"""Soft-mutation operator and associated tools"""
import inspect
import json
import numpy as np
from scipy.spatial.distance import cdist
from ase.data import covalent_radii
from ase.ga.offspring_creator import OffspringCreator
from ase.ga.utilities import atoms_too_close, gather_atoms_by_tag
from ase.neighborlist import NeighborList
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. This mutation hence acts in a deterministic way, in contrast
to most other genetic operators.
If you find this implementation useful in your work,
please consider citing:
`Van den Bossche, Gronbeck, Hammer, J. Chem. Theory Comput. 14 (2018)`__
__ https://dx.doi.org/10.1021/acs.jctc.8b00039
in addition to the paper mentioned above.
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 OSError:
# 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) as fd:
modes = json.load(fd)
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 fd:
json.dump(self.used_modes, fd)
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.calc = 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