The Interpenetration Index and Its Applications in Chemistry
摘要
We introduce the interpenetration index (pAB) as a unified metric for quantifying and comparing interatomic interactions across an extensive range of chemical systems. Building on the idea of representing each atom by three concentric spheres (core, valence, and van der Waals), we define the interpenetration index that measures the overlap of the outermost (van der Waals) regions of two nearby atoms. This approach yields a size-corrected parameter that places all interactions – from van der Waals contacts in noble gas dimers to multiple bonds in main-group, transition-metal, and actinide complexes – on a single, continuous scale. Through computational and experimental case studies, we show that pAB can successfully distinguish weak dispersion-driven associations, moderate hydrogen and σ-hole bonds, and strong single or multiple covalent bonds. Specifically, van der Waals systems map onto low or near-zero penetrations, while covalent and ionic bonds exhibit penetrations of 100% or higher. The method also accounts for more complex scenarios, such as proton transfer in hydrogen bonds and high-order metal–metal or actinyl bonds with unusually large overlaps. This framework offers a simple yet robust way to interpret and predict structure–property relationships in diverse chemical contexts, emphasizing that bonding should be viewed as a continuum rather than discrete categories.