## 3 Results and Discussion
### Hydrogen-Adsorption Properties
In the case of oxygen vacancies, the introduction of a vacancy disrupted the balance of charge within the system (Figure S19, Supplementary Material), leading to an increase in the negative charge at neighboring oxygen sites. This increased negative charge on the remaining oxygen atoms can enhance the electrostatic attraction with neutral hydrogen, resulting in a more negative \(\Delta G_{\rm H^{*}}\) and enhanced hydrogen adsorption. This is consistent with the trend observed in the 1 Vo-ZnO/graphene structure, where specific oxygen sites exhibit more negative \(\Delta G_{\rm H^{*}}\) values, indicating stronger hydrogen binding due to the increased negative charge at these sites. Conversely, the incorporation of Fe  
Figure 7: Panel (**a**) displays the oxygen- and zinc-adsorption sites for the 2D ZnO/graphene heterostructure and the sequence in which they become occupied by hydrogen species. Heatmaps of predicted Gibbs free energy of adsorption, \(\Delta G_{\rm H^{*}}\), for the Volmer step on oxygen- (**b**) and zinc (**c**) adsorption sites of 2 DZnO/graphene. Dependence of hydrogen-adsorption energy on hydrogen coverage for (**d**) Zn and (**e**) O sites of 2 DZnO/graphene. The insets demonstrate the optimized geometrical configurations of 2 DZnO/graphene with maximum acceptable H coverage for both Zn and O sites. dopants reduced the negative charge at the oxygen sites compared to the pristine structure (Figure S19, Supplementary Material). As a result, the electrostatic attraction between oxygen and hydrogen can weaken, leading to a decrease in the absolute value of \(\Delta G_{\text{H}^{*}}\) and indicating a weaker binding of hydrogen. The observed trends support the notion that the charge distribution, influenced by the presence of oxygen vacancies and Fe dopants, plays a crucial role in modulating the strength of hydrogen binding and catalytic activity within the heterostructures. Upon analyzing the data obtained from free-standing defect-engineered ZnO monolayers, notable trends emerge. Firstly, for the Zn sites adjacent to oxygen vacancy sites in vacancy-containing systems, the presence of graphene leads to more negative values of \(\Delta G_{\text{H}^{*}}\) compared to its absence (Figure S20, Supplementary Material). Conversely, for other Zn sites in systems without graphene, \(\Delta G_{\text{H}^{*}}\) becomes even less negative. These observations suggest that the presence of graphene not only enhances hydrogen adsorption at specific Zn sites, but also amplifies the heterogeneity in the adsorption behavior of Zn sites. In contrast, for all O sites, the values of \(\Delta G_{\text{H}^{*}}\) exhibited greater negativity in the  
Figure 8: Heatmaps of predicted Gibbs free energy of adsorption, \(\Delta G_{\text{H}^{*}}\), for the Volmer step on zinc-adsorption sites of defect-engineered 2 DZnO/graphene heterostructure: (**a**,**b**) oxygen vacancies and (**c**,**d**) Fe dopants, respectively. presence of graphene. This indicates that graphene contributes to an increased stability and stronger binding of hydrogen at oxygen sites. The enhanced negative values of \(\Delta G_{\text{H}^{*}}\) further underscore the influence of graphene in facilitating hydrogen adsorption at the oxygen sites. Iron-containing systems exhibit two distinct and contrasting trends (Figure S21, Supplementary Material): the presence of graphene substantially reduces the absolute value of \(\Delta G_{\text{H}^{*}}\) for hydrogen adsorption at Zn sites, while simultaneously augmenting the adsorption capacity of O sites, thereby promoting a stronger affinity between hydrogen atoms and the substrate.