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

TL;DR

This paper introduces a topological data analysis method to identify and distinguish axial and toroidal vortices in the magnetically-induced current density of molecules, demonstrated on LiH, using scalar field topology.

Contribution

It presents a novel approach combining scalar function selection and topological data analysis to extract vortex types in molecular current densities, advancing molecular topology analysis.

Findings

Successfully distinguishes AV and TV vortices in LiH

Uses persistent topological features for robust vortex identification

Demonstrates applicability of TDA in molecular current density analysis

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 $\Omega^{B_\alpha}$ based on the velocity-gradient $\Omega$ method known in research on classical flows. The Topological Data Analysis (TDA) is then used to analyze the $\Omega^{B_\alpha}$ 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 \emph{persistent} features of the topologically-simplified $\Omega^{B_\alpha}$ scalar field.