Enhanced Climbing Image Nudged Elastic Band method with Hessian Eigenmode Alignment

2026-01-19

AI Summary

This work proposes an adaptive hybrid algorithm that dynamically integrates the climbing image nudged elastic band (CI-NEB) and the minimum mode following (MMF) methods to overcome the limitations of conventional transition state search techniques. While traditional double-ended approaches like CI-NEB are computationally expensive and prone to stagnation on complex potential energy surfaces, single-ended methods such as MMF, though efficient, may converge to irrelevant saddle points. The proposed method employs Hessian eigenvector alignment with the reaction path direction and an intelligent switching strategy to balance relevance and efficiency. Coupled with a machine-learned potential (PET-MAD) and Bayesian performance analysis, the algorithm reduces the median number of energy and force evaluations by 46% on the Baker–Chan benchmark set and by 28% across 59 migration cases of Pt(111) heptamer islands, significantly accelerating high-throughput discovery of atomic rearrangements.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Matrix & Tensor Methods
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Accurate determination of transition states is central to an understanding of reaction kinetics. Double-endpoint methods where both initial and final states are specified, such as the climbing image nudged elastic band (CI-NEB), identify the minimum energy path between the two and thereby the saddle point on the energy surface that is relevant for the given transition, thus providing an estimate of the transition state within harmonic transition state theory. Such calculations can, however, incur high computational costs and may suffer stagnation on exceptionally flat or rough energy surfaces. Conversely, methods that only require specification of an initial set of atomic coordinates, such as the minimum mode following (MMF) method, offer efficiency but can converge on saddle points that are not relevant for the transition of interest. Here, we present an adaptive hybrid algorithm that switches between the CI-NEB and the MMF method so as to get faster convergence to the relevant saddle point. The method is benchmarked for the Baker-Chan (BC) saddle point test set using the PET-MAD machine-learned potential as well as 59 transitions of a heptamer island on Pt(111) from the OptBench set. A Bayesian analysis of the performance shows a median reduction of energy and force calculations by 46% [95% CrI: -55%, -37%] relative to CI-NEB for the BC set, while a 28% reduction is found for the transitions of the heptamer island. Calculations of the BC set where a simple switch from the CI-NEB to the MMF method is made when the magnitude of the atomic forces drops below 0.5 eV/AA requires 30% more force calculations than the OCI-NEB algorithm. These results show that an adaptive hybrid method mixing CI-NEB and MMF can be a highly efficient tool for high-throughput automated chemical discovery of atomic rearrangements.

Problem

• transition state
• saddle point
• reaction kinetics
• energy surface
• minimum energy path

Innovation

• CI-NEB
• minimum mode following
• Hessian eigenmode alignment
• transition state search
• adaptive hybrid algorithm