Issue 8, 2023

Topological data analysis of vortices in the magnetically-induced current density in LiH molecule

Abstract

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 ΩBα based on the velocity-gradient Ω method known in research on classical flows. The Topological Data Analysis (TDA) is then used to analyze the ΩBα 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 ΩBα scalar field.

Graphical abstract: Topological data analysis of vortices in the magnetically-induced current density in LiH molecule

Article information

Article type
Communication
Submitted
16 Dec 2022
Accepted
16 Jan 2023
First published
20 Jan 2023

Phys. Chem. Chem. Phys., 2023,25, 5942-5947

Topological data analysis of vortices in the magnetically-induced current density in LiH molecule

M. Olejniczak and J. Tierny, Phys. Chem. Chem. Phys., 2023, 25, 5942 DOI: 10.1039/D2CP05893F

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