The σ delocalization in planar boron clusters

The sigma 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 sigma and pi electrons follow different patterns of delocalization. For sigma electrons the delocalization is mainly due to the p(sigma) radial overlapping which decreases with ring size, thus, considerable delocalization is expected for small rings, while for the pi subsystem, the Hückel rule of organic chemistry works successfully regardless of the cluster size.