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Formation of the quasi-planar B56 boron cluster: topological path from B12 and disk aromaticity.

Formation and stability of the B56 boron cluster were investigated using a topological approach and the disk aromaticity model. An extensive global energy minimum search for the B56 system which was carried out by means of the Mexican Enhanced Genetic Algorithm (MEGA) in conjunction with density functional theory computations, confirms a quasi-planar structure as its energetically most stable isomer. Such a structural motif is derived by applying a topological leapfrog operation to a B12 form. Its high thermodynamic stability can be explained by the disk aromaticity model in which the delocalization of its π orbitals can be assigned to the levels of a particle in a circular box with the [(1σ)2 (1π)4 (1δ)4 (1φ)4 (2σ)2 (1γ)4 (2π)4 (2δ)4 (1η)4 (2φ)4 (1θ)2] electronic configuration. This π delocalization is confirmed by other delocalization indices. While the B56 has a similar electron delocalization to that of the quasi-planar B50, they have opposite magnetic ring current properties because of the symmetry selection rules of their HOMO-LUMO electronic transitions. The π delocalization in the boron clusters is larger at long distances as compared to carbon clusters at similar sizes, but such a trend is reversed at shorter distances.