Source code for pymatgen.analysis.local_env

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

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

import math
import warnings
import os
import json

import ruamel.yaml as yaml
import numpy as np

from copy import deepcopy
from math import pow, pi, asin, sqrt, exp, sin, cos, acos, fabs, atan2
from collections import namedtuple, defaultdict
from functools import lru_cache
from typing import Union, List, Optional
from bisect import bisect_left

from scipy.spatial import Voronoi
from monty.dev import deprecated
from monty.dev import requires
from monty.serialization import loadfn

from pymatgen import Element, Structure, IStructure
from pymatgen.analysis.bond_valence import BV_PARAMS, BVAnalyzer
from pymatgen.core.structure import PeriodicNeighbor
from pymatgen.analysis.molecule_structure_comparator import CovalentRadius
from pymatgen.core.sites import PeriodicSite, Site

try:
    from openbabel import openbabel as ob
except Exception:
    ob = None

__author__ = "Shyue Ping Ong, Geoffroy Hautier, Sai Jayaraman," + \
             " Nils E. R. Zimmermann, Bharat Medasani, Evan Spotte-Smith"
__copyright__ = "Copyright 2011, The Materials Project"
__version__ = "1.0"
__maintainer__ = "Nils E. R. Zimmermann"
__email__ = "nils.e.r.zimmermann@gmail.com"
__status__ = "Production"
__date__ = "August 17, 2017"

_directory = os.path.join(os.path.dirname(__file__))

with open(os.path.join(_directory, 'op_params.yaml'), "rt") as f:
    default_op_params = yaml.safe_load(f)

with open(os.path.join(_directory, 'cn_opt_params.yaml'), 'r') as f:
    cn_opt_params = yaml.safe_load(f)

with open(os.path.join(_directory, 'ionic_radii.json'), 'r') as fp:
    _ion_radii = json.load(fp)


[docs]class ValenceIonicRadiusEvaluator: """ Computes site valences and ionic radii for a structure using bond valence analyzer """ def __init__(self, structure): """ Args: structure: pymatgen.core.structure.Structure """ self._structure = structure.copy() self._valences = self._get_valences() self._ionic_radii = self._get_ionic_radii() @property def radii(self): """ List of ionic radii of elements in the order of sites. """ el = [site.species_string for site in self._structure.sites] radii_dict = dict(zip(el, self._ionic_radii)) # print radii_dict return radii_dict @property def valences(self): """ List of oxidation states of elements in the order of sites. """ el = [site.species_string for site in self._structure.sites] valence_dict = dict(zip(el, self._valences)) return valence_dict @property def structure(self): """ Returns oxidation state decorated structure. """ return self._structure.copy() def _get_ionic_radii(self): """ Computes ionic radii of elements for all sites in the structure. If valence is zero, atomic radius is used. """ radii = [] vnn = VoronoiNN() def nearest_key(sorted_vals, key): i = bisect_left(sorted_vals, key) if i == len(sorted_vals): return sorted_vals[-1] if i == 0: return sorted_vals[0] before = sorted_vals[i - 1] after = sorted_vals[i] if after - key < key - before: return after else: return before for i in range(len(self._structure.sites)): site = self._structure.sites[i] if isinstance(site.specie, Element): radius = site.specie.atomic_radius # Handle elements with no atomic_radius # by using calculated values instead. if radius is None: radius = site.specie.atomic_radius_calculated if radius is None: raise ValueError( "cannot assign radius to element {}".format( site.specie)) radii.append(radius) continue el = site.specie.symbol oxi_state = int(round(site.specie.oxi_state)) coord_no = int(round(vnn.get_cn(self._structure, i))) try: tab_oxi_states = sorted(map(int, _ion_radii[el].keys())) oxi_state = nearest_key(tab_oxi_states, oxi_state) radius = _ion_radii[el][str(oxi_state)][str(coord_no)] except KeyError: if vnn.get_cn(self._structure, i) - coord_no > 0: new_coord_no = coord_no + 1 else: new_coord_no = coord_no - 1 try: radius = _ion_radii[el][str(oxi_state)][str(new_coord_no)] coord_no = new_coord_no except Exception: tab_coords = sorted( map(int, _ion_radii[el][str(oxi_state)].keys())) new_coord_no = nearest_key(tab_coords, coord_no) i = 0 for val in tab_coords: if val > coord_no: break i = i + 1 if i == len(tab_coords): key = str(tab_coords[-1]) radius = _ion_radii[el][str(oxi_state)][key] elif i == 0: key = str(tab_coords[0]) radius = _ion_radii[el][str(oxi_state)][key] else: key = str(tab_coords[i - 1]) radius1 = _ion_radii[el][str(oxi_state)][key] key = str(tab_coords[i]) radius2 = _ion_radii[el][str(oxi_state)][key] radius = (radius1 + radius2) / 2 # implement complex checks later radii.append(radius) return radii def _get_valences(self): """ Computes ionic valences of elements for all sites in the structure. """ try: bv = BVAnalyzer() self._structure = bv.get_oxi_state_decorated_structure( self._structure) valences = bv.get_valences(self._structure) except Exception: try: bv = BVAnalyzer(symm_tol=0.0) self._structure = bv.get_oxi_state_decorated_structure( self._structure) valences = bv.get_valences(self._structure) except Exception: valences = [] for site in self._structure.sites: if len(site.specie.common_oxidation_states) > 0: valences.append(site.specie.common_oxidation_states[0]) # Handle noble gas species # which have no entries in common_oxidation_states. else: valences.append(0) if sum(valences): valences = [0] * self._structure.num_sites else: self._structure.add_oxidation_state_by_site(valences) # raise # el = [site.specie.symbol for site in self._structure.sites] # el = [site.species_string for site in self._structure.sites] # el = [site.specie for site in self._structure.sites] # valence_dict = dict(zip(el, valences)) # print valence_dict return valences
[docs]class NearNeighbors: """ Base class to determine near neighbors that typically include nearest neighbors and others that are within some tolerable distance. """ def __eq__(self, other): if type(other) is type(self): return self.__dict__ == other.__dict__ return False def __hash__(self): return len(self.__dict__.items()) @property def structures_allowed(self): """ Boolean property: can this NearNeighbors class be used with Structure objects? """ raise NotImplementedError("structures_allowed" " is not defined!") @property def molecules_allowed(self): """ Boolean property: can this NearNeighbors class be used with Molecule objects? """ raise NotImplementedError("molecules_allowed" " is not defined!") @property def extend_structure_molecules(self): """ Boolean property: Do Molecules need to be converted to Structures to use this NearNeighbors class? Note: this property is not defined for classes for which molecules_allowed == False. """ raise NotImplementedError("extend_structures_molecule" " is not defined!")
[docs] def get_cn(self, structure, n, use_weights=False): """ Get coordination number, CN, of site with index n in structure. Args: structure (Structure): input structure. n (integer): index of site for which to determine CN. use_weights (boolean): flag indicating whether (True) to use weights for computing the coordination number or not (False, default: each coordinated site has equal weight). Returns: cn (integer or float): coordination number. """ siw = self.get_nn_info(structure, n) return sum([e['weight'] for e in siw]) if use_weights else len(siw)
[docs] def get_cn_dict(self, structure, n, use_weights=False): """ Get coordination number, CN, of each element bonded to site with index n in structure Args: structure (Structure): input structure n (integer): index of site for which to determine CN. use_weights (boolean): flag indicating whether (True) to use weights for computing the coordination number or not (False, default: each coordinated site has equal weight). Returns: cn (dict): dictionary of CN of each element bonded to site """ siw = self.get_nn_info(structure, n) cn_dict = {} for i in siw: site_element = i['site'].species_string if site_element not in cn_dict: if use_weights: cn_dict[site_element] = i['weight'] else: cn_dict[site_element] = 1 else: if use_weights: cn_dict[site_element] += i['weight'] else: cn_dict[site_element] += 1 return cn_dict
[docs] def get_nn(self, structure, n): """ Get near neighbors of site with index n in structure. Args: structure (Structure): input structure. n (integer): index of site in structure for which to determine neighbors. Returns: sites (list of Site objects): near neighbors. """ return [e['site'] for e in self.get_nn_info(structure, n)]
[docs] def get_weights_of_nn_sites(self, structure, n): """ Get weight associated with each near neighbor of site with index n in structure. Args: structure (Structure): input structure. n (integer): index of site for which to determine the weights. Returns: weights (list of floats): near-neighbor weights. """ return [e['weight'] for e in self.get_nn_info(structure, n)]
[docs] def get_nn_images(self, structure, n): """ Get image location of all near neighbors of site with index n in structure. Args: structure (Structure): input structure. n (integer): index of site for which to determine the image location of near neighbors. Returns: images (list of 3D integer array): image locations of near neighbors. """ return [e['image'] for e in self.get_nn_info(structure, n)]
[docs] def get_nn_info(self, structure, n): """ Get all near-neighbor sites as well as the associated image locations and weights of the site with index n. Args: structure (Structure): input structure. n (integer): index of site for which to determine near-neighbor information. Returns: siw (list of dicts): each dictionary provides information about a single near neighbor, where key 'site' gives access to the corresponding Site object, 'image' gives the image location, and 'weight' provides the weight that a given near-neighbor site contributes to the coordination number (1 or smaller), 'site_index' gives index of the corresponding site in the original structure. """ raise NotImplementedError("get_nn_info(structure, n)" " is not defined!")
[docs] def get_all_nn_info(self, structure): """Get a listing of all neighbors for all sites in a structure Args: structure (Structure): Input structure Return: List of NN site information for each site in the structure. Each entry has the same format as `get_nn_info` """ return [self.get_nn_info(structure, n) for n in range(len(structure))]
[docs] def get_nn_shell_info(self, structure, site_idx, shell): """Get a certain nearest neighbor shell for a certain site. Determines all non-backtracking paths through the neighbor network computed by `get_nn_info`. The weight is determined by multiplying the weight of the neighbor at each hop through the network. For example, a 2nd-nearest-neighbor that has a weight of 1 from its 1st-nearest-neighbor and weight 0.5 from the original site will be assigned a weight of 0.5. As this calculation may involve computing the nearest neighbors of atoms multiple times, the calculation starts by computing all of the neighbor info and then calling `_get_nn_shell_info`. If you are likely to call this method for more than one site, consider calling `get_all_nn` first and then calling this protected method yourself. Args: structure (Structure): Input structure site_idx (int): index of site for which to determine neighbor information. shell (int): Which neighbor shell to retrieve (1 == 1st NN shell) Returns: list of dictionaries. Each entry in the list is information about a certain neighbor in the structure, in the same format as `get_nn_info`. """ all_nn_info = self.get_all_nn_info(structure) sites = self._get_nn_shell_info(structure, all_nn_info, site_idx, shell) # Update the site positions # Did not do this during NN options because that can be slower output = [] for info in sites: orig_site = structure[info['site_index']] info['site'] = PeriodicSite(orig_site.species, np.add(orig_site.frac_coords, info['image']), structure.lattice, properties=orig_site.properties) output.append(info) return output
def _get_nn_shell_info(self, structure, all_nn_info, site_idx, shell, _previous_steps=frozenset(), _cur_image=(0, 0, 0)): """Private method for computing the neighbor shell information Args: structure (Structure) - Structure being assessed all_nn_info ([[dict]]) - Results from `get_all_nn_info` site_idx (int) - index of site for which to determine neighbor information. shell (int) - Which neighbor shell to retrieve (1 == 1st NN shell) _previous_step ({(site_idx, image}) - Internal use only: Set of sites that have already been traversed. _cur_image (tuple) - Internal use only Image coordinates of current atom Returns: list of dictionaries. Each entry in the list is information about a certain neighbor in the structure, in the same format as `get_nn_info`. Does not update the site positions """ if shell <= 0: raise ValueError('Shell must be positive') # Append this site to the list of previously-visited sites _previous_steps = _previous_steps.union({(site_idx, _cur_image)}) # Get all the neighbors of this site possible_steps = list(all_nn_info[site_idx]) for i, step in enumerate(possible_steps): # Update the image information # Note: We do not update the site position yet, as making a # PeriodicSite for each intermediate step is too costly step = dict(step) step['image'] = tuple(np.add(step['image'], _cur_image).tolist()) possible_steps[i] = step # Get only the non-backtracking steps allowed_steps = [x for x in possible_steps if (x['site_index'], x['image']) not in _previous_steps] # If we are the last step (i.e., shell == 1), done! if shell == 1: # No further work needed, just package these results return allowed_steps else: # If not, Get the N-1 NNs of these allowed steps terminal_neighbors = [self._get_nn_shell_info(structure, all_nn_info, x['site_index'], shell - 1, _previous_steps, x['image']) for x in allowed_steps] # Each allowed step results in many terminal neighbors # And, different first steps might results in the same neighbor # Now, we condense those neighbors into a single entry per neighbor all_sites = dict() for first_site, term_sites in zip(allowed_steps, terminal_neighbors): for term_site in term_sites: key = (term_site['site_index'], tuple(term_site['image'])) # The weight for this site is equal to the weight of the # first step multiplied by the weight of the terminal neighbor term_site['weight'] *= first_site['weight'] # Check if this site is already known value = all_sites.get(key) if value is not None: # If so, add to its weight value['weight'] += term_site['weight'] else: # If not, prepare to add it value = term_site all_sites[key] = value return list(all_sites.values()) @staticmethod def _get_image(structure, site): """Private convenience method for get_nn_info, gives lattice image from provided PeriodicSite and Structure. Image is defined as displacement from original site in structure to a given site. i.e. if structure has a site at (-0.1, 1.0, 0.3), then (0.9, 0, 2.3) -> jimage = (1, -1, 2). Note that this method takes O(number of sites) due to searching an original site. Args: structure: Structure Object site: PeriodicSite Object Returns: image: ((int)*3) Lattice image """ original_site = structure[ NearNeighbors._get_original_site(structure, site)] image = np.around( np.subtract(site.frac_coords, original_site.frac_coords)) image = tuple(image.astype(int)) return image @staticmethod def _get_original_site(structure, site): """Private convenience method for get_nn_info, gives original site index from ProvidedPeriodicSite.""" for i, s in enumerate(structure): if site.is_periodic_image(s): return i raise Exception('Site not found!')
[docs] def get_bonded_structure(self, structure, decorate=False, weights=True): """ Obtain a StructureGraph object using this NearNeighbor class. Requires the optional dependency networkx (pip install networkx). Args: structure: Structure object. decorate (bool): whether to annotate site properties with order parameters using neighbors determined by this NearNeighbor class weights (bool): whether to include edge weights from NearNeighbor class in StructureGraph Returns: a pymatgen.analysis.graphs.StructureGraph object """ # requires optional dependency which is why it's not a top-level import from pymatgen.analysis.graphs import StructureGraph if decorate: # Decorate all sites in the underlying structure # with site properties that provides information on the # coordination number and coordination pattern based # on the (current) structure of this graph. order_parameters = [self.get_local_order_parameters(structure, n) for n in range(len(structure))] structure.add_site_property('order_parameters', order_parameters) sg = StructureGraph.with_local_env_strategy(structure, self, weights=weights) return sg
[docs] def get_local_order_parameters(self, structure, n): """ Calculate those local structure order parameters for the given site whose ideal CN corresponds to the underlying motif (e.g., CN=4, then calculate the square planar, tetrahedral, see-saw-like, rectangular see-saw-like order paramters). Args: structure: Structure object n (int): site index. Returns (Dict[str, float]): A dict of order parameters (values) and the underlying motif type (keys; for example, tetrahedral). """ # code from @nisse3000, moved here from graphs to avoid circular # import, also makes sense to have this as a general NN method cn = self.get_cn(structure, n) if cn in [int(k_cn) for k_cn in cn_opt_params.keys()]: names = [k for k in cn_opt_params[cn].keys()] types = [] params = [] for name in names: types.append(cn_opt_params[cn][name][0]) tmp = cn_opt_params[cn][name][1] \ if len(cn_opt_params[cn][name]) > 1 else None params.append(tmp) lostops = LocalStructOrderParams(types, parameters=params) sites = [structure[n]] + self.get_nn(structure, n) lostop_vals = lostops.get_order_parameters( sites, 0, indices_neighs=[i for i in range(1, cn + 1)]) d = {} for i, lostop in enumerate(lostop_vals): d[names[i]] = lostop return d else: return None
[docs]class VoronoiNN(NearNeighbors): """ Uses a Voronoi algorithm to determine near neighbors for each site in a structure. """ def __init__(self, tol=0, targets=None, cutoff=13.0, allow_pathological=False, weight='solid_angle', extra_nn_info=True, compute_adj_neighbors=True): """ Args: tol (float): tolerance parameter for near-neighbor finding. Faces that are smaller than `tol` fraction of the largest face are not included in the tessellation. (default: 0). targets (Element or list of Elements): target element(s). cutoff (float): cutoff radius in Angstrom to look for near-neighbor atoms. Defaults to 13.0. allow_pathological (bool): whether to allow infinite vertices in determination of Voronoi coordination. weight (string) - Statistic used to weigh neighbors (see the statistics available in get_voronoi_polyhedra) extra_nn_info (bool) - Add all polyhedron info to `get_nn_info` compute_adj_neighbors (bool) - Whether to compute which neighbors are adjacent. Turn off for faster performance """ super().__init__() self.tol = tol self.cutoff = cutoff self.allow_pathological = allow_pathological self.targets = targets self.weight = weight self.extra_nn_info = extra_nn_info self.compute_adj_neighbors = compute_adj_neighbors @property def structures_allowed(self): """ Boolean property: can this NearNeighbors class be used with Structure objects? """ return True @property def molecules_allowed(self): """ Boolean property: can this NearNeighbors class be used with Molecule objects? """ return False
[docs] def get_voronoi_polyhedra(self, structure, n): """ Gives a weighted polyhedra around a site. See ref: A Proposed Rigorous Definition of Coordination Number, M. O'Keeffe, Acta Cryst. (1979). A35, 772-775 Args: structure (Structure): structure for which to evaluate the coordination environment. n (integer): site index. Returns: A dict of sites sharing a common Voronoi facet with the site n mapped to a directory containing statistics about the facet: - solid_angle - Solid angle subtended by face - angle_normalized - Solid angle normalized such that the faces with the largest - area - Area of the facet - face_dist - Distance between site n and the facet - volume - Volume of Voronoi cell for this face - n_verts - Number of vertices on the facet """ # Assemble the list of neighbors used in the tessellation # Gets all atoms within a certain radius if self.targets is None: targets = structure.composition.elements else: targets = self.targets center = structure[n] cutoff = self.cutoff # max cutoff is the longest diagonal of the cell + room for noise corners = [[1, 1, 1], [-1, 1, 1], [1, -1, 1], [1, 1, -1]] d_corners = [np.linalg.norm(structure.lattice.get_cartesian_coords(c)) for c in corners] max_cutoff = max(d_corners) + 0.01 while True: try: neighbors = structure.get_sites_in_sphere( center.coords, cutoff) neighbors = [i[0] for i in sorted(neighbors, key=lambda s: s[1])] # Run the Voronoi tessellation qvoronoi_input = [s.coords for s in neighbors] voro = Voronoi( qvoronoi_input) # can give seg fault if cutoff is too small # Extract data about the site in question cell_info = self._extract_cell_info( structure, 0, neighbors, targets, voro, self.compute_adj_neighbors) break except RuntimeError as e: if cutoff >= max_cutoff: if e.args and "vertex" in e.args[0]: # pass through the error raised by _extract_cell_info raise e else: raise RuntimeError("Error in Voronoi neighbor finding; " "max cutoff exceeded") cutoff = min(cutoff * 2, max_cutoff + 0.001) return cell_info
[docs] def get_all_voronoi_polyhedra(self, structure): """Get the Voronoi polyhedra for all site in a simulation cell Args: structure (Structure): Structure to be evaluated Returns: A dict of sites sharing a common Voronoi facet with the site n mapped to a directory containing statistics about the facet: - solid_angle - Solid angle subtended by face - angle_normalized - Solid angle normalized such that the faces with the largest - area - Area of the facet - face_dist - Distance between site n and the facet - volume - Volume of Voronoi cell for this face - n_verts - Number of vertices on the facet """ # Special case: For atoms with 1 site, the atom in the root image is not included # in the get_all_neighbors output. Rather than creating logic to add that atom # to the neighbor list, which requires detecting whether it will be translated # to reside within the unit cell before neighbor detection, it is less complex # to just call the one-by-one operation if len(structure) == 1: return [self.get_voronoi_polyhedra(structure, 0)] # Assemble the list of neighbors used in the tessellation if self.targets is None: targets = structure.composition.elements else: targets = self.targets # Initialize the list of sites with the atoms in the origin unit cell # The `get_all_neighbors` function returns neighbors for each site's image in the # original unit cell. We start off with these central atoms to ensure they are # included in the tessellation sites = [x.to_unit_cell() for x in structure] indices = [(i, 0, 0, 0) for i, _ in enumerate(structure)] # Get all neighbors within a certain cutoff # Record both the list of these neighbors, and the site indices all_neighs = structure.get_all_neighbors(self.cutoff, include_index=True, include_image=True) for neighs in all_neighs: sites.extend([x[0] for x in neighs]) indices.extend([(x[2],) + x[3] for x in neighs]) # Get the non-duplicates (using the site indices for performance/numerical stability) indices = np.array(indices, dtype=np.int) indices, uniq_inds = np.unique(indices, return_index=True, axis=0) sites = np.array(sites)[uniq_inds] # Sort array such that atoms in the root image are first # Exploit the fact that the array is sorted by the unique operation such that # the images associated with atom 0 are first, followed by atom 1, etc. root_images, = np.nonzero(np.abs(indices[:, 1:]).max(axis=1) == 0) del indices # Save memory (tessellations can be costly) # Run the tessellation qvoronoi_input = [s.coords for s in sites] voro = Voronoi(qvoronoi_input) # Get the information for each neighbor return [self._extract_cell_info(structure, i, sites, targets, voro, self.compute_adj_neighbors) for i in root_images.tolist()]
def _get_elements(self, site): """ Get the list of elements for a Site Args: site (Site): Site to assess Returns: [Element]: List of elements """ try: if isinstance(site.specie, Element): return [site.specie] return [Element(site.specie)] except Exception: return site.species.elements def _is_in_targets(self, site, targets): """ Test whether a site contains elements in the target list Args: site (Site): Site to assess targets ([Element]) List of elements Returns: (boolean) Whether this site contains a certain list of elements """ elems = self._get_elements(site) for elem in elems: if elem not in targets: return False return True def _extract_cell_info(self, structure, site_idx, sites, targets, voro, compute_adj_neighbors=False): """Get the information about a certain atom from the results of a tessellation Args: structure (Structure) - Structure being assessed site_idx (int) - Index of the atom in question sites ([Site]) - List of all sites in the tessellation targets ([Element]) - Target elements voro - Output of qvoronoi compute_adj_neighbors (boolean) - Whether to compute which neighbors are adjacent Returns: A dict of sites sharing a common Voronoi facet. Key is facet id (not useful) and values are dictionaries containing statistics about the facet: - site: Pymatgen site - solid_angle - Solid angle subtended by face - angle_normalized - Solid angle normalized such that the faces with the largest - area - Area of the facet - face_dist - Distance between site n and the facet - volume - Volume of Voronoi cell for this face - n_verts - Number of vertices on the facet - adj_neighbors - Facet id's for the adjacent neighbors """ # Get the coordinates of every vertex all_vertices = voro.vertices # Get the coordinates of the central site center_coords = sites[site_idx].coords # Iterate through all the faces in the tessellation results = {} for nn, vind in voro.ridge_dict.items(): # Get only those that include the site in question if site_idx in nn: other_site = nn[0] if nn[1] == site_idx else nn[1] if -1 in vind: # -1 indices correspond to the Voronoi cell # missing a face if self.allow_pathological: continue else: raise RuntimeError("This structure is pathological," " infinite vertex in the voronoi " "construction") # Get the solid angle of the face facets = [all_vertices[i] for i in vind] angle = solid_angle(center_coords, facets) # Compute the volume of associated with this face volume = 0 # qvoronoi returns vertices in CCW order, so I can break # the face up in to segments (0,1,2), (0,2,3), ... to compute # its area where each number is a vertex size for j, k in zip(vind[1:], vind[2:]): volume += vol_tetra(center_coords, all_vertices[vind[0]], all_vertices[j], all_vertices[k]) # Compute the distance of the site to the face face_dist = np.linalg.norm( center_coords - sites[other_site].coords) / 2 # Compute the area of the face (knowing V=Ad/3) face_area = 3 * volume / face_dist # Compute the normal of the facet normal = np.subtract(sites[other_site].coords, center_coords) normal /= np.linalg.norm(normal) # Store by face index results[other_site] = { 'site': sites[other_site], 'normal': normal, 'solid_angle': angle, 'volume': volume, 'face_dist': face_dist, 'area': face_area, 'n_verts': len(vind) } # If we are computing which neighbors are adjacent, store the vertices if compute_adj_neighbors: results[other_site]['verts'] = vind # all sites should have atleast two connected ridges in periodic system if not results: raise ValueError("No Voronoi neighbours found for site - try increasing cutoff") # Get only target elements resultweighted = {} for nn_index, nstats in results.items(): # Check if this is a target site nn = nstats['site'] if nn.is_ordered: if nn.specie in targets: resultweighted[nn_index] = nstats else: # is nn site is disordered for disordered_sp in nn.species.keys(): if disordered_sp in targets: resultweighted[nn_index] = nstats # If desired, determine which neighbors are adjacent if compute_adj_neighbors: # Initialize storage for the adjacent neighbors adj_neighbors = dict((i, []) for i in resultweighted.keys()) # Find the neighbors that are adjacent by finding those # that contain exactly two vertices for a_ind, a_nninfo in resultweighted.items(): # Get the indices for this site a_verts = set(a_nninfo['verts']) # Loop over all neighbors that have an index lower that this one # The goal here is to exploit the fact that neighbor adjacency is symmetric # (if A is adj to B, B is adj to A) for b_ind, b_nninfo in resultweighted.items(): if b_ind > a_ind: continue if len(a_verts.intersection(b_nninfo['verts'])) == 2: adj_neighbors[a_ind].append(b_ind) adj_neighbors[b_ind].append(a_ind) # Store the results in the nn_info for key, neighbors in adj_neighbors.items(): resultweighted[key]['adj_neighbors'] = neighbors return resultweighted
[docs] def get_nn_info(self, structure, n): """ Get all near-neighbor sites as well as the associated image locations and weights of the site with index n in structure using Voronoi decomposition. Args: structure (Structure): input structure. n (integer): index of site for which to determine near-neighbor sites. Returns: siw (list of tuples (Site, array, float)): tuples, each one of which represents a coordinated site, its image location, and its weight. """ # Run the tessellation nns = self.get_voronoi_polyhedra(structure, n) # Extract the NN info return self._extract_nn_info(structure, nns)
[docs] def get_all_nn_info(self, structure): """ Args: structure (Structure): input structure. Returns: All nn info for all sites. """ all_voro_cells = self.get_all_voronoi_polyhedra(structure) return [self._extract_nn_info(structure, cell) for cell in all_voro_cells]
def _extract_nn_info(self, structure, nns): """Given Voronoi NNs, extract the NN info in the form needed by NearestNeighbors Args: structure (Structure): Structure being evaluated nns ([dicts]): Nearest neighbor information for a structure Returns: (list of tuples (Site, array, float)): See nn_info """ # Get the target information if self.targets is None: targets = structure.composition.elements else: targets = self.targets # Extract the NN info siw = [] max_weight = max(nn[self.weight] for nn in nns.values()) for nstats in nns.values(): site = nstats['site'] if nstats[self.weight] > self.tol * max_weight \ and self._is_in_targets(site, targets): nn_info = {'site': site, 'image': self._get_image(structure, site), 'weight': nstats[self.weight] / max_weight, 'site_index': self._get_original_site( structure, site)} if self.extra_nn_info: # Add all the information about the site poly_info = nstats del poly_info['site'] nn_info['poly_info'] = poly_info siw.append(nn_info) return siw
@deprecated(replacement=VoronoiNN, message='Use VoronoiNN instead, and set "tol" to 0.5') class VoronoiNN_modified(VoronoiNN): """ Modified VoronoiNN that only considers neighbors with more than 50% of the maximum weight """ def __init__(self, targets=None, cutoff=10.0, allow_pathological=False, weight='solid_angle', extra_nn_info=True): """ Args: targets (Element or list of Elements): target element(s). cutoff (float): cutoff radius in Angstrom to look for near-neighbor atoms. Defaults to 10.0. allow_pathological (bool): whether to allow infinite vertices in determination of Voronoi coordination. weight (string) - Statistic used to weigh neighbors (see the statistics available in get_voronoi_polyhedra) extra_nn_info (bool) - Add all polyhedron info to `get_nn_info` """ super().__init__(0.5, targets, cutoff, allow_pathological, weight, extra_nn_info)
[docs]class JmolNN(NearNeighbors): """ Determine near-neighbor sites and coordination number using an emulation of Jmol's default autoBond() algorithm. This version of the algorithm does not take into account any information regarding known charge states. """ def __init__(self, tol=0.56, min_bond_distance=0.4, el_radius_updates=None): """ Args: tol (float): tolerance parameter for bond determination (default: 0.56). el_radius_updates: (dict) symbol->float to override default atomic radii table values """ self.tol = tol self.min_bond_distance = min_bond_distance # Load elemental radii table bonds_file = os.path.join(os.path.dirname(os.path.abspath(__file__)), "bonds_jmol_ob.yaml") with open(bonds_file, 'r') as f: self.el_radius = yaml.safe_load(f) # Update any user preference elemental radii if el_radius_updates: self.el_radius.update(el_radius_updates) @property def structures_allowed(self): """ Boolean property: can this NearNeighbors class be used with Structure objects? """ return True @property def molecules_allowed(self): """ Boolean property: can this NearNeighbors class be used with Molecule objects? """ return True @property def extend_structure_molecules(self): """ Boolean property: Do Molecules need to be converted to Structures to use this NearNeighbors class? Note: this property is not defined for classes for which molecules_allowed == False. """ return True
[docs] def get_max_bond_distance(self, el1_sym, el2_sym): """ Use Jmol algorithm to determine bond length from atomic parameters Args: el1_sym: (str) symbol of atom 1 el2_sym: (str) symbol of atom 2 Returns: (float) max bond length """ return sqrt( (self.el_radius[el1_sym] + self.el_radius[el2_sym] + self.tol) ** 2)
[docs] def get_nn_info(self, structure, n): """ Get all near-neighbor sites as well as the associated image locations and weights of the site with index n using the bond identification algorithm underlying Jmol. Args: structure (Structure): input structure. n (integer): index of site for which to determine near neighbors. Returns: siw (list of tuples (Site, array, float)): tuples, each one of which represents a neighbor site, its image location, and its weight. """ site = structure[n] # Determine relevant bond lengths based on atomic radii table bonds = {} for el in structure.composition.elements: bonds[site.specie, el] = self.get_max_bond_distance( site.specie.symbol, el.symbol) # Search for neighbors up to max bond length + tolerance max_rad = max(bonds.values()) + self.tol min_rad = min(bonds.values()) siw = [] for nn in structure.get_neighbors(site, max_rad): dist = nn.nn_distance # Confirm neighbor based on bond length specific to atom pair if dist <= (bonds[(site.specie, nn.specie)]) and ( nn.nn_distance > self.min_bond_distance): weight = min_rad / dist siw.append({'site': nn, 'image': self._get_image(structure, nn), 'weight': weight, 'site_index': self._get_original_site(structure, nn)}) return siw
[docs]class MinimumDistanceNN(NearNeighbors): """ Determine near-neighbor sites and coordination number using the nearest neighbor(s) at distance, d_min, plus all neighbors within a distance (1 + tol) * d_min, where tol is a (relative) distance tolerance parameter. """ def __init__(self, tol=0.1, cutoff=10.0, get_all_sites=False): """ Args: tol (float): tolerance parameter for neighbor identification (default: 0.1). cutoff (float): cutoff radius in Angstrom to look for trial near-neighbor sites (default: 10.0). get_all_sites (boolean): If this is set to True then the neighbor sites are only determined by the cutoff radius, tol is ignored """ self.tol = tol self.cutoff = cutoff self.get_all_sites = get_all_sites @property def structures_allowed(self): """ Boolean property: can this NearNeighbors class be used with Structure objects? """ return True @property def molecules_allowed(self): """ Boolean property: can this NearNeighbors class be used with Molecule objects? """ return True @property def extend_structure_molecules(self): """ Boolean property: Do Molecules need to be converted to Structures to use this NearNeighbors class? Note: this property is not defined for classes for which molecules_allowed == False. """ return True
[docs] def get_nn_info(self, structure, n): """ Get all near-neighbor sites as well as the associated image locations and weights of the site with index n using the closest neighbor distance-based method. Args: structure (Structure): input structure. n (integer): index of site for which to determine near neighbors. Returns: siw (list of tuples (Site, array, float)): tuples, each one of which represents a neighbor site, its image location, and its weight. """ site = structure[n] neighs_dists = structure.get_neighbors(site, self.cutoff) siw = [] if self.get_all_sites: for nn in neighs_dists: w = nn.nn_distance siw.append({'site': nn, 'image': self._get_image(structure, nn), 'weight': w, 'site_index': self._get_original_site(structure, nn)}) else: min_dist = min([nn.nn_distance for nn in neighs_dists]) for nn in neighs_dists: dist = nn.nn_distance if dist < (1.0 + self.tol) * min_dist: w = min_dist / dist siw.append({'site': nn, 'image': self._get_image(structure, nn), 'weight': w, 'site_index': self._get_original_site(structure, nn)}) return siw
[docs]class OpenBabelNN(NearNeighbors): """ Determine near-neighbor sites and bond orders using OpenBabel API. NOTE: This strategy is only appropriate for molecules, and not for structures. """ @requires(ob, "BabelMolAdaptor requires openbabel to be installed with " "Python bindings. Please get it at http://openbabel.org " "(version >=3.0.0).") def __init__(self, order=True): """ Args: order (bool): True if bond order should be returned as a weight, False if bond length should be used as a weight. """ self.order = order @property def structures_allowed(self): """ Boolean property: can this NearNeighbors class be used with Structure objects? """ return False @property def molecules_allowed(self): """ Boolean property: can this NearNeighbors class be used with Molecule objects? """ return True @property def extend_structure_molecules(self): """ Boolean property: Do Molecules need to be converted to Structures to use this NearNeighbors class? Note: this property is not defined for classes for which molecules_allowed == False. """ return False
[docs] def get_nn_info(self, structure, n): """ Get all near-neighbor sites and weights (orders) of bonds for a given atom. :param molecule: input Molecule. :param n: index of site for which to determine near neighbors. :return: [dict] representing a neighboring site and the type of bond present between site n and the neighboring site. """ from pymatgen.io.babel import BabelMolAdaptor obmol = BabelMolAdaptor(structure).openbabel_mol siw = [] # Get only the atom of interest site_atom = [a for i, a in enumerate(ob.OBMolAtomDFSIter(obmol)) if [a.GetX(), a.GetY(), a.GetZ()] == list( structure[n].coords)][0] for neighbor in ob.OBAtomAtomIter(site_atom): coords = [neighbor.GetX(), neighbor.GetY(), neighbor.GetZ()] site = [a for a in structure if list(a.coords) == coords][0] index = structure.index(site) bond = site_atom.GetBond(neighbor) if self.order: obmol.PerceiveBondOrders() weight = bond.GetBondOrder() else: weight = bond.GetLength() siw.append({"site": site, "image": (0, 0, 0), "weight": weight, "site_index": index}) return siw
[docs] def get_bonded_structure(self, structure, decorate=False): """ Obtain a MoleculeGraph object using this NearNeighbor class. Requires the optional dependency networkx (pip install networkx). Args: structure: Molecule object. decorate (bool): whether to annotate site properties with order parameters using neighbors determined by this NearNeighbor class Returns: a pymatgen.analysis.graphs.MoleculeGraph object """ # requires optional dependency which is why it's not a top-level import from pymatgen.analysis.graphs import MoleculeGraph if decorate: # Decorate all sites in the underlying structure # with site properties that provides information on the # coordination number and coordination pattern based # on the (current) structure of this graph. order_parameters = [self.get_local_order_parameters(structure, n) for n in range(len(structure))] structure.add_site_property('order_parameters', order_parameters) mg = MoleculeGraph.with_local_env_strategy(structure, self) return mg
[docs] def get_nn_shell_info(self, structure, site_idx, shell): """Get a certain nearest neighbor shell for a certain site. Determines all non-backtracking paths through the neighbor network computed by `get_nn_info`. The weight is determined by multiplying the weight of the neighbor at each hop through the network. For example, a 2nd-nearest-neighbor that has a weight of 1 from its 1st-nearest-neighbor and weight 0.5 from the original site will be assigned a weight of 0.5. As this calculation may involve computing the nearest neighbors of atoms multiple times, the calculation starts by computing all of the neighbor info and then calling `_get_nn_shell_info`. If you are likely to call this method for more than one site, consider calling `get_all_nn` first and then calling this protected method yourself. Args: structure (Molecule): Input structure site_idx (int): index of site for which to determine neighbor information. shell (int): Which neighbor shell to retrieve (1 == 1st NN shell) Returns: list of dictionaries. Each entry in the list is information about a certain neighbor in the structure, in the same format as `get_nn_info`. """ all_nn_info = self.get_all_nn_info(structure) sites = self._get_nn_shell_info(structure, all_nn_info, site_idx, shell) # Update the site positions # Did not do this during NN options because that can be slower output = [] for info in sites: orig_site = structure[info['site_index']] info['site'] = Site(orig_site.species, orig_site._coords, properties=orig_site.properties) output.append(info) return output
[docs]class CovalentBondNN(NearNeighbors): """ Determine near-neighbor sites and bond orders using built-in pymatgen.Molecule CovalentBond functionality. NOTE: This strategy is only appropriate for molecules, and not for structures. """ def __init__(self, tol=0.2, order=True): """ Args: tol (float): Tolerance for covalent bond checking. order (bool): If True (default), this class will compute bond orders. If False, bond lengths will be computed """ self.tol = tol self.order = order self.bonds = None @property def structures_allowed(self): """ Boolean property: can this NearNeighbors class be used with Structure objects? """ return False @property def molecules_allowed(self): """ Boolean property: can this NearNeighbors class be used with Molecule objects? """ return True @property def extend_structure_molecules(self): """ Boolean property: Do Molecules need to be converted to Structures to use this NearNeighbors class? Note: this property is not defined for classes for which molecules_allowed == False. """ return False
[docs] def get_nn_info(self, structure, n): """ Get all near-neighbor sites and weights (orders) of bonds for a given atom. :param structure: input Molecule. :param n: index of site for which to determine near neighbors. :return: [dict] representing a neighboring site and the type of bond present between site n and the neighboring site. """ # This is unfortunately inefficient, but is the best way to fit the # current NearNeighbors scheme self.bonds = structure.get_covalent_bonds(tol=self.tol) siw = [] for bond in self.bonds: capture_bond = False if bond.site1 == structure[n]: site = bond.site2 capture_bond = True elif bond.site2 == structure[n]: site = bond.site1 capture_bond = True if capture_bond: index = structure.index(site) if self.order: weight = bond.get_bond_order() else: weight = bond.length siw.append({"site": site, "image": (0, 0, 0), "weight": weight, "site_index": index}) return siw
[docs] def get_bonded_structure(self, structure, decorate=False): """ Obtain a MoleculeGraph object using this NearNeighbor class. Args: structure: Molecule object. decorate (bool): whether to annotate site properties with order parameters using neighbors determined by this NearNeighbor class Returns: a pymatgen.analysis.graphs.MoleculeGraph object """ # requires optional dependency which is why it's not a top-level import from pymatgen.analysis.graphs import MoleculeGraph if decorate: # Decorate all sites in the underlying structure # with site properties that provides information on the # coordination number and coordination pattern based # on the (current) structure of this graph. order_parameters = [self.get_local_order_parameters(structure, n) for n in range(len(structure))] structure.add_site_property('order_parameters', order_parameters) mg = MoleculeGraph.with_local_env_strategy(structure, self) return mg
[docs] def get_nn_shell_info(self, structure, site_idx, shell): """Get a certain nearest neighbor shell for a certain site. Determines all non-backtracking paths through the neighbor network computed by `get_nn_info`. The weight is determined by multiplying the weight of the neighbor at each hop through the network. For example, a 2nd-nearest-neighbor that has a weight of 1 from its 1st-nearest-neighbor and weight 0.5 from the original site will be assigned a weight of 0.5. As this calculation may involve computing the nearest neighbors of atoms multiple times, the calculation starts by computing all of the neighbor info and then calling `_get_nn_shell_info`. If you are likely to call this method for more than one site, consider calling `get_all_nn` first and then calling this protected method yourself. Args: structure (Molecule): Input structure site_idx (int): index of site for which to determine neighbor information. shell (int): Which neighbor shell to retrieve (1 == 1st NN shell) Returns: list of dictionaries. Each entry in the list is information about a certain neighbor in the structure, in the same format as `get_nn_info`. """ all_nn_info = self.get_all_nn_info(structure) sites = self._get_nn_shell_info(structure, all_nn_info, site_idx, shell) # Update the site positions # Did not do this during NN options because that can be slower output = [] for info in sites: orig_site = structure[info['site_index']] info['site'] = Site(orig_site.species, orig_site._coords, properties=orig_site.properties) output.append(info) return output
[docs]class MinimumOKeeffeNN(NearNeighbors): """ Determine near-neighbor sites and coordination number using the neighbor(s) at closest relative distance, d_min_OKeffee, plus some relative tolerance, where bond valence parameters from O'Keeffe's bond valence method (J. Am. Chem. Soc. 1991, 3226-3229) are used to calculate relative distances. """ def __init__(self, tol=0.1, cutoff=10.0): """ Args: tol (float): tolerance parameter for neighbor identification (default: 0.1). cutoff (float): cutoff radius in Angstrom to look for trial near-neighbor sites (default: 10.0). """ self.tol = tol self.cutoff = cutoff @property def structures_allowed(self): """ Boolean property: can this NearNeighbors class be used with Structure objects? """ return True @property def molecules_allowed(self): """ Boolean property: can this NearNeighbors class be used with Molecule objects? """ return True @property def extend_structure_molecules(self): """ Boolean property: Do Molecules need to be converted to Structures to use this NearNeighbors class? Note: this property is not defined for classes for which molecules_allowed == False. """ return True
[docs] def get_nn_info(self, structure, n): """ Get all near-neighbor sites as well as the associated image locations and weights of the site with index n using the closest relative neighbor distance-based method with O'Keeffe parameters. Args: structure (Structure): input structure. n (integer): index of site for which to determine near neighbors. Returns: siw (list of tuples (Site, array, float)): tuples, each one of which represents a neighbor site, its image location, and its weight. """ site = structure[n] neighs_dists = structure.get_neighbors(site, self.cutoff) try: eln = site.specie.element except Exception: eln = site.species_string reldists_neighs = [] for nn in neighs_dists: neigh = nn dist = nn.nn_distance try: el2 = neigh.specie.element except Exception: el2 = neigh.species_string reldists_neighs.append([dist / get_okeeffe_distance_prediction( eln, el2), neigh]) siw = [] min_reldist = min([reldist for reldist, neigh in reldists_neighs]) for reldist, s in reldists_neighs: if reldist < (1.0 + self.tol) * min_reldist: w = min_reldist / reldist siw.append({'site': s, 'image': self._get_image(structure, s), 'weight': w, 'site_index': self._get_original_site(structure, s)}) return siw
[docs]class MinimumVIRENN(NearNeighbors): """ Determine near-neighbor sites and coordination number using the neighbor(s) at closest relative distance, d_min_VIRE, plus some relative tolerance, where atom radii from the ValenceIonicRadiusEvaluator (VIRE) are used to calculate relative distances. """ def __init__(self, tol=0.1, cutoff=10.0): """ Args: tol (float): tolerance parameter for neighbor identification (default: 0.1). cutoff (float): cutoff radius in Angstrom to look for trial near-neighbor sites (default: 10.0). """ self.tol = tol self.cutoff = cutoff @property def structures_allowed(self): """ Boolean property: can this NearNeighbors class be used with Structure objects? """ return True @property def molecules_allowed(self): """ Boolean property: can this NearNeighbors class be used with Molecule objects? """ return False
[docs] def get_nn_info(self, structure, n): """ Get all near-neighbor sites as well as the associated image locations and weights of the site with index n using the closest relative neighbor distance-based method with VIRE atomic/ionic radii. Args: structure (Structure): input structure. n (integer): index of site for which to determine near neighbors. Returns: siw (list of tuples (Site, array, float)): tuples, each one of which represents a neighbor site, its image location, and its weight. """ vire = _get_vire(structure) site = vire.structure[n] neighs_dists = vire.structure.get_neighbors(site, self.cutoff) rn = vire.radii[vire.structure[n].species_string] reldists_neighs = [] for nn in neighs_dists: reldists_neighs.append([nn.nn_distance / ( vire.radii[nn.species_string] + rn), nn]) siw = [] min_reldist = min([reldist for reldist, neigh in reldists_neighs]) for reldist, s in reldists_neighs: if reldist < (1.0 + self.tol) * min_reldist: w = min_reldist / reldist siw.append({'site': s, 'image': self._get_image(vire.structure, s), 'weight': w, 'site_index': self._get_original_site( vire.structure, s)}) return siw
def _get_vire(structure: Union[Structure, IStructure]): """Get the ValenceIonicRadiusEvaluator object for an structure taking advantage of caching. Args: structure: A structure. Returns: Output of `ValenceIonicRadiusEvaluator(structure)` """ # pymatgen does not hash Structure objects, so we need # to cast from Structure to the immutable IStructure if isinstance(structure, Structure): structure = IStructure.from_sites(structure) return _get_vire_istructure(structure) @lru_cache(maxsize=1) def _get_vire_istructure(structure: IStructure): """Get the ValenceIonicRadiusEvaluator object for an immutable structure taking advantage of caching. Args: structure: A structure. Returns: Output of `ValenceIonicRadiusEvaluator(structure)` """ return ValenceIonicRadiusEvaluator(structure)
[docs]def solid_angle(center, coords): """ Helper method to calculate the solid angle of a set of coords from the center. Args: center (3x1 array): Center to measure solid angle from. coords (Nx3 array): List of coords to determine solid angle. Returns: The solid angle. """ # Compute the displacement from the center r = [np.subtract(c, center) for c in coords] # Compute the magnitude of each vector r_norm = [np.linalg.norm(i) for i in r] # Compute the solid angle for each tetrahedron that makes up the facet # Following: https://en.wikipedia.org/wiki/Solid_angle#Tetrahedron angle = 0 for i in range(1, len(r) - 1): j = i + 1 tp = np.abs(np.dot(r[0], np.cross(r[i], r[j]))) de = (r_norm[0] * r_norm[i] * r_norm[j] + r_norm[j] * np.dot(r[0], r[i]) + r_norm[i] * np.dot(r[0], r[j]) + r_norm[0] * np.dot(r[i], r[j])) if de == 0: my_angle = 0.5 * pi if tp > 0 else -0.5 * pi else: my_angle = np.arctan(tp / de) angle += (my_angle if my_angle > 0 else my_angle + np.pi) * 2 return angle
[docs]def vol_tetra(vt1, vt2, vt3, vt4): """ Calculate the volume of a tetrahedron, given the four vertices of vt1, vt2, vt3 and vt4. Args: vt1 (array-like): coordinates of vertex 1. vt2 (array-like): coordinates of vertex 2. vt3 (array-like): coordinates of vertex 3. vt4 (array-like): coordinates of vertex 4. Returns: (float): volume of the tetrahedron. """ vol_tetra = np.abs(np.dot((vt1 - vt4), np.cross((vt2 - vt4), (vt3 - vt4)))) / 6 return vol_tetra
[docs]def get_okeeffe_params(el_symbol): """ Returns the elemental parameters related to atom size and electronegativity which are used for estimating bond-valence parameters (bond length) of pairs of atoms on the basis of data provided in 'Atoms Sizes and Bond Lengths in Molecules and Crystals' (O'Keeffe & Brese, 1991). Args: el_symbol (str): element symbol. Returns: (dict): atom-size ('r') and electronegativity-related ('c') parameter. """ el = Element(el_symbol) if el not in list(BV_PARAMS.keys()): raise RuntimeError("Could not find O'Keeffe parameters for element" " \"{}\" in \"BV_PARAMS\"dictonary" " provided by pymatgen".format(el_symbol)) return BV_PARAMS[el]
[docs]def get_okeeffe_distance_prediction(el1, el2): """ Returns an estimate of the bond valence parameter (bond length) using the derived parameters from 'Atoms Sizes and Bond Lengths in Molecules and Crystals' (O'Keeffe & Brese, 1991). The estimate is based on two experimental parameters: r and c. The value for r is based off radius, while c is (usually) the Allred-Rochow electronegativity. Values used are *not* generated from pymatgen, and are found in 'okeeffe_params.json'. Args: el1, el2 (Element): two Element objects Returns: a float value of the predicted bond length """ el1_okeeffe_params = get_okeeffe_params(el1) el2_okeeffe_params = get_okeeffe_params(el2) r1 = el1_okeeffe_params['r'] r2 = el2_okeeffe_params['r'] c1 = el1_okeeffe_params['c'] c2 = el2_okeeffe_params['c'] return r1 + r2 - r1 * r2 * pow(sqrt(c1) - sqrt(c2), 2) / (c1 * r1 + c2 * r2)
[docs]def get_neighbors_of_site_with_index(struct, n, approach="min_dist", delta=0.1, cutoff=10.0): """ Returns the neighbors of a given site using a specific neighbor-finding method. Args: struct (Structure): input structure. n (int): index of site in Structure object for which motif type is to be determined. approach (str): type of neighbor-finding approach, where "min_dist" will use the MinimumDistanceNN class, "voronoi" the VoronoiNN class, "min_OKeeffe" the MinimumOKeeffe class, and "min_VIRE" the MinimumVIRENN class. delta (float): tolerance involved in neighbor finding. cutoff (float): (large) radius to find tentative neighbors. Returns: neighbor sites. """ if approach == "min_dist": return MinimumDistanceNN(tol=delta, cutoff=cutoff).get_nn( struct, n) elif approach == "voronoi": return VoronoiNN(tol=delta, cutoff=cutoff).get_nn( struct, n) elif approach == "min_OKeeffe": return MinimumOKeeffeNN(tol=delta, cutoff=cutoff).get_nn( struct, n) elif approach == "min_VIRE": return MinimumVIRENN(tol=delta, cutoff=cutoff).get_nn( struct, n) else: raise RuntimeError("unsupported neighbor-finding method ({}).".format( approach))
[docs]def site_is_of_motif_type(struct, n, approach="min_dist", delta=0.1, cutoff=10.0, thresh=None): """ Returns the motif type of the site with index n in structure struct; currently featuring "tetrahedral", "octahedral", "bcc", and "cp" (close-packed: fcc and hcp) as well as "square pyramidal" and "trigonal bipyramidal". If the site is not recognized, "unrecognized" is returned. If a site should be assigned to two different motifs, "multiple assignments" is returned. Args: struct (Structure): input structure. n (int): index of site in Structure object for which motif type is to be determined. approach (str): type of neighbor-finding approach, where "min_dist" will use the MinimumDistanceNN class, "voronoi" the VoronoiNN class, "min_OKeeffe" the MinimumOKeeffe class, and "min_VIRE" the MinimumVIRENN class. delta (float): tolerance involved in neighbor finding. cutoff (float): (large) radius to find tentative neighbors. thresh (dict): thresholds for motif criteria (currently, required keys and their default values are "qtet": 0.5, "qoct": 0.5, "qbcc": 0.5, "q6": 0.4). Returns: motif type (str). """ if thresh is None: thresh = { "qtet": 0.5, "qoct": 0.5, "qbcc": 0.5, "q6": 0.4, "qtribipyr": 0.8, "qsqpyr": 0.8} ops = LocalStructOrderParams([ "cn", "tet", "oct", "bcc", "q6", "sq_pyr", "tri_bipyr"]) neighs_cent = get_neighbors_of_site_with_index( struct, n, approach=approach, delta=delta, cutoff=cutoff) neighs_cent.append(struct.sites[n]) opvals = ops.get_order_parameters( neighs_cent, len(neighs_cent) - 1, indices_neighs=[ i for i in range(len(neighs_cent) - 1)]) cn = int(opvals[0] + 0.5) motif_type = "unrecognized" nmotif = 0 if cn == 4 and opvals[1] > thresh["qtet"]: motif_type = "tetrahedral" nmotif += 1 if cn == 5 and opvals[5] > thresh["qsqpyr"]: motif_type = "square pyramidal" nmotif += 1 if cn == 5 and opvals[6] > thresh["qtribipyr"]: motif_type = "trigonal bipyramidal" nmotif += 1 if cn == 6 and opvals[2] > thresh["qoct"]: motif_type = "octahedral" nmotif += 1 if cn == 8 and (opvals[3] > thresh["qbcc"] and opvals[1] < thresh["qtet"]): motif_type = "bcc" nmotif += 1 if cn == 12 and (opvals[4] > thresh["q6"] and opvals[1] < thresh["q6"] and opvals[2] < thresh["q6"] and opvals[3] < thresh["q6"]): motif_type = "cp" nmotif += 1 if nmotif > 1: motif_type = "multiple assignments" return motif_type
[docs]def gramschmidt(vin, uin): """ Returns that part of the first input vector that is orthogonal to the second input vector. The output vector is not normalized. Args: vin (numpy array): first input vector uin (numpy array): second input vector """ vin_uin = np.inner(vin, uin) uin_uin = np.inner(uin, uin) if uin_uin <= 0.0: raise ValueError("Zero or negative inner product!") return vin - (vin_uin / uin_uin) * uin
[docs]class LocalStructOrderParams: """ This class permits the calculation of various types of local structure order parameters. """ __supported_types = ( "cn", "sgl_bd", "bent", "tri_plan", "tri_plan_max", "reg_tri", "sq_plan", "sq_plan_max", "pent_plan", "pent_plan_max", "sq", "tet", "tet_max", "tri_pyr", "sq_pyr", "sq_pyr_legacy", "tri_bipyr", "sq_bipyr", "oct", "oct_legacy", "pent_pyr", "hex_pyr", "pent_bipyr", "hex_bipyr", "T", "cuboct", "cuboct_max", "see_saw_rect", "bcc", "q2", "q4", "q6", "oct_max", "hex_plan_max", "sq_face_cap_trig_pris") def __init__(self, types, parameters=None, cutoff=-10.0): """ Args: types ([string]): list of strings representing the types of order parameters to be calculated. Note that multiple mentions of the same type may occur. Currently available types recognize following environments: "cn": simple coordination number---normalized if desired; "sgl_bd": single bonds; "bent": bent (angular) coordinations (Zimmermann & Jain, in progress, 2017); "T": T-shape coordinations; "see_saw_rect": see saw-like coordinations; "tet": tetrahedra (Zimmermann et al., submitted, 2017); "oct": octahedra (Zimmermann et al., submitted, 2017); "bcc": body-centered cubic environments (Peters, J. Chem. Phys., 131, 244103, 2009); "tri_plan": trigonal planar environments; "sq_plan": square planar environments; "pent_plan": pentagonal planar environments; "tri_pyr": trigonal pyramids (coordinated atom is in the center of the basal plane); "sq_pyr": square pyramids; "pent_pyr": pentagonal pyramids; "hex_pyr": hexagonal pyramids; "tri_bipyr": trigonal bipyramids; "sq_bipyr": square bipyramids; "pent_bipyr": pentagonal bipyramids; "hex_bipyr": hexagonal bipyramids; "cuboct": cuboctahedra; "q2": motif-unspecific bond orientational order parameter (BOOP) of weight l=2 (Steinhardt et al., Phys. Rev. B, 28, 784-805, 1983); "q4": BOOP of weight l=4; "q6": BOOP of weight l=6. "reg_tri": regular triangle with varying height to basal plane; "sq": square coordination (cf., "reg_tri"); "oct_legacy": original Peters-style OP recognizing octahedral coordination environments (Zimmermann et al., J. Am. Chem. Soc., 137, 13352-13361, 2015) that can, however, produce small negative values sometimes. "sq_pyr_legacy": square pyramids (legacy); parameters ([dict]): list of dictionaries that store float-type parameters associated with the definitions of the different order parameters (length of list = number of OPs). If an entry is None, default values are used that are read from the op_params.yaml file. With few exceptions, 9 different parameters are used across all OPs: "norm": normalizing constant (used in "cn" (default value: 1)). "TA": target angle (TA) in fraction of 180 degrees ("bent" (1), "tet" (0.6081734479693927), "tri_plan" (0.66666666667), "pent_plan" (0.6), "sq_pyr_legacy" (0.5)). "IGW_TA": inverse Gaussian width (IGW) for penalizing angles away from the target angle in inverse fractions of 180 degrees to ("bent" and "tet" (15), "tri_plan" (13.5), "pent_plan" (18), "sq_pyr_legacy" (30)). "IGW_EP": IGW for penalizing angles away from the equatorial plane (EP) at 90 degrees ("T", "see_saw_rect", "oct", "sq_plan", "tri_pyr", "sq_pyr", "pent_pyr", "hex_pyr", "tri_bipyr", "sq_bipyr", "pent_bipyr", "hex_bipyr", and "oct_legacy" (18)). "fac_AA": factor applied to azimuth angle (AA) in cosine term ("T", "tri_plan", and "sq_plan" (1), "tet", "tri_pyr", and "tri_bipyr" (1.5), "oct", "sq_pyr", "sq_bipyr", and "oct_legacy" (2), "pent_pyr" and "pent_bipyr" (2.5), "hex_pyr" and "hex_bipyr" (3)). "exp_cos_AA": exponent applied to cosine term of AA ("T", "tet", "oct", "tri_plan", "sq_plan", "tri_pyr", "sq_pyr", "pent_pyr", "hex_pyr", "tri_bipyr", "sq_bipyr", "pent_bipyr", "hex_bipyr", and "oct_legacy" (2)). "min_SPP": smallest angle (in radians) to consider a neighbor to be at South pole position ("see_saw_rect", "oct", "bcc", "sq_plan", "tri_bipyr", "sq_bipyr", "pent_bipyr", "hex_bipyr", "cuboct", and "oct_legacy" (2.792526803190927)). "IGW_SPP": IGW for penalizing angles away from South pole position ("see_saw_rect", "oct", "bcc", "sq_plan", "tri_bipyr", "sq_bipyr", "pent_bipyr", "hex_bipyr", "cuboct", and "oct_legacy" (15)). "w_SPP": weight for South pole position relative to equatorial positions ("see_saw_rect" and "sq_plan" (1), "cuboct" (1.8), "tri_bipyr" (2), "oct", "sq_bipyr", and "oct_legacy" (3), "pent_bipyr" (4), "hex_bipyr" (5), "bcc" (6)). cutoff (float): Cutoff radius to determine which nearest neighbors are supposed to contribute to the order parameters. If the value is negative the neighboring sites found by distance and cutoff radius are further pruned using the get_nn method from the VoronoiNN class. """ for t in types: if t not in LocalStructOrderParams.__supported_types: raise ValueError("Unknown order parameter type (" + t + ")!") self._types = tuple(types) self._comp_azi = False self._params = [] for i, t in enumerate(self._types): d = deepcopy(default_op_params[t]) if default_op_params[t] is not None else None if parameters is None: self._params.append(d) elif parameters[i] is None: self._params.append(d) else: self._params.append(deepcopy(parameters[i])) self._computerijs = self._computerjks = self._geomops = False self._geomops2 = self._boops = False self._max_trig_order = -1 # Add here any additional flags to be used during calculation. if "sgl_bd" in self._types: self._computerijs = True if not set(self._types).isdisjoint( ["tet", "oct", "bcc", "sq_pyr", "sq_pyr_legacy", "tri_bipyr", "sq_bipyr", "oct_legacy", "tri_plan", "sq_plan", "pent_plan", "tri_pyr", "pent_pyr", "hex_pyr", "pent_bipyr", "hex_bipyr", "T", "cuboct", "oct_max", "tet_max", "tri_plan_max", "sq_plan_max", "pent_plan_max", "cuboct_max", "bent", "see_saw_rect", "hex_plan_max", "sq_face_cap_trig_pris"]): self._computerijs = self._geomops = True if "sq_face_cap_trig_pris" in self._types: self._comp_azi = True if not set(self._types).isdisjoint(["reg_tri", "sq"]): self._computerijs = self._computerjks = self._geomops2 = True if not set(self._types).isdisjoint(["q2", "q4", "q6"]): self._computerijs = self._boops = True if "q2" in self._types: self._max_trig_order = 2 if "q4" in self._types: self._max_trig_order = 4 if "q6" in self._types: self._max_trig_order = 6 # Finish parameter treatment. if cutoff < 0.0: self._cutoff = -cutoff self._voroneigh = True elif cutoff > 0.0: self._cutoff = cutoff self._voroneigh = False else: raise ValueError("Cutoff radius is zero!") # Further variable definitions. self._last_nneigh = -1 self._pow_sin_t = {} self._pow_cos_t = {} self._sin_n_p = {} self._cos_n_p = {} @property def num_ops(self): """ Returns: int: the number of different order parameters that are targeted to be calculated. """ return len(self._types) @property def last_nneigh(self): """ Returns: int: the number of neighbors encountered during the most recent order parameter calculation. A value of -1 indicates that no such calculation has yet been performed for this instance. """ return len(self._last_nneigh)
[docs] def compute_trigonometric_terms(self, thetas, phis): """ Computes trigonometric terms that are required to calculate bond orientational order parameters using internal variables. Args: thetas ([float]): polar angles of all neighbors in radians. phis ([float]): azimuth angles of all neighbors in radians. The list of azimuth angles of all neighbors in radians. The list of azimuth angles is expected to have the same size as the list of polar angles; otherwise, a ValueError is raised. Also, the two lists of angles have to be coherent in order. That is, it is expected that the order in the list of azimuth angles corresponds to a distinct sequence of neighbors. And, this sequence has to equal the sequence of neighbors in the list of polar angles. """ if len(thetas) != len(phis): raise ValueError("List of polar and azimuthal angles have to be" " equal!") self._pow_sin_t.clear() self._pow_cos_t.clear() self._sin_n_p.clear() self._cos_n_p.clear() self._pow_sin_t[1] = [sin(float(t)) for t in thetas] self._pow_cos_t[1] = [cos(float(t)) for t in thetas] self._sin_n_p[1] = [sin(float(p)) for p in phis] self._cos_n_p[1] = [cos(float(p)) for p in phis] for i in range(2, self._max_trig_order + 1): self._pow_sin_t[i] = [e[0] * e[1] for e in zip( self._pow_sin_t[i - 1], self._pow_sin_t[1])] self._pow_cos_t[i] = [e[0] * e[1] for e in zip( self._pow_cos_t[i - 1], self._pow_cos_t[1])] self._sin_n_p[i] = [sin(float(i) * float(p)) for p in phis] self._cos_n_p[i] = [cos(float(i) * float(p)) for p in phis]
[docs] def get_q2(self, thetas=None, phis=None): """ Calculates the value of the bond orientational order parameter of weight l=2. If the function is called with non-empty lists of polar and azimuthal angles the corresponding trigonometric terms are computed afresh. Otherwise, it is expected that the compute_trigonometric_terms function has been just called. Args: thetas ([float]): polar angles of all neighbors in radians. phis ([float]): azimuth angles of all neighbors in radians. Returns: float: bond orientational order parameter of weight l=2 corresponding to the input angles thetas and phis. """ if thetas is not None and phis is not None: self.compute_trigonometric_terms(thetas, phis) nnn = len(self._pow_sin_t[1]) nnn_range = range(nnn) sqrt_15_2pi = sqrt(15.0 / (2.0 * pi)) sqrt_5_pi = sqrt(5.0 / pi) pre_y_2_2 = [0.25 * sqrt_15_2pi * val for val in self._pow_sin_t[2]] pre_y_2_1 = [0.5 * sqrt_15_2pi * val[0] * val[1] for val in zip(self._pow_sin_t[1], self._pow_cos_t[1])] acc = 0.0 # Y_2_-2 real = imag = 0.0 for i in nnn_range: real += pre_y_2_2[i] * self._cos_n_p[2][i] imag -= pre_y_2_2[i] * self._sin_n_p[2][i] acc += (real * real + imag * imag) # Y_2_-1 real = imag = 0.0 for i in nnn_range: real += pre_y_2_1[i] * self._cos_n_p[1][i] imag -= pre_y_2_1[i] * self._sin_n_p[1][i] acc += (real * real + imag * imag) # Y_2_0 real = imag = 0.0 for i in nnn_range: real += 0.25 * sqrt_5_pi * (3.0 * self._pow_cos_t[2][i] - 1.0) acc += (real * real) # Y_2_1 real = imag = 0.0 for i in nnn_range: real -= pre_y_2_1[i] * self._cos_n_p[1][i] imag -= pre_y_2_1[i] * self._sin_n_p[1][i] acc += (real * real + imag * imag) # Y_2_2 real = imag = 0.0 for i in nnn_range: real += pre_y_2_2[i] * self._cos_n_p[2][i] imag += pre_y_2_2[i] * self._sin_n_p[2][i] acc += (real * real + imag * imag) q2 = sqrt(4.0 * pi * acc / (5.0 * float(nnn * nnn))) return q2
[docs] def get_q4(self, thetas=None, phis=None): """ Calculates the value of the bond orientational order parameter of weight l=4. If the function is called with non-empty lists of polar and azimuthal angles the corresponding trigonometric terms are computed afresh. Otherwise, it is expected that the compute_trigonometric_terms function has been just called. Args: thetas ([float]): polar angles of all neighbors in radians. phis ([float]): azimuth angles of all neighbors in radians. Returns: float: bond orientational order parameter of weight l=4 corresponding to the input angles thetas and phis. """ if thetas is not None and phis is not None: self.compute_trigonometric_terms(thetas, phis) nnn = len(self._pow_sin_t[1]) nnn_range = range(nnn) i16_3 = 3.0 / 16.0 i8_3 = 3.0 / 8.0 sqrt_35_pi = sqrt(35.0 / pi) sqrt_35_2pi = sqrt(35.0 / (2.0 * pi)) sqrt_5_pi = sqrt(5.0 / pi) sqrt_5_2pi = sqrt(5.0 / (2.0 * pi)) sqrt_1_pi = sqrt(1.0 / pi) pre_y_4_4 = [i16_3 * sqrt_35_2pi * val for val in self._pow_sin_t[4]] pre_y_4_3 = [i8_3 * sqrt_35_pi * val[0] * val[1] for val in zip(self._pow_sin_t[3], self._pow_cos_t[1])] pre_y_4_2 = [i8_3 * sqrt_5_2pi * val[0] * (7.0 * val[1] - 1.0) for val in zip(self._pow_sin_t[2], self._pow_cos_t[2])] pre_y_4_1 = [i8_3 * sqrt_5_pi * val[0] * (7.0 * val[1] - 3.0 * val[2]) for val in zip(self._pow_sin_t[1], self._pow_cos_t[3], self._pow_cos_t[1])] acc = 0.0 # Y_4_-4 real = imag = 0.0 for i in nnn_range: real += pre_y_4_4[i] * self._cos_n_p[4][i] imag -= pre_y_4_4[i] * self._sin_n_p[4][i] acc += (real * real + imag * imag) # Y_4_-3 real = imag = 0.0 for i in nnn_range: real += pre_y_4_3[i] * self._cos_n_p[3][i] imag -= pre_y_4_3[i] * self._sin_n_p[3][i] acc += (real * real + imag * imag) # Y_4_-2 real = imag = 0.0 for i in nnn_range: real += pre_y_4_2[i] * self._cos_n_p[2][i] imag -= pre_y_4_2[i] * self._sin_n_p[2][i] acc += (real * real + imag * imag) # Y_4_-1 real = imag = 0.0 for i in nnn_range: real += pre_y_4_1[i] * self._cos_n_p[1][i] imag -= pre_y_4_1[i] * self._sin_n_p[1][i] acc += (real * real + imag * imag) # Y_4_0 real = imag = 0.0 for i in nnn_range: real += i16_3 * sqrt_1_pi * (35.0 * self._pow_cos_t[4][i] - 30.0 * self._pow_cos_t[2][i] + 3.0) acc += (real * real) # Y_4_1 real = imag = 0.0 for i in nnn_range: real -= pre_y_4_1[i] * self._cos_n_p[1][i] imag -= pre_y_4_1[i] * self._sin_n_p[1][i] acc += (real * real + imag * imag) # Y_4_2 real = imag = 0.0 for i in nnn_range: real += pre_y_4_2[i] * self._cos_n_p[2][i] imag += pre_y_4_2[i] * self._sin_n_p[2][i] acc += (real * real + imag * imag) # Y_4_3 real = imag = 0.0 for i in nnn_range: real -= pre_y_4_3[i] * self._cos_n_p[3][i] imag -= pre_y_4_3[i] * self._sin_n_p[3][i] acc += (real * real + imag * imag) # Y_4_4 real = imag = 0.0 for i in nnn_range: real += pre_y_4_4[i] * self._cos_n_p[4][i] imag += pre_y_4_4[i] * self._sin_n_p[4][i] acc += (real * real + imag * imag) q4 = sqrt(4.0 * pi * acc / (9.0 * float(nnn * nnn))) return q4
[docs] def get_q6(self, thetas=None, phis=None): """ Calculates the value of the bond orientational order parameter of weight l=6. If the function is called with non-empty lists of polar and azimuthal angles the corresponding trigonometric terms are computed afresh. Otherwise, it is expected that the compute_trigonometric_terms function has been just called. Args: thetas ([float]): polar angles of all neighbors in radians. phis ([float]): azimuth angles of all neighbors in radians. Returns: float: bond orientational order parameter of weight l=6 corresponding to the input angles thetas and phis. """ if thetas is not None and phis is not None: self.compute_trigonometric_terms(thetas, phis) nnn = len(self._pow_sin_t[1]) nnn_range = range(nnn) i64 = 1.0 / 64.0 i32 = 1.0 / 32.0 i32_3 = 3.0 / 32.0 i16 = 1.0 / 16.0 sqrt_3003_pi = sqrt(3003.0 / pi) sqrt_1001_pi = sqrt(1001.0 / pi) sqrt_91_2pi = sqrt(91.0 / (2.0 * pi)) sqrt_1365_pi = sqrt(1365.0 / pi) sqrt_273_2pi = sqrt(273.0 / (2.0 * pi)) sqrt_13_pi = sqrt(13.0 / pi) pre_y_6_6 = [i64 * sqrt_3003_pi * val for val in self._pow_sin_t[6]] pre_y_6_5 = [i32_3 * sqrt_1001_pi * val[0] * val[1] for val in zip(self._pow_sin_t[5], self._pow_cos_t[1])] pre_y_6_4 = [i32_3 * sqrt_91_2pi * val[0] * (11.0 * val[1] - 1.0) for val in zip(self._pow_sin_t[4], self._pow_cos_t[2])] pre_y_6_3 = [ i32 * sqrt_1365_pi * val[0] * (11.0 * val[1] - 3.0 * val[2]) for val in zip(self._pow_sin_t[3], self._pow_cos_t[3], self._pow_cos_t[1])] pre_y_6_2 = [i64 * sqrt_1365_pi * val[0] * (33.0 * val[1] - 18.0 * val[2] + 1.0) for val in zip(self._pow_sin_t[2], self._pow_cos_t[4], self._pow_cos_t[2])] pre_y_6_1 = [i16 * sqrt_273_2pi * val[0] * (33.0 * val[1] - 30.0 * val[2] + 5.0 * val[ 3]) for val in zip(self._pow_sin_t[1], self._pow_cos_t[5], self._pow_cos_t[3], self._pow_cos_t[1])] acc = 0.0 # Y_6_-6 real = 0.0 imag = 0.0 for i in nnn_range: real += pre_y_6_6[i] * self._cos_n_p[6][i] # cos(x) = cos(-x) imag -= pre_y_6_6[i] * self._sin_n_p[6][i] # sin(x) = -sin(-x) acc += (real * real + imag * imag) # Y_6_-5 real = 0.0 imag = 0.0 for i in nnn_range: real += pre_y_6_5[i] * self._cos_n_p[5][i] imag -= pre_y_6_5[i] * self._sin_n_p[5][i] acc += (real * real + imag * imag) # Y_6_-4 real = 0.0 imag = 0.0 for i in nnn_range: real += pre_y_6_4[i] * self._cos_n_p[4][i] imag -= pre_y_6_4[i] * self._sin_n_p[4][i] acc += (real * real + imag * imag) # Y_6_-3 real = 0.0 imag = 0.0 for i in nnn_range: real += pre_y_6_3[i] * self._cos_n_p[3][i] imag -= pre_y_6_3[i] * self._sin_n_p[3][i] acc += (real * real + imag * imag) # Y_6_-2 real = 0.0 imag = 0.0 for i in nnn_range: real += pre_y_6_2[i] * self._cos_n_p[2][i] imag -= pre_y_6_2[i] * self._sin_n_p[2][i] acc += (real * real + imag * imag) # Y_6_-1 real = 0.0 imag = 0.0 for i in nnn_range: real += pre_y_6_1[i] * self._cos_n_p[1][i] imag -= pre_y_6_1[i] * self._sin_n_p[1][i] acc += (real * real + imag * imag) # Y_6_0 real = 0.0 imag = 0.0 for i in nnn_range: real += i32 * sqrt_13_pi * (231.0 * self._pow_cos_t[6][i] - 315.0 * self._pow_cos_t[4][i] + 105.0 * self._pow_cos_t[2][i] - 5.0) acc += (real * real) # Y_6_1 real = 0.0 imag = 0.0 for i in nnn_range: real -= pre_y_6_1[i] * self._cos_n_p[1][i] imag -= pre_y_6_1[i] * self._sin_n_p[1][i] acc += (real * real + imag * imag) # Y_6_2 real = 0.0 imag = 0.0 for i in nnn_range: real += pre_y_6_2[i] * self._cos_n_p[2][i] imag += pre_y_6_2[i] * self._sin_n_p[2][i] acc += (real * real + imag * imag) # Y_6_3 real = 0.0 imag = 0.0 for i in nnn_range: real -= pre_y_6_3[i] * self._cos_n_p[3][i] imag -= pre_y_6_3[i] * self._sin_n_p[3][i] acc += (real * real + imag * imag) # Y_6_4 real = 0.0 imag = 0.0 for i in nnn_range: real += pre_y_6_4[i] * self._cos_n_p[4][i] imag += pre_y_6_4[i] * self._sin_n_p[4][i] acc += (real * real + imag * imag) # Y_6_5 real = 0.0 imag = 0.0 for i in nnn_range: real -= pre_y_6_5[i] * self._cos_n_p[5][i] imag -= pre_y_6_5[i] * self._sin_n_p[5][i] acc += (real * real + imag * imag) # Y_6_6 real = 0.0 imag = 0.0 for i in nnn_range: real += pre_y_6_6[i] * self._cos_n_p[6][i] imag += pre_y_6_6[i] * self._sin_n_p[6][i] acc += (real * real + imag * imag) q6 = sqrt(4.0 * pi * acc / (13.0 * float(nnn * nnn))) return q6
[docs] def get_type(self, index): """ Return type of order parameter at the index provided and represented by a short string. Args: index (int): index of order parameter for which type is to be returned. Returns: str: OP type. """ if index < 0 or index >= len(self._types): raise ValueError("Index for getting order parameter type" " out-of-bounds!") return self._types[index]
[docs] def get_parameters(self, index): """ Returns list of floats that represents the parameters associated with calculation of the order parameter that was defined at the index provided. Attention: the parameters do not need to equal those originally inputted because of processing out of efficiency reasons. Args: index (int): index of order parameter for which associated parameters are to be returned. Returns: [float]: parameters of a given OP. """ if index < 0 or index >= len(self._types): raise ValueError("Index for getting parameters associated with" " order parameter calculation out-of-bounds!") return self._params[index]
[docs] def get_order_parameters(self, structure, n, indices_neighs=None, tol=0.0, target_spec=None): """ Compute all order parameters of site n. Args: structure (Structure): input structure. n (int): index of site in input structure, for which OPs are to be calculated. Note that we do not use the sites iterator here, but directly access sites via struct[index]. indices_neighs ([int]): list of indices of those neighbors in Structure object structure that are to be considered for OP computation. This optional argument overwrites the way neighbors are to be determined as defined in the constructor (i.e., Voronoi coordination finder via negative cutoff radius vs constant cutoff radius if cutoff was positive). We do not use information about the underlying structure lattice if the neighbor indices are explicitly provided. This has two important consequences. First, the input Structure object can, in fact, be a simple list of Site objects. Second, no nearest images of neighbors are determined when providing an index list. Note furthermore that this neighbor determination type ignores the optional target_spec argument. tol (float): threshold of weight (= solid angle / maximal solid angle) to determine if a particular pair is considered neighbors; this is relevant only in the case when Voronoi polyhedra are used to determine coordination target_spec (Specie): target species to be considered when calculating the order parameters of site n; None includes all species of input structure. Returns: [floats]: representing order parameters. Should it not be possible to compute a given OP for a conceptual reason, the corresponding entry is None instead of a float. For Steinhardt et al.'s bond orientational OPs and the other geometric OPs ("tet", "oct", "bcc", etc.), this can happen if there is a single neighbor around site n in the structure because that does not permit calculation of angles between multiple neighbors. """ # Do error-checking and initialization. if n < 0: raise ValueError("Site index smaller zero!") if n >= len(structure): raise ValueError("Site index beyond maximum!") if indices_neighs is not None: for index in indices_neighs: if index >= len(structure): raise ValueError("Neighbor site index beyond maximum!") if tol < 0.0: raise ValueError("Negative tolerance for weighted solid angle!") left_of_unity = 1.0 - 1.0e-12 # The following threshold has to be adapted to non-Angstrom units. very_small = 1.0e-12 fac_bcc = 1.0 / exp(-0.5) # Find central site and its neighbors. # Note that we adopt the same way of accessing sites here as in # VoronoiNN; that is, not via the sites iterator. centsite = structure[n] if indices_neighs is not None: neighsites = [structure[index] for index in indices_neighs] elif self._voroneigh: vnn = VoronoiNN(tol=tol, targets=target_spec) neighsites = vnn.get_nn(structure, n) else: # Structure.get_sites_in_sphere --> also other periodic images neighsitestmp = [i[0] for i in structure.get_sites_in_sphere( centsite.coords, self._cutoff)] neighsites = [] if centsite not in neighsitestmp: raise ValueError("Could not find center site!") else: neighsitestmp.remove(centsite) if target_spec is None: neighsites = list(neighsitestmp) else: neighsites[:] = [site for site in neighsitestmp if site.specie.symbol == target_spec] nneigh = len(neighsites) self._last_nneigh = nneigh # Prepare angle calculations, if applicable. rij = [] rjk = [] rijnorm = [] rjknorm = [] dist = [] distjk_unique = [] distjk = [] centvec = centsite.coords if self._computerijs: for j, neigh in enumerate(neighsites): rij.append((neigh.coords - centvec)) dist.append(np.linalg.norm(rij[j])) rijnorm.append((rij[j] / dist[j])) if self._computerjks: for j, neigh in enumerate(neighsites): rjk.append([]) rjknorm.append([]) distjk.append([]) kk = 0 for k in range(len(neighsites)): if j != k: rjk[j].append(neighsites[k].coords - neigh.coords) distjk[j].append(np.linalg.norm(rjk[j][kk])) if k > j: distjk_unique.append(distjk[j][kk]) rjknorm[j].append(rjk[j][kk] / distjk[j][kk]) kk = kk + 1 # Initialize OP list and, then, calculate OPs. ops = [0.0 for t in self._types] # norms = [[[] for j in range(nneigh)] for t in self._types] # First, coordination number and distance-based OPs. for i, t in enumerate(self._types): if t == "cn": ops[i] = nneigh / self._params[i]['norm'] elif t == "sgl_bd": dist_sorted = sorted(dist) if len(dist_sorted) == 1: ops[i] = 1.0 elif len(dist_sorted) > 1: ops[i] = 1.0 - dist_sorted[0] / dist_sorted[1] # Then, bond orientational OPs based on spherical harmonics # according to Steinhardt et al., Phys. Rev. B, 28, 784-805, 1983. if self._boops: thetas = [] phis = [] for j, vec in enumerate(rijnorm): # z is North pole --> theta between vec and (0, 0, 1)^T. # Because vec is normalized, dot product is simply vec[2]. thetas.append(acos(max(-1.0, min(vec[2], 1.0)))) tmpphi = 0.0 # Compute phi only if it is not (almost) perfectly # aligned with z-axis. if -left_of_unity < vec[2] < left_of_unity: # x is prime meridian --> phi between projection of vec # into x-y plane and (1, 0, 0)^T tmpphi = acos(max(-1.0, min(vec[0] / (sqrt( vec[0] * vec[0] + vec[1] * vec[1])), 1.0))) if vec[1] < 0.0: tmpphi = -tmpphi phis.append(tmpphi) # Note that None flags that we have too few neighbors # for calculating BOOPS. for i, t in enumerate(self._types): if t == "q2": ops[i] = self.get_q2(thetas, phis) if len( thetas) > 0 else None elif t == "q4": ops[i] = self.get_q4(thetas, phis) if len( thetas) > 0 else None elif t == "q6": ops[i] = self.get_q6(thetas, phis) if len( thetas) > 0 else None # Then, deal with the Peters-style OPs that are tailor-made # to recognize common structural motifs # (Peters, J. Chem. Phys., 131, 244103, 2009; # Zimmermann et al., J. Am. Chem. Soc., under revision, 2015). if self._geomops: gaussthetak = [0.0 for t in self._types] # not used by all OPs qsptheta = [[[] for j in range(nneigh)] for t in self._types] norms = [[[] for j in range(nneigh)] for t in self._types] ipi = 1.0 / pi piover2 = pi / 2.0 onethird = 1.0 / 3.0 twothird = 2.0 / 3.0 for j in range(nneigh): # Neighbor j is put to the North pole. zaxis = rijnorm[j] kc = 0 for k in range(nneigh): # From neighbor k, we construct if j != k: # the prime meridian. for i in range(len(self._types)): qsptheta[i][j].append(0.0) norms[i][j].append(0) tmp = max( -1.0, min(np.inner(zaxis, rijnorm[k]), 1.0)) thetak = acos(tmp) xaxis = gramschmidt(rijnorm[k], zaxis) if np.linalg.norm(xaxis) < very_small: flag_xaxis = True else: xaxis = xaxis / np.linalg.norm(xaxis) flag_xaxis = False if self._comp_azi: flag_yaxis = True yaxis = np.cross(zaxis, xaxis) if np.linalg.norm(yaxis) > very_small: yaxis = yaxis / np.linalg.norm(yaxis) flag_yaxis = False # Contributions of j-i-k angles, where i represents the # central atom and j and k two of the neighbors. for i, t in enumerate(self._types): if t in ["bent", "sq_pyr_legacy"]: tmp = self._params[i]['IGW_TA'] * ( thetak * ipi - self._params[i]['TA']) qsptheta[i][j][kc] += exp(-0.5 * tmp * tmp) norms[i][j][kc] += 1 elif t in ["tri_plan", "tri_plan_max", "tet", "tet_max"]: tmp = self._params[i]['IGW_TA'] * ( thetak * ipi - self._params[i]['TA']) gaussthetak[i] = exp(-0.5 * tmp * tmp) if t in ["tri_plan_max", "tet_max"]: qsptheta[i][j][kc] += gaussthetak[i] norms[i][j][kc] += 1 elif t in ["T", "tri_pyr", "sq_pyr", "pent_pyr", "hex_pyr"]: tmp = self._params[i]['IGW_EP'] * ( thetak * ipi - 0.5) qsptheta[i][j][kc] += exp(-0.5 * tmp * tmp) norms[i][j][kc] += 1 elif t in ["sq_plan", "oct", "oct_legacy", "cuboct", "cuboct_max"]: if thetak >= self._params[i]['min_SPP']: tmp = self._params[i]['IGW_SPP'] * ( thetak * ipi - 1.0) qsptheta[i][j][kc] += ( self._params[i]['w_SPP'] * exp(-0.5 * tmp * tmp)) norms[i][j][kc] += self._params[i]['w_SPP'] elif t in ["see_saw_rect", "tri_bipyr", "sq_bipyr", "pent_bipyr", "hex_bipyr", "oct_max", "sq_plan_max", "hex_plan_max"]: if thetak < self._params[i]['min_SPP']: tmp = self._params[i]['IGW_EP'] * ( thetak * ipi - 0.5) if t != "hex_plan_max" else \ self._params[i]['IGW_TA'] * ( fabs(thetak * ipi - 0.5) - self._params[i]['TA']) qsptheta[i][j][kc] += exp( -0.5 * tmp * tmp) norms[i][j][kc] += 1 elif t in ["pent_plan", "pent_plan_max"]: tmp = 0.4 if thetak <= self._params[i][ 'TA'] * pi \ else 0.8 tmp2 = self._params[i]['IGW_TA'] * ( thetak * ipi - tmp) gaussthetak[i] = exp(-0.5 * tmp2 * tmp2) if t == "pent_plan_max": qsptheta[i][j][kc] += gaussthetak[i] norms[i][j][kc] += 1 elif t == "bcc" and j < k: if thetak >= self._params[i]['min_SPP']: tmp = self._params[i]['IGW_SPP'] * ( thetak * ipi - 1.0) qsptheta[i][j][kc] += ( self._params[i]['w_SPP'] * exp(-0.5 * tmp * tmp)) norms[i][j][kc] += self._params[i]['w_SPP'] elif t == "sq_face_cap_trig_pris": if thetak < self._params[i]['TA3']: tmp = self._params[i]['IGW_TA1'] * (thetak * ipi - self._params[i]['TA1']) qsptheta[i][j][kc] += exp(-0.5 * tmp * tmp) norms[i][j][kc] += 1 for m in range(nneigh): if (m != j) and (m != k) and (not flag_xaxis): tmp = max(-1.0, min(np.inner(zaxis, rijnorm[m]), 1.0)) thetam = acos(tmp) xtwoaxistmp = gramschmidt(rijnorm[m], zaxis) l = np.linalg.norm(xtwoaxistmp) if l < very_small: flag_xtwoaxis = True else: xtwoaxis = xtwoaxistmp / l phi = acos(max(-1.0, min(np.inner(xtwoaxis, xaxis), 1.0))) flag_xtwoaxis = False if self._comp_azi: phi2 = atan2(np.dot(xtwoaxis, yaxis), np.dot(xtwoaxis, xaxis)) # South pole contributions of m. if t in ["tri_bipyr", "sq_bipyr", "pent_bipyr", "hex_bipyr", "oct_max", "sq_plan_max", "hex_plan_max", "see_saw_rect"]: if thetam >= self._params[i]['min_SPP']: tmp = self._params[i]['IGW_SPP'] * ( thetam * ipi - 1.0) qsptheta[i][j][kc] += exp( -0.5 * tmp * tmp) norms[i][j][kc] += 1 # Contributions of j-i-m angle and # angles between plane j-i-k and i-m vector. if not flag_xaxis and not flag_xtwoaxis: for i, t in enumerate(self._types): if t in ["tri_plan", "tri_plan_max", "tet", "tet_max"]: tmp = self._params[i]['IGW_TA'] * (thetam * ipi - self._params[i]['TA']) tmp2 = cos(self._params[i]['fac_AA'] * phi) ** self._params[i]['exp_cos_AA'] tmp3 = 1 if t in ["tri_plan_max", "tet_max"] else gaussthetak[i] qsptheta[i][j][kc] += tmp3 * exp(-0.5 * tmp * tmp) * tmp2 norms[i][j][kc] += 1 elif t in ["pent_plan", "pent_plan_max"]: tmp = 0.4 if thetam <= self._params[i]['TA'] * pi else 0.8 tmp2 = self._params[i]['IGW_TA'] * (thetam * ipi - tmp) tmp3 = cos(phi) tmp4 = 1 if t == "pent_plan_max" else gaussthetak[i] qsptheta[i][j][kc] += tmp4 * exp(-0.5 * tmp2 * tmp2) * tmp3 * tmp3 norms[i][j][kc] += 1 elif t in ["T", "tri_pyr", "sq_pyr", "pent_pyr", "hex_pyr"]: tmp = cos(self._params[i]['fac_AA'] * phi) ** self._params[i]['exp_cos_AA'] tmp3 = self._params[i]['IGW_EP'] * (thetam * ipi - 0.5) qsptheta[i][j][kc] += tmp * exp( -0.5 * tmp3 * tmp3) norms[i][j][kc] += 1 elif t in ["sq_plan", "oct", "oct_legacy"]: if thetak < self._params[i]['min_SPP'] and \ thetam < self._params[i]['min_SPP']: tmp = cos(self._params[i]['fac_AA'] * phi) ** self._params[i][ 'exp_cos_AA'] tmp2 = self._params[i]['IGW_EP'] * (thetam * ipi - 0.5) qsptheta[i][j][kc] += tmp * exp(-0.5 * tmp2 * tmp2) if t == "oct_legacy": qsptheta[i][j][kc] -= tmp * self._params[i][6] * self._params[i][7] norms[i][j][kc] += 1 elif t in ["tri_bipyr", "sq_bipyr", "pent_bipyr", "hex_bipyr", "oct_max", "sq_plan_max", "hex_plan_max"]: if thetam < self._params[i]['min_SPP']: if thetak < self._params[i]['min_SPP']: tmp = cos(self._params[i][ 'fac_AA'] * phi) ** \ self._params[i][ 'exp_cos_AA'] tmp2 = self._params[i][ 'IGW_EP'] * ( thetam * ipi - 0.5) if t != "hex_plan_max" else \ self._params[i][ 'IGW_TA'] * ( fabs( thetam * ipi - 0.5) - self._params[i][ 'TA']) qsptheta[i][j][ kc] += tmp * exp( -0.5 * tmp2 * tmp2) norms[i][j][kc] += 1 elif t == "bcc" and j < k: if thetak < self._params[i]['min_SPP']: if thetak > piover2: fac = 1.0 else: fac = -1.0 tmp = (thetam - piover2) / asin( 1 / 3) qsptheta[i][j][kc] += fac * cos(3.0 * phi) * fac_bcc * \ tmp * exp(-0.5 * tmp * tmp) norms[i][j][kc] += 1 elif t == "see_saw_rect": if thetam < self._params[i]['min_SPP']: if thetak < self._params[i]['min_SPP'] and phi < 0.75 * pi: tmp = cos(self._params[i][ 'fac_AA'] * phi) ** \ self._params[i][ 'exp_cos_AA'] tmp2 = self._params[i][ 'IGW_EP'] * ( thetam * ipi - 0.5) qsptheta[i][j][kc] += tmp * exp(-0.5 * tmp2 * tmp2) norms[i][j][kc] += 1.0 elif t in ["cuboct", "cuboct_max"]: if thetam < self._params[i]['min_SPP'] and \ thetak > self._params[i][4] and \ thetak < self._params[i][2]: if thetam > self._params[i][4] and thetam < self._params[i][2]: tmp = cos(phi) tmp2 = self._params[i][ 5] * ( thetam * ipi - 0.5) qsptheta[i][j][ kc] += tmp * tmp * exp( -0.5 * tmp2 * tmp2) norms[i][j][kc] += 1.0 elif thetam < self._params[i][4]: tmp = 0.0556 * (cos(phi - 0.5 * pi) - 0.81649658) tmp2 = self._params[i][6] * (thetam * ipi - onethird) qsptheta[i][j][kc] += exp( -0.5 * tmp * tmp) * exp(-0.5 * tmp2 * tmp2) norms[i][j][kc] += 1.0 elif thetam > self._params[i][2]: tmp = 0.0556 * (cos(phi - 0.5 * pi) - 0.81649658) tmp2 = self._params[i][6] * ( thetam * ipi - twothird) qsptheta[i][j][kc] += exp( -0.5 * tmp * tmp) * exp(-0.5 * tmp2 * tmp2) norms[i][j][kc] += 1.0 elif t == "sq_face_cap_trig_pris" and not flag_yaxis: if thetak < self._params[i]['TA3']: if thetam < self._params[i]['TA3']: tmp = cos(self._params[i]['fac_AA1'] * phi2) ** \ self._params[i]['exp_cos_AA1'] tmp2 = self._params[i]['IGW_TA1'] * (thetam * ipi - self._params[i]['TA1']) else: tmp = cos(self._params[i]['fac_AA2'] * (phi2 + self._params[i]['shift_AA2'])) ** \ self._params[i]['exp_cos_AA2'] tmp2 = self._params[i][ 'IGW_TA2'] * ( thetam * ipi - self._params[ i][ 'TA2']) qsptheta[i][j][kc] += tmp * exp( -0.5 * tmp2 * tmp2) norms[i][j][kc] += 1 kc += 1 # Normalize Peters-style OPs. for i, t in enumerate(self._types): if t in ["tri_plan", "tet", "bent", "sq_plan", "oct", "oct_legacy", "cuboct", "pent_plan"]: ops[i] = tmp_norm = 0.0 for j in range(nneigh): ops[i] += sum(qsptheta[i][j]) tmp_norm += float(sum(norms[i][j])) ops[i] = ops[i] / tmp_norm if tmp_norm > 1.0e-12 else None elif t in ["T", "tri_pyr", "see_saw_rect", "sq_pyr", "tri_bipyr", "sq_bipyr", "pent_pyr", "hex_pyr", "pent_bipyr", "hex_bipyr", "oct_max", "tri_plan_max", "tet_max", "sq_plan_max", "pent_plan_max", "cuboct_max", "hex_plan_max", "sq_face_cap_trig_pris"]: ops[i] = None if nneigh > 1: for j in range(nneigh): for k in range(len(qsptheta[i][j])): qsptheta[i][j][k] = qsptheta[i][j][k] / norms[i][j][k] \ if norms[i][j][k] > 1.0e-12 else 0.0 ops[i] = max(qsptheta[i][j]) if j == 0 \ else max(ops[i], max(qsptheta[i][j])) elif t == "bcc": ops[i] = 0.0 for j in range(nneigh): ops[i] += sum(qsptheta[i][j]) ops[i] = ops[i] / float(0.5 * float( nneigh * (6 + (nneigh - 2) * (nneigh - 3)))) \ if nneigh > 3 else None elif t == "sq_pyr_legacy": if nneigh > 1: dmean = np.mean(dist) acc = 0.0 for d in dist: tmp = self._params[i][2] * (d - dmean) acc = acc + exp(-0.5 * tmp * tmp) for j in range(nneigh): ops[i] = max(qsptheta[i][j]) if j == 0 \ else max(ops[i], max(qsptheta[i][j])) ops[i] = acc * ops[i] / float(nneigh) # nneigh * (nneigh - 1)) else: ops[i] = None # Then, deal with the new-style OPs that require vectors between # neighbors. if self._geomops2: # Compute all (unique) angles and sort the resulting list. aij = [] for ir, r in enumerate(rijnorm): for j in range(ir + 1, len(rijnorm)): aij.append( acos(max(-1.0, min(np.inner(r, rijnorm[j]), 1.0)))) aijs = sorted(aij) # Compute height, side and diagonal length estimates. neighscent = np.array([0.0, 0.0, 0.0]) for j, neigh in enumerate(neighsites): neighscent = neighscent + neigh.coords if nneigh > 0: neighscent = (neighscent / float(nneigh)) h = np.linalg.norm(neighscent - centvec) b = min(distjk_unique) if len(distjk_unique) > 0 else 0 dhalf = max(distjk_unique) / 2.0 if len(distjk_unique) > 0 else 0 for i, t in enumerate(self._types): if t == "reg_tri" or t == "sq": if nneigh < 3: ops[i] = None else: ops[i] = 1.0 if t == "reg_tri": a = 2.0 * asin(b / (2.0 * sqrt(h * h + (b / ( 2.0 * cos(3.0 * pi / 18.0))) ** 2.0))) nmax = 3 elif t == "sq": a = 2.0 * asin( b / (2.0 * sqrt(h * h + dhalf * dhalf))) nmax = 4 for j in range(min([nneigh, nmax])): ops[i] = ops[i] * exp(-0.5 * (( aijs[j] - a) * self._params[i][ 0]) ** 2) return ops
[docs]class BrunnerNN_reciprocal(NearNeighbors): """ Determine coordination number using Brunner's algorithm which counts the atoms that are within the largest gap in differences in real space interatomic distances. This algorithm uses Brunner's method of largest reciprocal gap in interatomic distances. """ def __init__(self, tol=1.0e-4, cutoff=8.0): """ Args: tol (float): tolerance parameter for bond determination (default: 1E-4). cutoff (float): cutoff radius in Angstrom to look for near-neighbor atoms. Defaults to 8.0. """ self.tol = tol self.cutoff = cutoff @property def structures_allowed(self): """ Boolean property: can this NearNeighbors class be used with Structure objects? """ return True @property def molecules_allowed(self): """ Boolean property: can this NearNeighbors class be used with Molecule objects? """ return False
[docs] def get_nn_info(self, structure, n): """ Get all near-neighbor sites as well as the associated image locations and weights of the site with index n in structure. Args: structure (Structure): input structure. n (integer): index of site for which to determine near-neighbor sites. Returns: siw (list of tuples (Site, array, float)): tuples, each one of which represents a coordinated site, its image location, and its weight. """ site = structure[n] neighs_dists = structure.get_neighbors(site, self.cutoff) ds = [i.nn_distance for i in neighs_dists] ds.sort() ns = [1.0 / ds[i] - 1.0 / ds[i + 1] for i in range(len(ds) - 1)] d_max = ds[ns.index(max(ns))] siw = [] for nn in neighs_dists: s, dist = nn, nn.nn_distance if dist < d_max + self.tol: w = ds[0] / dist siw.append({'site': s, 'image': self._get_image(structure, s), 'weight': w, 'site_index': self._get_original_site(structure, s)}) return siw
[docs]class BrunnerNN_relative(NearNeighbors): """ Determine coordination number using Brunner's algorithm which counts the atoms that are within the largest gap in differences in real space interatomic distances. This algorithm uses Brunner's method of of largest relative gap in interatomic distances. """ def __init__(self, tol=1.0e-4, cutoff=8.0): """ Args: tol (float): tolerance parameter for bond determination (default: 1E-4). cutoff (float): cutoff radius in Angstrom to look for near-neighbor atoms. Defaults to 8.0. """ self.tol = tol self.cutoff = cutoff @property def structures_allowed(self): """ Boolean property: can this NearNeighbors class be used with Structure objects? """ return True @property def molecules_allowed(self): """ Boolean property: can this NearNeighbors class be used with Molecule objects? """ return False
[docs] def get_nn_info(self, structure, n): """ Get all near-neighbor sites as well as the associated image locations and weights of the site with index n in structure. Args: structure (Structure): input structure. n (integer): index of site for which to determine near-neighbor sites. Returns: siw (list of tuples (Site, array, float)): tuples, each one of which represents a coordinated site, its image location, and its weight. """ site = structure[n] neighs_dists = structure.get_neighbors(site, self.cutoff) ds = [i.nn_distance for i in neighs_dists] ds.sort() ns = [ds[i + 1] / ds[i] for i in range(len(ds) - 1)] d_max = ds[ns.index(max(ns))] siw = [] for nn in neighs_dists: s, dist = nn, nn.nn_distance if dist < d_max + self.tol: w = ds[0] / dist siw.append({'site': s, 'image': self._get_image(structure, s), 'weight': w, 'site_index': self._get_original_site(structure, s)}) return siw
[docs]class BrunnerNN_real(NearNeighbors): """ Determine coordination number using Brunner's algorithm which counts the atoms that are within the largest gap in differences in real space interatomic distances. This algorithm uses Brunner's method of largest gap in interatomic distances. """ def __init__(self, tol=1.0e-4, cutoff=8.0): """ Args: tol (float): tolerance parameter for bond determination (default: 1E-4). cutoff (float): cutoff radius in Angstrom to look for near-neighbor atoms. Defaults to 8.0. """ self.tol = tol self.cutoff = cutoff @property def structures_allowed(self): """ Boolean property: can this NearNeighbors class be used with Structure objects? """ return True @property def molecules_allowed(self): """ Boolean property: can this NearNeighbors class be used with Molecule objects? """ return False
[docs] def get_nn_info(self, structure, n): """ Get all near-neighbor sites as well as the associated image locations and weights of the site with index n in structure. Args: structure (Structure): input structure. n (integer): index of site for which to determine near-neighbor sites. Returns: siw (list of tuples (Site, array, float)): tuples, each one of which represents a coordinated site, its image location, and its weight. """ site = structure[n] neighs_dists = structure.get_neighbors(site, self.cutoff) ds = [i.nn_distance for i in neighs_dists] ds.sort() ns = [ds[i + 1] - ds[i] for i in range(len(ds) - 1)] d_max = ds[ns.index(max(ns))] siw = [] for nn in neighs_dists: s, dist = nn, nn.nn_distance if dist < d_max + self.tol: w = ds[0] / dist siw.append({'site': s, 'image': self._get_image(structure, s), 'weight': w, 'site_index': self._get_original_site(structure, s)}) return siw
[docs]class EconNN(NearNeighbors): """ Determines the average effective coordination number for each cation in a given structure using Hoppe's algorithm. This method follows the procedure outlined in: Hoppe, Rudolf. "Effective coordination numbers (ECoN) and mean fictive ionic radii (MEFIR)." Zeitschrift für Kristallographie-Crystalline Materials 150.1-4 (1979): 23-52. """ def __init__( self, tol: float = 0.2, cutoff: float = 10.0, cation_anion: bool = False, use_fictive_radius: bool = False ): """ Args: tol: Tolerance parameter for bond determination. cutoff: Cutoff radius in Angstrom to look for near-neighbor atoms. cation_anion: If set to True, will restrict bonding targets to sites with opposite or zero charge. Requires an oxidation states on all sites in the structure. use_fictive_radius: Whether to use the fictive radius in the EcoN calculation. If False, the bond distance will be used. """ self.tol = tol self.cutoff = cutoff self.cation_anion = cation_anion self.use_fictive_radius = use_fictive_radius @property def structures_allowed(self): """ Boolean property: can this NearNeighbors class be used with Structure objects? """ return True @property def molecules_allowed(self): """ Boolean property: can this NearNeighbors class be used with Molecule objects? """ return True @property def extend_structure_molecules(self): """ Boolean property: Do Molecules need to be converted to Structures to use this NearNeighbors class? Note: this property is not defined for classes for which molecules_allowed == False. """ return True
[docs] def get_nn_info(self, structure, n): """ Get all near-neighbor sites as well as the associated image locations and weights of the site with index n in structure. Args: structure (Structure): input structure. n (integer): index of site for which to determine near-neighbor sites. Returns: siw (list of tuples (Site, array, float)): tuples, each one of which represents a coordinated site, its image location, and its weight. """ site = structure[n] neighbors = structure.get_neighbors(site, self.cutoff) if self.cation_anion and hasattr(site.specie, "oxi_state"): # filter out neighbor of like charge (except for neutral sites) if site.specie.oxi_state >= 0: neighbors = [n for n in neighbors if n.oxi_state <= 0] elif site.specie.oxi_state <= 0: neighbors = [n for n in neighbors if n.oxi_state >= 0] if self.use_fictive_radius: # calculate fictive ionic radii firs = [_get_fictive_ionic_radius(site, neighbor) for neighbor in neighbors] else: # just use the bond distance firs = [neighbor.nn_distance for neighbor in neighbors] # calculate mean fictive ionic radius mefir = _get_mean_fictive_ionic_radius(firs) # # iteratively solve MEFIR; follows equation 4 in Hoppe's EconN paper prev_mefir = float("inf") while abs(prev_mefir - mefir) > 1e-4: # this is guaranteed to converge prev_mefir = mefir mefir = _get_mean_fictive_ionic_radius(firs, minimum_fir=mefir) siw = [] for nn, fir in zip(neighbors, firs): if nn.nn_distance < self.cutoff: w = exp(1 - (fir / mefir) ** 6) if w > self.tol: bonded_site = { 'site': nn, 'image': self._get_image(structure, nn), 'weight': w, 'site_index': self._get_original_site(structure, nn) } siw.append(bonded_site) return siw
def _get_fictive_ionic_radius(site: Site, neighbor: PeriodicNeighbor) -> float: """ Get fictive ionic radius. Follows equation 1 of: Hoppe, Rudolf. "Effective coordination numbers (ECoN) and mean fictive ionic radii (MEFIR)." Zeitschrift für Kristallographie-Crystalline Materials 150.1-4 (1979): 23-52. Args: site: The central site. neighbor neighboring site. Returns: Hoppe's fictive ionic radius. """ r_h = _get_radius(site) if r_h == 0: r_h = _get_default_radius(site) r_i = _get_radius(neighbor) if r_i == 0: r_i = _get_default_radius(neighbor) return neighbor.nn_distance * (r_h / (r_h + r_i)) def _get_mean_fictive_ionic_radius( fictive_ionic_radii: List[float], minimum_fir: Optional[float] = None, ) -> float: """ Returns the mean fictive ionic radius. Follows equation 2: Hoppe, Rudolf. "Effective coordination numbers (ECoN) and mean fictive ionic radii (MEFIR)." Zeitschrift für Kristallographie-Crystalline Materials 150.1-4 (1979): 23-52. Args: fictive_ionic_radii: List of fictive ionic radii for a center site and its neighbors. minimum_fir: Minimum fictive ionic radius to use. Returns: Hoppe's mean fictive ionic radius. """ if not minimum_fir: minimum_fir = min(fictive_ionic_radii) weighted_sum = 0.0 total_sum = 0.0 for fir in fictive_ionic_radii: weighted_sum += fir * exp(1 - (fir / minimum_fir) ** 6) total_sum += exp(1 - (fir / minimum_fir) ** 6) return weighted_sum / total_sum
[docs]class CrystalNN(NearNeighbors): """ This is custom near neighbor method intended for use in all kinds of periodic structures (metals, minerals, porous structures, etc). It is based on a Voronoi algorithm and uses the solid angle weights to determine the probability of various coordination environments. The algorithm can also modify probability using smooth distance cutoffs as well as Pauling electronegativity differences. The output can either be the most probable coordination environment or a weighted list of coordination environments. """ NNData = namedtuple("nn_data", ["all_nninfo", "cn_weights", "cn_nninfo"]) def __init__(self, weighted_cn=False, cation_anion=False, distance_cutoffs=(0.5, 1), x_diff_weight=3.0, porous_adjustment=True, search_cutoff=7, fingerprint_length=None): """ Initialize CrystalNN with desired parameters. Default parameters assume "chemical bond" type behavior is desired. For geometric neighbor finding (e.g., structural framework), set (i) distance_cutoffs=None, (ii) x_diff_weight=0.0 and (optionally) (iii) porous_adjustment=False which will disregard the atomic identities and perform best for a purely geometric match. Args: weighted_cn: (bool) if set to True, will return fractional weights for each potential near neighbor. cation_anion: (bool) if set True, will restrict bonding targets to sites with opposite or zero charge. Requires an oxidation states on all sites in the structure. distance_cutoffs: ([float, float]) - if not None, penalizes neighbor distances greater than sum of covalent radii plus distance_cutoffs[0]. Distances greater than covalent radii sum plus distance_cutoffs[1] are enforced to have zero weight. x_diff_weight: (float) - if multiple types of neighbor elements are possible, this sets preferences for targets with higher electronegativity difference. porous_adjustment: (bool) - if True, readjusts Voronoi weights to better describe layered / porous structures search_cutoff: (float) cutoff in Angstroms for initial neighbor search; this will be adjusted if needed internally fingerprint_length: (int) if a fixed_length CN "fingerprint" is desired from get_nn_data(), set this parameter """ self.weighted_cn = weighted_cn self.cation_anion = cation_anion self.distance_cutoffs = distance_cutoffs self.x_diff_weight = x_diff_weight if x_diff_weight is not None else 0 self.search_cutoff = search_cutoff self.porous_adjustment = porous_adjustment self.fingerprint_length = fingerprint_length @property def structures_allowed(self): """ Boolean property: can this NearNeighbors class be used with Structure objects? """ return True @property def molecules_allowed(self): """ Boolean property: can this NearNeighbors class be used with Molecule objects? """ return False
[docs] def get_nn_info(self, structure, n): """ Get all near-neighbor information. Args: structure: (Structure) pymatgen Structure n: (int) index of target site Returns: siw (list of dicts): each dictionary provides information about a single near neighbor, where key 'site' gives access to the corresponding Site object, 'image' gives the image location, and 'weight' provides the weight that a given near-neighbor site contributes to the coordination number (1 or smaller), 'site_index' gives index of the corresponding site in the original structure. """ nndata = self.get_nn_data(structure, n) if not self.weighted_cn: max_key = max(nndata.cn_weights, key=lambda k: nndata.cn_weights[k]) nn = nndata.cn_nninfo[max_key] for entry in nn: entry["weight"] = 1 return nn else: for entry in nndata.all_nninfo: weight = 0 for cn in nndata.cn_nninfo: for cn_entry in nndata.cn_nninfo[cn]: if entry["site"] == cn_entry["site"]: weight += nndata.cn_weights[cn] entry["weight"] = weight return nndata.all_nninfo
[docs] def get_nn_data(self, structure, n, length=None): """ The main logic of the method to compute near neighbor. Args: structure: (Structure) enclosing structure object n: (int) index of target site to get NN info for length: (int) if set, will return a fixed range of CN numbers Returns: a namedtuple (NNData) object that contains: - all near neighbor sites with weights - a dict of CN -> weight - a dict of CN -> associated near neighbor sites """ length = length or self.fingerprint_length # determine possible bond targets target = None if self.cation_anion: target = [] m_oxi = structure[n].specie.oxi_state for site in structure: if site.specie.oxi_state * m_oxi <= 0: # opposite charge target.append(site.specie) if not target: raise ValueError( "No valid targets for site within cation_anion constraint!") # get base VoronoiNN targets cutoff = self.search_cutoff vnn = VoronoiNN(weight="solid_angle", targets=target, cutoff=cutoff) nn = vnn.get_nn_info(structure, n) # solid angle weights can be misleading in open / porous structures # adjust weights to correct for this behavior if self.porous_adjustment: for x in nn: x["weight"] *= x["poly_info"][ "solid_angle"] / x["poly_info"]["area"] # adjust solid angle weight based on electronegativity difference if self.x_diff_weight > 0: for entry in nn: X1 = structure[n].specie.X X2 = entry["site"].specie.X if math.isnan(X1) or math.isnan(X2): chemical_weight = 1 else: # note: 3.3 is max deltaX between 2 elements chemical_weight = 1 + self.x_diff_weight * \ math.sqrt(abs(X1 - X2) / 3.3) entry["weight"] = entry["weight"] * chemical_weight # sort nearest neighbors from highest to lowest weight nn = sorted(nn, key=lambda x: x["weight"], reverse=True) if nn[0]["weight"] == 0: return self.transform_to_length(self.NNData([], {0: 1.0}, {0: []}), length) # renormalize weights so the highest weight is 1.0 highest_weight = nn[0]["weight"] for entry in nn: entry["weight"] = entry["weight"] / highest_weight # adjust solid angle weights based on distance if self.distance_cutoffs: r1 = _get_radius(structure[n]) for entry in nn: r2 = _get_radius(entry["site"]) if r1 > 0 and r2 > 0: d = r1 + r2 else: warnings.warn( "CrystalNN: cannot locate an appropriate radius, " "covalent or atomic radii will be used, this can lead " "to non-optimal results.") d = _get_default_radius(structure[n]) + \ _get_default_radius(entry["site"]) dist = np.linalg.norm( structure[n].coords - entry["site"].coords) dist_weight = 0 cutoff_low = d + self.distance_cutoffs[0] cutoff_high = d + self.distance_cutoffs[1] if dist <= cutoff_low: dist_weight = 1 elif dist < cutoff_high: dist_weight = (math.cos((dist - cutoff_low) / ( cutoff_high - cutoff_low) * math.pi) + 1) * 0.5 entry["weight"] = entry["weight"] * dist_weight # sort nearest neighbors from highest to lowest weight nn = sorted(nn, key=lambda x: x["weight"], reverse=True) if nn[0]["weight"] == 0: return self.transform_to_length(self.NNData([], {0: 1.0}, {0: []}), length) for entry in nn: entry["weight"] = round(entry["weight"], 3) del entry["poly_info"] # trim # remove entries with no weight nn = [x for x in nn if x["weight"] > 0] # get the transition distances, i.e. all distinct weights dist_bins = [] for entry in nn: if not dist_bins or dist_bins[-1] != entry["weight"]: dist_bins.append(entry["weight"]) dist_bins.append(0) # main algorithm to determine fingerprint from bond weights cn_weights = {} # CN -> score for that CN cn_nninfo = {} # CN -> list of nearneighbor info for that CN for idx, val in enumerate(dist_bins): if val != 0: nn_info = [] for entry in nn: if entry["weight"] >= val: nn_info.append(entry) cn = len(nn_info) cn_nninfo[cn] = nn_info cn_weights[cn] = self._semicircle_integral(dist_bins, idx) # add zero coord cn0_weight = 1.0 - sum(cn_weights.values()) if cn0_weight > 0: cn_nninfo[0] = [] cn_weights[0] = cn0_weight return self.transform_to_length(self.NNData(nn, cn_weights, cn_nninfo), length)
[docs] def get_cn(self, structure, n, use_weights=False): """ Get coordination number, CN, of site with index n in structure. Args: structure (Structure): input structure. n (integer): index of site for which to determine CN. use_weights (boolean): flag indicating whether (True) to use weights for computing the coordination number or not (False, default: each coordinated site has equal weight). Returns: cn (integer or float): coordination number. """ if self.weighted_cn != use_weights: raise ValueError("The weighted_cn parameter and use_weights " "parameter should match!") return super().get_cn(structure, n, use_weights)
[docs] def get_cn_dict(self, structure, n, use_weights=False): """ Get coordination number, CN, of each element bonded to site with index n in structure Args: structure (Structure): input structure n (integer): index of site for which to determine CN. use_weights (boolean): flag indicating whether (True) to use weights for computing the coordination number or not (False, default: each coordinated site has equal weight). Returns: cn (dict): dictionary of CN of each element bonded to site """ if self.weighted_cn != use_weights: raise ValueError("The weighted_cn parameter and use_weights " "parameter should match!") return super().get_cn_dict(structure, n, use_weights)
@staticmethod def _semicircle_integral(dist_bins, idx): """ An internal method to get an integral between two bounds of a unit semicircle. Used in algorithm to determine bond probabilities. Args: dist_bins: (float) list of all possible bond weights idx: (float) index of starting bond weight Returns: (float) integral of portion of unit semicircle """ r = 1 x1 = dist_bins[idx] x2 = dist_bins[idx + 1] if dist_bins[idx] == 1: area1 = 0.25 * math.pi * r ** 2 else: area1 = 0.5 * ((x1 * math.sqrt(r ** 2 - x1 ** 2)) + ( r ** 2 * math.atan(x1 / math.sqrt(r ** 2 - x1 ** 2)))) area2 = 0.5 * ((x2 * math.sqrt(r ** 2 - x2 ** 2)) + ( r ** 2 * math.atan(x2 / math.sqrt(r ** 2 - x2 ** 2)))) return (area1 - area2) / (0.25 * math.pi * r ** 2)
[docs] @staticmethod def transform_to_length(nndata, length): """ Given NNData, transforms data to the specified fingerprint length Args: nndata: (NNData) length: (int) desired length of NNData """ if length is None: return nndata if length: for cn in range(length): if cn not in nndata.cn_weights: nndata.cn_weights[cn] = 0 nndata.cn_nninfo[cn] = [] return nndata
def _get_default_radius(site): """ An internal method to get a "default" covalent/element radius Args: site: (Site) Returns: Covalent radius of element on site, or Atomic radius if unavailable """ try: return CovalentRadius.radius[site.specie.symbol] except Exception: return site.specie.atomic_radius def _get_radius(site): """ An internal method to get the expected radius for a site with oxidation state. Args: site: (Site) Returns: Oxidation-state dependent radius: ionic, covalent, or atomic. Returns 0 if no oxidation state or appropriate radius is found. """ if hasattr(site.specie, 'oxi_state'): el = site.specie.element oxi = site.specie.oxi_state if oxi == 0: return _get_default_radius(site) elif oxi in el.ionic_radii: return el.ionic_radii[oxi] # e.g., oxi = 2.667, average together 2+ and 3+ radii elif int(math.floor(oxi)) in el.ionic_radii and \ int(math.ceil(oxi)) in el.ionic_radii: oxi_low = el.ionic_radii[int(math.floor(oxi))] oxi_high = el.ionic_radii[int(math.ceil(oxi))] x = oxi - int(math.floor(oxi)) return (1 - x) * oxi_low + x * oxi_high elif oxi > 0 and el.average_cationic_radius > 0: return el.average_cationic_radius elif el.average_anionic_radius > 0 > oxi: return el.average_anionic_radius else: warnings.warn( "No oxidation states specified on sites! For better results, set " "the site oxidation states in the structure." ) return 0
[docs]class CutOffDictNN(NearNeighbors): """ A very basic NN class using a dictionary of fixed cut-off distances. Can also be used with no dictionary defined for a Null/Empty NN class. """ def __init__(self, cut_off_dict=None): """ Args: cut_off_dict (Dict[str, float]): a dictionary of cut-off distances, e.g. {('Fe','O'): 2.0} for a maximum Fe-O bond length of 2.0 Angstroms. Note that if your structure is oxidation state decorated, the cut-off distances will have to explicitly include the oxidation state, e.g. {('Fe2+', 'O2-'): 2.0} """ self.cut_off_dict = cut_off_dict or {} # for convenience self._max_dist = 0.0 lookup_dict = defaultdict(dict) for (sp1, sp2), dist in self.cut_off_dict.items(): lookup_dict[sp1][sp2] = dist lookup_dict[sp2][sp1] = dist if dist > self._max_dist: self._max_dist = dist self._lookup_dict = lookup_dict @property def structures_allowed(self): """ Boolean property: can this NearNeighbors class be used with Structure objects? """ return True @property def molecules_allowed(self): """ Boolean property: can this NearNeighbors class be used with Molecule objects? """ return True @property def extend_structure_molecules(self): """ Boolean property: Do Molecules need to be converted to Structures to use this NearNeighbors class? Note: this property is not defined for classes for which molecules_allowed == False. """ return True
[docs] @staticmethod def from_preset(preset): """ Initialise a CutOffDictNN according to a preset set of cut-offs. Args: preset (str): A preset name. The list of supported presets are: - "vesta_2019": The distance cut-offs used by the VESTA visualisation program. Returns: A CutOffDictNN using the preset cut-off dictionary. """ if preset == 'vesta_2019': cut_offs = loadfn(os.path.join(_directory, 'vesta_cutoffs.yaml')) return CutOffDictNN(cut_off_dict=cut_offs) else: raise ValueError("Unrecognised preset: {}".format(preset))
[docs] def get_nn_info(self, structure, n): """ Get all near-neighbor sites as well as the associated image locations and weights of the site with index n in structure. Args: structure (Structure): input structure. n (integer): index of site for which to determine near-neighbor sites. Returns: siw (list of tuples (Site, array, float)): tuples, each one of which represents a coordinated site, its image location, and its weight. """ site = structure[n] neighs_dists = structure.get_neighbors(site, self._max_dist) nn_info = [] for nn in neighs_dists: n_site = nn dist = nn.nn_distance neigh_cut_off_dist = self._lookup_dict \ .get(site.species_string, {}) \ .get(n_site.species_string, 0.0) if dist < neigh_cut_off_dist: nn_info.append({ 'site': n_site, 'image': self._get_image(structure, n_site), 'weight': dist, 'site_index': self._get_original_site(structure, n_site) }) return nn_info
[docs]class Critic2NN(NearNeighbors): """ Performs a topological analysis using critic2 to obtain neighbor information, using a sum of atomic charge densities. If an actual charge density is available (e.g. from a VASP CHGCAR), see Critic2Caller directly instead. """ def __init__(self): """ Init for Critic2NN. """ # we cache the last-used structure, in case user # calls get_nn_info() repeatedly for different # sites in the same structure to save redundant # computations self.__last_structure = None self.__last_bonded_structure = None @property def structures_allowed(self): """ Boolean property: can this NearNeighbors class be used with Structure objects? """ return True @property def molecules_allowed(self): """ Boolean property: can this NearNeighbors class be used with Molecule objects? """ return True @property def extend_structure_molecules(self): """ Boolean property: Do Molecules need to be converted to Structures to use this NearNeighbors class? Note: this property is not defined for classes for which molecules_allowed == False. """ return True
[docs] def get_bonded_structure(self, structure, decorate=False): """ :param structure: Input structure :param decorate: Whether to decorate the structure :return: Bonded structure """ # not a top-level import because critic2 is an optional # dependency, only want to raise an import error if # Critic2NN() is used from pymatgen.command_line.critic2_caller import Critic2Caller if structure == self.__last_structure: sg = self.__last_bonded_structure else: c2_output = Critic2Caller(structure).output sg = c2_output.structure_graph() self.__last_structure = structure self.__last_bonded_structure = sg if decorate: order_parameters = [self.get_local_order_parameters(structure, n) for n in range(len(structure))] sg.structure.add_site_property('order_parameters', order_parameters) return sg
[docs] def get_nn_info(self, structure, n): """ Get all near-neighbor sites as well as the associated image locations and weights of the site with index n in structure. Args: structure (Structure): input structure. n (integer): index of site for which to determine near-neighbor sites. Returns: siw (list of tuples (Site, array, float)): tuples, each one of which represents a coordinated site, its image location, and its weight. """ sg = self.get_bonded_structure(structure) return [ { 'site': connected_site.site, 'image': connected_site.jimage, 'weight': connected_site.weight, 'site_index': connected_site.index } for connected_site in sg.get_connected_sites(n) ]