Centre of New Technologies, University of Warsaw, S. Banacha 2c, Warsaw 02-097, Poland.
CNRS, Sorbonne Université, Laboratoire d'Informatique de Paris 6, LIP6, Paris F-75005, France.
Phys Chem Chem Phys. 2023 Feb 22;25(8):5942-5947. doi: 10.1039/d2cp05893f.
A novel strategy for extracting axial (AV) and toroidal (TV) vortices in the magnetically-induced current density (MICD) in molecular systems is introduced, and its pilot application to LiH molecule is demonstrated. It exploits differences in the topologies of AV and TV cores and involves two key steps: selecting a scalar function that can describe vortex cores in MICD and its subsequent topological analysis. The scalar function of choice is based on the velocity-gradient method known in research on classical flows. The Topological Data Analysis (TDA) is then used to analyze the scalar field. In particular, TDA robustly assigns distinct topological features of this field to different vortex types in LiH: AV to saddle-maximum separatrices which connect maxima to 2-saddles located on the domain's boundary, TV to a 1-cycle of the super-level sets of the input data. Both are extracted as the most persistent features of the topologically-simplified scalar field.
介绍了一种在分子系统中提取磁感应电流密度（MICD）中轴向（AV）和环向（TV）涡旋的新策略，并将其初步应用于 LiH 分子。该策略利用了 AV 和 TV 核拓扑结构的差异，涉及两个关键步骤：选择可以描述 MICD 中涡核的标量函数及其随后的拓扑分析。所选的标量函数基于在经典流研究中已知的速度梯度方法。然后使用拓扑数据分析（TDA）来分析标量场。特别是，TDA 将该场的不同拓扑特征稳健地分配给 LiH 中的不同涡类型：AV 分配给鞍点极大值分离物，鞍点极大值分离物将极大值与位于域边界上的 2-鞍点连接起来，TV 分配给输入数据的超水平集的一个 1-环。这两者都作为拓扑简化标量场的最持久特征被提取出来。
