# coding: utf-8
# Copyright (c) Pymatgen Development Team.
# Distributed under the terms of the MIT License.
"""
This module provides classes to perform topological analyses of structures.
"""
__author__ = "Shyue Ping Ong, Geoffroy Hautier, Sai Jayaraman"
__copyright__ = "Copyright 2011, The Materials Project"
from math import pi, acos
import numpy as np
import itertools
import collections
from monty.dev import deprecated
from warnings import warn
from scipy.spatial import Voronoi
from pymatgen import PeriodicSite
from pymatgen import Element, Specie, Composition
from pymatgen.util.num import abs_cap
from pymatgen.symmetry.analyzer import SpacegroupAnalyzer
from pymatgen.core.surface import SlabGenerator
from pymatgen.analysis.local_env import VoronoiNN, JmolNN
[docs]def average_coordination_number(structures, freq=10):
"""
Calculates the ensemble averaged Voronoi coordination numbers
of a list of Structures using VoronoiNN.
Typically used for analyzing the output of a Molecular Dynamics run.
Args:
structures (list): list of Structures.
freq (int): sampling frequency of coordination number [every freq steps].
Returns:
Dictionary of elements as keys and average coordination numbers as values.
"""
coordination_numbers = {}
for spec in structures[0].composition.as_dict().keys():
coordination_numbers[spec] = 0.0
count = 0
for t in range(len(structures)):
if t % freq != 0:
continue
count += 1
vnn = VoronoiNN()
for atom in range(len(structures[0])):
cn = vnn.get_cn(structures[t], atom, use_weights=True)
coordination_numbers[structures[t][atom].species_string] += cn
elements = structures[0].composition.as_dict()
for el in coordination_numbers:
coordination_numbers[el] = coordination_numbers[el] / elements[
el] / count
return coordination_numbers
[docs]class VoronoiAnalyzer:
"""
Performs a statistical analysis of Voronoi polyhedra around each site.
Each Voronoi polyhedron is described using Schaefli notation.
That is a set of indices {c_i} where c_i is the number of faces with i
number of vertices. E.g. for a bcc crystal, there is only one polyhedron
notation of which is [0,6,0,8,0,0,...].
In perfect crystals, these also corresponds to the Wigner-Seitz cells.
For distorted-crystals, liquids or amorphous structures, rather than one-type,
there is a statistical distribution of polyhedra.
See ref: Microstructure and its relaxation in Fe-B amorphous system
simulated by molecular dynamics,
Stepanyuk et al., J. Non-cryst. Solids (1993), 159, 80-87.
"""
def __init__(self, cutoff=5.0, qhull_options="Qbb Qc Qz"):
"""
Args:
cutoff (float): cutoff distance to search for neighbors of a given atom
(default = 5.0)
qhull_options (str): options to pass to qhull (optional)
"""
self.cutoff = cutoff
self.qhull_options = qhull_options
[docs] def analyze(self, structure, n=0):
"""
Performs Voronoi analysis and returns the polyhedra around atom n
in Schlaefli notation.
Args:
structure (Structure): structure to analyze
n (int): index of the center atom in structure
Returns:
voronoi index of n: <c3,c4,c6,c6,c7,c8,c9,c10>
where c_i denotes number of facets with i vertices.
"""
center = structure[n]
neighbors = structure.get_sites_in_sphere(center.coords, self.cutoff)
neighbors = [i[0] for i in sorted(neighbors, key=lambda s: s[1])]
qvoronoi_input = np.array([s.coords for s in neighbors])
voro = Voronoi(qvoronoi_input, qhull_options=self.qhull_options)
vor_index = np.array([0, 0, 0, 0, 0, 0, 0, 0])
for key in voro.ridge_dict:
if 0 in key: # This means if the center atom is in key
if -1 in key: # This means if an infinity point is in key
raise ValueError("Cutoff too short.")
else:
try:
vor_index[len(voro.ridge_dict[key]) - 3] += 1
except IndexError:
# If a facet has more than 10 edges, it's skipped here.
pass
return vor_index
[docs] def analyze_structures(self, structures, step_freq=10,
most_frequent_polyhedra=15):
"""
Perform Voronoi analysis on a list of Structures.
Note that this might take a significant amount of time depending on the
size and number of structures.
Args:
structures (list): list of Structures
cutoff (float: cutoff distance around an atom to search for
neighbors
step_freq (int): perform analysis every step_freq steps
qhull_options (str): options to pass to qhull
most_frequent_polyhedra (int): this many unique polyhedra with
highest frequences is stored.
Returns:
A list of tuples in the form (voronoi_index,frequency)
"""
voro_dict = {}
step = 0
for structure in structures:
step += 1
if step % step_freq != 0:
continue
v = []
for n in range(len(structure)):
v.append(str(self.analyze(structure, n=n).view()))
for voro in v:
if voro in voro_dict:
voro_dict[voro] += 1
else:
voro_dict[voro] = 1
return sorted(voro_dict.items(),
key=lambda x: (x[1], x[0]),
reverse=True)[:most_frequent_polyhedra]
[docs] @staticmethod
def plot_vor_analysis(voronoi_ensemble):
"""
Plot the Voronoi analysis.
:param voronoi_ensemble:
:return: matplotlib.pyplot
"""
t = zip(*voronoi_ensemble)
labels = t[0]
val = list(t[1])
tot = np.sum(val)
val = [float(j) / tot for j in val]
pos = np.arange(len(val)) + .5 # the bar centers on the y axis
import matplotlib.pyplot as plt
plt.figure()
plt.barh(pos, val, align='center', alpha=0.5)
plt.yticks(pos, labels)
plt.xlabel('Count')
plt.title('Voronoi Spectra')
plt.grid(True)
return plt
[docs]class RelaxationAnalyzer:
"""
This class analyzes the relaxation in a calculation.
"""
def __init__(self, initial_structure, final_structure):
"""
Please note that the input and final structures should have the same
ordering of sites. This is typically the case for most computational
codes.
Args:
initial_structure (Structure): Initial input structure to
calculation.
final_structure (Structure): Final output structure from
calculation.
"""
if final_structure.formula != initial_structure.formula:
raise ValueError("Initial and final structures have different " +
"formulas!")
self.initial = initial_structure
self.final = final_structure
[docs] def get_percentage_volume_change(self):
"""
Returns the percentage volume change.
Returns:
Volume change in percentage, e.g., 0.055 implies a 5.5% increase.
"""
initial_vol = self.initial.lattice.volume
final_vol = self.final.lattice.volume
return final_vol / initial_vol - 1
[docs] def get_percentage_lattice_parameter_changes(self):
"""
Returns the percentage lattice parameter changes.
Returns:
A dict of the percentage change in lattice parameter, e.g.,
{'a': 0.012, 'b': 0.021, 'c': -0.031} implies a change of 1.2%,
2.1% and -3.1% in the a, b and c lattice parameters respectively.
"""
initial_latt = self.initial.lattice
final_latt = self.final.lattice
d = {l: getattr(final_latt, l) / getattr(initial_latt, l) - 1
for l in ["a", "b", "c"]}
return d
[docs] def get_percentage_bond_dist_changes(self, max_radius=3.0):
"""
Returns the percentage bond distance changes for each site up to a
maximum radius for nearest neighbors.
Args:
max_radius (float): Maximum radius to search for nearest
neighbors. This radius is applied to the initial structure,
not the final structure.
Returns:
Bond distance changes as a dict of dicts. E.g.,
{index1: {index2: 0.011, ...}}. For economy of representation, the
index1 is always less than index2, i.e., since bonding between
site1 and siten is the same as bonding between siten and site1,
there is no reason to duplicate the information or computation.
"""
data = collections.defaultdict(dict)
for inds in itertools.combinations(list(range(len(self.initial))), 2):
(i, j) = sorted(inds)
initial_dist = self.initial[i].distance(self.initial[j])
if initial_dist < max_radius:
final_dist = self.final[i].distance(self.final[j])
data[i][j] = final_dist / initial_dist - 1
return data
[docs]class VoronoiConnectivity:
"""
Computes the solid angles swept out by the shared face of the voronoi
polyhedron between two sites.
"""
def __init__(self, structure, cutoff=10):
"""
Args:
structure (Structure): Input structure
cutoff (float) Cutoff distance.
"""
self.cutoff = cutoff
self.s = structure
recp_len = np.array(self.s.lattice.reciprocal_lattice.abc)
i = np.ceil(cutoff * recp_len / (2 * pi))
offsets = np.mgrid[-i[0]:i[0] + 1, -i[1]:i[1] + 1, -i[2]:i[2] + 1].T
self.offsets = np.reshape(offsets, (-1, 3))
# shape = [image, axis]
self.cart_offsets = self.s.lattice.get_cartesian_coords(self.offsets)
@property
def connectivity_array(self):
"""
Provides connectivity array.
Returns:
connectivity: An array of shape [atomi, atomj, imagej]. atomi is
the index of the atom in the input structure. Since the second
atom can be outside of the unit cell, it must be described
by both an atom index and an image index. Array data is the
solid angle of polygon between atomi and imagej of atomj
"""
# shape = [site, axis]
cart_coords = np.array(self.s.cart_coords)
# shape = [site, image, axis]
all_sites = cart_coords[:, None, :] + self.cart_offsets[None, :, :]
vt = Voronoi(all_sites.reshape((-1, 3)))
n_images = all_sites.shape[1]
cs = (len(self.s), len(self.s), len(self.cart_offsets))
connectivity = np.zeros(cs)
vts = np.array(vt.vertices)
for (ki, kj), v in vt.ridge_dict.items():
atomi = ki // n_images
atomj = kj // n_images
imagei = ki % n_images
imagej = kj % n_images
if imagei != n_images // 2 and imagej != n_images // 2:
continue
if imagei == n_images // 2:
# atomi is in original cell
val = solid_angle(vt.points[ki], vts[v])
connectivity[atomi, atomj, imagej] = val
if imagej == n_images // 2:
# atomj is in original cell
val = solid_angle(vt.points[kj], vts[v])
connectivity[atomj, atomi, imagei] = val
if -10.101 in vts[v]:
warn('Found connectivity with infinite vertex. '
'Cutoff is too low, and results may be '
'incorrect')
return connectivity
@property
def max_connectivity(self):
"""
returns the 2d array [sitei, sitej] that represents
the maximum connectivity of site i to any periodic
image of site j
"""
return np.max(self.connectivity_array, axis=2)
[docs] def get_connections(self):
"""
Returns a list of site pairs that are Voronoi Neighbors, along
with their real-space distances.
"""
con = []
maxconn = self.max_connectivity
for ii in range(0, maxconn.shape[0]):
for jj in range(0, maxconn.shape[1]):
if maxconn[ii][jj] != 0:
dist = self.s.get_distance(ii, jj)
con.append([ii, jj, dist])
return con
[docs] def get_sitej(self, site_index, image_index):
"""
Assuming there is some value in the connectivity array at indices
(1, 3, 12). sitei can be obtained directly from the input structure
(structure[1]). sitej can be obtained by passing 3, 12 to this function
Args:
site_index (int): index of the site (3 in the example)
image_index (int): index of the image (12 in the example)
"""
atoms_n_occu = self.s[site_index].species
lattice = self.s.lattice
coords = self.s[site_index].frac_coords + self.offsets[image_index]
return PeriodicSite(atoms_n_occu, coords, lattice)
[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.
"""
o = np.array(center)
r = [np.array(c) - o for c in coords]
r.append(r[0])
n = [np.cross(r[i + 1], r[i]) for i in range(len(r) - 1)]
n.append(np.cross(r[1], r[0]))
vals = []
for i in range(len(n) - 1):
v = -np.dot(n[i], n[i + 1]) \
/ (np.linalg.norm(n[i]) * np.linalg.norm(n[i + 1]))
vals.append(acos(abs_cap(v)))
phi = sum(vals)
return phi + (3 - len(r)) * pi
[docs]def get_max_bond_lengths(structure, el_radius_updates=None):
"""
Provides max bond length estimates for a structure based on the JMol
table and algorithms.
Args:
structure: (structure)
el_radius_updates: (dict) symbol->float to update atomic radii
Returns: (dict) - (Element1, Element2) -> float. The two elements are
ordered by Z.
"""
# jmc = JMolCoordFinder(el_radius_updates)
jmnn = JmolNN(el_radius_updates=el_radius_updates)
bonds_lens = {}
els = sorted(structure.composition.elements, key=lambda x: x.Z)
for i1 in range(len(els)):
for i2 in range(len(els) - i1):
bonds_lens[els[i1], els[i1 + i2]] = jmnn.get_max_bond_distance(
els[i1].symbol, els[i1 + i2].symbol)
return bonds_lens
@deprecated(message=("find_dimension has been moved to"
"pymatgen.analysis.dimensionality.get_dimensionality_gorai"
" this method will be removed in pymatgen v2019.1.1."))
def get_dimensionality(structure, max_hkl=2, el_radius_updates=None,
min_slab_size=5, min_vacuum_size=5,
standardize=True, bonds=None):
"""
This method returns whether a structure is 3D, 2D (layered), or 1D (linear
chains or molecules) according to the algorithm published in Gorai, P.,
Toberer, E. & Stevanovic, V. Computational Identification of Promising
Thermoelectric Materials Among Known Quasi-2D Binary Compounds. J. Mater.
Chem. A 2, 4136 (2016).
Note that a 1D structure detection might indicate problems in the bonding
algorithm, particularly for ionic crystals (e.g., NaCl)
Users can change the behavior of bonds detection by passing either
el_radius_updates to update atomic radii for auto-detection of max bond
distances, or bonds to explicitly specify max bond distances for atom pairs.
Note that if you pass both, el_radius_updates are ignored.
Args:
structure: (Structure) structure to analyze dimensionality for
max_hkl: (int) max index of planes to look for layers
el_radius_updates: (dict) symbol->float to update atomic radii
min_slab_size: (float) internal surface construction parameter
min_vacuum_size: (float) internal surface construction parameter
standardize (bool): whether to standardize the structure before
analysis. Set to False only if you already have the structure in a
convention where layers / chains will be along low <hkl> indexes.
bonds ({(specie1, specie2): max_bond_dist}: bonds are
specified as a dict of tuples: float of specie1, specie2
and the max bonding distance. For example, PO4 groups may be
defined as {("P", "O"): 3}.
Returns: (int) the dimensionality of the structure - 1 (molecules/chains),
2 (layered), or 3 (3D)
"""
if standardize:
structure = SpacegroupAnalyzer(structure). \
get_conventional_standard_structure()
if not bonds:
bonds = get_max_bond_lengths(structure, el_radius_updates)
num_surfaces = 0
for h in range(max_hkl):
for k in range(max_hkl):
for l in range(max_hkl):
if max([h, k, l]) > 0 and num_surfaces < 2:
sg = SlabGenerator(structure, (h, k, l),
min_slab_size=min_slab_size,
min_vacuum_size=min_vacuum_size)
slabs = sg.get_slabs(bonds)
for _ in slabs:
num_surfaces += 1
return 3 - min(num_surfaces, 2)
[docs]def contains_peroxide(structure, relative_cutoff=1.1):
"""
Determines if a structure contains peroxide anions.
Args:
structure (Structure): Input structure.
relative_cutoff: The peroxide bond distance is 1.49 Angstrom.
Relative_cutoff * 1.49 stipulates the maximum distance two O
atoms must be to each other to be considered a peroxide.
Returns:
Boolean indicating if structure contains a peroxide anion.
"""
ox_type = oxide_type(structure, relative_cutoff)
if ox_type == "peroxide":
return True
else:
return False
[docs]class OxideType:
"""
Separate class for determining oxide type.
"""
def __init__(self, structure, relative_cutoff=1.1):
"""
Args:
structure: Input structure.
relative_cutoff: Relative_cutoff * act. cutoff stipulates the max.
distance two O atoms must be from each other. Default value is
1.1. At most 1.1 is recommended, nothing larger, otherwise the
script cannot distinguish between superoxides and peroxides.
"""
self.structure = structure
self.relative_cutoff = relative_cutoff
self.oxide_type, self.nbonds = self.parse_oxide()
[docs] def parse_oxide(self):
"""
Determines if an oxide is a peroxide/superoxide/ozonide/normal oxide.
Returns:
oxide_type (str): Type of oxide
ozonide/peroxide/superoxide/hydroxide/None.
nbonds (int): Number of peroxide/superoxide/hydroxide bonds in
structure.
"""
structure = self.structure
relative_cutoff = self.relative_cutoff
o_sites_frac_coords = []
h_sites_frac_coords = []
lattice = structure.lattice
if isinstance(structure.composition.elements[0], Element):
comp = structure.composition
elif isinstance(structure.composition.elements[0], Specie):
elmap = collections.defaultdict(float)
for site in structure:
for species, occu in site.species.items():
elmap[species.element] += occu
comp = Composition(elmap)
if Element("O") not in comp or comp.is_element:
return "None", 0
for site in structure:
syms = [sp.symbol for sp in site.species.keys()]
if "O" in syms:
o_sites_frac_coords.append(site.frac_coords)
if "H" in syms:
h_sites_frac_coords.append(site.frac_coords)
if h_sites_frac_coords:
dist_matrix = lattice.get_all_distances(o_sites_frac_coords,
h_sites_frac_coords)
if np.any(dist_matrix < relative_cutoff * 0.93):
return "hydroxide", len(
np.where(dist_matrix < relative_cutoff * 0.93)[0]) / 2.0
dist_matrix = lattice.get_all_distances(o_sites_frac_coords,
o_sites_frac_coords)
np.fill_diagonal(dist_matrix, 1000)
is_superoxide = False
is_peroxide = False
is_ozonide = False
if np.any(dist_matrix < relative_cutoff * 1.35):
bond_atoms = np.where(dist_matrix < relative_cutoff * 1.35)[0]
is_superoxide = True
elif np.any(dist_matrix < relative_cutoff * 1.49):
is_peroxide = True
bond_atoms = np.where(dist_matrix < relative_cutoff * 1.49)[0]
if is_superoxide:
if len(bond_atoms) > len(set(bond_atoms)):
is_superoxide = False
is_ozonide = True
try:
nbonds = len(set(bond_atoms))
except UnboundLocalError:
nbonds = 0.0
if is_ozonide:
str_oxide = "ozonide"
elif is_superoxide:
str_oxide = "superoxide"
elif is_peroxide:
str_oxide = "peroxide"
else:
str_oxide = "oxide"
if str_oxide == "oxide":
nbonds = comp["O"]
return str_oxide, nbonds
[docs]def oxide_type(structure, relative_cutoff=1.1, return_nbonds=False):
"""
Determines if an oxide is a peroxide/superoxide/ozonide/normal oxide
Args:
structure (Structure): Input structure.
relative_cutoff (float): Relative_cutoff * act. cutoff stipulates the
max distance two O atoms must be from each other.
return_nbonds (bool): Should number of bonds be requested?
"""
ox_obj = OxideType(structure, relative_cutoff)
if return_nbonds:
return ox_obj.oxide_type, ox_obj.nbonds
else:
return ox_obj.oxide_type
[docs]def sulfide_type(structure):
"""
Determines if a structure is a sulfide/polysulfide
Args:
structure (Structure): Input structure.
Returns:
(str) sulfide/polysulfide/sulfate
"""
structure = structure.copy()
structure.remove_oxidation_states()
s = Element("S")
comp = structure.composition
if comp.is_element or s not in comp:
return None
finder = SpacegroupAnalyzer(structure, symprec=0.1)
symm_structure = finder.get_symmetrized_structure()
s_sites = [sites[0] for sites in symm_structure.equivalent_sites if
sites[0].specie == s]
def process_site(site):
# in an exceptionally rare number of structures, the search
# radius needs to be increased to find a neighbor atom
search_radius = 4
neighbors = []
while len(neighbors) == 0:
neighbors = structure.get_neighbors(site, search_radius)
search_radius *= 2
if search_radius > max(structure.lattice.abc) * 2:
break
neighbors = sorted(neighbors, key=lambda n: n.nn_distance)
dist = neighbors[0].nn_distance
coord_elements = [nn.specie for nn in neighbors
if nn.nn_distance < dist + 0.4][:4]
avg_electroneg = np.mean([e.X for e in coord_elements])
if avg_electroneg > s.X:
return "sulfate"
elif avg_electroneg == s.X and s in coord_elements:
return "polysulfide"
else:
return "sulfide"
types = set([process_site(site) for site in s_sites])
if "sulfate" in types:
return None
elif "polysulfide" in types:
return "polysulfide"
else:
return "sulfide"