Decoding Chemical Resonance in π-Conjugated Systems

The quantum rationale for chemical resonance and bond delocalization in π-conjugated systems remains largely uncharted. Conventional computational models and magnetic response analyses often obscure the resonance logic, reducing it to heuristic electron-bookkeeping rules or localized-orbital snapshots. Here, we introduce the π-Bond Delocalization Function (BDFπ), a density-based framework that reveals resonance bonding patterns directly from the electronic wavefunction. By decomposing the π-electron density into localized and delocalized contributions, BDFπ generates spatially resolved, chemically intuitive maps that ex-pose the internal coherence — or fragmentation — of π-conjugated frameworks. This method bypasses the need for formal π-counting or current-based indicators, instead reconstructing the structure of resonance from first principles. Applied to a set of structurally diverse (and architecturally elegant) π-systems, BDFπ offers a deeper understanding of π-electron behavior in regimes where traditional aromaticity metrics fall short. It not only clarifies where electrons go - but why they choose to stay.