The Curiously Stable Cluster and its Neutral and Anionic Counterparts:  The Advantages of Planarity

The cationic, neutral, and anionic charge states of the B13 cluster are examined through the use of density functional theory. Several different isomers are studied and compared with a special emphasis given to the electronic structure of the lowest lying isomers. Included among the isomers are three which have been proposed earlier and a pair of new ones. While no minima that corresponded to a filled icosahedron could be found for the cluster, an intriguing atom-in-a-cage structure was found that is a local minimum on the cationic, neutral, and anionic surfaces. The structure found for the anionic cluster has D3h symmetry, and the 12 external boron atoms are arranged as three six-membered rings back-to-back. The planar and quasi-planar structures are seen to be more stable than three-dimensional isomers, but the ordering by stability of the planar and quasi-planar structures changes depending on the charge. Relative energies, selected geometric features, ionization potentials, and electron affinities are reported for these structures and some justification for the differences seen among the isomers is given. The planar structures benefit from π delocalization. In the case of the global minimum of the B13+ cationic cluster this delocalization is reminiscent of aromaticity.