The nudged elastic band (NEB) is a method for finding saddle points and
minimum energy paths between known reactants and products. The method
works by optimizing a number of intermediate images along the reaction
path. Each image finds the lowest energy possible while maintaining
equal spacing to neighboring images. This constrained optimization is
done by adding spring forces along the band between images and by
projecting out the component of the force due to the potential
perpendicular to the band.
Difference from the implementation in VASP
There are a few improvements to the NEB method which
are not yet included in the current version of vasp. A new tangent definition
and a climbing image method combine to allow for the more accurate finding
of saddle points using the NEB with fewer images than the original method.
The setup and operation of this implementation can be identical to what is
described in the vasp manual under the
elastic band section.
The new tangent is implemented by default, and the climbing image method
can be turned by setting LCLIMB=.TRUE. in the INCAR file.
The climbing image is a small modification to the NEB method in which the
highest energy image is driven up to the saddle point.
This image does not feel the spring
forces along the band. Instead, the true force at this image along the tangent
is inverted. In this way, the image tries to maximize it's energy along the
band, and minimize in all other directions. When this image converges, it will
be at the exact saddle point.
Because the highest image is moved to the saddle point and it does not feel
the spring forces, the spacing of images on either side of this image will be
different. It can be important to do some minimization with the regular NEB
method before this flag is turned on, both to have a good estimate of the reaction
co-ordinate around the saddle point, and so that the highest image is close
to the saddle point. If the maximum image is initially very far from the saddle
point, and the climbing image was used from the outset, the path would develop
very different spacing on either side of the saddle point.
To use the climbing image, set LCLIMB=.True.
The graph on the right shows an NEB calculation (blue) and a climbing
image cNEB calculation* (red).
The system is an Al adatom on an Al(100) surface. The process is an exchange
between the adatom and a substraight atom, leading to adatom diffusion.
Notice how the climbing image calculation has shifted the position of
the images (by compressing the images on the left) so that one image sits
right at the saddle point.
*The cNEB energies have been shifted by 0.05 eV so that the two curves
|ICHAIN||0||Indicates which method to run. NEB (ICHAIN=0) is the default|
|IMAGES||Number of images in the band, excluding endpoints|
|SPRING||-5.0 eV/A2||Spring force between images; negative value turns on nudging|
|LCLIMB||.TRUE.||Flag to turn on the climbing image algorithm|
|LTANGENTOLD||.FALSE.||Flag to turn on the old central difference tangent|
|LDNEB||.FALSE.||Flag to turn on modified doubble nudging|
|LNEBCELL||.FALSE.||Flag to turn on SS-NEB. Used with ISIF=3 and IOPT=3.|
|JACOBIAN||(Ω/N)1/3N1/2||Controls weight of lattice to atomic motion. Ω is volume and N is the number of atoms.|