import sys
import threading
import warnings
from abc import ABC, abstractmethod
import numpy as np
import ase.parallel
from ase.build import minimize_rotation_and_translation
from ase.calculators.calculator import Calculator
from ase.calculators.singlepoint import SinglePointCalculator
from ase.geometry import find_mic
from ase.optimize import MDMin
from ase.utils import lazyproperty, deprecated
from ase.utils.forcecurve import fit_images
class Spring:
def __init__(self, atoms1, atoms2, energy1, energy2, k):
self.atoms1 = atoms1
self.atoms2 = atoms2
self.energy1 = energy1
self.energy2 = energy2
self.k = k
def _find_mic(self):
pos1 = self.atoms1.get_positions()
pos2 = self.atoms2.get_positions()
# XXX If we want variable cells we will need to edit this.
mic, _ = find_mic(pos2 - pos1, self.atoms1.cell, self.atoms1.pbc)
return mic
@lazyproperty
def t(self):
return self._find_mic()
@lazyproperty
def nt(self):
return np.linalg.norm(self.t)
class NEBState:
def __init__(self, neb, images, energies):
self.neb = neb
self.images = images
self.energies = energies
def spring(self, i):
return Spring(self.images[i], self.images[i + 1],
self.energies[i], self.energies[i + 1],
self.neb.k[i])
@lazyproperty
def imax(self):
return 1 + np.argsort(self.energies[1:-1])[-1]
@property
def emax(self):
return self.energies[self.imax]
@lazyproperty
def eqlength(self):
images = self.images
beeline = (images[self.neb.nimages - 1].get_positions() -
images[0].get_positions())
beelinelength = np.linalg.norm(beeline)
return beelinelength / (self.neb.nimages - 1)
class NEBMethod(ABC):
def __init__(self, neb):
self.neb = neb
@abstractmethod
def get_tangent(self, state, spring1, spring2, i):
...
@abstractmethod
def add_image_force(self, state, tangential_force, tangent, imgforce,
spring1, spring2, i):
...
class ImprovedTangent(NEBMethod):
"""Tangent estimates are improved according to Eqs. 8-11 in paper I.
Tangents are weighted at extrema to ensure smooth transitions between
the positive and negative tangents."""
def get_tangent(self, state, spring1, spring2, i):
energies = state.energies
if energies[i + 1] > energies[i] > energies[i - 1]:
tangent = spring2.t.copy()
elif energies[i + 1] < energies[i] < energies[i - 1]:
tangent = spring1.t.copy()
else:
deltavmax = max(abs(energies[i + 1] - energies[i]),
abs(energies[i - 1] - energies[i]))
deltavmin = min(abs(energies[i + 1] - energies[i]),
abs(energies[i - 1] - energies[i]))
if energies[i + 1] > energies[i - 1]:
tangent = spring2.t * deltavmax + spring1.t * deltavmin
else:
tangent = spring2.t * deltavmin + spring1.t * deltavmax
# Normalize the tangent vector
tangent /= np.linalg.norm(tangent)
return tangent
def add_image_force(self, state, tangential_force, tangent, imgforce,
spring1, spring2, i):
imgforce -= tangential_force * tangent
# Improved parallel spring force (formula 12 of paper I)
imgforce += (spring2.nt * spring2.k - spring1.nt * spring1.k) * tangent
class ASENEB(NEBMethod):
"""Standard NEB implementation in ASE. The tangent of each image is
estimated from the spring closest to the saddle point in each
spring pair."""
def get_tangent(self, state, spring1, spring2, i):
imax = self.neb.imax
if i < imax:
tangent = spring2.t
elif i > imax:
tangent = spring1.t
else:
tangent = spring1.t + spring2.t
return tangent
def add_image_force(self, state, tangential_force, tangent, imgforce,
spring1, spring2, i):
tangent_mag = np.vdot(tangent, tangent) # Magnitude for normalizing
factor = tangent / tangent_mag
imgforce -= tangential_force * factor
imgforce -= np.vdot(
spring1.t * spring1.k -
spring2.t * spring2.k, tangent) * factor
class EB(NEBMethod):
"""Elastic band method. The full spring force is included."""
def get_tangent(self, state, spring1, spring2, i):
# Tangents are bisections of spring-directions
# (formula C8 of paper III)
tangent = spring1.t / spring1.nt + spring2.t / spring2.nt
tangent /= np.linalg.norm(tangent)
return tangent
def add_image_force(self, state, tangential_force, tangent, imgforce,
spring1, spring2, i):
imgforce -= tangential_force * tangent
energies = state.energies
# Spring forces
# Eqs. C1, C5, C6 and C7 in paper III)
f1 = -(spring1.nt -
state.eqlength) * spring1.t / spring1.nt * spring1.k
f2 = (spring2.nt - state.eqlength) * spring2.t / spring2.nt * spring2.k
if self.neb.climb and abs(i - self.neb.imax) == 1:
deltavmax = max(abs(energies[i + 1] - energies[i]),
abs(energies[i - 1] - energies[i]))
deltavmin = min(abs(energies[i + 1] - energies[i]),
abs(energies[i - 1] - energies[i]))
imgforce += (f1 + f2) * deltavmin / deltavmax
else:
imgforce += f1 + f2
def get_neb_method(neb, method):
if method == 'eb':
return EB(neb)
elif method == 'aseneb':
return ASENEB(neb)
elif method == 'improvedtangent':
return ImprovedTangent(neb)
else:
raise ValueError(f'Bad method: {method}')
class BaseNEB:
def __init__(self, images, k=0.1, climb=False, parallel=False,
remove_rotation_and_translation=False, world=None,
method='aseneb', allow_shared_calculator=False):
self.images = images
self.climb = climb
self.parallel = parallel
self.allow_shared_calculator = allow_shared_calculator
for img in images:
if len(img) != self.natoms:
raise ValueError('Images have different numbers of atoms')
if np.any(img.pbc != images[0].pbc):
raise ValueError('Images have different boundary conditions')
if np.any(img.get_atomic_numbers() !=
images[0].get_atomic_numbers()):
raise ValueError('Images have atoms in different orders')
if np.any(np.abs(img.get_cell() - images[0].get_cell()) > 1e-8):
raise NotImplementedError("Variable cell NEB is not "
"implemented yet")
self.emax = np.nan
self.remove_rotation_and_translation = remove_rotation_and_translation
self.method = method
self.neb_method = get_neb_method(self, method)
if isinstance(k, (float, int)):
k = [k] * (self.nimages - 1)
self.k = list(k)
if world is None:
world = ase.parallel.world
self.world = world
if parallel:
assert world.size == 1 or world.size % (self.nimages - 2) == 0
if self.allow_shared_calculator:
raise RuntimeError(
"Cannot use shared calculators in parallel in NEB.")
self.real_forces = None # ndarray of shape (nimages, natom, 3)
self.energies = None # ndarray of shape (nimages,)
@property
def natoms(self):
return len(self.images[0])
@property
def nimages(self):
return len(self.images)
@staticmethod
def freeze_results_on_image(atoms: ase.Atoms,
**results_to_include):
atoms.calc = SinglePointCalculator(atoms=atoms, **results_to_include)
def interpolate(self, method='linear', mic=False):
"""Interpolate the positions of the interior images between the
initial state (image 0) and final state (image -1).
method: str
Method by which to interpolate: 'linear' or 'idpp'.
linear provides a standard straight-line interpolation, while
idpp uses an image-dependent pair potential.
mic: bool
Use the minimum-image convention when interpolating.
"""
if self.remove_rotation_and_translation:
minimize_rotation_and_translation(self.images[0], self.images[-1])
interpolate(self.images, mic)
if method == 'idpp':
idpp_interpolate(images=self, traj=None, log=None, mic=mic)
@deprecated("Please use NEB's interpolate(method='idpp') method or "
"directly call the idpp_interpolate function from ase.neb")
def idpp_interpolate(self, traj='idpp.traj', log='idpp.log', fmax=0.1,
optimizer=MDMin, mic=False, steps=100):
idpp_interpolate(self, traj=traj, log=log, fmax=fmax,
optimizer=optimizer, mic=mic, steps=steps)
def get_positions(self):
positions = np.empty(((self.nimages - 2) * self.natoms, 3))
n1 = 0
for image in self.images[1:-1]:
n2 = n1 + self.natoms
positions[n1:n2] = image.get_positions()
n1 = n2
return positions
def set_positions(self, positions):
n1 = 0
for image in self.images[1:-1]:
n2 = n1 + self.natoms
image.set_positions(positions[n1:n2])
n1 = n2
def get_forces(self):
"""Evaluate and return the forces."""
images = self.images
if not self.allow_shared_calculator:
calculators = [image.calc for image in images
if image.calc is not None]
if len(set(calculators)) != len(calculators):
msg = ('One or more NEB images share the same calculator. '
'Each image must have its own calculator. '
'You may wish to use the ase.neb.SingleCalculatorNEB '
'class instead, although using separate calculators '
'is recommended.')
raise ValueError(msg)
forces = np.empty(((self.nimages - 2), self.natoms, 3))
energies = np.empty(self.nimages)
if self.remove_rotation_and_translation:
for i in range(1, self.nimages):
minimize_rotation_and_translation(images[i - 1], images[i])
if self.method != 'aseneb':
energies[0] = images[0].get_potential_energy()
energies[-1] = images[-1].get_potential_energy()
if not self.parallel:
# Do all images - one at a time:
for i in range(1, self.nimages - 1):
energies[i] = images[i].get_potential_energy()
forces[i - 1] = images[i].get_forces()
elif self.world.size == 1:
def run(image, energies, forces):
energies[:] = image.get_potential_energy()
forces[:] = image.get_forces()
threads = [threading.Thread(target=run,
args=(images[i],
energies[i:i + 1],
forces[i - 1:i]))
for i in range(1, self.nimages - 1)]
for thread in threads:
thread.start()
for thread in threads:
thread.join()
else:
# Parallelize over images:
i = self.world.rank * (self.nimages - 2) // self.world.size + 1
try:
energies[i] = images[i].get_potential_energy()
forces[i - 1] = images[i].get_forces()
except Exception:
# Make sure other images also fail:
error = self.world.sum(1.0)
raise
else:
error = self.world.sum(0.0)
if error:
raise RuntimeError('Parallel NEB failed!')
for i in range(1, self.nimages - 1):
root = (i - 1) * self.world.size // (self.nimages - 2)
self.world.broadcast(energies[i:i + 1], root)
self.world.broadcast(forces[i - 1], root)
# Save for later use in iterimages:
self.energies = energies
self.real_forces = np.zeros((self.nimages, self.natoms, 3))
self.real_forces[1:-1] = forces
state = NEBState(self, images, energies)
# Can we get rid of self.energies, self.imax, self.emax etc.?
self.imax = state.imax
self.emax = state.emax
spring1 = state.spring(0)
for i in range(1, self.nimages - 1):
spring2 = state.spring(i)
tangent = self.neb_method.get_tangent(state, spring1, spring2, i)
imgforce = forces[i - 1]
# Get overlap between PES-derived force and tangent
tangential_force = np.vdot(imgforce, tangent)
if i == self.imax and self.climb:
"""The climbing image, imax, is not affected by the spring
forces. This image feels the full PES-derived force,
but the tangential component is inverted:
see Eq. 5 in paper II."""
if self.method == 'aseneb':
tangent_mag = np.vdot(tangent, tangent) # For normalizing
imgforce -= 2 * tangential_force / tangent_mag * tangent
else:
imgforce -= 2 * tangential_force * tangent
else:
self.neb_method.add_image_force(state, tangential_force,
tangent, imgforce, spring1,
spring2, i)
spring1 = spring2
return forces.reshape((-1, 3))
def get_potential_energy(self, force_consistent=False):
"""Return the maximum potential energy along the band.
Note that the force_consistent keyword is ignored and is only
present for compatibility with ase.Atoms.get_potential_energy."""
return self.emax
def set_calculators(self, calculators):
"""Set new calculators to the images.
Parameters
----------
calculators : Calculator / list(Calculator)
calculator(s) to attach to images
- single calculator, only if allow_shared_calculator=True
list of calculators if length:
- length nimages, set to all images
- length nimages-2, set to non-end images only
"""
if not isinstance(calculators, list):
if self.allow_shared_calculator:
calculators = [calculators] * self.nimages
else:
raise RuntimeError("Cannot set shared calculator to NEB "
"with allow_shared_calculator=False")
n = len(calculators)
if n == self.nimages:
for i in range(self.nimages):
self.images[i].calc = calculators[i]
elif n == self.nimages - 2:
for i in range(1, self.nimages - 1):
self.images[i].calc = calculators[i - 1]
else:
raise RuntimeError(
'len(calculators)=%d does not fit to len(images)=%d'
% (n, self.nimages))
def __len__(self):
# Corresponds to number of optimizable degrees of freedom, i.e.
# virtual atom count for the optimization algorithm.
return (self.nimages - 2) * self.natoms
def iterimages(self):
# Allows trajectory to convert NEB into several images
for i, atoms in enumerate(self.images):
if i == 0 or i == self.nimages - 1:
yield atoms
else:
atoms = atoms.copy()
self.freeze_results_on_image(
atoms, energy=self.energies[i],
forces=self.real_forces[i])
yield atoms
[docs]class DyNEB(BaseNEB):
def __init__(self, images, k=0.1, fmax=0.05, climb=False, parallel=False,
remove_rotation_and_translation=False, world=None,
dynamic_relaxation=True, scale_fmax=0., method='aseneb',
allow_shared_calculator=False):
"""
Subclass of NEB that allows for scaled and dynamic optimizations of
images. This method, which only works in series, does not perform
force calls on images that are below the convergence criterion.
The convergence criteria can be scaled with a displacement metric
to focus the optimization on the saddle point region.
'Scaled and Dynamic Optimizations of Nudged Elastic Bands',
P. Lindgren, G. Kastlunger and A. A. Peterson,
J. Chem. Theory Comput. 15, 11, 5787-5793 (2019).
dynamic_relaxation: bool
True skips images with forces below the convergence criterion.
This is updated after each force call; if a previously converged
image goes out of tolerance (due to spring adjustments between
the image and its neighbors), it will be optimized again.
False reverts to the default NEB implementation.
fmax: float
Must be identical to the fmax of the optimizer.
scale_fmax: float
Scale convergence criteria along band based on the distance between
an image and the image with the highest potential energy. This
keyword determines how rapidly the convergence criteria are scaled.
"""
super().__init__(
images, k=k, climb=climb, parallel=parallel,
remove_rotation_and_translation=remove_rotation_and_translation,
world=world, method=method,
allow_shared_calculator=allow_shared_calculator)
self.fmax = fmax
self.dynamic_relaxation = dynamic_relaxation
self.scale_fmax = scale_fmax
if not self.dynamic_relaxation and self.scale_fmax:
msg = ('Scaled convergence criteria only implemented in series '
'with dynamic relaxation.')
raise ValueError(msg)
def set_positions(self, positions):
if not self.dynamic_relaxation:
return super().set_positions(positions)
n1 = 0
for i, image in enumerate(self.images[1:-1]):
if self.parallel:
msg = ('Dynamic relaxation does not work efficiently '
'when parallelizing over images. Try AutoNEB '
'routine for freezing images in parallel.')
raise ValueError(msg)
else:
forces_dyn = self._fmax_all(self.images)
if forces_dyn[i] < self.fmax:
n1 += self.natoms
else:
n2 = n1 + self.natoms
image.set_positions(positions[n1:n2])
n1 = n2
def _fmax_all(self, images):
"""Store maximum force acting on each image in list. This is used in
the dynamic optimization routine in the set_positions() function."""
n = self.natoms
forces = self.get_forces()
fmax_images = [
np.sqrt((forces[n * i:n + n * i] ** 2).sum(axis=1)).max()
for i in range(self.nimages - 2)]
return fmax_images
def get_forces(self):
forces = super().get_forces()
if not self.dynamic_relaxation:
return forces
"""Get NEB forces and scale the convergence criteria to focus
optimization on saddle point region. The keyword scale_fmax
determines the rate of convergence scaling."""
n = self.natoms
for i in range(self.nimages - 2):
n1 = n * i
n2 = n1 + n
force = np.sqrt((forces[n1:n2] ** 2.).sum(axis=1)).max()
n_imax = (self.imax - 1) * n # Image with highest energy.
positions = self.get_positions()
pos_imax = positions[n_imax:n_imax + n]
"""Scale convergence criteria based on distance between an
image and the image with the highest potential energy."""
rel_pos = np.sqrt(((positions[n1:n2] - pos_imax) ** 2).sum())
if force < self.fmax * (1 + rel_pos * self.scale_fmax):
if i == self.imax - 1:
# Keep forces at saddle point for the log file.
pass
else:
# Set forces to zero before they are sent to optimizer.
forces[n1:n2, :] = 0
return forces
def _check_deprecation(keyword, kwargs):
if keyword in kwargs:
warnings.warn(f'Keyword {keyword} of NEB is deprecated. '
'Please use the DyNEB class instead for dynamic '
'relaxation', FutureWarning)
[docs]class NEB(DyNEB):
def __init__(self, images, k=0.1, climb=False, parallel=False,
remove_rotation_and_translation=False, world=None,
method='aseneb', allow_shared_calculator=False, **kwargs):
"""Nudged elastic band.
Paper I:
G. Henkelman and H. Jonsson, Chem. Phys, 113, 9978 (2000).
https://doi.org/10.1063/1.1323224
Paper II:
G. Henkelman, B. P. Uberuaga, and H. Jonsson, Chem. Phys,
113, 9901 (2000).
https://doi.org/10.1063/1.1329672
Paper III:
E. L. Kolsbjerg, M. N. Groves, and B. Hammer, J. Chem. Phys,
145, 094107 (2016)
https://doi.org/10.1063/1.4961868
images: list of Atoms objects
Images defining path from initial to final state.
k: float or list of floats
Spring constant(s) in eV/Ang. One number or one for each spring.
climb: bool
Use a climbing image (default is no climbing image).
parallel: bool
Distribute images over processors.
remove_rotation_and_translation: bool
TRUE actives NEB-TR for removing translation and
rotation during NEB. By default applied non-periodic
systems
method: string of method
Choice betweeen three method:
* aseneb: standard ase NEB implementation
* improvedtangent: Paper I NEB implementation
* eb: Paper III full spring force implementation
allow_shared_calculator: bool
Allow images to share the same calculator between them.
Incompatible with parallelisation over images.
"""
for keyword in 'dynamic_relaxation', 'fmax', 'scale_fmax':
_check_deprecation(keyword, kwargs)
defaults = dict(dynamic_relaxation=False,
fmax=0.05,
scale_fmax=0.0)
defaults.update(kwargs)
# Only reason for separating BaseNEB/NEB is that we are
# deprecating dynamic_relaxation.
#
# We can turn BaseNEB into NEB once we get rid of the
# deprecated variables.
#
# Then we can also move DyNEB into ase.dyneb without cyclic imports.
# We can do that in ase-3.22 or 3.23.
super().__init__(
images, k=k, climb=climb, parallel=parallel,
remove_rotation_and_translation=remove_rotation_and_translation,
world=world, method=method,
allow_shared_calculator=allow_shared_calculator,
**defaults,
)
class IDPP(Calculator):
"""Image dependent pair potential.
See:
Improved initial guess for minimum energy path calculations.
Søren Smidstrup, Andreas Pedersen, Kurt Stokbro and Hannes Jónsson
Chem. Phys. 140, 214106 (2014)
"""
implemented_properties = ['energy', 'forces']
def __init__(self, target, mic):
Calculator.__init__(self)
self.target = target
self.mic = mic
def calculate(self, atoms, properties, system_changes):
Calculator.calculate(self, atoms, properties, system_changes)
P = atoms.get_positions()
d = []
D = []
for p in P:
Di = P - p
if self.mic:
Di, di = find_mic(Di, atoms.get_cell(), atoms.get_pbc())
else:
di = np.sqrt((Di ** 2).sum(1))
d.append(di)
D.append(Di)
d = np.array(d)
D = np.array(D)
dd = d - self.target
d.ravel()[::len(d) + 1] = 1 # avoid dividing by zero
d4 = d ** 4
e = 0.5 * (dd ** 2 / d4).sum()
f = -2 * ((dd * (1 - 2 * dd / d) / d ** 5)[..., np.newaxis] * D).sum(
0)
self.results = {'energy': e, 'forces': f}
@deprecated("SingleCalculatorNEB is deprecated. "
"Please use NEB(allow_shared_calculator=True) instead.")
class SingleCalculatorNEB(NEB):
def __init__(self, images, *args, **kwargs):
kwargs["allow_shared_calculator"] = True
super().__init__(images, *args, **kwargs)
[docs]def interpolate(images, mic=False, interpolate_cell=False,
use_scaled_coord=False):
"""Given a list of images, linearly interpolate the positions of the
interior images.
mic: bool
Map movement into the unit cell by using the minimum image convention.
interpolate_cell: bool
Interpolate the three cell vectors linearly just like the atomic
positions. Not implemented for NEB calculations!
use_scaled_coord: bool
Use scaled/internal/fractional coordinates instead of real ones for the
interpolation. Not implemented for NEB calculations!
"""
if use_scaled_coord:
pos1 = images[0].get_scaled_positions(wrap=mic)
pos2 = images[-1].get_scaled_positions(wrap=mic)
else:
pos1 = images[0].get_positions()
pos2 = images[-1].get_positions()
d = pos2 - pos1
if not use_scaled_coord and mic:
d = find_mic(d, images[0].get_cell(), images[0].pbc)[0]
d /= (len(images) - 1.0)
if interpolate_cell:
cell1 = images[0].get_cell()
cell2 = images[-1].get_cell()
cell_diff = cell2 - cell1
cell_diff /= (len(images) - 1.0)
for i in range(1, len(images) - 1):
# first the new cell, otherwise scaled positions are wrong
if interpolate_cell:
images[i].set_cell(cell1 + i * cell_diff)
new_pos = pos1 + i * d
if use_scaled_coord:
images[i].set_scaled_positions(new_pos)
else:
images[i].set_positions(new_pos)
[docs]def idpp_interpolate(images, traj='idpp.traj', log='idpp.log', fmax=0.1,
optimizer=MDMin, mic=False, steps=100):
"""Interpolate using the IDPP method. 'images' can either be a plain
list of images or an NEB object (containing a list of images)."""
if hasattr(images, 'interpolate'):
neb = images
else:
neb = NEB(images)
d1 = neb.images[0].get_all_distances(mic=mic)
d2 = neb.images[-1].get_all_distances(mic=mic)
d = (d2 - d1) / (neb.nimages - 1)
real_calcs = []
for i, image in enumerate(neb.images):
real_calcs.append(image.calc)
image.calc = IDPP(d1 + i * d, mic=mic)
with optimizer(neb, trajectory=traj, logfile=log) as opt:
opt.run(fmax=fmax, steps=steps)
for image, calc in zip(neb.images, real_calcs):
image.calc = calc
class NEBtools(NEBTools):
@deprecated('NEBtools has been renamed; please use NEBTools.')
def __init__(self, images):
NEBTools.__init__(self, images)
@deprecated('Please use NEBTools.plot_band_from_fit.')
def plot_band_from_fit(s, E, Sfit, Efit, lines, ax=None):
NEBTools.plot_band_from_fit(s, E, Sfit, Efit, lines, ax=None)
def fit0(*args, **kwargs):
raise DeprecationWarning('fit0 is deprecated. Use `fit_raw` from '
'`ase.utils.forcecurve` instead.')