# NEB: Computing a minimum energy path

Nudged Elastic Band (NEB) is a method which can be used to find the minimum energy path (MEP) and the transition state which connects reactants to products. Reactants and products are considered in their local minima and their states need to be provided by the user.

The algorithm works as following. A set of images (i.e a specific geometric configuration of the atoms) connecting the initial (reactant) and final (product) states are linearly interpolated.

Each image is connected to the other by a spring. Then, the energy of this string of images is minimized. The perpendicular component of the spring force is removed to avoid interference with relaxation to the MEP when minimizing. If the minimization converges, one obtains a guess of the minimum energy path.

For example, for the $\sf{H+H_2}\rightarrow\sf{H_2+H}$ reaction, the blue images (see below) would be interpolations between start and end geometries. During minimization the intermediate configurations will change until the MEP is found.

NEB path for a reaction

Here I will describe how to write input files to submit an NEB calculation using TeraChem (http://www.petachem.com/products.html).

To begin one minimizes the reactant and products to get a converged geometry in their local minima.

Here is an example of the input file for TeraChem minimization:

coordinates     reactants.xyz
charge          0
method          rhf
basis           6-31g*
run             minimize
min_coordinates cartesian
end

When the simulation converges, the output file in scr/optim.xyz will contain the geometry of reactants at each optimization step. The last frame is the optimized frame.The same type of minimization is repeated for the products. The two optimized geometries are inserted into a coordinates.xyz file, first the reactant geometry then the product geometry. This file is used as input for the NEB calculation, here is the NEB input file:

coordinates     coordinates.xyz
charge          0
method          rhf
basis           6-31g*
run             ts
ts_method       neb_frozen
maxit           200
nstep           200
min_image       10
end

The main difference is the keyword ts_method used to select the NEB method with frozen end points. When the algorithm converges, the TS optimized geometry can be found in the optim.xyz file of the scr/ directory.