Source code for acat.build.ordering

from acat.utilities import numbers_from_ratio
from ase.geometry import get_distances
from ase.io import Trajectory, read, write
from asap3.analysis import FullCNA 
from collections import defaultdict
from itertools import product, combinations
import numpy as np
import random
import math


[docs]class SymmetricOrderingGenerator(object): """`SymmetricOrderingGenerator` is a class for generating symmetric chemical orderings for a nanoalloy. As for now only support clusters without fixing the composition, but there is no limitation of the number of metal components. Please align the z direction to the symmetry axis of the cluster. Parameters ---------- atoms : ase.Atoms object The nanoparticle to use as a template to generate symmetric chemical orderings. Accept any ase.Atoms object. No need to be built-in. elements : list of strs The metal elements of the nanoalloy. symmetry : str, default 'spherical' Support 8 symmetries: 'spherical' = centrosymmetry (shells defined by the distances to the geometric center); 'cylindrical' = cylindrical symmetry around z axis (shells defined by the distances to the z axis); 'planar' = planar symmetry around z axis (shells defined by the z coordinates), common for phase-separated nanoalloys; 'reflective_planar' = reflective planar symmetry around both z and xy plane (shells defined by the absolute z coordinate), high symmetry subset of 'planar'; 'circular' = ring symmetry around z axis (shells defined by both z coordinate and distance to z axis); 'reflective_circular' = reflective ring symmetry around both z and xy plane (shells defined by both absolute z coordinate and distance to z axis); 'chemical' = symmetry w.r.t chemical environment (shells defined by vertex / edge / fcc111 / fcc100 / bulk identified by CNA analysis); 'conventional' = conventional definition of shells (surface / subsurface, subsubsurface, ..., core). cutoff: float, default 1.0 Minimum distance (in Angstrom) that the code can distinguish between two neighbor shells. If symmetry='chemical' or symmetry='conventional', this is the cutoff radius (in Angstrom) for CNA and will automatically use a reasonable cutoff based on the lattice constant of the material if cutoff < 1. If the structure is distorted, please use a larger cutoff. secondary_symmetry : str, default None Add a secondary symmetry check to define shells hierarchically. For example, even if two atoms are classifed in the same shell defined by the primary symmetry, they can still end up in different shells if they fall into two different shells defined by the secondary symmetry. Support 6 symmetries: 'spherical', 'cylindrical', 'planar', 'reflective_planar', 'chemical' and 'conventional'. Note that secondary symmetry has the same importance as the primary symmetry, so you can set either of the two symmetries of interest as the secondary symmetry. Useful for combining chemical environment with geometric symmetry or combining symmetries with different cutoffs. secondary_cutoff : float, default 1.0 Same as cutoff, except that it is for the secondary symmetry. composition: dict, None Generate symmetric orderings only at a certain composition. The dictionary contains the metal elements as keys and their concentrations as values. Generate orderings at all compositions if not specified. Note that the computational cost scales badly with the number of shells for a fixed-composition search. shell_threshold : int, default 20 Number of shells to switch to stochastic mode automatically. trajectory : str, default 'orderings.traj' The name of the output ase trajectory file. append_trajectory : bool, default False Whether to append structures to the existing trajectory. """ def __init__(self, atoms, elements, symmetry='spherical', cutoff=1., secondary_symmetry=None, secondary_cutoff=1., composition=None, shell_threshold=20, trajectory='orderings.traj', append_trajectory=False): self.atoms = atoms self.elements = elements self.symmetry = symmetry self.cutoff = cutoff assert secondary_symmetry not in ['circular', 'reflective_circular'] self.secondary_symmetry = secondary_symmetry self.secondary_cutoff = secondary_cutoff self.composition = composition if self.composition is not None: ks = list(self.composition.keys()) assert set(ks) == set(self.elements) vs = list(self.composition.values()) nums = numbers_from_ratio(len(self.atoms), vs) self.num_dict = {ks[i]: nums[i] for i in range(len(ks))} self.shell_threshold = shell_threshold if isinstance(trajectory, str): self.trajectory = trajectory self.append_trajectory = append_trajectory self.shells = self.get_shells()
[docs] def get_sorted_indices(self, symmetry): """Returns the indices sorted by the metric that defines different shells, together with the corresponding vlues, given a specific symmetry. Returns the indices sorted by chemical environment if symmetry='chemical'. Returns the indices sorted by surface, subsurface, subsubsurface, ..., core. Parameters ---------- symmetry : str Support 6 symmetries: spherical, cylindrical, planar, reflective_planar, chemical, conventional. """ atoms = self.atoms.copy() atoms.center() geo_mid = [(atoms.cell/2.)[0][0], (atoms.cell/2.)[1][1], (atoms.cell/2.)[2][2]] if symmetry == 'spherical': dists = get_distances(atoms.positions, [geo_mid])[1][:,0] elif symmetry == 'cylindrical': dists = np.asarray([math.sqrt((a.position[0] - geo_mid[0])**2 + (a.position[1] - geo_mid[1])**2) for a in atoms]) elif symmetry == 'planar': dists = atoms.positions[:, 2] elif symmetry == 'reflective_planar': dists = abs(atoms.positions[:, 2] - geo_mid[2]) elif symmetry == 'chemical': if self.symmetry == 'chemical': rCut = None if self.cutoff < 1. else self.cutoff elif self.secondary_symmetry == 'chemical': rCut = None if self.secondary_cutoff < 1. else self.secondary_cutoff atoms.center(vacuum=5.) fcna = FullCNA(atoms, rCut=rCut).get_normal_cna() d = defaultdict(list) for i, x in enumerate(fcna): if sum(x.values()) < 12: d[str(x)].append(i) else: d['bulk'].append(i) return list(d.values()), None elif symmetry == 'conventional': if self.symmetry == 'conventional': rCut = None if self.cutoff < 1. else self.cutoff elif self.secondary_symmetry == 'conventional': rCut = None if self.secondary_cutoff < 1. else self.secondary_cutoff def view1D(a, b): # a, b are arrays a = np.ascontiguousarray(a) b = np.ascontiguousarray(b) void_dt = np.dtype((np.void, a.dtype.itemsize * a.shape[1])) return a.view(void_dt).ravel(), b.view(void_dt).ravel() def argwhere_nd_searchsorted(a,b): A,B = view1D(a,b) sidxB = B.argsort() mask = np.isin(A,B) cm = A[mask] idx0 = np.flatnonzero(mask) idx1 = sidxB[np.searchsorted(B,cm, sorter=sidxB)] return idx0, idx1 # idx0 : indices in A, idx1 : indices in B def get_surf_ids(a): fcna = FullCNA(a, rCut=rCut).get_normal_cna() surf_ids, bulk_ids = [], [] for i in range(len(a)): if sum(fcna[i].values()) < 12: surf_ids.append(i) else: bulk_ids.append(i) shell_ids = list(argwhere_nd_searchsorted(atoms.positions, a.positions[surf_ids])[0]) conv_shells.append(shell_ids) if not bulk_ids: return get_surf_ids(a[bulk_ids]) conv_shells = [] atoms.center(vacuum=5.) get_surf_ids(atoms) return conv_shells, None else: raise NotImplementedError("Symmetry '{}' is not supported".format(symmetry)) sorted_indices = np.argsort(np.ravel(dists)) return sorted_indices, dists[sorted_indices]
[docs] def get_shells(self): """Get the shells (a list of lists of atom indices) that divided by the symmetry.""" if self.symmetry == 'circular': symmetry = 'planar' elif self.symmetry == 'reflective_circular': symmetry = 'reflective_planar' else: symmetry = self.symmetry indices, dists = self.get_sorted_indices(symmetry=symmetry) if self.symmetry in ['chemical', 'conventional']: shells = indices else: shells = [] old_dist = -10. for i, dist in zip(indices, dists): if abs(dist - old_dist) > self.cutoff: shells.append([i]) old_dist = dist else: shells[-1].append(i) if self.symmetry in ['circular', 'reflective_circular']: indices0, dists0 = self.get_sorted_indices(symmetry='cylindrical') shells0 = [] old_dist0 = -10. for j, dist0 in zip(indices0, dists0): if abs(dist0 - old_dist0) > self.cutoff: shells0.append([j]) old_dist0 = dist0 else: shells0[-1].append(j) res = [] for shell in shells: res0 = [] for shell0 in shells0: match = [i for i in shell if i in shell0] if match: res0.append(match) res += res0 shells = res if self.secondary_symmetry is not None: indices2, dists2 = self.get_sorted_indices(symmetry= self.secondary_symmetry) if self.secondary_symmetry in ['chemical', 'conventional']: shells2 = indices2 else: shells2 = [] old_dist2 = -10. for j, dist2 in zip(indices2, dists2): if abs(dist2 - old_dist2) > self.secondary_cutoff: shells2.append([j]) old_dist2 = dist2 else: shells2[-1].append(j) res = [] for shell in shells: res2 = [] for shell2 in shells2: match = [i for i in shell if i in shell2] if match: res2.append(match) res += res2 shells = res return shells
[docs] def run(self, max_gen=None, mode='systematic', verbose=False): """Run the chemical ordering generator. Parameters ---------- max_gen : int, default None Maximum number of chemical orderings to generate. Enumerate all symetric patterns if not specified. mode : str, default 'systematic' Mode 'systematic' = enumerate all possible chemical orderings. Mode 'stochastic' = sample chemical orderings stochastically. Stocahstic mode is recommended when there are many shells. verbose : bool, default False Whether to print out information about number of shells and number of generated structures. """ traj_mode = 'a' if self.append_trajectory else 'w' traj = Trajectory(self.trajectory, mode=traj_mode) atoms = self.atoms shells = self.shells nshells = len(shells) n_write = 0 if verbose: print('{} shells classified'.format(nshells)) if self.composition is not None: def bipartitions(shells, total): n = len(shells) for k in range(n + 1): for combo in combinations(range(n), k): if sum(len(shells[i]) for i in combo) == total: set_combo = set(combo) yield sorted(shells[i] for i in combo), sorted( shells[i] for i in range(n) if i not in set_combo) def partitions_into_totals(shells, totals): assert totals if len(totals) == 1: yield [shells] else: for first, remaining_shells in bipartitions(shells, totals[0]): for rest in partitions_into_totals(remaining_shells, totals[1:]): yield [first] + rest keys = list(self.num_dict.keys()) totals = list(self.num_dict.values()) if max_gen is None: max_gen = -1 for part in partitions_into_totals(shells, totals): for j in range(len(totals)): ids = [i for shell in part[j] for i in shell] atoms.symbols[ids] = len(ids) * keys[j] traj.write(atoms) n_write += 1 if n_write == max_gen: break else: # When the number of shells is too large (> 20), systematic enumeration # is not feasible. Stochastic sampling is the only option if mode == 'systematic': if nshells > self.shell_threshold: if verbose: print('{} shells is infeasible for systematic'.format(nshells), 'generator. Use stochastic generator instead') mode = 'stochastic' else: combos = list(product(self.elements, repeat=nshells)) random.shuffle(combos) for combo in combos: for j, spec in enumerate(combo): atoms.symbols[shells[j]] = spec traj.write(atoms) n_write += 1 if max_gen is not None: if n_write == max_gen: break if mode == 'stochastic': combos = set() too_few = (2 ** nshells * 0.95 <= max_gen) if too_few and verbose: print('Too few shells. The generated images are not all unique.') while True: combo = tuple(np.random.choice(self.elements, size=nshells)) if combo not in combos or too_few: combos.add(combo) for j, spec in enumerate(combo): atoms.symbols[shells[j]] = spec traj.write(atoms) n_write += 1 if max_gen is not None: if n_write == max_gen: break if verbose: print('{} symmetric chemical orderings generated'.format(n_write))
[docs]class RandomOrderingGenerator(object): """`RandomOrderingGenerator` is a class for generating random chemical orderings for an alloy catalyst. The function is generalized for both periodic and non-periodic systems, and there is no limitation of the number of metal components. Parameters ---------- atoms : ase.Atoms object The nanoparticle or surface slab to use as a template to generate random chemical orderings. Accept any ase.Atoms object. No need to be built-in. elements : list of strs The metal elements of the alloy catalyst. composition: dict, None Generate random orderings only at a certain composition. The dictionary contains the metal elements as keys and their concentrations as values. Generate orderings at all compositions if not specified. trajectory : str, default 'patterns.traj' The name of the output ase trajectory file. append_trajectory : bool, default False Whether to append structures to the existing trajectory. """ def __init__(self, atoms, elements, composition=None, trajectory='orderings.traj', append_trajectory=False): self.atoms = atoms self.elements = elements self.composition = composition if self.composition is not None: ks = list(self.composition.keys()) assert set(ks) == set(self.elements) vs = list(self.composition.values()) nums = numbers_from_ratio(len(self.atoms), vs) self.num_dict = {ks[i]: nums[i] for i in range(len(ks))} if isinstance(trajectory, str): self.trajectory = trajectory self.append_trajectory = append_trajectory
[docs] def randint_with_sum(self): """Return a randomly chosen list of N positive integers i summing to the number of atoms. N is the number of elements. Each such list is equally likely to occur.""" N = len(self.elements) total = len(self.atoms) dividers = sorted(random.sample(range(1, total), N - 1)) return [a - b for a, b in zip(dividers + [total], [0] + dividers)]
[docs] def random_split_indices(self): """Generate random chunks of indices given sizes of each chunk.""" indices = list(range(len(self.atoms))) random.shuffle(indices) res = {} pointer = 0 for k, v in self.num_dict.items(): res[k] = indices[pointer:pointer+v] pointer += v return res
[docs] def run(self, num_gen): """Run the chemical ordering generator. Parameters ---------- num_gen : int Number of chemical orderings to generate. """ traj_mode = 'a' if self.append_trajectory else 'w' traj = Trajectory(self.trajectory, mode=traj_mode) atoms = self.atoms natoms = len(atoms) for _ in range(num_gen): if self.composition is None: rands = self.randint_with_sum() self.num_dict = {e: rands[i] for i, e in enumerate(self.elements)} chunks = self.random_split_indices() indi = atoms.copy() for e, ids in chunks.items(): indi.symbols[ids] = e traj.write(indi)