# Nudged elastic band¶

The Nudged Elastic Band method is a technique for finding transition paths (and corresponding energy barriers) between given initial and final states. The method involves constructing a “chain” of “replicas” or “images” of the system and relaxing them in a certain way.

Relevant literature References:

1. H. Jonsson, G. Mills, and K. W. Jacobsen, in ‘Classical and Quantum Dynamics in Condensed Phase Systems’, edited by B. J. Berne, G. Cicotti, and D. F. Coker, World Scientific, 1998 [standard formulation]

2. ‘Improved Tangent Estimate in the NEB method for Finding Minimum Energy Paths and Saddle Points’, G. Henkelman and H. Jonsson, J. Chem. Phys. 113, 9978 (2000) [improved tangent estimates]

3. ‘A Climbing-Image NEB Method for Finding Saddle Points and Minimum Energy Paths’, G. Henkelman, B. P. Uberuaga and H. Jonsson, J. Chem. Phys. 113, 9901 (2000)

4. ‘Improved initial guess for minimum energy path calculations.’, S. Smidstrup, A. Pedersen, K. Stokbro and H. Jonsson, J. Chem. Phys. 140, 214106 (2014)

## The NEB class¶

This module defines one class:

class ase.neb.NEB(images, k=0.1, fmax=0.05, climb=False, parallel=False, remove_rotation_and_translation=False, world=None, method='aseneb', dynamic_relaxation=False, scale_fmax=0.0)[source]

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

dynamic_relaxation: bool

TRUE calculates the norm of the forces acting on each image in the band. An image is optimized only if its norm is above the convergence criterion. The list fmax_images is updated every 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. This routine can speed up calculations if convergence is non-uniform. Convergence criterion should be the same as that given to the optimizer. Not efficient when parallelizing over images.

scale_fmax: float

Scale convergence criteria along band based on the distance between a state and the state with the highest potential energy.

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

Example of use, between initial and final state which have been previously saved in A.traj and B.traj:

from ase import io
from ase.neb import NEB
from ase.optimize import MDMin
# Read initial and final states:
# Make a band consisting of 5 images:
images = [initial]
images += [initial.copy() for i in range(3)]
images += [final]
neb = NEB(images)
# Interpolate linearly the potisions of the three middle images:
neb.interpolate()
# Set calculators:
for image in images[1:4]:
image.set_calculator(MyCalculator(...))
# Optimize:
optimizer = MDMin(neb, trajectory='A2B.traj')
optimizer.run(fmax=0.04)


Be sure to use the copy method (or similar) to create new instances of atoms within the list of images fed to the NEB. Do not use something like [initial for i in range(3)], as it will only create references to the original atoms object.

Notice the use of the interpolate() method to obtain an initial guess for the path from A to B.

## Interpolation¶

NEB.interpolate()[source]

Interpolate path linearly from initial to final state.

NEB.interpolate('idpp')[source]

From a linear interpolation, create an improved path from initial to final state using the IDPP approach [4].

NEB.idpp_interpolate()[source]

Generate an idpp pathway from a set of images. This differs from above in that an initial guess for the IDPP, other than linear interpolation can be provided.

Only the internal images (not the endpoints) need have calculators attached.

ase.optimize:

Information about energy minimization (optimization). Note that you cannot use the default optimizer, BFGSLineSearch, with NEBs. (This is the optimizer imported when you import QuasiNewton.) If you would like a quasi-newton optimizer, use BFGS instead.

ase.calculators:

How to use calculators.

Note

If there are $$M$$ images and each image has $$N$$ atoms, then the NEB object behaves like one big Atoms object with $$MN$$ atoms, so its get_positions() method will return a $$MN \times 3$$ array.

## Trajectories¶

The code:

from ase.optimize import BFGS
opt = BFGS(neb, trajectory='A2B.traj')


will write all images to one file. The Trajectory object knows about NEB calculations, so it will write $$M$$ images with $$N$$ atoms at every iteration and not one big configuration containing $$MN$$ atoms.

The result of the latest iteration can now be analysed with this command: ase gui A2B.traj@-5:.

For the example above, you can write the images to individual trajectory files like this:

for i in range(1, 4):
opt.attach(io.Trajectory('A2B-%d.traj' % i, 'w', images[i]))


The result of the latest iteration can be analysed like this: