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

Formation and stability of the B-56 boron cluster were investigated using a topological approach and the disk aromaticity model. An extensive global energy minimum search for the B-56 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 B-12 form. Its high thermodynamic stability can be explained by the disk aromaticity model in which the delocalization of its pi orbitals can be assigned to the levels of a particle in a circular box with the [(1 sigma)(2) (1 pi)(4) (1 delta)(4) (1 phi)(4) (2 sigma)(2) (1 gamma)(4) (2 pi)(4) (2 delta)(4) (1 eta)(4) (2 phi)(4) (1 theta)(2)] electronic configuration. This pi delocalization is confirmed by other delocalization indices. While the B-56 has a similar electron delocalization to that of the quasi-planar B-50, they have opposite magnetic ring current properties because of the symmetry selection rules of their HOMO-LUMO electronic transitions. The pi 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.

Automated summary

The formation and stability of the B-56 boron cluster was studied using a topological approach and the disk aromaticity model. The cluster's quasi-planar structure was confirmed as the most stable isomer, with high thermodynamic stability explained by pi delocalization. Another key finding is the cluster's larger pi delocalization at long distances compared to carbon clusters of similar sizes, with reversed trends at shorter distances.