Source code for hiphive.core.get_clusters

# Contains the get_clusters function which generates clusters

from ase.neighborlist import NeighborList
import numpy as np
import itertools as it
from collections import defaultdict

from .utilities import BiMap
from ..io.logging import logger

logger = logger.getChild('get_clusters')


# TODO: This function could be made a bit more general
[docs]def get_clusters(atoms, cutoffs, nPrim, multiplicity=True, use_geometrical_order=False): '''Generate a list of all clusters in the atoms object which includes the center atoms with positions within the cell metric. The cutoff determines up to which order and range clusters should be generated. With multiplicity set to True clusters like `[0,0]` and `[3,3,4` etc will be generated. This is useful when doing force constants but not so much for cluster expansions. The geometrical order is the total number of different atoms in the cluster. `[0,0,1]` would have geometrical order 2 and `[1,2,3,4]` would have order 4. If the key word is True the cutoff criteria will be based on the geometrical order of the cluster. This is based on the observation that many body interactions decrease fast with cutoff but anharmonic interactions can be quite long ranged. Parameters ---------- atoms : ASE Atoms object can be a general atoms object but must have pbc=False. cutoffs : dict the keys specify the order while the values specify the cutoff radii multiplicity : bool includes clusters where same atom appears more than once geometrical_order : bool specifies if the geometrical order should be used as cutoff_order, otherwise the normal order of the cluster is used Returns ------- list of tuples a list of clusters where each entry is a tuple of indices, which refer to the atoms in the input supercell ''' logger.debug('Generating clusters...') cluster_dict = defaultdict(list) for i in range(nPrim): for order in cutoffs.orders: cluster = (i,) * order cluster_dict[order].append(cluster) for nbody in range(2, cutoffs.max_nbody + 1): cutoff = cutoffs.max_nbody_cutoff(nbody) nbody_clusters, nbody_cutoffs = \ generate_geometrical_clusters(atoms, nPrim, cutoff, nbody) for order in range(nbody, cutoffs.max_nbody_order(nbody) + 1): for cluster, cutoff in zip(nbody_clusters, nbody_cutoffs): if cutoff < cutoffs.get_cutoff(nbody=nbody, order=order): clusters = extend_cluster(cluster, order) cluster_dict[order].extend(clusters) cluster_list = BiMap() for key in sorted(cluster_dict): for cluster in sorted(cluster_dict[key]): cluster_list.append(cluster) return cluster_list
[docs]def generate_geometrical_clusters(atoms, nPrim, cutoff, order): nm, dm = create_neighbor_matrices(atoms, cutoff) clusters = [] cutoffs = [] i, j = 0, 0 for tup in it.combinations(range(len(atoms)), r=order): if tup[0] >= nPrim: break if not nm[tup[i], tup[j]]: continue for i, j in it.combinations(range(order), r=2): if not nm[tup[i], tup[j]]: break else: clusters.append(tup) cutoffs.append(np.max(dm[tup, :][:, tup])) return clusters, cutoffs
[docs]def create_neighbor_matrices(atoms, cutoff): atoms = atoms.copy() atoms.pbc = False nAtoms = len(atoms) nl = NeighborList([cutoff / 2] * nAtoms, skin=0, bothways=True) nl.update(atoms) neighbor_matrix = np.eye(nAtoms, dtype=bool) distance_matrix = np.zeros((nAtoms, nAtoms)) for i in range(nAtoms): indices, _ = nl.get_neighbors(i) neighbor_matrix[i, indices] = True distance_matrix[i, indices] = atoms.get_distances(i, indices) return neighbor_matrix, distance_matrix
[docs]def extend_cluster(cluster, order): clusters = [] cluster = tuple(cluster) nbody = len(cluster) r = order - nbody for tup in it.combinations_with_replacement(cluster, r): new_cluster = sorted(cluster + tup) clusters.append(tuple(new_cluster)) return clusters