VASP calculation of Nudged Elastic Band (NEB)

Series of try VASP sample: “Nudged Elastic Band Method”.

Nudged Elastic Band Method

Now, we think that an atom which is located on a surface of lattice or in a lattice moves to the next position. Atoms are located at the most stable position, of which the potential energy is the lowest, and atoms are required to go up to the mountain of potential and go down to the next position, as shown in the following image.

The frequency to move to the next site is shown as:

(1)   \begin{equation*}  \nu = \nu_0 \exp \left(- \frac{\Delta E}{kT}\right)  \end{equation*}

when \Delta E is activation energy to move. The activation energy is the same as the height of the mountain. The way to calculate the activation energy by DFT is Nudged Elastic Band (NEB) calculation.

The way of NEB in VASP is to prepare the POSCAR files of the first position, the last position, and the intermediate positions. The intermediate positions are called images. These images are linked by springs. The relaxation calculation is carried out with the same force of left and right spring (shown with red color in the following figure) of each atom. I’m worry that this is just “elastic band method” and the atom move to the next position without the minimum energy path (MEP). So, springs are added to the vertical direction (shown with blue color in the following figure), and the relaxation calculation is carried out as the vertical force is also zero. This is called Nudged Elastic Band calculation. (If I misunderstand, please let me know…)

Try NEB according to the sample of VASP.

In this sample, the motion of platinum (Pt) atom located on 001 surface to the next site is calculated as shown in the following figure.

The following figure is the top view.

INCAR

The following 2 parameters are added to the relaxation calculation.

SPRING:The constant of spring. If the value is 0, each image is only allowed to move into the direction perpendicular to the current hyper-tangent, which is calculated as the normal vector between two neighboring images. When the value is negative, the nudged elastic band calculation is performed. The default value is -5.
IMAGES:The number of intermediate positions.

Sub directory

For NEB, the number of images + 2 directories are required. For example, when IMAGE = 2, “00”, “01”, “02”, “03” directories are required. “00” directory is for first position and “03” directory is for the last position. POSCAR for each position is need to be prepared in each directory. You can make POSCARs by yourself or you can use “interpolatePOSCAR” script in the sample page. I don’t understand awk well, so I made it by myself.

INCAR, KPOINTS, POTCAR is prepared in the main directory. (not need for each sub directory)

Execute

NEB calculation is performed when you run VASP in the main directory. Very easy!

Result

The relaxation calculation is performed for the intermediate position. The first and the last position are not calculated. The result is the following.

I should calculate with the odd number of images. I don’t get the energy of the top of the mountain… Anyway, the energy between 00 and 01 is about 0.85 eV.

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