“Ultrasmall” ZrO ₂ Nanoparticles: Disentangling Core and Surface Contributions to Structural and Electronic Properties through First-Principles Modeling

We resort to first-principles molecular dynamics (FPMD) and density functional theory (DFT) calculations at the PBE and PBE0 levels of theory to examine the structure, stability, and electronic properties of zirconia nanoparticles (NPs) with diameters ranging from 0.9 to 2.0 nm. A procedure based on the use of water molecules and an appropriate MD thermal annealing cycle is developed to generate [ZrO₂] _<i>n</i> models with different sizes (<i>n</i> = 14, 16, 43, 80, and 141) and different surface passivation states. It is shown that the rate of passivation has a significant influence on the NP structure and that NP models corresponding to saturated passivation exhibit the best structural characteristics, featuring close agreement with experimental atomic pair distribution functions (PDFs). It is also found that the Zr-O bond length varies as a function of the position of Zr and O atoms from the core to the surface of NPs, providing a descriptor capable of separating core and surface regions in ZrO₂ NPs. A core-shell structure has been demonstrated for NP models as small as 1.3 nm, while for even smaller NPs, no separation between the core and shell is possible. For the largest NP models, the core atoms show local environments closer to the cubic phase of zirconia, while the local structure of atoms close to the surface shows a large similarity with the monoclinic phase. Finally, the study of electronic properties has shown that ZrO₂ NPs exhibit very moderate quantum confinement effects. Moreover, the evolution of the band gap as a function of size does not correspond well with the <i>d</i> ^-2 trend expected from the effective mass approximation model. These differences can only be partly attributed to the shell atoms, which induce a slight decrease in the band gap compared to the contribution of the core atoms.