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 the harmonic approximation of 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 transition of interest. Here, we present an adaptive hybrid algorithm that integrates the CI-NEB with 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 benchmark set. A Bayesian analysis of the performance shows a median reduction in energy and force calculations of 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. These results establish this hybrid method as a highly effective tool for high-throughput automated chemical discovery of atomic rearrangements.

翻译：过渡态的精确确定对于理解反应动力学至关重要。双端点方法（如爬升图像微动弹性带方法）需同时指定初始态和终态，通过寻找两者间的最小能量路径来定位势能面上与特定过渡相关的鞍点，从而在过渡态理论的谐波近似下提供过渡态的估计。然而，此类计算可能产生高昂的计算成本，并在异常平坦或粗糙的势能面上陷入停滞。相反，仅需指定初始原子坐标集的方法（如最小模跟踪方法）虽具有高效性，但可能收敛至与目标过渡无关的鞍点。本文提出一种自适应混合算法，将爬升图像微动弹性带方法与最小模跟踪方法相结合，以实现向相关鞍点的快速收敛。该方法使用PET-MAD机器学习势能对Baker-Chan鞍点测试集进行了基准测试，并基于OptBench基准集中的Pt(111)表面七聚体岛59个过渡过程进行了验证。贝叶斯性能分析表明：对于Baker-Chan测试集，相较于爬升图像微动弹性带方法，能量和力计算量中位数减少46%[95%可信区间：-55%, -37%]；对于七聚体岛过渡过程，计算量减少28%。这些结果证明该混合方法是实现原子重排高通量自动化化学发现的高效工具。