"""Mutation operations intended for bulk structures.
If you find this implementation useful in your work,
please consider citing:
M. Van den Bossche, Henrik Gronbeck, B. Hammer,
J. Chem. Theory Comput., doi:10.1021/acs.jctc.8b00039
in addition to the papers mentioned in the docstrings."""
import inspect
import json
import numpy as np
from random import gauss
from ase.data import covalent_radii
from ase.neighborlist import NeighborList
from ase.build import niggli_reduce
from ase.ga.offspring_creator import OffspringCreator, CombinationMutation
from ase.ga.utilities import (atoms_too_close, atoms_too_close_two_sets,
gather_atoms_by_tag)
from ase.ga.bulk_utilities import get_rotation_matrix
from scipy.spatial.distance import cdist
[docs]class StrainMutation(OffspringCreator):
""" Mutates a candidate by applying a randomly generated strain.
For more information, see also:
* `Glass, Oganov, Hansen, Comp. Phys. Comm. 175 (2006) 713-720`__
__ https://doi.org/10.1016/j.cpc.2006.07.020
* `Lonie, Zurek, Comp. Phys. Comm. 182 (2011) 372-387`__
__ https://doi.org/10.1016/j.cpc.2010.07.048
After initialization of the mutation, a scaling volume
(to which each mutated structure is scaled before checking the
constraints) is typically generated from the population,
which is then also occasionally updated in the course of the
GA run.
Parameters:
blmin: dict
The closest allowed interatomic distances on the form:
{(Z, Z*): dist, ...}, where Z and Z* are atomic numbers.
cellbounds: ase.ga.bulk_utilities.CellBounds instance
Describing limits on the cell shape, see
:class:`~ase.ga.bulk_utilities.CellBounds`.
stddev: float
Standard deviation used in the generation of the
strain matrix elements.
use_tags: boolean
Whether to use the atomic tags to preserve molecular identity.
"""
def __init__(self, blmin, cellbounds=None, stddev=0.7, use_tags=False,
verbose=False):
OffspringCreator.__init__(self, verbose)
self.blmin = blmin
self.cellbounds = cellbounds
self.stddev = stddev
self.use_tags = use_tags
self.scaling_volume = None
self.descriptor = 'StrainMutation'
self.min_inputs = 1
def update_scaling_volume(self, population, w_adapt=0.5, n_adapt=0):
"""Function to initialize or update the scaling volume in a GA run."""
if not n_adapt:
# if not set, take best 20% of the population
n_adapt = int(round(0.2 * len(population)))
v_new = np.mean([a.get_volume() for a in population[:n_adapt]])
if not self.scaling_volume:
self.scaling_volume = v_new
else:
volumes = [self.scaling_volume, v_new]
weights = [1 - w_adapt, w_adapt]
self.scaling_volume = np.average(volumes, weights=weights)
def get_new_individual(self, parents):
f = parents[0]
indi = self.mutate(f)
if indi is None:
return indi, 'mutation: strain'
indi = self.initialize_individual(f, indi)
indi.info['data']['parents'] = [f.info['confid']]
return self.finalize_individual(indi), 'mutation: strain'
def mutate(self, atoms):
""" Does the actual mutation. """
cell_ref = atoms.get_cell()
pos_ref = atoms.get_positions()
vol = atoms.get_volume()
if self.use_tags:
tags = atoms.get_tags()
gather_atoms_by_tag(atoms)
pos = atoms.get_positions()
mutant = atoms.copy()
if self.cellbounds is not None:
if not self.cellbounds.is_within_bounds(cell_ref):
niggli_reduce(mutant)
count = 0
too_close = True
maxcount = 1000
while too_close and count < maxcount:
mutant.set_cell(cell_ref, scale_atoms=False)
mutant.set_positions(pos_ref)
# generating the strain matrix:
strain = np.identity(3)
for i in range(3):
for j in range(i + 1):
if i == j:
strain[i, j] += gauss(0, self.stddev)
else:
epsilon = 0.5 * gauss(0, self.stddev)
strain[i, j] += epsilon
strain[j, i] += epsilon
# applying the strain:
cell_new = np.dot(strain, cell_ref)
# volume scaling:
v = abs(np.linalg.det(cell_new))
if self.scaling_volume is None:
cell_new *= (vol / v)**(1. / 3)
else:
cell_new *= (self.scaling_volume / v)**(1. / 3)
# check cell dimensions:
if not self.cellbounds.is_within_bounds(cell_new):
continue
if self.use_tags:
transfo = np.linalg.solve(cell_ref, cell_new)
for tag in np.unique(tags):
select = np.where(tags == tag)
cop = np.mean(pos[select], axis=0)
disp = np.dot(cop, transfo) - cop
mutant.positions[select] += disp
mutant.set_cell(cell_new, scale_atoms=not self.use_tags)
# check distances:
too_close = atoms_too_close(mutant, self.blmin,
use_tags=self.use_tags)
count += 1
if count == maxcount:
mutant = None
return mutant
[docs]class PermuStrainMutation(CombinationMutation):
""" Combination of PermutationMutation and StrainMutation.
For more information, see also:
* `Lonie, Zurek, Comp. Phys. Comm. 182 (2011) 372-387`__
__ https://doi.org/10.1016/j.cpc.2010.07.048
Parameters:
permutationmutation: OffspringCreator instance
A mutation that permutes atom types.
strainmutation: OffspringCreator instance
A mutation that mutates by straining.
"""
def __init__(self, permutationmutation, strainmutation, verbose=False):
super(PermuStrainMutation, self).__init__(permutationmutation,
strainmutation,
verbose=verbose)
self.descriptor = 'permustrain'
class TagFilter:
''' Filter which constrains same-tag atoms to behave
like internally rigid moieties '''
def __init__(self, atoms):
self.atoms = atoms
gather_atoms_by_tag(self.atoms)
self.tags = self.atoms.get_tags()
self.unique_tags = np.unique(self.tags)
self.n = len(self.unique_tags)
def get_positions(self):
all_pos = self.atoms.get_positions()
cop_pos = np.zeros((self.n, 3))
for i in range(self.n):
indices = np.where(self.tags == self.unique_tags[i])
cop_pos[i] = np.average(all_pos[indices], axis=0)
return cop_pos
def set_positions(self, positions, **kwargs):
cop_pos = self.get_positions()
all_pos = self.atoms.get_positions()
assert np.all(np.shape(positions) == np.shape(cop_pos))
for i in range(self.n):
indices = np.where(self.tags == self.unique_tags[i])
shift = positions[i] - cop_pos[i]
all_pos[indices] += shift
self.atoms.set_positions(all_pos, **kwargs)
def get_forces(self, *args, **kwargs):
f = self.atoms.get_forces()
forces = np.zeros((self.n, 3))
for i in range(self.n):
indices = np.where(self.tags == self.unique_tags[i])
forces[i] = np.sum(f[indices], axis=0)
return forces
def get_masses(self):
m = self.atoms.get_masses()
masses = np.zeros(self.n)
for i in range(self.n):
indices = np.where(self.tags == self.unique_tags[i])
masses[i] = np.sum(m[indices])
return masses
def __len__(self):
return self.n
class PairwiseHarmonicPotential:
""" Parent class for interatomic potentials of the type
E(r_ij) = 0.5 * k_ij * (r_ij - r0_ij) ** 2 """
def __init__(self, atoms, rcut=10.):
self.atoms = atoms
self.pos0 = atoms.get_positions()
self.rcut = rcut
# build neighborlist
nat = len(self.atoms)
self.nl = NeighborList([self.rcut / 2.] * nat, skin=0., bothways=True,
self_interaction=False)
self.nl.update(self.atoms)
self.calculate_force_constants()
def calculate_force_constants(self):
msg = 'Child class needs to define a calculate_force_constants() ' \
'method which computes the force constants and stores them ' \
'in self.force_constants (as a list which contains, for every ' \
'atom, a list of the atom\'s force constants with its neighbors.'
raise NotImplementedError(msg)
def get_forces(self, atoms):
pos = atoms.get_positions()
cell = atoms.get_cell()
forces = np.zeros_like(pos)
for i, p in enumerate(pos):
indices, offsets = self.nl.get_neighbors(i)
p = pos[indices] + np.dot(offsets, cell)
r = cdist(p, [pos[i]])
v = (p - pos[i]) / r
p0 = self.pos0[indices] + np.dot(offsets, cell)
r0 = cdist(p0, [self.pos0[i]])
dr = r - r0
forces[i] = np.dot(self.force_constants[i].T, dr * v)
return forces
def get_number_of_valence_electrons(Z):
""" Return the number of valence electrons for the element with
atomic number Z, simply based on its periodic table group """
groups = [[], [1, 3, 11, 19, 37, 55, 87], [2, 4, 12, 20, 38, 56, 88],
[21, 39, 57, 89]]
for i in range(9):
groups.append(i + np.array([22, 40, 72, 104]))
for i in range(6):
groups.append(i + np.array([5, 13, 31, 49, 81, 113]))
for i, group in enumerate(groups):
if Z in group:
nval = i if i < 13 else i - 10
break
else:
raise ValueError('Z=%d not included in this dataset.' % Z)
return nval
class BondElectroNegativityModel(PairwiseHarmonicPotential):
""" Pairwise harmonic potential where the force constants are
determined using the "bond electronegativity" model, see:
* `Lyakhov, Oganov, Valle, Comp. Phys. Comm. 181 (2010) 1623-1632`__
__ https://dx.doi.org/10.1016/j.cpc.2010.06.007
* `Lyakhov, Oganov, Phys. Rev. B 84 (2011) 092103`__
__ https://dx.doi.org/10.1103/PhysRevB.84.092103
"""
def calculate_force_constants(self):
cell = self.atoms.get_cell()
pos = self.atoms.get_positions()
num = self.atoms.get_atomic_numbers()
nat = len(self.atoms)
nl = self.nl
# computing the force constants
s_norms = []
valence_states = []
r_cov = []
for i in range(nat):
indices, offsets = nl.get_neighbors(i)
p = pos[indices] + np.dot(offsets, cell)
r = cdist(p, [pos[i]])
r_ci = covalent_radii[num[i]]
s = 0.
for j, index in enumerate(indices):
d = r[j] - r_ci - covalent_radii[num[index]]
s += np.exp(-d / 0.37)
s_norms.append(s)
valence_states.append(get_number_of_valence_electrons(num[i]))
r_cov.append(r_ci)
self.force_constants = []
for i in range(nat):
indices, offsets = nl.get_neighbors(i)
p = pos[indices] + np.dot(offsets, cell)
r = cdist(p, [pos[i]])[:, 0]
fc = []
for j, ii in enumerate(indices):
d = r[j] - r_cov[i] - r_cov[ii]
chi_ik = 0.481 * valence_states[i] / (r_cov[i] + 0.5 * d)
chi_jk = 0.481 * valence_states[ii] / (r_cov[ii] + 0.5 * d)
cn_ik = s_norms[i] / np.exp(-d / 0.37)
cn_jk = s_norms[ii] / np.exp(-d / 0.37)
fc.append(np.sqrt(chi_ik * chi_jk / (cn_ik * cn_jk)))
self.force_constants.append(np.array(fc))
[docs]class SoftMutation(OffspringCreator):
"""
Mutates the structure by displacing it along the lowest (nonzero)
frequency modes found by vibrational analysis, as in:
* `Lyakhov, Oganov, Valle, Comp. Phys. Comm. 181 (2010) 1623-1632`__
__ https://dx.doi.org/10.1016/j.cpc.2010.06.007
As in the reference above, the next-lowest mode is used if the
structure has already been softmutated along the current-lowest
mode.
Parameters:
blmin: dict
The closest allowed interatomic distances on the form:
{(Z, Z*): dist, ...}, where Z and Z* are atomic numbers.
bounds: list
Lower and upper limits (in Angstrom) for the largest
atomic displacement in the structure. For a given mode,
the algorithm starts at zero amplitude and increases
it until either blmin is violated or the largest
displacement exceeds the provided upper bound).
If the largest displacement in the resulting structure
is lower than the provided lower bound, the mutant is
considered too similar to the parent and None is
returned.
calculator: ASE calculator object
The calculator to be used in the vibrational
analysis. The default is to use a calculator
based on pairwise harmonic potentials with force
constants from the "bond electronegativity"
model described in the reference above.
Any calculator with a working :func:`get_forces()`
method will work.
rcut: float
Cutoff radius in Angstrom for the pairwise harmonic
potentials.
used_modes_file: str or None
Name of json dump file where previously used
modes will be stored (and read). If None,
no such file will be used. Default is to use
the filename 'used_modes.json'.
use_tags: boolean
Whether to use the atomic tags to preserve molecular identity.
"""
def __init__(self, blmin, bounds=[0.5, 2.0],
calculator=BondElectroNegativityModel, rcut=10.,
used_modes_file='used_modes.json', use_tags=False,
verbose=False):
OffspringCreator.__init__(self, verbose)
self.blmin = blmin
self.bounds = bounds
self.calc = calculator
self.rcut = rcut
self.used_modes_file = used_modes_file
self.use_tags = use_tags
self.descriptor = 'SoftMutation'
self.used_modes = {}
if self.used_modes_file is not None:
try:
self.read_used_modes(self.used_modes_file)
except IOError:
# file doesn't exist (yet)
pass
def _get_hessian(self, atoms, dx):
"""
Returns the Hessian matrix d2E/dxi/dxj using a first-order
central difference scheme with displacements dx.
"""
N = len(atoms)
pos = atoms.get_positions()
hessian = np.zeros((3 * N, 3 * N))
for i in range(3 * N):
row = np.zeros(3 * N)
for direction in [-1, 1]:
disp = np.zeros(3)
disp[i % 3] = direction * dx
pos_disp = np.copy(pos)
pos_disp[i // 3] += disp
atoms.set_positions(pos_disp)
f = atoms.get_forces()
row += -1 * direction * f.flatten()
row /= (2. * dx)
hessian[i] = row
hessian += np.copy(hessian).T
hessian *= 0.5
atoms.set_positions(pos)
return hessian
def _calculate_normal_modes(self, atoms, dx=0.02, massweighing=False):
"""Performs the vibrational analysis."""
hessian = self._get_hessian(atoms, dx)
if massweighing:
m = np.array([np.repeat(atoms.get_masses()**-0.5, 3)])
hessian *= (m * m.T)
eigvals, eigvecs = np.linalg.eigh(hessian)
modes = {eigval: eigvecs[:, i] for i, eigval in enumerate(eigvals)}
return modes
def animate_mode(self, atoms, mode, nim=30, amplitude=1.0):
"""Returns an Atoms object showing an animation of the mode."""
pos = atoms.get_positions()
mode = mode.reshape(np.shape(pos))
animation = []
for i in range(nim):
newpos = pos + amplitude * mode * np.sin(i * 2 * np.pi / nim)
image = atoms.copy()
image.positions = newpos
animation.append(image)
return animation
def read_used_modes(self, filename):
""" Read used modes from json file. """
with open(filename, 'r') as f:
modes = json.load(f)
self.used_modes = {int(k): modes[k] for k in modes}
return
def write_used_modes(self, filename):
""" Dump used modes to json file. """
with open(filename, 'w') as f:
json.dump(self.used_modes, f)
return
def get_new_individual(self, parents):
f = parents[0]
indi = self.mutate(f)
if indi is None:
return indi, 'mutation: soft'
indi = self.initialize_individual(f, indi)
indi.info['data']['parents'] = [f.info['confid']]
return self.finalize_individual(indi), 'mutation: soft'
def mutate(self, atoms):
""" Does the actual mutation. """
a = atoms.copy()
if inspect.isclass(self.calc):
assert issubclass(self.calc, PairwiseHarmonicPotential)
calc = self.calc(atoms, rcut=self.rcut)
else:
calc = self.calc
a.set_calculator(calc)
if self.use_tags:
a = TagFilter(a)
pos = a.get_positions()
modes = self._calculate_normal_modes(a)
# Select the mode along which we want to move the atoms;
# The first 3 translational modes as well as previously
# applied modes are discarded.
keys = np.array(sorted(modes))
index = 3
confid = atoms.info['confid']
if confid in self.used_modes:
while index in self.used_modes[confid]:
index += 1
self.used_modes[confid].append(index)
else:
self.used_modes[confid] = [index]
if self.used_modes_file is not None:
self.write_used_modes(self.used_modes_file)
key = keys[index]
mode = modes[key].reshape(np.shape(pos))
# Find a suitable amplitude for translation along the mode;
# at every trial amplitude both positive and negative
# directions are tried.
mutant = atoms.copy()
amplitude = 0.
increment = 0.1
direction = 1
largest_norm = np.max(np.apply_along_axis(np.linalg.norm, 1, mode))
def expand(atoms, positions):
if isinstance(atoms, TagFilter):
a.set_positions(positions)
return a.atoms.get_positions()
else:
return positions
while amplitude * largest_norm < self.bounds[1]:
pos_new = pos + direction * amplitude * mode
pos_new = expand(a, pos_new)
mutant.set_positions(pos_new)
mutant.wrap()
too_close = atoms_too_close(mutant, self.blmin,
use_tags=self.use_tags)
if too_close:
amplitude -= increment
pos_new = pos + direction * amplitude * mode
pos_new = expand(a, pos_new)
mutant.set_positions(pos_new)
mutant.wrap()
break
if direction == 1:
direction = -1
else:
direction = 1
amplitude += increment
if amplitude * largest_norm < self.bounds[0]:
mutant = None
return mutant
[docs]class RotationalMutation(OffspringCreator):
""" Mutates a candidate by applying random rotations
to multi-atom moieties in the structure (atoms with
the same tag are considered part of one such moiety).
Only performs whole-molecule rotations, no internal
rotations.
For more information, see also:
* `Zhu Q., Oganov A.R., Glass C.W., Stokes H.T,
Acta Cryst. (2012), B68, 215-226.`__
__ https://dx.doi.org/10.1107/S0108768112017466
Parameters:
blmin: dict
The closest allowed interatomic distances on the form:
{(Z, Z*): dist, ...}, where Z and Z* are atomic numbers.
n_top: int or None
The number of atoms to optimize (None = include all).
fraction: float
Fraction of the moieties to be rotated.
tags: None or list of integers
Specifies, respectively, whether all moieties or only those
with matching tags are eligible for rotation.
min_angle: float
Minimal angle (in radians) for each rotation;
should lie in the interval [0, pi].
test_dist_to_slab: boolean
Whether also the distances to the slab
should be checked to satisfy the blmin.
"""
def __init__(self, blmin, n_top=None, fraction=0.33, tags=None,
min_angle=1.57, test_dist_to_slab=True, verbose=False):
OffspringCreator.__init__(self, verbose)
self.blmin = blmin
self.n_top = n_top
self.fraction = fraction
self.tags = tags
self.min_angle = min_angle
self.test_dist_to_slab = test_dist_to_slab
self.descriptor = 'RotationalMutation'
self.min_inputs = 1
def get_new_individual(self, parents):
f = parents[0]
indi = self.mutate(f)
if indi is None:
return indi, 'mutation: rotational'
indi = self.initialize_individual(f, indi)
indi.info['data']['parents'] = [f.info['confid']]
return self.finalize_individual(indi), 'mutation: rotational'
def mutate(self, atoms):
""" Does the actual mutation. """
N = len(atoms) if self.n_top is None else self.n_top
slab = atoms[:len(atoms) - N]
atoms = atoms[-N:]
mutant = atoms.copy()
gather_atoms_by_tag(mutant)
pos = mutant.get_positions()
tags = mutant.get_tags()
eligible_tags = tags if self.tags is None else self.tags
indices = {}
for tag in np.unique(tags):
hits = np.where(tags == tag)[0]
if len(hits) > 1 and tag in eligible_tags:
indices[tag] = hits
n_rot = int(np.ceil(len(indices) * self.fraction))
chosen_tags = np.random.choice(list(indices.keys()), size=n_rot,
replace=False)
too_close = True
count = 0
maxcount = 10000
while too_close and count < maxcount:
newpos = np.copy(pos)
for tag in chosen_tags:
p = np.copy(newpos[indices[tag]])
cop = np.mean(p, axis=0)
if len(p) == 2:
line = (p[1] - p[0]) / np.linalg.norm(p[1] - p[0])
while True:
axis = np.random.random(3)
axis /= np.linalg.norm(axis)
a = np.arccos(np.dot(axis, line))
if np.pi / 4 < a < np.pi * 3 / 4:
break
else:
axis = np.random.random(3)
axis /= np.linalg.norm(axis)
angle = self.min_angle
angle += 2 * (np.pi - self.min_angle) * np.random.random()
m = get_rotation_matrix(axis, angle)
newpos[indices[tag]] = np.dot(m, (p - cop).T).T + cop
mutant.set_positions(newpos)
mutant.wrap()
too_close = atoms_too_close(mutant, self.blmin, use_tags=True)
count += 1
if not too_close and self.test_dist_to_slab:
too_close = atoms_too_close_two_sets(slab, mutant, self.blmin)
if count == maxcount:
mutant = None
else:
mutant = slab + mutant
return mutant
[docs]class RattleRotationalMutation(CombinationMutation):
""" Combination of RattleMutation and RotationalMutation.
Parameters:
rattlemutation: OffspringCreator instance
A mutation that rattles atoms.
rotationalmutation: OffspringCreator instance
A mutation that rotates moieties.
"""
def __init__(self, rattlemutation, rotationalmutation, verbose=False):
super(RattleRotationalMutation, self).__init__(rattlemutation,
rotationalmutation,
verbose=verbose)
self.descriptor = 'rattlerotational'