Interpreting Ring Currents from Hückel-Guided σ- and π-Electron Delocalization in Small Boron Rings

The aromaticity of small boron clusters remains under scrutiny due to persistent inconsistencies between magnetic and electronic descriptors. Here, we reexamine B₃^-, B₃⁺, B₄, B₄²⁺, and B₄^2- using a multidimensional approach that integrates Adaptive Natural Density Partitioning, Electron Density of Delocalized Bonds, magnetically induced current density, and the z-component of the induced magnetic field. We introduce a model in which σ-aromaticity arises from two distinct delocalization topologies: a radial 2e^- σ-pathway and a tangential multicenter circuit formed by alternating filled and vacant sp² orbitals. This framework accounts for the evolution of aromaticity upon oxidation or reduction, preserving coherence between electronic structure and magnetic response. B₃^- features cooperative radial and tangential σ-delocalization, together with a delocalized 2e^- π-bond, yielding robust double aromaticity. B₃⁺ retains σ- and π-aromaticity, but only via a tangential 6e^- σ-framework, leading to a more compact delocalization and slightly attenuated ring currents. In B₄, the presence of a radial 2e^- σ-bond and a 4c-2e π-bond confers partial aromatic character, while the tangential 8e^- σ-framework satisfies the 4n rule and induces a paratropic current. In contrast, B₄²⁺ lacks the radial σ-component but retains a tangential 8e^- σ-circuit and a 2e^- 4c-2e π-bond, leading to a σ-antiaromatic and π-aromatic configuration. Finally, B₄^2-, exhibits delocalized π- and σ-circuits, yielding consistent diatropic ring currents, which confirms its fully doubly aromatic nature. Altogether, this analysis underscores the importance of resolving σ-framework topology and demonstrates that, when radial and tangential contributions are correctly distinguished, Hückel's rule remains a powerful tool for interpreting aromaticity in small boron rings.