Persistent Path Homology for Quantitative Analysis of Carboranes

Persistent path homology represents an advanced mathematical approach explicitly tailored for directed systems. With its remarkable ability to characterize unbalanced or asymmetrical relationships within data, this method demonstrates great promise in qualitative analysis of the intrinsic topological features present in materials and molecules. In this work, we introduce persistent path homology at the first time for carborane analysis. Intrinsic path topological features are used to predict the stability of closo-carboranes. We qualitatively explain the connection between path topological features and properties on o-C 2 B[Formula: see text]H[Formula: see text], m-C 2 B[Formula: see text]H[Formula: see text] and p-C 2 B[Formula: see text]H[Formula: see text]. The correlation coefficients between linear predictions based on persistent path homology and thermodynamic stability are higher than 0.95, and that for chemical stability are about 0.85. While the correlation coefficients based on nonlinear models are increased to 0.99 and 0.95, respectively. These results indicate that persistent path homology shows excellent capabilities in structural and stability analysis of multi-element cluster physics.