Real Space Delocalization, Resonance and Aromaticity

When chemists want to explain a molecule’s stability and reactivity, they often refer to the concepts of delocalization, resonance, and aromaticity. Resonance is commonly discussed within the electronic structure framework of valence bond theory as the stabilizing effect of mixing different Lewis structures. Yet, most computational chemists work with delocalized molecular orbitals, which are also usually employed to explain the concept of aromaticity, a special kind of ring delocalization that shows up in cyclic planar systems which abide certain number rules. As an intuitive picture for aromaticity, an electronic ring current has been hypothesized. However, all three concepts lack a real space definition, that is not reliant on orbitals or specific wave function expansions. Here, we outline a redefinition from first principles: the concepts are of kinetic nature and related to saddle points of the all-electron probability density |Ψ|². Delocalization means that likely electron arrangements are connected via paths of high probability density in the many-electron real space. In this picture, resonance is the consideration of additional electron arrangements, which offer alternative paths of higher probability. Most notably, the concept of aromatic ring currents in absence of a magnetic field is rejected and the famous 4n+2 Hückel rule is derived from nothing but the antisymmetry of fermionic wave functions. The analysis developed in this work allows for a quantitative discussion of important chemical concepts that were previously only accessible qualitatively or restricted to specific electronic structure frameworks.