## 3 Results and Discussion
### Hydrogen-Adsorption Properties
On the other hand, the \(\Delta G_{\text{H^{*}}}\) value for oxygen sites became less negative with increasing the hydrogen coverage (Figure 7e). Furthermore, the hydrogen adsorption induced the significant deformation/corrugation of the 2D ZnO layer (please see the inset of Figure 7e). The geometry optimization in full-coverage conditions did not converge correctly. For this reason, in this work, only low and moderate hydrogen-coverage conditions on O-sites of 2D ZnO were considered. While the absence of graphene had minimal impact on the relationship between \(\Delta G_{\text{H^{*}}}\) and hydrogen coverage on Zn sites (left panel, Figure S17, Supplementary Material), it significantly altered the trend for oxygen sites. Specifically, it was observed that the absolute value of \(\Delta G_{\text{H^{*}}}\) tended to increase as the hydrogen coverage at oxygen sites increased (right panel, Figure S17, Supplementary Material). The comparison of \(\Delta G_{\text{H^{*}}}\) heatmaps for defect-engineered 2 DZnO/graphene heterostructures enables us to understand the effect of oxygen vacancies and Fe dopants on hydrogen adsorption (Figure 8). The adsorption energies of zinc sites adjacent to oxygen vacancy sites on V\({}_{\text{O}}\)-containing surfaces (Figure 8a,b) were much stronger compared to those on the pristine 2D ZnO surface. When discussing Fe-doped systems (Figure 8c,d), it is observed that H-adsorption energies are significantly stronger at Fe sites than Zn sites, resulting in preferential H adsorption at Fe sites over Zn sites. Notably, for surfaces with one Fe substitutional defect (Figure 8c), Zn sites next to an Fe site (labeled as 1 and 9) have much lower \(\Delta G_{\text{H^{*}}}\) values than neighboring Fe and Zn sites, implying that H can preferentially bind at Zn sites adjacent to Fe. However, for the surface where two Fe sites are incorporated into 2D ZnO (Figure 8d), the situation is different. Although Fe sites still exhibit significantly higher \(\Delta G_{\text{H^{*}}}\) values, the Gibbs free energy of hydrogen-adsorption energies becomes considerably stronger at all Zn sites than those of the 1 Fe-doped 2D ZnO system. This suggests that the distance between Fe dopants in 2D ZnO can significantly affect the HER performance of 2 DZnO/graphene heterogeneous catalysts. It is important to note that the \(\Delta G_{\text{H^{*}}}\) value should approach zero for an ideal catalyst, and systems with isolated Fe substitutional defects appear to be more promising for HER catalysis, requiring careful further investigation. Figure S18 (Supplementary Material) illustrates the impact of oxygen vacancies and Fe dopants on \(\Delta G_{\rm H^{*}}\) values for hydrogen adsorption at different oxygen sites within the studied structures. The introduction of oxygen vacancies generally results in an increase in the absolute value of \(\Delta G_{\rm H^{*}}\), indicating enhanced hydrogen adsorption at the remaining oxygen sites. This effect was particularly pronounced in the 1 Vo-ZnO/graphene structure, as evidenced by the more negative \(\Delta G_{\rm H^{*}}\) values observed for specific oxygen sites. Conversely, the incorporation of Fe dopants in the ZnO/graphene structure led to a decrease in the absolute value of \(\Delta G_{\rm H^{*}}\) at oxygen sites compared to the pristine structure. The influence of Fe dopants becomes more intricate in the case of 2 Fe-ZnO/graphene, with some sites showing reduced adsorption energies (approximately \(-0.57\) eV and \(-1.42\) eV), while others exhibit more negative \(\Delta G_{\rm H^{*}}\) values (\(\geq-2.4\) eV). These findings highlight the diverse effects of Fe dopants on hydrogen-adsorption properties within the heterostructures, indicating site-dependent variations in the catalytic activity. To shed more light on the nature of the site-dependent properties, the Hirshfeld population analysis was performed. There was a correlation between the charge at oxygen sites and the \(\Delta G_{\rm H^{*}}\) values for hydrogen adsorption.