The Σ delocalization in planar boron clusters

The Σ delocalization plays an important role in the stability of small boron clusters; therefore, it is important to establish under which circumstances this delocalization contributes to the aromaticity of these molecules. In this work, using electron localization function (ELF) calculations, we show that Σ and Π electrons follow different patterns of delocalization. For Σ electrons the delocalization is mainly due to the p_Σ radial overlapping which decreases with ring size, thus, considerable delocalization is expected for small rings, while for the Π subsystem, the HÜckel rule of organic chemistry works successfully regardless of the cluster size.