## 3 Results and Discussion  
### Structural Properties  
Figure 1 shows the optimized geometrical configurations of the 2D ZnO/graphene heterostructure predicted by DFT, highlighting the effect of defects (oxygen vacancies and substitutional Fe\({}_{\text{Zn}}\) atoms) on the 2D ZnO morphology and interlayer distance. The equilibrium distance between the pristine ZnO monolayer and graphene was estimated to be 2.931 A, which was smaller than the same parameter reported by other authors (DFT-D2+U: 3.134 A [38], GGA(PBE)-D2: 3.556 A [13]). The fact that the structural parameters and electronic properties of 2D materials are usually method- and functional-dependent mainly explains this difference. However, a unique stacking configuration of a bilayer heterostructure modeled within this work could not be ruled out as a possible factor influencing the interlayer interaction. It was also observed that, independently on the defect type, 2D ZnO layers lay flat on the graphene surface. Table S2 (Supplementary Material) summarizes the \(z\)-coordinates of graphene carbon atoms in the considered systems. The observed similarity in the coordinates of carbon atoms in all models suggests that the local structure of graphene was hardly affected by the surrounding environment, including the presence of defects and doping in ZnO. When separately considering vacancy-containing and Fe-doped systems, it was evident that the stronger interaction between defective 2D ZnO and graphene, compared to that between pristine 2D ZnO and graphene, was manifested by a shorter interlayer distance. The structures, including 2 oxygen vacancies and 2 Fe\({}_{\text{Zn}}\) substitutional atoms, were characterized by the smallest values of the interlayer distance: 2.913 A and 2.912 A, respectively. This was consistent with the calculations of the adhesion energy. More specifically, the adhesion energy of pristine 2D ZnO on the graphene surface was predicted to be \(-\)0.076 eV per atom. While for the systems with 2 oxygen vacancies and 2 Fe\({}_{\text{Zn}}\) substitutional atoms, \(E_{\text{adh}}\) achieved more negative values (Table 1), pointing out a stronger interaction between the 2D ZnO layer and graphene.  
It is interesting to note that the energy cost associated with the removal of oxygen atoms and the Fe-to-Zn substitution mechanism was compensated by the elongation of the Zn-O bonds (Table 1). In the case of heterostructures comprising the oxygen vacancies, zinc atoms that surrounded the vacant site(s) tended to approach each other, thereby causing a redistribution of chemical bonds in the overall structure. On the other hand, in the Fe-containing complexes, the local formation of the Fe-O bonds, which are generally stronger and shorter than Zn-O bonds (\(-1.9\) A vs. \(-2.0\) A), was the main reason for the increase in the mean Zn-O bond length. The observed difference in the bond length can be understood in terms of atomic radii and electronic configuration. Indeed, since the iron atom has a smaller atomic radius compared to the Zn atom, it can exert a stronger attractive force on the oxygen atom's electrons compared to the zinc. Furthermore, compared to the completely filled \(d\)-orbital of the Zn atom, the partially filled \(d\)-orbital of Fe made it more effective in bonding with the oxygen (a more efficient overlap with the oxygen \(p\)-orbitals was expected). The combination of these factors explains the shorter and stronger Fe-O bond compared to the Zn-O bond.