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), [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