Eur. Phys. J. D 43, 221–224 (2007) DOI: 10.1140/epjd/e2007-00087-7 T HE EUROPEAN P HYSICAL JOURNAL D Rings, towers, cages of ZnO A.C. Reber 1 , S.N. Khanna 1 , J.S. Hunjan 2 , and M.R. Beltran 2, a 1 Physics Department, Virginia Commonwealth University, Richmond, Va. 23284-2000, USA 2 Instituto de Investigaciones en Materiales, Universidad Nacional Aut´onoma de M´ exico A.P. 70-360, C.P. 04510, M´ exico Received 24 July 2006 / Received in final form 10 October 2006 Published online 24 May 2007 – c  EDP Sciences, Societ`a Italiana di Fisica, Springer-Verlag 2007 Abstract. Theoretical electronic structure studies on (ZnO)n (n = 2–18, 21) have been carried out to show that the transition from an elementary ZnO molecule to the bulk wurtzite ZnO proceeds via hollow rings, towers, and cages. Our first principles electronic structure calculations carried out within a gradient corrected density functional framework show that small ZnnOn (n = 2–7) clusters form single, highly stable rings. Zn3O3 and the symmetric cage Zn12O12 are shown to be particularly stable clusters. Among larger clusters, the most stable are oblong cages, Zn15O15, Zn18O18, and Zn21O21, which are reminiscent of nanotubes. PACS. 31.15.Ar Ab initio calculations – 31.15.Ew Density-functional theory – 36.40.Qv Stability and fragmentation of clusters – 36.40.Cg Electronic and magnetic properties of clusters The recent discovery of one-dimensional nano-struct- ures [1,2] in semiconducting oxides has created consid- erable excitement. By controlling the experimental condi- tions, it is now possible to form nanobelts [3], nanorods [4], nanosprings [5] and a variety of other one dimensional structures [6] of varying sizes. The interest in these sys- tems is largely by the fact that the quantum confinement and the new topologies lead to novel behaviors. For ex- ample, the nanobelts [3] and nanosprings [4] are found to exhibit interesting piezoelectric behavior. The exciton binding energy is found to be substantially enhanced and many of these oxides can be doped with transition metal impurities to form magnetic semiconductors [7–10]. One of the materials that have drawn considerable interest is ZnO. The bulk has a wurtzite structure and is a wide band gap semiconductor. Are there different families of struc- tures with novel properties that can be formed at smaller sizes? The purpose of this paper is to take a bottom up approach where we consider the evolution of the struc- tures as individual formula units (ZnO) are brought to- gether. As previous calculations by Matxain et al. [11,12], Behrman [13], we also found that at the molecular sizes, the formula units first assemble to form hollow rings. We show that starting around Zn 8 O 8 , the single hollow rings begin to transform to hollow drums. An analysis of the energy binding shows that the intra-ring interactions are stronger than inter-ring bonding. As the size increases, the drums ultimately take the form of cages and oblong a e-mail: mbeltran@servidor.unam.mx cages reminiscent of nanotubes. The physical properties are shown to change discontinuously with size and many of the structures exhibit large band gaps and ionization potentials. Matxain et al. [11,12], Behrman [13] have pre- viously reported studies on Zn i O i clusters containing up to 15 units. Reporting ground state geometries and their isomers. We on the other hand, focus on the evolution of bonding and physical properties with size. The geometries for our smallest cluster, n = 1–9 reproduce fairly closely to those found earlier by Matxain et al. [11,12], but we found different structures where n = 10, 13, and 14. In an earlier work [10], the present authors have emphasized magnetic doping in on ZnOn clusters, while the present work focuses on geometric evolution and electronic prop- erties, and includes additional larger clusters. As we show, it is by going to larger sizes that one can truly understand the role of intra and inter-ring interactions and their effect on physical properties. The theoretical calculations are carried out within a density functional formalism [14] that incorporates exchange and correlation effects within the generalized gradient approximation (GGA) of Perdew, Burke and Ernzerhof [15]. In particular, the Gaussian basis sets are employed to construct atomic wave function while the cluster wave function is formed from a linear combination of atomic orbitals. All calculations were performed using the NRLMOL software [16–18]. Supplemental calculations were performed using the deMon code of Koester [19–22] et al. In each case, the basis set was supplemented by a diffuse Gaussian. For details, the reader is referred to original papers [16–22]. A Fair search of a total 200 initial