# Efficient Chain-of-States Approach for Locating Transition State via Spherical Optimization

## TL;DR

This paper introduces a spherical optimization-based method to efficiently locate transition states in complex chemical reactions, significantly reducing computational cost compared to traditional chain-of-states methods.

## Contribution

The authors propose a novel spherical optimization approach that generates model end structures for NEB calculations, improving efficiency and robustness in challenging transition state searches.

## Key findings

- SOPT-based NEB consistently converges to correct MEPs in tested examples.
- The method reduces computational cost compared to regular NEB.
- It is effective even when traditional NEB fails.

## Abstract

The Chain-of-states(CoS) methods like nudge elastic band(NEB) method can be used to determine the minimum energy path (MEP) and transition state (TS) between two end local minima. However, the CoS methods are inefficient for difficult cases where the two ends are far apart with chemically insignificant part(s) in the MEP. We present here a method based on spherical optimization (SOPT), in which the SOPT method generates model end structures for CoS methods under the constraint of constant root-mean-square distance (RMSD) between two ends that is chosen to cover only the chemically significant part. We demonstrate the robustness and efficiency of our method with two examples, the CHOH dissociation channel and the first step of Aldol reaction. In both cases, the SOPT-based NEB calculations always reach the convergence to the correct MEPs with much less computational cost, whereas the regular NEB calculations fail under certain setups.