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

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 ΔESC in bonded-ALMO-EDA, VXC in IQA, ΔECT 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.