A many-electron perspective on aromaticity: investigating delocalization using probability density analysis

Aromaticity is a key concept in chemistry, understood as the cyclic delocalization of electrons. Yet despite its importance, it lacks an unambiguous definition, as no single measure can fully capture it. In this work, we utilize probability density analysis (PDA), which examines the topology of the many-electron probability density |Ψ|², to study aromaticity, providing a real-space perspective. Building on previous work deriving and generalizing Hückel's rule from the antisymmetry of the wave function, the electron delocalization in σ- and π-aromatic as well as antiaromatic systems is investigated. We uncover characteristic many-electron rotations, resembling the cyclic electronic delocalization associated with aromaticity. For the systems considered, aromatic compounds display independent same-spin rotations that are unaffected by the opposite-spin, whereas antiaromatic compounds exhibit coupled rotations involving opposite-spin electrons.