Stability and bonding nature for icosahedral or planar cluster of hydrogenated boron or aluminum

Ab initio molecular orbital calculations are performed for B13−, Al13−, B12H122−, Al12H122−, Si10, and Si10H16 clusters. The highest occupied molecular orbital (HOMO) of stable and unstable clusters is bonding and antibonding orbitals, respectively. The cluster size dependences of the orbital energies are almost the same for B13− and Al13− icosahedral clusters, when the size and the energy are properly normalized. The normalized factors for size and energy are almost coincident with the ratios of those of the atomic outer s orbitals. On the other hand, the most stable size of B13− is smaller than that of Al13−, and this ratio of the stable size seems to be affected by the ratio of the sizes of the atomic outer p orbitals. As a result, B13− and Al13− icosahedral clusters have antibonding and bonding orbitals for HOMOs and so are unstable and stable, respectively. The situation for B13− and Al13− planar clusters is opposite to that discussed above for the icosahedral clusters. The orbital energies for the metallic bonding Al13− icosahedral and Si10 clusters can be reproduced by the Woods–Saxon model; however, those for the unstable B13− icosahedral and covalent bonding B12H122−, Al12H122−, and Si10H16 clusters cannot be reproduced by the Woods–Saxon model. After optimization of the parameters of the Woods–Saxon model for the Al13− icosahedral and Si10 clusters, the orbital energies are reproduced very well and the sizes and shapes of the potential are reasonable.