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.