Introduction
The purpose of this Tutorial is to introduce the user to the effective use of the NEB (nudged elastic band) method for finding transition states.
It is recommended that the user be somewhat familiar with the use of the code for single configuration (non-NEB) calculations before using NEB.
Units
The default units for energy are Rydberg (1 Rydberg = 0.5 Hartree = 13.605 eV), and for distances are bohr (1 bohr = 0.52918 Ang = 0.052918 nm). All input coordinates will be in these units, though one can use the scaling functions in the code to aid in the conversions.
Input files
The code uses one main input file that the user must construct. Atom (potential+basis) files, which will need to be listed in the input file, can be obtained from atom libraries. The input file is a text-rich keyword-driven document that, once constructed, is self-documenting. The input is a sequence of keyword lines with the indicated data on following lines. Only the first few (6 or 8) characters of the keyword line are significant. The remainder of a keyword line can be used for additional documentation. The data itself, in general, is free-format. The input in the setup data section is highly structured, and requires its input in a very specific order. Other sections take their data in any order. If you miss putting something in the right place in the input, not to worry. The code will very happily process the input file, and stop when it cannot find required input in the right place. It echoes the input file as it reads it, and will politely tell you what it was looking for when it runs into a problem. Interspersed among the required inputs, are a variety of usually invisible optional input sections. The code uses a variety of defaults that can be overridden in the input file.
Brief overview of NEB calculations
Generally, NEB is used when the goal is to gain insight into mechanisms, and determine activation energies for processes such as chemical reactions or diffusion. Briefly, the method works as follows: A chain of images is generated between two minima on a potential energy surface, by interpolating the coordinates of the atoms from one minimum to another. Neighboring images interact via a harmonic potential along the direction of the path described by the chain. The forces on the ions are further modified such that the original forces parallel to the path and the inter-image spring forces perpendicular to the path are removed (this is the path "nudging"). The entire chain is then relaxed as a unit. The saddle point geometry may be refined by using the climbing image method, which works by inverting the parallel force on images that are higher in energy than either of their neighbors. This method robustly finds a saddle point on a given path, given that there are sufficient images to describe the path topology. The implementation of NEB available in the code will work with cluster, slab or bulk calculations. The example is a cluster calculation, and should be able to run on a single processor in a few hours.
Example:Reaction of ethylene and H2
Illustrated in this example is a file for doing a simple finite (cluster) calculation of the gas phase reaction of ethylene and hydrogen:
H2 + C2H4 &rarr C2H6
Before performing an NEB calculation, you need to have endpoints for the chain. Before setting up this example, I ran two separate cluster calculations corresponding to the reactant (H2 + C2H4), and product (C6H6) states of the reaction. The reactant state is assigned to the initial NEB endpoint, and the product to the final NEB endpoint. Since the NEB calculation will be subject to some constraints, I ran both endpoints subject to the same constraints. It is necessary to think ahead when setting up the endpoints for an NEB run. For example, if you are planning to have a subset of atoms frozen at specific set of coordinates, those coordinates should be the same in both endpoint calculations.
See the Cluster Tutorial for details about how to set up molecular calculations.
Command options
The NEB method is invoked by including the command option "do neb." NEB will work with most of the available command options. The "do relax" is mandatory. The "do cell" is not permitted. Both chain endpoints and all the intermediate images must have the same fixed cell. The "do dynamics" is currently not supported with NEB.
Setup phase data
The input here is the same as a regular, non-NEB run. The atom position may be superceded by later input in the neb data, atom type is not. In an NEB run, you may encounter difficulties with some functions:symmetry – Use of symmetry with NEB is tricky. Not only both endpoints, but the entire chain must have the same symmetry. While this is sometime possible, particularly for molecules, it requires careful thought.LMCC – This method assumes a fixed location for the localized charge, and current implementation does not allow for motion of the charge within the cell from image to image.
Run phase data
Again, the code will accept any of the regular input options. For this example, I use a few options in the geometry section.
First, the use of the "frame" option is especially helpful for molecular calculations.
frame 1 2 3
I have frozen atom 1, (a carbon atom), fixed the direction of the vector between the atom 1 and 2 (the 2 carbon atoms), and fixed the plane of atoms 1, 2 and 3. This eliminates translational and rotational degrees of freedom, and keeps the molecules from "running away" to avoid the saddle point during the NEB calculation. These constraints are often not necessary for a bulk calculation. Important: The initial endpoint calculations were performed using the same frame constraints.
Second, I use Accelerated Steepest Descent (ASD) for the geometry relaxation method.
gmethod ASD
The is the recommended (and the default) option for NEB relaxation.
The Broyden method, default for single image relaxations, will often fail for the more complex NEB calculations, and should not be invoked for an NEB calculation.
The calculation is allowed to run for 25 steps. This is not sufficient to converge to a saddle point, but will provide input for a further calculation, described below.
neb data
This section begins with the line "neb data" and ends with the line "end neb data". This section contains chain coordinates, and allows the user to select options to control the NEB run.
At the beginning of this section, the user first sets the number of intermediate images in the NEB chain. I have used
images 6
which results in 6 intermediate geometries to be relaxed between the fixed chain endpoints. A useful NEB chain usually needs at least 3 intermediate images. The maximum number of images is currently limited to 12 (but could be increased by redimensioning and recompiling).
Next, the code requires information about the chain endpoints. The required input is the energies (in Rydberg!) of the initial and final chain geometries, einitial, efinal and coordinates of the final chain endpoint. In this example, I have included coordinates for the initial state geometry. I have used the format atom, types, and position, and the coordinates for the initial image are identical to those in the setup phase. Different coordinates will override the setup phase coordinates. I chose this input format for convenience. The geometries are transferred directly from the lcao.geom output files of the initial preparatory runs to obtain the converged endpoints. Notice that the coordinates of the first 3 atoms in the initial and final geometries meet the same frame constraints.
Important: The code obtains the atom types from the input in the setup phase, and this is not overridden here. It is up to the user to make sure that the setup phase and neb section have consistent ordering of atom types.
Next comes optional input. I have used
antikink
which uses a more efficient definition of the path tangent. This is the recommended setting.
do setup
do iters
do force
do relax
do neb
setup data
notes
An example NEB calculation.
end_notes
dimension of system (0=cluster ... 3=bulk)
0
primitive lattice vectors
25.0000000000 0.0000000000 0.0000000000
0.0000000000 30.0000000000 0.0000000000
0.0000000000 0.0000000000 25.0000000000
grid dimensions
90 100 90
atom types
2
atom file
H = h_ps.atm
atom file
C = c.atm
number of atoms in unit cell
8
atom, type, position;
1 C 0.0000000000 0.0000000000 -1.2453000000
2 C 0.0000000000 0.0000000000 1.2489100943
3 H -1.7584758285 0.0000000000 -2.3301860262
4 H 1.7584653078 0.0100205966 -2.3301646065
5 H -1.7585064612 -0.0008441341 2.3338084172
6 H 1.7584894664 0.0097791574 2.3337979751
7 H 0.0003487181 5.6228197807 -0.7233840640
8 H 0.0003518424 5.6189301345 0.7229545354
end setup phase data
run phase input data
convergence criterion
0.000500
geometry relaxation
frame
1 2 3
gsteps
25
gmethod
ASD
end geometry relaxation
end run phase data
neb data
images
6
einitial
-29.6690869400
atom, type, position; H2 molecule plus C2H4
1 C 0.0000000000 0.0000000000 -1.2453000000
2 C 0.0000000000 0.0000000000 1.2489100943
3 H -1.7584758285 0.0000000000 -2.3301860262
4 H 1.7584653078 0.0100205966 -2.3301646065
5 H -1.7585064612 -0.0008441341 2.3338084172
6 H 1.7584894664 0.0097791574 2.3337979751
7 H 0.0003487181 5.6228197807 -0.7233840640
8 H 0.0003518424 5.6189301345 0.7229545354
efinal
-29.8262256994
atom, type, position; C2H6
1 C 0.0000000000 0.0000000000 -1.2453000000
2 C 0.0000000000 0.0000000000 1.6127026368
3 H -1.9325347853 0.0000000000 -2.0125327795
4 H 0.9274168890 -1.7039832670 -1.9973680549
5 H -1.3457830207 -1.3888791220 2.3776347814
6 H 1.8745031884 -0.4702321383 2.3799786218
7 H 1.0056057745 1.6427026553 -2.0259990122
8 H -0.5350756401 1.8581263113 2.3819664428
antikink
end neb data
Using the climb option to get closer to the saddlepoint and including intermediate image coordinates in the input file
In order to better approach the saddlepoint, use the "climb" option. It is often advisable to first run the NEB for a few steps without the climb option, to allow the chain to relax away from any possible high-energy initial configurations. Notice that the format for the coordinates in the neb data section is different this time: the chain coordinates were transferred directly from the lcao.neb_geom file output from the previous run.
do setup
do iters
do force
do relax
do neb
setup data
notes
Illustration of the "climb" option with the NEB
end_notes
dimension of system (0=cluster ... 3=bulk)
0
primitive lattice vectors
25.0000000000 0.0000000000 0.0000000000
0.0000000000 30.0000000000 0.0000000000
0.0000000000 0.0000000000 25.0000000000
grid dimensions
90 100 90
atom types
2
atom file
H = h_ps.atm
atom file
C = c.atm
number of atoms in unit cell
8
atom, type, position;
1 C 0.0000000000 0.0000000000 -1.2453000000
2 C 0.0000000000 0.0000000000 1.2489100943
3 H -1.7584758285 0.0000000000 -2.3301860262
4 H 1.7584653078 0.0100205966 -2.3301646065
5 H -1.7585064612 -0.0008441341 2.3338084172
6 H 1.7584894664 0.0097791574 2.3337979751
7 H 0.0003487181 5.6228197807 -0.7233840640
8 H 0.0003518424 5.6189301345 0.7229545354
end setup phase data
run phase input data
convergence criterion
0.000500
geometry relaxation
frame
1 2 3
gsteps
50
gmethod
ASD
end geometry relaxation
end run phase data
neb data
images, and number of atoms
6 8
einitial - energy for start-point
-29.66908694
coordinates for start-point
0.0000000000 0.0000000000 -1.2453000000
0.0000000000 0.0000000000 1.2489100943
-1.7584758285 0.0000000000 -2.3301860262
1.7584653078 0.0100205966 -2.3301646065
-1.7585064612 -0.0008441341 2.3338084172
1.7584894664 0.0097791574 2.3337979751
0.0003487181 5.6228197807 -0.7233840640
0.0003518424 5.6189301345 0.7229545354
efinal - energy for end-product
-29.82622570
coordinates for end-product
0.0000000000 0.0000000000 -1.2453000000
0.0000000000 0.0000000000 1.6127026368
-1.9325347853 0.0000000000 -2.0125327795
0.9274168890 -1.7039832670 -1.9973680549
-1.3457830207 -1.3888791220 2.3776347814
1.8745031884 -0.4702321383 2.3799786218
1.0056057745 1.6427026553 -2.0259990122
-0.5350756401 1.8581263113 2.3819664428
antikink
climb
image number in NEB
1
coordinates for this image
0.0000000000 0.0000000000 -1.2453000000
0.0000000000 0.0000000000 1.2479195030
-1.7682784683 0.0000000000 -2.3154236486
1.7500419238 -0.1247043290 -2.3383997023
-1.7493045783 -0.0109300541 2.3478654821
1.7619199452 -0.0750451854 2.3268306341
0.1890350370 4.8191631072 -0.6616504543
-0.0660714094 4.8901759400 0.7542001906
image number in NEB
2
coordinates for this image
0.0000000000 0.0000000000 -1.2453000000
0.0000000000 0.0000000000 1.2541414187
-1.7819797665 0.0000000000 -2.2930748462
1.7356773201 -0.2685628527 -2.3430631839
-1.7279616325 -0.1694757922 2.3846761056
1.7653405529 -0.1311556516 2.3339633442
0.2703519792 4.1177421581 -0.6024806639
-0.0208934101 4.0826842503 0.7962020009
image number in NEB
3
coordinates for this image
0.0000000000 0.0000000000 -1.2453000000
0.0000000000 0.0000000000 1.3180638612
-1.7938737354 0.0000000000 -2.2704139519
1.7002459021 -0.4502238630 -2.3286795024
-1.7053842796 -0.3467362060 2.4710612762
1.7840583963 -0.1906836189 2.3977228119
0.2594739311 3.4283310041 -0.7017886632
-0.0033894971 3.3388665739 0.8930933197
image number in NEB
4
coordinates for this image
0.0000000000 0.0000000000 -1.2453000000
0.0000000000 0.0000000000 1.5444241806
-1.7907946750 0.0000000000 -2.2695930873
1.6742300910 -0.5409416714 -2.3270244692
-1.7285814109 -0.4690410031 2.5205993441
1.8118215409 -0.2315843468 2.4462524518
0.2813849417 3.0236504843 -1.0905114021
-0.0573080325 2.8605801098 1.2868029533
image number in NEB
5
coordinates for this image
0.0000000000 0.0000000000 -1.2453000000
0.0000000000 0.0000000000 1.5869071781
-1.8088017879 0.0000000000 -2.2450191195
1.6305034787 -0.6796305224 -2.3191696089
-1.7125118531 -0.5948140327 2.5549212425
1.8259490870 -0.3255847865 2.4736259746
0.3494746795 2.4863018167 -1.3937245145
-0.1060411804 2.3304575331 1.6256081269
image number in NEB
6
coordinates for this image
0.0000000000 0.0000000000 -1.2453000000
0.0000000000 0.0000000000 1.6105030358
-1.8847231299 0.0000000000 -2.1180612900
1.3877240462 -1.1601595177 -2.2467239353
-1.5674330749 -0.9943891796 2.5274907833
1.8215855438 -0.5150435933 2.4533053967
0.5550633906 1.9941659708 -1.6992747907
-0.2522113539 2.0254380432 2.0768958092
end neb data
Calculations using periodic boundary conditions
When using NEB in a periodic calculation, avoid running chains across the periodic boundaries, as the results can be unpredictable.
Additional issues
NEB calculations can be quite difficult to converge. It is good to keep in mind that the primary goal is usually to find a transition state. Rather than trying to fully optimize the entire path, it is more important to monitor the behavior at or near the saddle point geometry.NEB will find the minimum energy path that is closest to the initial path geometry. You should think about what other mechanisms may occur and try to generate paths to check them. Also, if the initial path is nonsensical, the MEP will be as well.
Also see NEB Troubleshooting.