Comprehensive analysis of chemical bonding in boron clusters

We present a comprehensive analysis of chemical bonding in pure boron clusters. It is now established in joint experimental and theoretical studies that pure boron clusters are planar or quasi-planar at least up to twenty atoms. Their planarity or quasi-planarity was usually discussed in terms of pi-delocalization or pi-aromaticity. In the current article, we demonstrated that one cannot ignore sigma-electrons and that the presence of two-center two-electron (2c--2e) peripheral B--B bonds together with the globally delocalized sigma-electrons must be taken into consideration when the shape of pure boron cluster is discussed. The global aromaticity (or global antiaromaticity) can be assigned on the basis of the 4n+2 (or 4n) electron counting rule for either pi- or sigma-electrons in the planar structures. We showed that pure boron clusters could have double (sigma- and pi-) aromaticity (B3-, B4, B5+, B6(2+), B7+, B7-, B8, B(8)2-, B9-, B10, B11+, B12, and B13+), double (sigma- and pi-) antiaromaticity (B6(2-), B15), or conflicting aromaticity (B5-,sigma-antiaromatic and pi-aromatic and B14, sigma-aromatic and pi-antiaromatic). Appropriate geometric fit is also an essential factor, which determines the shape of the most stable structures. In all the boron clusters considered here, the peripheral atoms form planar cycles. Peripheral 2c--2e B--B bonds are built up from s to p hybrid atomic orbitals and this enforces the planarity of the cycle. If the given number of central atoms (1, 2, 3, or 4) can perfectly fit the central cavity then the overall structure is planar. Otherwise, central atoms come out of the plane of the cycle and the overall structure is quasi-planar.