Why Boron clusters are Planar?

The origin of the unusual stability of planar and quasi-planar B12 and B13$^{+}$ clusters is explored. Our results demonstrate that in B$_{12}$ and B$_{13}^{+}$ clusters a 6$_{\pi }$-6$_{\sigma -delo}$-6$_{\sigma -3ring}$ trifurcation leads to the triple aromaticity, which is unique to these clusters. Most importantly, the H-L gaps of these clusters are strongly dependent on the strength of the interaction between the inner- and the outer-rings, which make up these clusters. Furthermore, the similarities and the differences between B$_{12}$ and other stable boron species, B$_{10}$ and B$_{14}$ clusters are also discussed. The implication of the current analysis is discussed with respect to Carbon, Silicon and Aluminum clusters.