Persistent Magnitude for the Quantitative Analysis of the Structure and Stability of Carboranes

Abstract

Magnitude, similar to concepts like volume, cardinality or Euler characteristic, has become a key focus in combinatorics and topology. Recent advancements in topological data analysis and persistent homology have emphasized its importance. Persistent magnitude, a newly highlighted invariant introduced by Govc and Hepworth, has emerged as a notable subject of interest. In this work, we apply persistent magnitude to analyze and predict the stability of closo-carborane structures. First, we assess the stability of carboranes by employing cross-validation with different magnitude features. The Pearson correlation coefficients for stability predictions using three distinct magnitude features are 0.900, 0.882 and 0.883, respectively. These results are comparable to the Pearson correlation coefficient of 0.881 obtained when using a single feature based on persistent homology. Second, the utilization of magnitude features to predict the HOMO, LUMO and HOMO–LUMO gaps of carboranes involves conducting eight gradient boosting regressions for each scenario. The lowest correlation coefficients observed are 0.9056, 0.9385 and 0.9427, respectively. These findings highlight the promising performance of persistent magnitude features in the analysis of material structure and stability.