Rings, Towers and Cages in Zn$_{n}$O$_{n}$ Clusters

It is shown that the transition from an elementary ZnO molecule to compact bulk wurtzite ZnO proceeds via hollow rings, towers, and cages. First principles electronic structure calculations within a gradient corrected density functional framework have been carried out to investigate the progression of geometries and electronic properties of Zn$_{n}$O$_{n}$ (n=2-12,15,16,21) clusters. It is shown that Zn$_{n}$O$_{n}$ (n=2, 3, 4, 5, 6, 7) clusters are all single, highly stable rings and that Zn$_{3}$O$_{3}$ is particularly stable. Starting at Zn$_{8}$O$_{8}$, these elementary rings begin to assemble into column structures that begin to distort at n=10. The ground states of Zn$_{12}$O$_{12}$, and Zn$_{16}$O$_{16}$ are single cages while the structure of Zn$_{11}$O$_{11}$, Zn$_{15}$O$_{15}$ and Zn$_{21}$O$_{21}$ can be described as barrels. The Zn$_{12}$O$_{12}$ cage has a high dissociation energy and a large highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) gap of 2.51 eV making it a potential candidate for cluster assemblies.