  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.
