Size-dependent electronic properties of nanomaterials: How this novel class of nanodescriptors supposed to be calculated?

In this study, the influence of the size on the electronic properties (e.g. electronic energy) of three nanometal oxides: ZnO, TiO 2 , and Al 2 O 3 were investigated. The wurtzite, rutile and corundum type of clusters were selected to represent ZnO, TiO 2 , and Al 2 O 3 , respectively. To study the effect of the size on the property, we have build several molecular cluster models with different number of atoms and performed for those clusters quantum–mechanical calculations. For small clusters, up to 40 atoms, the calculations at different levels of theory, including: density functional theory (DFT), Hartree–Fock method, and the semi-empirical PM6 method were carried out. The results from ab initio and DFT calculations were utilized to validate the less time-consuming PM6 approach. The PM6 method was then employed for larger clusters. Linear regression models were developed to describe the relationships between size (number of atoms in cluster) and the electronic properties. The developed and validated methodology is transferable and could be applied for other type of nanosized clusters to calculate properties that are considered as potential nanodescriptors for nano-QSAR modelling.