## 3 Results and Discussion
### Adsorption of Hydrogen Molecules on the Surface of Iron
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Distance (Å)** & **Top Site’s Energy (eV)** & **Hollow Site’s Energy (eV)** \\ \hline
0.5 & \(-\)10321.70 & \(-\)10378.46 \\
1 & \(-\)10376.92 & \(-\)10378.46 \\
1.5 & \(-\)10383.34 & \(-\)10382.77 \\
2 & \(-\)10383.33 & \(-\)10382.97 \\
2.5 & \(-\)10383.24 & \(-\)10383.15 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Energy of the system with hydrogen molecules at different positions. Figure 1: Energy-distance relationship diagram. 1.75 A, the variation in system energy stabilizes, indicating that past this juncture, the hydrogen molecule's inclination towards physical adsorption or interaction weakens as the distance increases [41]. Further research indicates that within the distance range of 2 A to 3 A, as the distance between the hydrogen molecule and the iron surface gradually increases, the system energy shows a stable upward trend. This suggests that the effective interaction between the hydrogen molecule and the iron surface is gradually weakening and tends towards a state of detaching from the adsorption on the iron surface. Meanwhile, according to experimental data or theoretical calculations, the physical adsorption distance of hydrogen molecules at the iron surface's hollow site is approximately 2.5 A. Based on this, we can reasonably infer that on the Fe(110) surface, the ideal physical adsorption distance of hydrogen molecules at the top site is approximately 1.75 A, while physical adsorption at the hollow site tends to occur around a distance of 2.5 A. This helps to identify the lowest energy adsorption sites for hydrogen molecules on the iron surface. During the geometric optimization of the Fe(110) interface system, the hydrogen-to-iron surface distance was initially set at 1.75 A to identify the lowest energy configuration of the system. This optimization led to significant alterations in the electronic structure, marked by dynamic shifts in the band structure and density of electronic states. Figure 2 illustrates the atomic configurations before and after optimization during hydrogen adsorption on the Fe(110) surface. In the unrelaxed state (Figure 2a), the H-H bond measures 0.74 A, with the molecular center located 1.75 A above the topmost iron layer. Upon partial relaxation (Figure 2b), the H-H bond elongates to 1.067 A, while the vertical distance to the surface contracts to 1.478 A, signaling the onset of molecular dissociation and the formation of incipient Fe-H bonds, with bond lengths around 1.68 A. Fully optimized configurations (Figure 2c) reveal that the hydrogen atoms have completely dissociated and migrated to hollow-bridge sites on the Fe surface, with Fe-H bonds stabilizing at approximately 1.612 A and the H-H separation expanding further to 2.189 A. Additionally, minor lateral displacements of Fe atoms are observed, consistent with structural reorganization induced by hydrogen chemisorption. Additionally, the iron atoms on the Fe(110) surface displayed  
Figure 2: Changes in atomic configurations of molecular structures before and after geometrical optimization. (**a**) initial configuration; (**b**) adsorption configuration; (**c**) dissociated configuration. slight positional adjustments as a result of the dissociative adsorption of hydrogen atoms. The computational findings align well with the literature, specifically references 14 and 29, affirming the model's accuracy [27; 42]. To gain a deeper understanding of the spontaneity of the reaction system, this paper will analyze the thermodynamic parameters of the reaction process. The change in Gibbs free energy \(\Delta G\) serves as a key thermodynamic quantity for determining whether a chemical reaction will proceed spontaneously and is calculated by comparing the free energies of the products and reactants [43]. The calculation of Gibbs free energy is presented in Equation (4).