From planar to three-dimensional structural transition in gold clusters and the spin–orbit coupling effect

The transition from the planar to three-dimensional structures in Au clusters occurs at the cluster consisting of 15 Au atoms, which is predicted based on the first-principles density functional theory (DFT) calculations including the spin–orbital coupling. The results show that the spin–orbit coupling does not alter the relative stability of Au clusters but increases the binding energy of the cluster by about 0.08 eV/atom for all the clusters studied here. The energy gap between the highest occupied and the lowest unoccupied orbitals, on the other hand, decreases when the spin–orbit coupling is included.