## 4 Conclusions  
In this study, the effects of different types of defects on the properties of 2D ZnO supported by graphene were investigated using GGA-PBE+U-D2 calculations. It was found that significant changes in the heterostructure properties, such as the alteration of the interlayer adhesion strength, the creation of mid-gap states and the modulation of the electronic band structure, and catalytic activity, were caused by the formation of defects. The alteration of not only the magnitude, but also the nature of the Schottky barrier, could be affected by the formation of defects in the 2D ZnO layer of the heterostructure. The transition from the \(p\)-type Schottky barrier to \(p\)-type ohmic behavior of the vdW contacts was identified when introducing Fe\({}_{\text{Zn}}\) substitutional defects into the system. The adsorption energy of hydrogen on pristine 2 DZnO/graphene was strongly influenced by the adsorption site, with a higher adsorption energy observed at oxygen sites than at zinc sites. Site energy inhomogeneity created by the charge transfer between 2D ZnO and graphene affected the hydrogen-adsorption energy. Zinc sites exhibited more negative hydrogen-adsorption energy with increasing hydrogen coverage, indicating negligibly lower repulsive interactions between the hydrogen species. Significantly larger \(\Delta G_{\text{H}^{*}}\) values were observed at Fe sites compared to Zn sites, and the HER performance of 2 DZnO/graphene heterogeneous catalysts could be significantly affected by the distance between Fe dopants in 2D ZnO. This study brings to light the substantial influence of graphene on the electronic properties and adsorption characteristics within 2D ZnO/graphene heterostructures. These findings underscore the critical role of defect engineering in tailoring the properties of graphene-supported 2D ZnO, thus enabling advancements in efficient hydrogen storage materials and catalytic hydrogen evolution reactions (HER) based on 2D ZnO/graphene systems. **Supplementary Materials:** The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app13127243/s1](https://www.mdpi.com/article/10.3390/app13127243/s1)]([https://www.mdpi.com/article/10.3390/app13127243/s1](https://www.mdpi.com/article/10.3390/app13127243/s1)), Table S1: A comparison of adhesion energies predicted at different convergence tolerances; Figure S1: Band structure and PDOS of the spin up and spin down channels for the pristine 2 DZnO/graphene heterostructure, predicted at different convergence tolerance: 0.01 eV/A and 0.02 eV/A, respectively; Figure S2: Band structure and PDOS of the spin up and spin down channels for the 1V\({}_{\text{O}}\)-2 DZnO/graphene heterostructure, predicted at different convergence tolerance: 0.01 eV/A and 0.02 eV/A, respectively; Figure S3: Band structure and PDOS of the spin up and spin down channels for the 2V\({}_{\text{O}}\)-2 DZnO/graphene heterostructure, predicted at different convergence tolerance: 0.01 eV/A and 0.02 eV/A, respectively; Figure S4: Band structure and PDOS of the spin up and spin down channels for the 1 Fe-2 DZnO/graphene heterostructure, predicted at different convergence tolerance: 0.01 eV/A and 0.02 eV/A, respectively; Figure S5: Band structure and PDOS of the spin up and spin down channels for the 2 Fe-2 DZnO/graphene heterostructure, predicted at different convergence tolerance: 0.01 eV/A and 0.02 eV/A, respectively; Table S2: A comparison of \(z\) coordinates of carbon atoms belonging to graphene in different 2 DZnO/G systems; Figure S6: Band structure and PDOS of the spin up and spin down channels for the free-standing pristine 2 DZnO. The size of each circle corresponds proportionally to the orbital contribution of each band; Figure S7: Band structure and PDOS of the spin up and spin down channels for the free-standing 1V\({}_{\text{O}}\)-2 DZnO.