Source code for hiphive.structure_generation.rattle

"""
Module for generating rattled structures. Rattle refers to displacing atoms
with a normal distribution with zero mean and some standard deviation.
"""

import numpy as np
from scipy.special import erf
from ase.neighborlist import NeighborList


[docs]def generate_rattled_structures(atoms, n_structures, rattle_std, seed=42): """Returns list of rattled configurations. Displacements are drawn from normal distributions for each Cartesian directions for each atom independently. Warning ------- Repeatedly calling this function *without* providing different seeds will yield identical or correlated results. To avoid this behavior it is recommended to specify a different seed for each call to this function. Parameters ---------- atoms : ase.Atoms prototype structure n_structures : int number of structures to generate rattle_std : float rattle amplitude (standard deviation of the normal distribution) seed : int seed for setting up NumPy random state from which random numbers are generated Returns ------- list of ase.Atoms generated structures """ rs = np.random.RandomState(seed) N = len(atoms) atoms_list = [] for _ in range(n_structures): atoms_tmp = atoms.copy() displacements = rs.normal(0.0, rattle_std, (N, 3)) atoms_tmp.positions += displacements atoms_list.append(atoms_tmp) return atoms_list
[docs]def generate_mc_rattled_structures(atoms, n_configs, rattle_std, d_min, seed=42, **kwargs): """Returns list of Monte Carlo rattled configurations. Rattling atom `i` is carried out as a Monte Carlo move that is accepted with a probability determined from the minimum interatomic distance :math:`d_{ij}`. If :math`\\min(d_{ij})` is smaller than :math:`d_{min}` the move is only accepted with a low probability. This process is repeated for each atom a number of times meaning the magnitude of the final displacements is not *directly* connected to `rattle_std`. Warning ------- Repeatedly calling this function *without* providing different seeds will yield identical or correlated results. To avoid this behavior it is recommended to specify a different seed for each call to this function. Notes ------ The procedure implemented here might not generate a symmetric distribution for the displacements `kwargs` will be forwarded to `mc_rattle` (see user guide for a detailed explanation) Parameters ---------- atoms : ase.Atoms prototype structure n_structures : int number of structures to generate rattle_std : float rattle amplitude (standard deviation in normal distribution); note this value is not *directly* connected to the final average displacement for the structures d_min : float interatomic distance used for computing the probability for each rattle move seed : int seed for setting up NumPy random state from which random numbers are generated Returns ------- list of ase.Atoms generated structures """ rs = np.random.RandomState(seed) atoms_list = [] for _ in range(n_configs): atoms_tmp = atoms.copy() seed = rs.randint(1, 1000000000) displacements = mc_rattle(atoms_tmp, rattle_std, d_min, seed=seed, **kwargs) atoms_tmp.positions += displacements atoms_list.append(atoms_tmp) return atoms_list
def _probability_mc_rattle(d, d_min, width): """ Monte Carlo probability function as an error function. Parameters ---------- d_min : float center value for the error function width : float width of error function """ return (erf((d-d_min)/width) + 1.0) / 2 def mc_rattle(atoms, rattle_std, d_min, width=0.1, n_iter=10, max_attempts=5000, max_disp=2.0, active_atoms=None, seed=42): """Generate displacements using the Monte Carlo rattle method Parameters ---------- atoms : ase.Atoms prototype structure rattle_std : float rattle amplitude (standard deviation in normal distribution) d_min : float interatomic distance used for computing the probability for each rattle move. Center position of the error function width : float width of the error function n_iter : int number of Monte Carlo cycle max_disp : float rattle moves that yields a displacement larger than max_disp will always be rejected. This rarley occurs and is more used as a safety net for not generating structures where two or more have swapped positions. max_attempts : int limit for how many attempted rattle moves are allowed a single atom; if this limit is reached an `Exception` is raised. active_atoms : list list of which atomic indices should undergo Monte Carlo rattling seed : int seed for setting up NumPy random state from which random numbers are generated Returns ------- numpy.ndarray atomic displacements (`Nx3`) """ rs = np.random.RandomState(seed) if active_atoms is None: active_atoms = range(len(atoms)) atoms_rattle = atoms.copy() reference_positions = atoms_rattle.get_positions() nbr_list = NeighborList([d_min]*len(atoms_rattle), skin=0.0, self_interaction=False, bothways=True) nbr_list.update(atoms_rattle) # run Monte Carlo for _ in range(n_iter): for i in active_atoms: i_nbrs = np.setdiff1d(nbr_list.get_neighbors(i)[0], [i]) for n in range(max_attempts): delta_disp = rs.normal(0.0, rattle_std, 3) atoms_rattle.positions[i] += delta_disp disp_i = atoms_rattle.positions[i] - reference_positions[i] if np.linalg.norm(disp_i) > max_disp: continue min_distance = np.min(atoms_rattle.get_distances(i, i_nbrs, mic=True)) if _probability_mc_rattle(min_distance, d_min, width) > \ rs.rand(): # accept disp_i break else: # revert disp_i atoms_rattle[i].position -= delta_disp else: raise Exception('Maxmium attempts for atom {}'.format(i)) displacements = atoms_rattle.positions - reference_positions return displacements