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.

中文翻译：

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相对论计算中非共价相互作用的拓扑数据分析视角

拓扑数据分析 (TDA) 是一种强大的数学理论，在理论化学中很大程度上尚未得到探索。在这项工作中，我们通过研究相对论对 Au4-S-C6H4-S'-Au'4 分子键合的影响，展示了 TDA 如何提供对电子密度和减小的密度梯度的拓扑特征的新见解。而最近对该物种的分析是根据分子中原子的量子理论 [Anderson et al., Chem. 欧元。J. 25, 2538, 2019] 得出结论，从电子密度中新拓扑特征的出现，相对论效应产生了金和氢原子之间的非共价相互作用，我们从它们的低持久性值（随着基组的增加而降低）大小）这些特征并不重要。对降低的密度梯度的进一步分析证实了 Au4-S-C6H4-S'-Au'4 中没有相对论诱导的非共价相互作用。我们认为 TDA 应该集成到电子结构分析方法中，并被视为开发基于拓扑的新方法的基础。