## 3 Results and Discussion
### Hydrogen-Adsorption Properties  
The changes in electronic properties induced by oxygen vacancies and Fe dopants were expected to enhance the sensitivity and catalytic activity of the 2D ZnO/graphene system, making it a promising material for sensing and catalytic applications. To verify this, hydrogen adsorption--the Volmer step of the hydrogen evolution reaction--onto pristine and defective 2D ZnO/graphene heterostructures was investigated as a model chemical process. The focus was on estimating the free energy of hydrogen adsorption (\(\Delta G_{\text{H}^{\ast}}\)), which is believed to be an essential factor describing the HER performance of catalysts. To accomplish this, the value of \(\Delta G_{\text{H}^{\ast}}\) was computed using the following equation: \(\Delta G_{\text{H}^{\ast}}=\Delta E_{\text{H}^{\ast}}+0.24\) eV. Here, \(\Delta E_{\text{H}^{\ast}}\) represents the hydrogen-adsorption energy, whereas the term 0.24 eV accounts for the changes in entropy and zero-point energy (ZPE) between gaseous and absorbed hydrogen. All possible adsorption sites were checked (please see Figure 7a, where the numbers designate the considered zinc and oxygen sites). The heatmaps presented in Figure 7b,c suggest that the hydrogen-adsorption energy is strongly influenced by the nature of the adsorption site of the pristine 2D ZnO/graphene heterostructure, with the oxygen sites exhibiting greater adsorption energy compared to the zinc sites. Oxygen sites bind to hydrogen atoms more strongly than zinc ones because of the difference in their electronegativities. Whereas the highly electronegative oxygen has a  
Figure 6: Spin-density distribution plot of (**a**) pristine 2D ZnO/graphene, (**b**) 1V\({}_{\text{O}}\)-2 DZnO/graphene, (**c**) 2V\({}_{\text{O}}\)-2 DZnO/graphene, (**d**) 1 Fe-2 DZnO/graphene, and (**c**) 2 Fe-2 DZnO/graphene heterostructures. For (**a**–**c**), the isosurface level is set to 10\({}^{-5}\) a.u., while for (**d**,e**), the isosurface corresponds to 0.001 a.u. strong ability to attract electrons to form a strong polar covalent bond, the relatively low electronegativity of zinc dictates its much weaker interaction with hydrogen. However, the \(\Delta G_{\text{H^{*}}}\) values for both adsorption site types were negative, indicating that this process was thermodynamically favorable. Notably, even chemically similar sites (zinc or oxygen sites) had different binding abilities. This was driven by the charge transfer between 2D ZnO and graphene, which brings the site-energy inhomogeneity to the system. It is of utmost importance to highlight that the presence of graphene plays a pivotal role in facilitating charge transfer at the interface. This becomes evident when examining the hydrogen-adsorption behavior in the absence of graphene, resulting in \(\Delta G_{\text{H^{*}}}\) becoming more negative for hydrogen adsorption at Zn sites and less negative for hydrogen adsorption at O sites, as depicted in Figure S16 (Supplementary Material). This finding not only highlights graphene's crucial function as a stabilizing and supportive substrate, but also underscores its influence on hydrogen adsorption. Figure 7d,e exhibit the dependence of hydrogen-adsorption energy for zinc and oxygen sites on hydrogen coverage. The results indicate that the hydrogen-adsorption energy for zinc sites becomes more negative with increasing hydrogen coverage, which may be indicative of negligibly small repulsive interactions between the hydrogen species. This is achieved through a 2D ZnO structure transformation from a flat to buckled geometry during the H-adsorption process and a formation of tilted chemical Zn-H bonds (see the inset of Figure 7d). Despite the 2D ZnO layer reconstruction upon H adsorption, no significant atomic fluctuations in the \(z\) direction for oxygen and zinc sublayers were observed. These findings have important implications for the development of efficient hydrogen storage materials based on 2D ZnO/graphene systems.