Integrating the Substituent Effect into the Wade-Mingos Rules for Dicarboranes

Abstract

This work revisits the Wade-Mingos (W-M) rules in carborane chemistry by showing that substituent effects, rather than skeletal electron pairs alone, determine ground-state architectures. We performed high-throughput computational analysis of 74613 six-vertex dicarboranes (C₂B₄R₆), using the newly proposed Seed and Mortise-Tenon model, achieving a prediction accuracy of 92.8%. Through this analysis, we derived a simple substituent-counting rule (P = n_M + 1.1n_H) that incorporates substituent electronegativity via connected-atom electronegativity (CAEN) to predict energetic stability. According to this rule, the previously underestimated trigonal-bipyramidal isomer emerges as the global ground state in 89.1% of the cases, whereas the W-M-predicted octahedral form accounts for only 9.1%. This inversion can be explained by electronic stabilization involving vacant orbitals of tricoordinate boron atoms. To rationalize these trends, we classified the studied carboranes into 28 domains defined by CAEN environments. Our analysis shows that substituent effects control the electronic balance between basic and acidic subfragments, a factor neglected in classical frameworks. The W-M rules fail in 27 of the 28 domains, remaining valid only for L-CAEN substituents (P = 0). Collectively, these results establish a substituent-guided design framework and showcase how data-driven approaches can refine bonding rules in cluster chemistry.

Keywords: Boranes; Carboranes; Electron counting rules; Wade–Mingos rule.