The B30 boron cluster has a bowl rather than a double-ring or a triple-ring tubular structure. This bowl isomer exhibits disk-aromaticity similar to that found for B20(2-) and B19(-) clusters. We confirmed that the concept of disk-aromaticity can be applied to both planar and non-planar systems.

We performed a systematic investigation on silicon-doped boron clusters BnSi (n = 8-14) in both neutral and anionic states using quantum chemical methods. Thermochemical properties of the lowest-lying isomers of BnSi(0/-) clusters such as total atomization energies, heats of formation at 0 and 298 K, average binding energies, dissociation energies, etc. were evaluated by using the composite G4 method. The growth pattern for BnSi(0/-) with n = 8-14 is established as follows: (i) BnSi(0/-) clusters tend to be constructed by substituting B atom by Si-atom or adding one Si-impurity into the parent Bn clusters with n to be even number, and (ii) Si favors an external position of the Bn frameworks. Our theoretical results reveal that B8Si, B9Si(-), B10Si and B13Si(-) are systems with enhanced stability due to having high average binding energies, second-order difference in energies and dissociation energies. Especially, by analyzing the MOs, ELF, and ring current maps, the enhanced stability of B8Si can be rationalized in terms of a triple aromaticity.

While the stability of planar elongated pure boron clusters is determined by their […σ2(n+1) π12(n+1) π22n] electronic configuration, the rectangle model can rationalize the π electronic configuration of rectangle-shaped structures.

We investigated the structures and properties of medium size silicon-doped boron clusters in both neutral and anionic states B n Si 0/− with n = 15−24. While geometries were optimized using DFT with both TPSSh and PBE functionals, energies were determined using the coupled-cluster theory (U)CCSD(T) with the 6-311+G(d) basis set, with a calibration using the 6-311+G(3df) basis set. Average binding energies, second-order energy differences, dissociation energies, and electron detachment energies were predicted by using the (U)CCSD(T) + ZPE energies for the entire series. The growth of the B n Si series considered does not follow a regular pattern, but a few trends can be established as follows: (i) most of the lowest-energy isomers of B n Si 0/− clusters arise from a replacement of a B atom of the B n+1 species by an Si atom or an addition of one Si atom into the neutral, anionic, or dianionic B n species; (ii) the predominance of the planar structures for B n Si 0/− clusters can be interpreted as a result of an effect of either the pure boron clusters or the Si dopant or also an effect of the negative charge; and (iii) the Si dopant prefers to be placed at an outer place of the B n framework in order to exchange for, or to connect to, the peripheral B atoms in forming a low coordination number. The B 19 Si − anion whose planar motif, MOs shapes, electron distribution, and magnetic ring current are similar to those of the pure anions, B 18 2− , B 19 − , and B 20 2− , can be considered as a disk aromatic species involving 12 valence π-electrons. The MOs and electron distribution of the pseudotubes B 20 Si, B 22 Si, and B 24 Si can be interpreted by the hollow cylinder model. The first stable pseudotubular shape was found for the size B 24 Si whose thermodynamic stability is enhanced by both σ and π aromatic characters.