Smallest Fullerene-like Structures of Boron with Cr, Mo, and W Encapsulation

Using density functional theory calculations, we study doping of a Cr, Mo, and W atom in boron clusters in the size range of 18-24 atoms and report the finding of metal atom encapsulated fullerene-like cage structures with 20 to 24 boron atoms in contrast to a fullerene-like structure of pure boron with 40 atoms. Our results show that bicapped drum-shaped structures are favored for neutral Cr@B$_{18}$, Mo@B$_{20}$, and W@B$_{20}$ clusters whereas a drum-shaped structure is preferred for neutral, cation, and anion of Mo@B$_{18}$ and W@B$_{18}$. Further, we find that B$_{20}$ is the smallest cage for Cr encapsulation, while B$_{22}$ is the smallest symmetric cage for Mo and W encapsulation and it is magic. Symmetric cage structures are also obtained for Mo@B$_{24}$ and W@B$_{24}$. A detailed analysis of the bonding character and molecular orbitals suggests that Cr@B$_{18}$, Cr@B$_{20}$, M@B$_{22}$ (M = Cr, Mo, and W) and M@B$_{24}$ (M = Mo and W) cages are stabilized with 18 $\pi$-bonded valence electrons whereas the drum-shaped M@B$_{18}$ (M = Mo and W) clusters are stabilized by 20 $\pi$-bonded valence electrons. Calculations with PBE0 functional in Gaussian 09 code show that in all cases of neutral clusters there is a large highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gap. In some cases the lowest energy isomer of the charged clusters is different from the one for the neutral. We discuss the calculated infrared and Raman spectra for the neutral and cation clusters as well as the electronic structure of the anion clusters. Also we report results for isoelectronic anion and neutral clusters doped with V, Nb, and Ta which are generally similar to those obtained for Mo and W doped clusters. These results would be helpful to confirm the formation of these doped boron clusters experimentally.