Geometries and Electronic Properties of Transition Metal Hafnium-Doped Boron Clusters: A Computational Investigation

Abstract

The geometries, stabilities, electronic properties, and bonding properties of the Hf-doped boron clusters at the size of n = 5–11 have been investigated systematically by using density functional theory. Emphasis is placed on studies that focus on the growth-pattern behaviors, dipole moments, fragmentation energies, aromatic properties, charge-transfer characteristics, and highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gaps. The optimized geometries show that the aromatic Hf-encapsulated negative Bn structures emerges as n = 10. The calculated fragmentation energies manifest that the magic numbers of stabilities are HfBn (n = 6, 9, and 11) and the HfB11 is the most stable isomer of all different sized clusters. Natural population analysis shows that the charges transfer from Hf atom to boron framework. It should be pointed out that the remarkable charge-transfer features of HfBn clusters are obviously different from those of transitional metal (TM = W and Mo) doped Bn clusters. In addition, the calculated HOMO-LUMO gaps indicate that the HfBn (n = 5, 9, and 11) clusters have dramatically enhanced stabilities; meanwhile, the cage-like HfB11 cluster is revealed and has the largest chemical hardness.