Hydrogenated caged clusters of Si, Ge, and Sn and their endohedral doping with atoms: Ab initio calculations

We report results of an ab initio study on the stability of hydrogenated empty cages XnHn with X=Si, Ge, and Sn, and n=8, 10, 12, 14, 16, 18, 20, 24, and 28. All these cages have large highest-occupied-lowest-unoccupied molecular orbital (HOMO-LUMO) gaps. The HOMO-LUMO gap for Ge cages is found to be even larger than the values for Si cages, though in bulk Ge has a smaller band gap than Si. Cages with n=16 and 20 are found to be particularly stable in the form of fullerene structures. The bonding in the dodecahedral X20H20 cage is very close to sp(3) type and it leads to the highest stability of this cage with perfect icosahedral symmetry. Endohedral doping of the empty cages such as SinHn (n=10-28), with different guest atoms shows that doping can be used to manipulate the HOMO-LUMO gap with the possibility of varying their optical properties as well as to prepare species with large magnetic moments. Depending upon the guest atom, the character of the HOMO and the LUMO states and their origins either from the cage or the guest atom changes. This could lead to their applications in sensors. In contrast to the metal-encapsulated silicon-caged clusters, the embedding energy of the guest atom in the hydrogenated silicon fullerenes is small in most cases due to the weak interactions with the cage and therefore these slaved guest atoms can keep their atomic properties to a large extent. We find that atoms with closed electronic shell configurations such as Ca, Ba,... generally occupy the center of the cage. However, Be and other open electronic shell atoms tend to drift towards the wall of the cage. Doping of halogens such as iodine and alkalis such as Na can be used to produce, respectively hole and electron doping while transition-metal atoms such as V, Cr, Mn, and Fe are shown to produce atomiclike magnetic moments in many cases. In most of these cases the HOMO-LUMO gap becomes small because the guest atom orbital(s) are only partially occupied. However, for Ni and Zn the HOMO-LUMO gap is large as the hybridized d orbitals become fully occupied. An interesting finding is that the endohedral doping can lead to a higher-energy undoped cage isomer to become the lowest-energy doped isomer. Implications of this result for endohedral fullerenes of carbon are also discussed.