Origin of the Unusual Stability of B12 and B13+ Clusters

A novel way to analyze the boron clusters is proposed in which the cluster is partitioned as inner and outer rings. Fragment molecular orbital analysis, based on this fragmentation, reveals that the delocalized valence electrons in B12 and B13+ clusters can be trifurcated as 6π−6σdelo−6σ3-ring, leading to triple aromaticity, which is unique to these clusters.