# A Topological Data Analysis Perspective on Non-Covalent Interactions in Relativistic Calculations

## TL;DR

This paper applies Topological Data Analysis to electron densities in relativistic calculations, revealing that previous claims of non-covalent interactions due to relativity are not supported by topological persistence measures.

## Contribution

It demonstrates the use of TDA in analyzing topological features of electron densities and challenges prior interpretations of relativistic effects on non-covalent interactions in a specific gold-containing molecule.

## Key findings

- TDA shows no significant topological features indicating non-covalent interactions due to relativity.
- Persistence values decrease with larger basis sets, suggesting features are not meaningful.
- Reduced density gradient analysis supports the absence of relativity-induced non-covalent interactions.

## Abstract

Topological Data Analysis (TDA) is a powerful mathematical theory, largely unexplored in theoretical chemistry. In this work we demonstrate how TDA provides new insights into topological features of electron densities and reduced density gradients, by investigating the effects of relativity on the bonding of the Au4-S-C6H4-S'-Au'4 molecule. Whereas recent analyses of this species carried out with the Quantum Theory of Atoms-In-Molecules [Anderson et al., Chem. Eur. J. 25, 2538, 2019] concluded, from the emergence of new topological features in the electron density, that relativistic effects yielded non-covalent interactions between gold and hydrogen atoms, we show from their low persistence values (which decrease with increased basis set size) these features are not significant. Further analysis of the reduced density gradient confirms no relativity-induced non-covalent interactions in Au4-S-C6H4-S'-Au'4. We argue TDA should be integrated into electronic structure analysis methods, and be considered as a basis for the development of new topology-based approaches.