**5. Conclusions**

We have constructed double-bubble clusters and frameworks of ZnO and GaN from a bottom up approach from cage structures analogous to fullerenes formed from hexagonal building units [15,16,22]. The four systems we have considered, (GaN)12@(ZnO)48, (ZnO)12@(GaN)48, (ZnO)12@(ZnO)48 and (GaN)12@(GaN)48, were first geometry optimized using a semi-empirical potential within the GULP code and then refined using FHI-aims (for the double bubble clusters) or VASP (for the frameworks) at the DFT level of theory using the PBEsol exchange-correlation functional. We found that although the average bond lengths of both ZnO and GaN are similar, the average bond lengths for ZnO inner bubbles were larger than the GaN inner bubbles of both the double bubble cluster systems and the frameworks. This relative size difference, we believe, means that the larger ZnO inner bubble fills in the space offered by the smaller GaN outer bubble better than the GaN counterpart. In addition, we found that the greater flexibility of the ZnO bubbles from calculations of bulk moduli, as compared with that of GaN bubbles, means that the size mismatch between the inner bubble and outer bubble is more readily accommodated by ZnO. Furthermore, the structural analysis of the pure ZnO double bubbles also showed the greater deformations. The average M-X inter-bubble bonds were found to exhibit a bi-modal distribution for both clusters and frameworks, except for the pure ZnO and (ZnO)12@(GaN)48 framework systems. These single-peak distributions were due to the larger ZnO inner bubble that has less freedom to move than in the inverse systems. The association energies of the double bubble clusters show that the systems investigated here are favourable when compared to individual bubbles, although when compared to bulk wurtzite phases, the clusters are less favourable.

The standard formation enthalpies for the framework systems are lower than those of carbon fullerenes. Therefore, we suggest that these double bubble systems should be thermodynamically accessible and could provide valuable material properties in the future.
