The 13-atom encapsulated gold cage clusters

The structure and the magnetic moment of transition metal encapsulated in a Au₁₂ cage cluster have been studied by using the density functional theory. The results show that all of the transition metal atoms (TMA) can embed into the Au₁₂ cage and increase the stability of the clusters except Mn. Half of them have the I_h or O_h symmetry. The curves of binding energy have oscillation characteristics when the extra-nuclear electrons increase; the reason for this may be the interaction between parity changes of extra-nuclear electrons and Au atoms. The curves of highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gap also have oscillation characteristics when the extra-nuclear electrons increase. The binding energies of many M@Au₁₂ clusters are much larger than that of the pure Au₁₃ cluster, while the gaps of some of them are less than that of Au₁₃, so maybe Cr@Au₁₂, Nb@Au₁₂, and W@Au₁₂ clusters are most stable in fact. For magnetic calculations, some clusters are quenched totally, but the Au₁₃ cluster has the largest magnetic moment of 5 μ _B. When the number of extra-nuclear electrons of the encapsulated TMA is even, the magnetic moment of relevant M@Au₁₂ cluster is even, and so are the odd ones.