A Topological Data Analysis perspective on noncovalent interactions in relativistic calculations

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 (a previous study) concluded, from the emergence of new topological features in the electron density, that relativistic effects yielded noncovalent 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 noncovalent 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.

Wasserstein Distances, Geodesics and Barycenters of Merge Trees

“…In that context, Topological Data Analysis (TDA) [32] forms a family of generic, robust, and efficient techniques whose utility has been demonstrated in a number of visualization tasks [55] for revealing the implicit structural patterns present in complex datasets. Examples of popular application fields include turbulent combustion [23,51,65], material sciences [40,53,54], nuclear energy [71], fluid dynamics [61], bioimaging [4,20,26], quantum chemistry [16,47,76] or astrophysics [103,105]. Among the data abstractions developed in TDA (see Sec.…”

The DIRAC code for relativistic molecular calculations

“…127 It is also possible to localize molecular orbitals, which is favorable for bonding analysis. 179 The visualization module in DIRAC makes it possible to export densities and their derivatives, as well as other quantities (such as property densities obtained from response calculations), to third-party visualization software commonly used by the theoretical chemistry community such as Molden, 182,183 as well as by less known analysis tools such as the Topology Toolkit (TTK), 184 with which we can perform a wide range of topological analyses, including atomsin-molecules (AIM) 185 with densities obtained with Hartree-Fock, DFT, and CCSD wave functions. DIRAC can export such data in the Gaussian cube file format, or over a custom grid.…”

Topological Analysis of Interaction Patterns in Cancer-Specific Gene Regulatory Network: Persistent Homology Approach

“…These constructions can be described by simplices of different dimensions and hence, can be studied in the framework of Balance Theory and Topological Data Analysis (TDA). From TDA, we employ the Persistent Homology (PH) analysis tool, which is based on algebraic topology and has been applied to problems in a variety of fields such as network science, physics, chemistry, biology, and medicine [18][19][20][21][22][23][24][25][26][27][27][28][29][30][31][32] . PH has been previously used to study protein-protein interaction networks to inform cancer therapy by determining the correlation between Betti numbers and the survival of cancer patients 33 .…”