delu_el”) where el is the name of the element.

      - delu_default (float) – Default value for all unset chemical potentials.

      - increments (int) – Number of data points between min/max or point of intersection. Defaults to 10 points.

      - no_clean (bool) – Some parameter, description missing.

      - no_doped (bool) – Some parameter, description missing.

    Returns:

      Plot of area frac on the Wulff shape for each facet vs chemical potential.

    Return type:

      plt.Axes

  static chempot_plot_addons(ax, xrange, ref_el, pad=2.4, rect=None, ylim=None)

    Helper function to a chempot plot look nicer.

    Parameters:

      - plt (Plot)

      - xrange (list) – xlim parameter

      - ref_el (str) – Element of the referenced chempot.

      - axes (axes)

      - pad (float)

      - rect (list) – For tight layout

      - ylim (ylim parameter)

    return (Plot): Modified plot with addons. return (Plot): Modified plot with addons.

  chempot_vs_gamma(ref_delu, chempot_range, miller_index=(), delu_dict=None, delu_default=0, JPERM2=False, show_unstable=False, ylim=None, plt=None, no_clean=False, no_doped=False, use_entry_labels=False, no_label=False)
    Plots the surface energy as a function of chemical potential.

      Each facet will be associated with its own distinct colors. Dashed lines will represent stoichiometries different from that of the mpid’s compound. Transparent lines indicates adsorption.

    Parameters:

      - ref_delu (sympy Symbol) – The range stability of each slab is based on the chempot range of this chempot. Should be a sympy Symbol object of the format: Symbol(“delu_el”) where el is the name of the element

      - chempot_range ([max_chempot, min_chempot]) – Range to consider the stability of the slabs.

      - miller_index (list) – Miller index for a specific facet to get a dictionary for.

      - delu_dict (dict) – Dictionary of the chemical potentials to be set as constant. Note the key should be a sympy Symbol object of the format: Symbol(“delu_el”) where el is the name of the element.

      - delu_default (float) – Default value for all unset chemical potentials

      - JPERM2 (bool) – Whether to plot surface energy in /m^2 (True) or eV/A^2 (False)

      - show_unstable (bool) – Whether or not to show parts of the surface energy plot outside the region of stability.

      - ylim ([ymax, ymin]) – Range of y axis

      - no_doped (bool) – Whether to plot for the clean slabs only.

      - no_clean (bool) – Whether to plot for the doped slabs only.

      - use_entry_labels (bool) – If True, will label each slab configuration according to their given label in the SlabEntry object.

      - no_label (bool) – Option to turn off labels.

    Returns:

      Plot of surface energy vs chempot for all entries.

    Return type:

      Plot

  chempot_vs_gamma_plot_one(ax: Axes, entry: SlabEntry, ref_delu: Symbol, chempot_range: list[float], delu_dict: dict[Symbol, float] | None = None, delu_default: float = 0, label: str = '', JPERM2: bool = False) → Axes

    Helper function to help plot the surface energy of a single SlabEntry as a function of chemical potential.

    Parameters:

      - ax (plt.Axes) – Matplotlib Axes instance for plotting.

      - entry – Entry of the slab whose surface energy we want to plot. (Add appropriate description for type)

      - ref_delu (Symbol) – The range stability of each slab is based on the chempot range of this chempot.

      - chempot_range (list[float]) – Range to consider the stability of the slabs.

      - delu_dict (dict[Symbol, float]) – Dictionary of the chemical potentials.

      - delu_default (float) – Default value for all unset chemical potentials.

      - label (str) – Label of the slab for the legend.

      - JPERM2 (bool) – Whether to plot surface energy in /m^2 (True) or eV/A^2 (False).

    Returns:

      Plot of surface energy vs chemical potential for one entry.

    Return type:

      plt.Axes

  color_palette_dict(alpha=0.35)

    Helper function to assign each facet a unique color using a dictionary.

    Parameters:

      alpha (float) – Degree of transparency

    return (dict): Dictionary of colors (r,g,b,a) when plotting surface

      energy stability. The keys are individual surface entries where clean surfaces have a solid color while the corresponding adsorbed surface will be transparent.

  get_stable_entry_at_u(miller_index, delu_dict=None, delu_default=0, no_doped=False, no_clean=False) → tuple[SlabEntry, float]
    Get the entry corresponding to the most stable slab for a particular

      facet at a specific chempot. We assume that surface energy is constant so all free variables must be set with delu_dict, otherwise they are assumed to be equal to delu_default.

    Parameters:

      - miller_index ((h, k,l)) – The facet to find the most stable slab in

      - delu_dict (dict) – Dictionary of the chemical potentials to be set as constant. Note the key should be a sympy Symbol object of the format: Symbol(“delu_el”) where el is the name of the element.

      - delu_default (float) – Default value for all unset chemical potentials

      - no_doped (bool) – Consider stability of clean slabs only.

      - no_clean (bool) – Consider stability of doped slabs only.

    Returns:

      The most stable slab entry and its surface energy.

    Return type:

      tuple[SlabEntry, float]

  get_surface_equilibrium(slab_entries, delu_dict=None)
    Takes in a list of SlabEntries and calculates the chemical potentials

      at which all slabs in the list coexists simultaneously. Useful for building surface phase diagrams. Note that to solve for x equations (x slab_entries), there must be x free variables (chemical potentials). Adjust delu_dict as need be to get the correct number of free variables.

    Parameters:

      - slab_entries (array) – The coefficients of the first equation

      - delu_dict (dict) – Dictionary of the chemical potentials to be set as constant. Note the key should be a sympy Symbol object of the format: Symbol(“delu_el”) where el is the name of the element.

    Returns:

      Array containing a solution to x equations with x

        variables (x-1 chemical potential and 1 surface energy)

    Return type:

      array

  monolayer_vs_BE(plot_eads=False)
    Plots the binding energy as a function of monolayers (ML), i.e.

      the fractional area adsorbate density for all facets. For each facet at a specific monolayer, only plot the lowest binding energy.

    Parameters:

      plot_eads (bool) – Option to plot the adsorption energy (binding energy multiplied by number of adsorbates) instead.

    Returns:

      Plot of binding energy vs monolayer for all facets.

    Return type:

      Plot

  set_all_variables(delu_dict, delu_default)
    Set all chemical potential values and returns a dictionary where

      the key is a sympy Symbol and the value is a float (chempot).

    Parameters:

      - entry (SlabEntry) – Computed structure entry of the slab

      - delu_dict (dict) – Dictionary of the chemical potentials to be set as constant. Note the key should be a sympy Symbol object of the format: Symbol(“delu_el”) where el is the name of the element.

      - delu_default (float) – Default value for all unset chemical potentials

    Returns:

      Dictionary of set chemical potential values

  stable_u_range_dict(chempot_range, ref_delu, no_doped=True, no_clean=False, delu_dict=None, miller_index=(), dmu_at_0=False, return_se_dict=False)

    Creates a dictionary where each entry is a key pointing to a chemical potential range where the surface of that entry is stable. Does so by enumerating through all possible solutions (intersect) for surface energies of a specific facet.

    Parameters:

      - chempot_range ([max_chempot, min_chempot]) – Range to consider the stability of the slabs.

      - ref_delu (sympy Symbol) – The range stability of each slab is based on the chempot range of this chempot. Should be a sympy Symbol object of the format: Symbol(“delu_el”) where el is the name of the element

      - no_doped (bool) – Consider stability of clean slabs only.

      - no_clean (bool) – Consider stability of doped slabs only.

      - delu_dict (dict) – Dictionary of the chemical potentials to be set as constant. Note the key should be a sympy Symbol object of the format: Symbol(“delu_el”) where el is the name of the element.

      - miller_index (list) – Miller index for a specific facet to get a dictionary for.

      - dmu_at_0 (bool) – If True, if the surface energies corresponding to the chemical potential range is between a negative and positive value, the value is a list of three chemical potentials with the one in the center corresponding a surface energy of 0. Uselful in identifying unphysical ranges of surface energies and their chemical potential range.

      - return_se_dict (bool) – Whether or not to return the corresponding dictionary of surface energies

  surface_chempot_range_map(elements, miller_index, ranges, incr=50, no_doped=False, no_clean=False, delu_dict=None, ax=None, annotate=True, show_unphysical_only=False, fontsize=10) → Axes
    Adapted from the get_chempot_range_map() method in the PhaseDiagram

      class. Plot the chemical potential range map based on surface energy stability. Currently works only for 2-component PDs. At the moment uses a brute force method by enumerating through the range of the first element chempot with a specified increment and determines the chempot range of the second element for each SlabEntry. Future implementation will determine the chempot range map first by solving systems of equations up to 3 instead of 2.

    Parameters:

      - elements (list) – Sequence of elements to be considered as independent variables. e.g. if you want to show the stability ranges of all Li-Co-O phases w.r.t. to duLi and duO, you will supply [Element(“Li”), Element(“O”)]

      - miller_index ([h, k, l]) – Miller index of the surface we are interested in

      - ranges ([[range1], [range2]]) – List of chempot ranges (max and min values) for the first and second element.

      - incr (int) – Number of points to sample along the range of the first chempot

      - no_doped (bool) – Whether or not to include doped systems.

      - no_clean (bool) – Whether or not to include clean systems.

      - delu_dict (dict) – Dictionary of the chemical potentials to be set as constant. Note the key should be a sympy Symbol object of the format: Symbol(“delu_el”) where el is the name of the element.

      - ax (plt.Axes) – Axes object to plot on. If None, will create a new plot.

      - annotate (bool) – Whether to annotate each “phase” with the label of the entry. If no label, uses the reduced formula

      - show_unphysical_only (bool) – Whether to only show the shaded region where surface energy is negative. Useful for drawing other chempot range maps.

      - fontsize (int) – Font size of the annotation

  wulff_from_chempot(delu_dict=None, delu_default=0, symprec=1e-05, no_clean=False, no_doped=False) → WulffShape

    Method to get the Wulff shape at a specific chemical potential.

    Parameters:

      - delu_dict (dict) – Dictionary of the chemical potentials to be set as constant. Note the key should be a sympy Symbol object of the format: Symbol(“delu_el”) where el is the name of the element.

      - delu_default (float) – Default value for all unset chemical potentials

      - symprec (float) – See WulffShape.

      - no_doped (bool) – Consider stability of clean slabs only.

      - no_clean (bool) – Consider stability of doped slabs only.

    Returns:

      The WulffShape at u_ref and u_ads.

    Return type:

      WulffShape

class WorkFunctionAnalyzer(structure: Structure, locpot_along_c, efermi, shift=0, blength=3.5)

  Bases: `object`

  A class used for calculating the work function from a slab model and visualizing the behavior of the local potential along the slab.

  efermi

    The Fermi energy.

    Type:

      float

  locpot_along_c

    Local potential in eV along points along the c axis.

    Type:

      list

  vacuum_locpot

    The maximum local potential along the c direction for the slab model, i.e. the potential at the vacuum.

    Type:

      float

  work_function

    The minimum energy needed to move an electron from the surface to infinity. Defined as the difference between the potential at the vacuum and the Fermi energy.

    Type:

      float

  slab

    The slab structure model.

    Type:

      Slab

  along_c

    Points along the c direction with same increments as the locpot in the c axis.

    Type:

      list

  ave_locpot

    Mean of the minimum and maximum (vacuum) locpot along c.

    Type:

      float

  sorted_sites

    List of sites from the slab sorted along the c direction.

    Type:

      list

  ave_bulk_p

    The average locpot of the slab region along the c direction.

    Type:

      float

  Initialize the WorkFunctionAnalyzer class.

  Parameters:

    - structure (Structure) – Structure object modelling the surface

    - locpot_along_c (list) – Local potential along the c direction

    - outcar (MSONable) – Outcar vasp output object

    - shift (float) – Parameter to translate the slab (and therefore the vacuum) of the slab structure, thereby translating the plot along the x axis.

    - blength (float (Ang)) – The longest bond length in the material. Used to handle pbc for noncontiguous slab layers

  classmethod from_files(poscar_filename, locpot_filename, outcar_filename, shift=0, blength=3.5) → Self

    Initialize a WorkFunctionAnalyzer from POSCAR, LOCPOT, and OUTCAR files.

    Parameters:

      - poscar_filename (str) – The path to the POSCAR file.

      - locpot_filename (str) – The path to the LOCPOT file.

      - outcar_filename (str) – The path to the OUTCAR file.

      - shift (float) – The shift value. Defaults to 0.

      - blength (float) – The longest bond length in the material. Used to handle pbc for noncontiguous slab layers. Defaults to 3.5.

    Returns:

      A WorkFunctionAnalyzer instance.

    Return type:

      WorkFunctionAnalyzer

  get_labels(plt, label_fontsize=10)

    Handles the optional labelling of the plot with relevant quantities.

    Parameters:

      - plt (plt) – Plot of the locpot vs c axis

      - label_fontsize (float) – Fontsize of labels

    Returns Labelled plt.

  get_locpot_along_slab_plot(label_energies=True, plt=None, label_fontsize=10)
    Get a plot of the local potential (eV) vs the

      position along the c axis of the slab model (Ang).

    Parameters:

      - label_energies (bool) – Whether to label relevant energy quantities such as the work function, Fermi energy, vacuum locpot, bulk-like locpot

      - plt (plt) – Matplotlib pyplot object

      - label_fontsize (float) – Fontsize of labels

    Returns plt of the locpot vs c axis

  is_converged(min_points_frac=0.015, tol: float = 0.0025)
    A well converged work function should have a flat electrostatic

      potential within some distance (min_point) about where the peak electrostatic potential is found along the c direction of the slab. This is dependent on the size of the slab.

    Parameters:

      - min_point (fractional coordinates) – The number of data points +/- the point of where the electrostatic potential is at its peak along the c direction.

      - tol (float) – If the electrostatic potential stays the same within this tolerance, within the min_points, it is converged.

    Returns a bool (whether or not the work function is converged)

entry_dict_from_list(all_slab_entries) → dict

  Converts a list of SlabEntry to an appropriate dictionary. It is assumed that if there is no adsorbate, then it is a clean SlabEntry and that adsorbed SlabEntry has the clean_entry parameter set.

  Parameters:

    all_slab_entries (list) – List of SlabEntry objects

  Returns:

    Dictionary of SlabEntry with the Miller index as the main

      key to a dictionary with a clean SlabEntry as the key to a list of adsorbed SlabEntry.

  Return type:

    dict

sub_chempots(gamma_dict, chempots)
  Uses dot product of numpy array to sub chemical potentials

    into the surface grand potential. This is much faster than using the subs function in sympy.

  Parameters:

    - gamma_dict (dict) – Surface grand potential equation as a coefficient dictionary

    - chempots (dict) – Dictionary assigning each chemical potential (key) in gamma a value

  Returns:

    Surface energy as a float

## pymatgen.analysis.thermochemistry module

A module to perform experimental thermochemical data analysis.

class ThermoData(data_type, cpdname, phaseinfo, formula, value, ref='', method='', temp_range=(298, 298), uncertainty=None)

  Bases: `object`

  Container for experimental thermo-chemical data.

  Parameters:

    - data_type – The thermochemical data type. Should be one of the following: fH - Formation enthalpy, S - Entropy, A, B, C, D, E, F, G, H - variables for use in the various equations for generating formation enthalpies or Cp at various temperatures.

    - cpdname (str) – A name for the compound. For example, hematite for Fe2O3.

    - phaseinfo (str) – Denoting the phase. For example, “solid”, “liquid”, “gas” or “tetragonal”.

    - formula (str) – A proper string formula, e.g. Fe2O3

    - value (float) – The value of the data.

    - ref (str) – A reference, if any, for the data.

    - method (str) – The method by which the data was determined, if available.

    - temp_range ([float, float]) – Temperature range of validity for the data in Kelvin. Defaults to 298 K only.

    - uncertainty (float) – An uncertainty for the data, if available.

  as_dict()

    Get MSONable dict.

  classmethod from_dict(dct: dict) → Self
    Parameters:

      dct (dict) – Dict representation.

    Returns:

      ThermoData

## pymatgen.analysis.transition_state module

Some reimplementation of Henkelman’s Transition State Analysis utilities, which are originally in Perl. Additional features beyond those offered by Henkelman’s utilities will be added.

class NEBAnalysis(r: ArrayLike, energies: ArrayLike, forces: ArrayLike, structures: list[Structure], spline_options: dict | None = None, zero_slope_saddle: bool = False)

  Bases: `MSONable`

  An NEBAnalysis class.

  Initialize an NEBAnalysis from the cumulative root mean squared distances between structures, the energies, the forces and the structures for the analysis.

  Parameters:

    - r (ArrayLike) – Root mean square distances between structures.

    - energies (ArrayLike) – Energies of each structure along reaction coordinate.

    - forces (ArrayLike) – Tangent forces along the reaction coordinate.

    - structures (list[Structure]) – Structures along reaction coordinate.

    - spline_options (dict, optional) – [Deprecated] Use zero_slope_saddle instead.

    - zero_slope_saddle (bool) – If True, enforces zero slope at saddle point.

  as_dict() → dict[str, Any]

    Dict representation of NEBAnalysis.

    Returns:

      JSON-serializable dict representation.

  classmethod from_dir(root_dir: PathLike, relaxation_dirs: tuple[PathLike, PathLike] | None = None, **kwargs) → Self

    Initialize an NEBAnalysis object from a directory of an NEB run.

    Note that OUTCARs must be present in all image directories. For the terminal OUTCARs from relaxation calculations, you can specify the locations using relaxation_dir. If these are not specified, the code will attempt to look for the OUTCARs in 00 and 0n directories, followed by subdirs (“start”, “end”) or (“initial”, “final”) in the root_dir. These are just some typical conventions used preferentially in Shyue Ping’s MAVRL research group.

    For the non-terminal points, the CONTCAR is read to obtain structures. For terminal points, the POSCAR is used. The image directories are assumed to be the only directories that can be resolved to integers. e.g. “00”, “01”, …, “06”. The minimum sub-directory structure that can be parsed is of the following form (a 5-image example is shown):

    > 00:

    >   - POSCAR

    >   - OUTCAR

    > 01-05:

    >   - CONTCAR

    >   - OUTCAR

    > 06:

    >   - POSCAR

    >   - OUTCAR

    Parameters:

      - root_dir (PathLike) – Path to the root directory of the NEB calculation.

      - relaxation_dirs (tuple) – The (start, end) directories from which the OUTCARs are read for the terminal points for the energies.

    Returns:

      NEBAnalysis object.

  classmethod from_outcars(outcars: list[Outcar], structures: list[Structure], **kwargs) → Self

    Initialize an NEBAnalysis from Outcar and Structure objects. Use the static constructors, e.g. from_dir instead if you prefer to have these automatically generated from a directory of NEB calculations.

    Parameters:

      - outcars (list[Outcar]) – Outcar objects. Note that these have to be ordered from start to end along reaction coordinates.

      - structures (list[Structure]) – Structures along reaction coordinate. Must be same length as outcars.

  get_extrema(normalize_rxn_coordinate: bool = True) → tuple[list[tuple[float, float]], list[tuple[float, float]]]

    Get the positions of the extrema in meV along the minimum energy path (MEP). Both local minimums and maximums are returned.

    Parameters:

      normalize_rxn_coordinate (bool) – Whether to normalize the reaction coordinate to between 0 and 1. Defaults to True.

    Returns:

      where the extrema are given as [(x1, y1), (x2, y2), …].

    Return type:

      tuple[min_extrema, max_extrema]

  get_plot(normalize_rxn_coordinate: bool = True, label_barrier: bool = True) → Axes

    Get an NEB plot. Uses Henkelman’s approach of spline fitting each section of the reaction path based on tangent force and energies.

    Parameters:

      - normalize_rxn_coordinate (bool) – Whether to normalize the reaction coordinate to between 0 and 1. Defaults to True.

      - label_barrier (bool) – Whether to label the maximum barrier. Defaults to True.

    Returns:

      matplotlib axes object.

    Return type:

      plt.Axes

  setup_spline(spline_options: dict | None = None, zero_slope_saddle: bool = False) → None

    Set up the cubic spline interpolation of the MEP.

    Parameters:

      - spline_options (dict, optional) – [Deprecated] Dictionary of options. Set to {“saddle_point”: “zero_slope”} to enforce zero slope at saddle.

      - zero_slope_saddle (bool) – New preferred argument. If True, enforces zero slope at the saddle point.

combine_neb_plots(neb_analyses: list[NEBAnalysis], arranged_neb_analyses: bool = False, reverse_plot: bool = False) → NEBAnalysis

  Combine NEB plots.

  Parameters:

    - neb_analyses – a list of NEBAnalysis objects.

    - arranged_neb_analyses – The code connects two end points with the smallest-energy difference. If all end points have very close energies, it’s likely to result in an inaccurate connection. Manually arrange neb_analyses if the combined plot is not as expected compared with all individual plots. e.g. if there are two NEBAnalysis objects to combine, arrange in such a way that the end-point energy of the first NEBAnalysis object is the start-point energy of the second NEBAnalysis object. Note that the barrier labeled in y-axis in the combined plot might be different from that in the individual plot due to the reference energy used. reverse_plot: reverse the plot or percolation direction.

  Returns:

    NEBAnalysis object

## pymatgen.analysis.wulff module

This module define a WulffShape class to generate the Wulff shape from a lattice, a list of indices and their corresponding surface energies, and the total area and volume of the Wulff shape, the weighted surface energy, the anisotropy and shape_factor can also be calculated. In support of plotting from a given view in terms of miller index.

The lattice is from the conventional unit cell, and (hkil) for hexagonal lattices.

If you use this code extensively, consider citing the following:

Tran, R.; Xu, Z.; Radhakrishnan, B.; Winston, D.; Persson, K. A.; Ong, S. P. (2016). Surface energies of elemental crystals. Scientific Data.

class WulffFacet(normal, e_surf, normal_pt, dual_pt, index, m_ind_orig, miller)

  Bases: `object`

  Helper container for each Wulff plane.

  Parameters:

    - normal

    - e_surf

    - normal_pt

    - dual_pt

    - index

    - m_ind_orig

    - miller

class WulffShape(lattice: Lattice, miller_list, e_surf_list, symprec=1e-05)

  Bases: `object`

  Generate Wulff Shape from list of miller index and surface energies, with given conventional unit cell. surface energy (Jm^2) is the length of normal.

  Wulff shape is the convex hull. Based on: https://docs.scipy.org/doc/scipy/reference/generated/scipy.spatial.ConvexHull.html

  Process:

    1. get Wulff simplices

    2. label with color

    3. get wulff_area and other properties

  debug

    Whether to print debug information.

    Type:

      bool

  alpha

    Transparency of the Wulff shape.

    Type:

      float

  color_set

    colors to use for facets.

    Type:

      list

  grid_off

    Whether to turn off the grid.

    Type:

      bool

  axis_off

    Whether to turn off the axis.

    Type:

      bool

  show_area

    Whether to show the area of each facet.

    Type:

      bool

  off_color

    Color of facets not on the Wulff shape.

    Type:

      str

  structure

    Input conventional unit cell (with H) from lattice.

    Type:

      Structure

  miller_list

    input Miller indices, for hcp in the form of hkil.

    Type:

      list

  hkl_list

    Modified Miller indices in the same order as input_miller.

    Type:

      list

  e_surf_list

    input surface energies in the same order as input_miller.

    Type:

      list

  lattice

    Input lattice for the conventional unit cell.

    Type:

      Lattice

  facets

    WulffFacet objects considering symmetry.

    Type:

      list

  dual_cv_simp

    Simplices from the dual convex hull (dual_pt).

    Type:

      list

  wulff_pt_list

    Wulff points.

    Type:

      list

  wulff_cv_simp

    Simplices from the convex hull of wulff_pt_list.

    Type:

      list

  on_wulff

    List for all input_miller, True if on the Wulff shape.

    Type:

      list

  color_area

    List for all input_miller, total area on the Wulff shape, off_wulff = 0.

    Type:

      list

  miller_area

    Dictionary of Miller indices and their corresponding areas.

    Type:

      dict

  Parameters:

    - lattice – Lattice object of the conventional unit cell

    - miller_list ([(hkl) – list of hkl or hkil for hcp

    - e_surf_list ([float]) – list of corresponding surface energies

    - symprec (float) – for reciprocal lattice operation, default is 1e-5.

  property anisotropy: float

    Returns: float: Coefficient of Variation from weighted surface energy. The ideal sphere is 0.

  property area_fraction_dict: dict[tuple, float]

    Returns: dict: {hkl: area_hkl/total area on wulff}.

  property effective_radius: float

    Radius of the WulffShape (in Angstroms) when the WulffShape is approximated as a sphere.

    Returns:

      radius R_eff

    Return type:

      float

  get_line_in_facet(facet)

    Get the sorted pts in a facet used to draw a line.

  get_plot(color_set='PuBu', grid_off=True, axis_off=True, show_area=False, alpha=1, off_color='red', direction=None, bar_pos=(0.75, 0.15, 0.05, 0.65), bar_on=False, units_in_JPERM2=True, legend_on=True, aspect_ratio=(8, 8), custom_colors=None)

    Get the Wulff shape plot.

    Parameters:

      - color_set – default is ‘PuBu’

      - grid_off (bool) – default is True

      - axis_off (bool) – default is True

      - show_area (bool) – default is False

      - alpha (float) – chosen from 0 to 1 (float), default is 1

      - off_color – Default color for facets not present on the Wulff shape.

      - direction – default is (1, 1, 1)

      - bar_pos – default is [0.75, 0.15, 0.05, 0.65]

      - bar_on (bool) – default is False

      - legend_on (bool) – default is True

      - aspect_ratio – default is (8, 8)

      - ({(h (custom_colors) – [r,g,b,alpha]}): Customize color of each facet with a dictionary. The key is the corresponding Miller index and value is the color. Undefined facets will use default color site. Note: If you decide to set your own colors, it probably won’t make any sense to have the color bar on.

      - k – [r,g,b,alpha]}): Customize color of each facet with a dictionary. The key is the corresponding Miller index and value is the color. Undefined facets will use default color site. Note: If you decide to set your own colors, it probably won’t make any sense to have the color bar on.

      - l} – [r,g,b,alpha]}): Customize color of each facet with a dictionary. The key is the corresponding Miller index and value is the color. Undefined facets will use default color site. Note: If you decide to set your own colors, it probably won’t make any sense to have the color bar on.

      - units_in_JPERM2 (bool) – Units of surface energy, defaults to Joules per square meter (True)

    Returns:

      3D plot of the Wulff shape.

    Return type:

      mpl_toolkits.mplot3d.Axes3D

  get_plotly(color_set='PuBu', off_color='red', alpha=1, custom_colors=None, units_in_JPERM2=True)

    Get the Wulff shape as a plotly Figure object.

    Parameters:

      - color_set – default is ‘PuBu’

      - alpha (float) – chosen from 0 to 1 (float), default is 1

      - off_color – Default color for facets not present on the Wulff shape.

      - ({(h (custom_colors) – [r,g,b,alpha}): Customize color of each facet with a dictionary. The key is the corresponding Miller index and value is the color. Undefined facets will use default color site. Note: If you decide to set your own colors, it probably won’t make any sense to have the color bar on.

      - k – [r,g,b,alpha}): Customize color of each facet with a dictionary. The key is the corresponding Miller index and value is the color. Undefined facets will use default color site. Note: If you decide to set your own colors, it probably won’t make any sense to have the color bar on.

      - l} – [r,g,b,alpha}): Customize color of each facet with a dictionary. The key is the corresponding Miller index and value is the color. Undefined facets will use default color site. Note: If you decide to set your own colors, it probably won’t make any sense to have the color bar on.

      - units_in_JPERM2 (bool) – Units of surface energy, defaults to Joules per square meter (True)

    Returns:

      (plotly.graph_objects.Figure)

  property miller_area_dict: dict[tuple, float]

    area_hkl on wulff}.

    Type:

      {hkl

  property miller_energy_dict: dict[tuple, float]

    surface energy_hkl}.

    Type:

      {hkl

  property shape_factor: float

    Determine the critical nucleus size. A large shape factor indicates great anisotropy. See Ballufi, R. W., Allen, S. M. & Carter, W. C. Kinetics

    > of Materials. (John Wiley & Sons, 2005), p.461.

    Returns:

      Shape factor.

    Return type:

      float

  show(*args, **kwargs)

    Show the Wulff plot.

    Parameters:

      - *args – Passed to get_plot.

      - **kwargs – Passed to get_plot.

  property surface_area: float

    Total surface area of Wulff shape.

  property tot_corner_sites

    The number of vertices in the convex hull. Useful for identifying catalytically active sites.

  property tot_edges

    The number of edges in the convex hull. Useful for identifying catalytically active sites.

  property total_surface_energy: float

    Total surface energy of the Wulff shape.

    Returns:

      sum(surface_energy_hkl * area_hkl)

    Return type:

      float

  property volume: float

    Volume of the Wulff shape.

  property weighted_surface_energy: float

    Returns: sum(surface_energy_hkl * area_hkl)/ sum(area_hkl).

get_tri_area(pts)

  Given a list of coords for 3 points, Compute the area of this triangle.

  Parameters:

    pts – [a, b, c] three points

hkl_tuple_to_str(hkl)

  Prepare for display on plots “(hkl)” for surfaces.

  Parameters:

    hkl – in the form of [h, k, l] or (h, k, l).

## pymatgen.analysis.xps module

This is a module for XPS analysis. It is modelled after the Galore package (https://github.com/SMTG-UCL/galore), but with some modifications for easier analysis from pymatgen itself. Please cite the following original work if you use this:

> Adam J. Jackson, Alex M. Ganose, Anna Regoutz, Russell G. Egdell, David O. Scanlon (2018). Galore: Broadening and weighting for simulation of photoelectron spectroscopy. Journal of Open Source Software, 3(26), 773, doi: 10.21105/joss.007733

You may wish to look at the optional dependency galore for more functionality such as plotting and other cross-sections. Note that the atomic_subshell_photoionization_cross_sections.csv has been reparsed from the original compilation:

> Yeh, J. J.; Lindau, I. Atomic Subshell Photoionization Cross Sections and Asymmetry Parameters: 1 ⩽ Z ⩽ 103. Atomic Data and Nuclear Data Tables 1985, 32 (1), 1-155. https://doi.org/10.1016/0092-640X(85)90016-6.

This version contains all detailed information for all orbitals.

class XPS(x: ArrayLike, y: ArrayLike, *args, **kwargs)

  Bases: `Spectrum`

  An X-ray photoelectron spectra.

  Parameters:

    - x (ndarray) – A ndarray of N values.

    - y (ndarray) – A ndarray of N x k values. The first dimension must be the same as that of x. Each of the k values are interpreted as separate.

    - *args – All subclasses should provide args other than x and y when calling super, e.g. super().__init__( x, y, arg1, arg2, kwarg1=val1, ..). This guarantees the +, -, *, etc. operators work properly.

    - **kwargs – Same as that for *args.

  XLABEL = 'Binding Energy (eV)'
  YLABEL = 'Intensity'
  classmethod from_dos(dos: CompleteDos) → Self
    Parameters:

      - dos – CompleteDos object with project element-orbital DOS.

      - Vasprun.get_complete_dos. (Can be obtained from)

      - sigma – Smearing for Gaussian.

    Returns:

      X-ray photoelectron spectrum.

    Return type:

      XPS