# Transition path calculation: NEB and string method

### This page gives hints on how to calculate transition paths with the ABINIT package.

##### Copyright (C) 2016-2017 ABINIT group (GG)

Mentioned in topic_GeoConstraints, help_features#4.

### Table of content:

- 1. Introduction.
- 2. Related lesson(s) of the tutorial.
- 3. Related input variables.
- 4. Selected input files.
- 5. References.

### 1. Introduction.

Similarly to the PIMD, finding minimum energy paths and in particular transition states for chemical transformations is of great importance in many different fields. In ABINIT we have implemented two different flavours based on interpolation methods [Weinan2007],[Henkelman2000], [Mills1994] and controlled by the keyword imgmov.

The calculation starts with the knowledge of the initial and final state (local minima in the configuration space) and an educated guess for the reaction pathway.

If the reaction path is not given, a linear interpolation between the reactants and final products is constructed by a series of images (configurations) that connect the two states, which are given by the keyword nimage.

The energy path that joins the series of images is then modified at each step to allow the search over the lowest energy path joining the reactants and products.

In the Nudged Elastic Band method (NEB), the images are connected through springs, with a spring constant that has to be chosen such that the images are uniformly spaced during the path search. The forces on each image come from the potential energy surface of that configuration and a spring force from the two closest configurations. The change in images is calculated by projecting out the true force perpendicular to the path and the parallel projection of the spring force with respect to the path [Henkelman2000].

The spring constant is obtained from the keyword neb_spring and the number of iterations is given by ntimimage. In the String method, the system set up is exactly the same as in the NEBM with the difference that no spring constant needs to be defined. In this case, the forces are obtained as in the NEB method from the true force perpendicular but now the configurations are equally redistributed along the path at each iteration [Weinan2007]. In both methods, the search stops if the number of predefined iterations (ntimimage) or the tolerance convergence criteria (tolimg) is reached.

As in the PIMD, each of the images can be treated in parallel and the requested parallelization mode is set with the keyword npimage.

Specified lattice parameters, or angles, or atomic positions, can be kept fixed if needed, see topic_GeoConstraints.
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### 2. Related lesson(s) of the tutorial.

- Parallelism based on "images", e.g. for the determination of transitions paths (string method), that can be activated on top of the "KGB" parallelism for force calculations.
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### 3. Related input variables.

Compulsory input variables:

... imgmov [IMaGe MOVEs]
... nimage [Number of IMAGEs]
... ntimimage [Number of TIME steps for IMAGE propagation]

Basic input variables:

... mep_solver [Minimal Energy Path ordinary differential equation SOLVER]
... tolimg [TOLerance on the mean total energy for IMaGes]

Useful input variables:

... mep_mxstep [Minimal Energy Path search: MaXimum allowed STEP size]
... neb_algo [Nudged Elastic Band ALGOrithm]
... neb_spring [Nudged Elastic Band: SPRING constant]
... npimage [Number of Processors at the IMAGE level]
... string_algo [STRING method ALGOrithm]

Input variables for experts:

... cineb_start [Climbing-Image Nudged Elastic Band: STARTing iteration]
... dynimage [DYNamics of the IMAGE]
... fxcartfactor [Forces to (X) CARTesian coordinates FACTOR]
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### 4. Selected input files.

WARNING : as of ABINITv8.6.x, the list of input files provided in the specific section of the topics Web pages is still to be reviewed/tuned. In some cases, it will be adequate, and in other cases, it might be incomplete, or perhaps even useless.
The user can find some related example input files in the ABINIT package in the directory /tests, or on the Web:

tests/v6/Input: t24.in t25.in

tests/paral/Input: t08.in
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### 5. References.

[Henkelman2000] G. Henkelman and H. Jónsson, "Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points", The Journal of chemical physics 113, 9978–9985 (2000).
[Mills1994] G. Mills and H. Jónsson, "Quantum and thermal effects in H2 dissociative adsorption: Evaluation of free energy barriers in multidimensional quantum systems", Phys. Rev. Lett. 72, 1124 (1994).
[Weinan2007] E. Weinan, W. Ren and E. Vanden-Eijnden, "Simplified and improved string method for computing the minimum energy paths in barrier-crossing events", The Journal of Chemical Physics 126, 164103 (2007).

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