Quantum rules for planar boron nanoclusters

This article presents the use of free particle models to obtain quantum rules for planar boron clusters, with nuclearities in the range from seven to twenty. The information obtained from the models is being compared with electronic structure calculations based on the DFT method. Separate rules for in-plane and out-of-plane bonding are derived. In-plane bonding is precise on the cluster boundary and forms a network of alternating triangular 3c-2e bonds on the inside. The out-of-plane bonding is strongly delocalized and only depends on the global shape and size of the cluster.