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−6σ_delo−6σ_3-ring, leading to triple aromaticity, which is unique to these clusters.