Sructures and stabilities B 9, B 9 + and B 9 - clusters

28 isomers of B 9 (1-10), B 9 + (1 +-8 +) and B 9 - (1 --10 -) clusters, including five isomers reported previously, have been optimized at the B3LYP/6-311+G* and MP2/6-311+G* levels of theory. To confirm the global minimum, some low-energy isomers were recalculated with CCSD(T)/AVDZ method. The CCSD(T)/AVDZ results suggest that B 9, B 9 + and B 9 - clusters have their global minima to be the D 7h-symmetry heptagonal bipyramid structure 2, the C s-symmetry wheel-shaped structure 1 + and the D gh-symmetry planar wheel-shaped structure 1 -, respectively. Natural bond orbital analysis suggests that multi-centered σ bonds and delocalized π bonding play an important role in stabilizing the most stable isomers of all the B 9/B 9 +/B 9 - clusters. The bonding nature and aromaticity of all the clusters are discussed according to their nucleus-independent chemical shifts. Moreover, the adiabatic ionization potentials and electron affinities are also calculated for various B 9 isomers, which express a proof for the clusters' stability.