import sys
import threading
import time
import warnings
from abc import ABC, abstractmethod
import numpy as np
from scipy.integrate import cumulative_trapezoid
from scipy.interpolate import CubicSpline
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.optimize.ode import ode12r
from ase.optimize.optimize import DEFAULT_MAX_STEPS, Optimizer
from ase.optimize.precon import Precon, PreconImages
from ase.optimize.sciopt import OptimizerConvergenceError
from ase.utils import deprecated, lazyproperty
from ase.utils.abc import Optimizable
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)
@lazyproperty
def nimages(self):
return len(self.images)
@property
def precon(self):
return self.neb.precon
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):
...
def adjust_positions(self, positions):
return positions
class ImprovedTangentMethod(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 ASENEBMethod(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):
# Magnitude for normalizing. Ensure it is not 0
tangent_mag = np.vdot(tangent, tangent) or 1
factor = tangent / tangent_mag
imgforce -= tangential_force * factor
imgforce -= np.vdot(
spring1.t * spring1.k -
spring2.t * spring2.k, tangent) * factor
class FullSpringMethod(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
class BaseSplineMethod(NEBMethod):
"""
Base class for SplineNEB and String methods
Can optionally be preconditioned, as described in the following article:
S. Makri, C. Ortner and J. R. Kermode, J. Chem. Phys.
150, 094109 (2019)
https://dx.doi.org/10.1063/1.5064465
"""
def __init__(self, neb):
NEBMethod.__init__(self, neb)
def get_tangent(self, state, spring1, spring2, i):
return state.precon.get_tangent(i)
def add_image_force(self, state, tangential_force, tangent, imgforce,
spring1, spring2, i):
# project out tangential component (Eqs 6 and 7 in Paper IV)
imgforce -= tangential_force * tangent
class SplineMethod(BaseSplineMethod):
"""
NEB using spline interpolation, plus optional preconditioning
"""
def add_image_force(self, state, tangential_force, tangent, imgforce,
spring1, spring2, i):
super().add_image_force(state, tangential_force,
tangent, imgforce, spring1, spring2, i)
eta = state.precon.get_spring_force(i, spring1.k, spring2.k, tangent)
imgforce += eta
class StringMethod(BaseSplineMethod):
"""
String method using spline interpolation, plus optional preconditioning
"""
def adjust_positions(self, positions):
# fit cubic spline to positions, reinterpolate to equispace images
# note this uses the preconditioned distance metric.
fit = self.neb.spline_fit(positions)
new_s = np.linspace(0.0, 1.0, self.neb.nimages)
new_positions = fit.x(new_s[1:-1]).reshape(-1, 3)
return new_positions
def get_neb_method(neb, method):
if method == 'eb':
return FullSpringMethod(neb)
elif method == 'aseneb':
return ASENEBMethod(neb)
elif method == 'improvedtangent':
return ImprovedTangentMethod(neb)
elif method == 'spline':
return SplineMethod(neb)
elif method == 'string':
return StringMethod(neb)
else:
raise ValueError(f'Bad method: {method}')
class NEBOptimizable(Optimizable):
def __init__(self, neb):
self.neb = neb
def get_forces(self):
return self.neb.get_forces()
def get_potential_energy(self):
return self.neb.get_potential_energy()
def is_neb(self):
return True
def get_positions(self):
return self.neb.get_positions()
def set_positions(self, positions):
self.neb.set_positions(positions)
def __len__(self):
return len(self.neb)
def iterimages(self):
return self.neb.iterimages()
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, precon=None):
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')
# check periodic cell directions
cell_ok = True
for pbc, vc, vc0 in zip(img.pbc, img.cell, images[0].cell):
if pbc and np.any(np.abs(vc - vc0) > 1e-8):
cell_ok = False
if not cell_ok:
raise NotImplementedError(
"Variable cell in periodic directions "
"is not implemented yet for NEB")
self.emax = np.nan
self.remove_rotation_and_translation = remove_rotation_and_translation
if method in ['aseneb', 'eb', 'improvedtangent', 'spline', 'string']:
self.method = method
else:
raise NotImplementedError(method)
if precon is not None and method not in ['spline', 'string']:
raise NotImplementedError(f'no precon implemented: {method}')
self.precon = precon
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:
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,)
self.residuals = None # ndarray of shape (nimages,)
def __ase_optimizable__(self):
return NEBOptimizable(self)
@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, apply_constraint=None):
"""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.
apply_constraint: bool
Controls if the constraints attached to the images
are ignored or applied when setting the interpolated positions.
Default value is None, in this case the resulting constrained
positions (apply_constraint=True) are compared with unconstrained
positions (apply_constraint=False),
if the positions are not the same
the user is required to specify the desired behaviour
by setting up apply_constraint keyword argument to False or True.
"""
if self.remove_rotation_and_translation:
minimize_rotation_and_translation(self.images[0], self.images[-1])
interpolate(self.images, mic, apply_constraint=apply_constraint)
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.mep")
def idpp_interpolate(self, traj='idpp.traj', log='idpp.log', fmax=0.1,
optimizer=MDMin, mic=False, steps=100):
"""
.. deprecated:: 3.23.0
Please use :class:`~ase.mep.NEB`'s ``interpolate(method='idpp')``
method
"""
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, adjust_positions=True):
if adjust_positions:
# optional reparameterisation step: some NEB methods need to adjust
# positions e.g. string method does this to equispace the images)
positions = self.neb_method.adjust_positions(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.mep.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):
forces[i - 1] = images[i].get_forces()
energies[i] = images[i].get_potential_energy()
elif self.world.size == 1:
def run(image, energies, forces):
forces[:] = image.get_forces()
energies[:] = image.get_potential_energy()
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:
forces[i - 1] = images[i].get_forces()
energies[i] = images[i].get_potential_energy()
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)
# if this is the first force call, we need to build the preconditioners
if self.precon is None or isinstance(self.precon, (str, Precon, list)):
self.precon = PreconImages(self.precon, images)
# apply preconditioners to transform forces
# for the default IdentityPrecon this does not change their values
precon_forces = self.precon.apply(forces, index=slice(1, -1))
# 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)
self.residuals = []
for i in range(1, self.nimages - 1):
spring2 = state.spring(i)
tangent = self.neb_method.get_tangent(state, spring1, spring2, i)
# Get overlap between full PES-derived force and tangent
tangential_force = np.vdot(forces[i - 1], tangent)
# from now on we use the preconditioned forces (equal for precon=ID)
imgforce = precon_forces[i - 1]
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)
# compute the residual - with ID precon, this is just max force
residual = self.precon.get_residual(i, imgforce)
self.residuals.append(residual)
spring1 = spring2
return precon_forces.reshape((-1, 3))
def get_residual(self):
"""Return residual force along the band.
Typically this the maximum force component on any image. For
non-trivial preconditioners, the appropriate preconditioned norm
is used to compute the residual.
"""
if self.residuals is None:
raise RuntimeError("get_residual() called before get_forces()")
return np.max(self.residuals)
def get_potential_energy(self):
"""Return the maximum potential energy along the band."""
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
def spline_fit(self, positions=None, norm='precon'):
"""
Fit a cubic spline to this NEB
Args:
norm (str, optional): Norm to use: 'precon' (default) or 'euclidean'
Returns:
fit: ase.precon.precon.SplineFit instance
"""
if norm == 'precon':
if self.precon is None or isinstance(self.precon, str):
self.precon = PreconImages(self.precon, self.images)
precon = self.precon
# if this is the first call, we need to build the preconditioners
elif norm == 'euclidean':
precon = PreconImages('ID', self.images)
else:
raise ValueError(f'unsupported norm {norm}')
return precon.spline_fit(positions)
def integrate_forces(self, spline_points=1000, bc_type='not-a-knot'):
"""Use spline fit to integrate forces along MEP to approximate
energy differences using the virtual work approach.
Args:
spline_points (int, optional): Number of points. Defaults to 1000.
bc_type (str, optional): Boundary conditions, default 'not-a-knot'.
Returns:
s: reaction coordinate in range [0, 1], with `spline_points` entries
E: result of integrating forces, on the same grid as `s`.
F: projected forces along MEP
"""
# note we use standard Euclidean rather than preconditioned norm
# to compute the virtual work
fit = self.spline_fit(norm='euclidean')
forces = np.array([image.get_forces().reshape(-1)
for image in self.images])
f = CubicSpline(fit.s, forces, bc_type=bc_type)
s = np.linspace(0.0, 1.0, spline_points, endpoint=True)
dE = f(s) * fit.dx_ds(s)
F = dE.sum(axis=1)
E = -cumulative_trapezoid(F, s, initial=0.0)
return s, E, F
[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, precon=None):
"""
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, precon=precon)
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,
precon=None, **kwargs):
"""Nudged elastic band.
Paper I:
G. Henkelman and H. Jonsson, Chem. Phys, 113, 9978 (2000).
:doi:`10.1063/1.1323224`
Paper II:
G. Henkelman, B. P. Uberuaga, and H. Jonsson, Chem. Phys,
113, 9901 (2000).
:doi:`10.1063/1.1329672`
Paper III:
E. L. Kolsbjerg, M. N. Groves, and B. Hammer, J. Chem. Phys,
145, 094107 (2016)
:doi:`10.1063/1.4961868`
Paper IV:
S. Makri, C. Ortner and J. R. Kermode, J. Chem. Phys.
150, 094109 (2019)
https://dx.doi.org/10.1063/1.5064465
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 five methods:
* aseneb: standard ase NEB implementation
* improvedtangent: Paper I NEB implementation
* eb: Paper III full spring force implementation
* spline: Paper IV spline interpolation (supports precon)
* string: Paper IV string method (supports precon)
allow_shared_calculator: bool
Allow images to share the same calculator between them.
Incompatible with parallelisation over images.
precon: string, :class:`ase.optimize.precon.Precon` instance or list of
instances. If present, enable preconditioing as in Paper IV. This is
possible using the 'spline' or 'string' methods only.
Default is no preconditioning (precon=None), which is converted to
a list of :class:`ase.precon.precon.IdentityPrecon` instances.
"""
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,
precon=precon,
**defaults)
class NEBOptimizer(Optimizer):
"""
This optimizer applies an adaptive ODE solver to a NEB
Details of the adaptive ODE solver are described in paper IV
"""
def __init__(self,
neb,
restart=None, logfile='-', trajectory=None,
master=None,
append_trajectory=False,
method='ODE',
alpha=0.01,
verbose=0,
rtol=0.1,
C1=1e-2,
C2=2.0):
super().__init__(atoms=neb, restart=restart,
logfile=logfile, trajectory=trajectory,
master=master,
append_trajectory=append_trajectory)
self.neb = neb
method = method.lower()
methods = ['ode', 'static', 'krylov']
if method not in methods:
raise ValueError(f'method must be one of {methods}')
self.method = method
self.alpha = alpha
self.verbose = verbose
self.rtol = rtol
self.C1 = C1
self.C2 = C2
def force_function(self, X):
positions = X.reshape((self.neb.nimages - 2) *
self.neb.natoms, 3)
self.neb.set_positions(positions)
forces = self.neb.get_forces().reshape(-1)
return forces
def get_residual(self, F=None, X=None):
return self.neb.get_residual()
def log(self):
fmax = self.get_residual()
T = time.localtime()
if self.logfile is not None:
name = f'{self.__class__.__name__}[{self.method}]'
if self.nsteps == 0:
args = (" " * len(name), "Step", "Time", "fmax")
msg = "%s %4s %8s %12s\n" % args
self.logfile.write(msg)
args = (name, self.nsteps, T[3], T[4], T[5], fmax)
msg = "%s: %3d %02d:%02d:%02d %12.4f\n" % args
self.logfile.write(msg)
self.logfile.flush()
def callback(self, X, F=None):
self.log()
self.call_observers()
self.nsteps += 1
def run_ode(self, fmax):
try:
ode12r(self.force_function,
self.neb.get_positions().reshape(-1),
fmax=fmax,
rtol=self.rtol,
C1=self.C1,
C2=self.C2,
steps=self.max_steps,
verbose=self.verbose,
callback=self.callback,
residual=self.get_residual)
return True
except OptimizerConvergenceError:
return False
def run_static(self, fmax):
X = self.neb.get_positions().reshape(-1)
for _ in range(self.max_steps):
F = self.force_function(X)
if self.neb.get_residual() <= fmax:
return True
X += self.alpha * F
self.callback(X)
return False
def run(self, fmax=0.05, steps=DEFAULT_MAX_STEPS, method=None):
"""
Optimize images to obtain the minimum energy path
Parameters
----------
fmax - desired force tolerance
steps - maximum number of steps
"""
self.max_steps = steps
if method is None:
method = self.method
if method == 'ode':
return self.run_ode(fmax)
elif method == 'static':
return self.run_static(fmax)
else:
raise ValueError(f'unknown method: {self.method}')
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):
"""
.. deprecated:: 3.23.0
Please use ``NEB(allow_shared_calculator=True)`` instead
"""
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, apply_constraint=None):
"""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!
apply_constraint: bool
Controls if the constraints attached to the images
are ignored or applied when setting the interpolated positions.
Default value is None, in this case the resulting constrained positions
(apply_constraint=True) are compared with unconstrained positions
(apply_constraint=False), if the positions are not the same
the user is required to specify the desired behaviour
by setting up apply_constraint keyword argument to False or True.
"""
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:
if apply_constraint is None:
unconstrained_image = images[i].copy()
unconstrained_image.set_positions(new_pos,
apply_constraint=False)
images[i].set_positions(new_pos, apply_constraint=True)
try:
np.testing.assert_allclose(unconstrained_image.positions,
images[i].positions)
except AssertionError:
raise RuntimeError(f"Constraint(s) in image number {i} \n"
"affect the interpolation results.\n"
"Please specify if you want to \n"
"apply or ignore the constraints \n"
"during the interpolation \n"
"with apply_constraint argument.")
else:
images[i].set_positions(new_pos,
apply_constraint=apply_constraint)
[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):
"""
.. deprecated:: 3.23.0
Please use :class:`~ase.mep.NEBTools`.
"""
NEBTools.__init__(self, images)
@deprecated('Please use NEBTools.plot_band_from_fit.')
def plot_band_from_fit(s, E, Sfit, Efit, lines, ax=None):
"""
.. deprecated:: 3.23.0
Please use :meth:`NEBTools.plot_band_from_fit`.
"""
NEBTools.plot_band_from_fit(s, E, Sfit, Efit, lines, ax=None)