The nudged elastic band (NEB) method is utilized to find reaction paths (RPs) using discretized intermediate structures called “images” between a reactant and a product. In fact, NEB calculations do not always converge because of the bent of RPs. Mathematically, more images are needed for complex curves, and here, we focused on the curvature. In this study, we propose a new method for calculating the curvature of the RPs as well as a method for weighting the spring constant of the NEB with the curvature, which we named the curvature weighted NEB (CW-NEB) method. In addition, we will propose the CW-NEB method with the climbing image (CI) method (CW-CI-NEB). To show the efficiency of our method, calculations for the ene-reaction of the CW-CI-NEB method were performed and compared with those of the CI-NEB methods. The CW-CI-NEB methods converged in shorter iteration times than the CI-NEB calculation, which was found by gathering the bent of RPs.

中文翻译：

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使用黎曼曲率的曲率加权微动弹性带方法

轻推弹性带 (NEB) 方法用于使用反应物和产物之间称为“图像”的离散化中间结构来寻找反应路径 (RP)。事实上，由于 RP 的弯曲，NEB 计算并不总是收敛。在数学上，复杂的曲线需要更多的图像，在这里，我们关注曲率。在这项研究中，我们提出了一种计算 RP 曲率的新方法以及一种用曲率对 NEB 的弹簧常数进行加权的方法，我们将其命名为曲率加权 NEB (CW-NEB) 方法。此外，我们将提出 CW-NEB 方法和爬升图像 (CI) 方法 (CW-CI-NEB)。为了显示我们方法的效率，对 CW-CI-NEB 方法的烯反应进行了计算，并与 CI-NEB 方法进行了比较。