Beyond bond distances: a purely geometrical descriptor correlating with covalency-related bonding terms

Abstract

Quantifying covalency remains a central challenge in understanding chemical bonding. Traditional distance–bond strength correlations often fail in diverse bonding regimes, and most existing metrics require computationally demanding electronic structure analyses. Here we introduce the penetration index, a purely geometrical, size-normalized descriptor derived from atomic positions and covalent/van der Waals radii, which is related to covalency. For a broad set of systems, including diatomic molecules and ions, phosphine chalcogenides, hydrogen- and halogen-bonded complexes, and halonium ions, the penetration index shows remarkably strong correlations (R² up to 0.99) with established computational covalency descriptors such as ΔE_SC in bonded-ALMO-EDA, V_XC in IQA, ΔE_CT in ALMO-EDA, DDEC6 bond orders, and 3c–4e bonding percentages. In all cases, it outperforms bare interatomic distances, transforming scattered trends into linear relationships. The penetration index thus offers a robust, low-cost, and transferable structural metric that correlates with covalency-related bonding terms for both covalent and noncovalent interactions.