## 3 Results and Discussion
### Analysis of Hydrogen-Gas and Iron Surface Interactions Based on First Principles  
The redistribution of charge density is crucial for understanding chemical reactions, especially in scenarios involving the transfer of electrons between molecules [44; 45]. This phenomenon is particularly pronounced in the dissociative adsorption reaction of hydrogen molecules on the iron surface. The interaction between hydrogen and iron atoms triggers the redistribution of electrons, thereby altering the layout of charge density within the system. This change directly affects the formation of chemical bonds [46]. Through density functional theory, an in-depth simulation analysis of the iron-hydrogen adsorption model was conducted, aiming to quantify the overall and orbit-specific changes in the electron state density during the dissociative adsorption process of hydrogen on the iron surface. As shown in Figure 3, by comparing the changes in the total state density before and after hydrogen dissociative adsorption (represented by the red and blue areas, respectively), we observed a significant increase in the total state density near the Fermi level (energy range from \(-5\) eV to \(5\) eV). This increase reflects an enhancement in the interaction strength between electrons, which could indicate the formation of new chemical bonds. The key changes in the electron state density provide important clues for understanding the microscopic mechanism of hydrogen's dissociative adsorption on the iron surface. To further deepen the analysis, the changes in the electron state density were subdivided into three energy intervals: \(-10\) eV to \(-5\) eV, \(-5\) eV to \(5\) eV, and above \(5\) eV. This subdivision helps in thoroughly discussing and analyzing the specific impacts of changes in electron state density within each energy interval. The change in the s-orbital electron state density before and after hydrogen adsorption can be observed (as shown in Figure 4). Before hydrogen adsorption, near the Fermi level (\(0\) eV), the state density diagram exhibits a sharp and high peak, reflecting the high state density of the lone electron on the hydrogen atom's s-orbital. After hydrogen adsorption, this sharp peak disappears, and a new, broader peak appears in a lower energy range (approximately \(-10\) eV to \(-5\) eV). This indicates that electrons from the hydrogen atom's s-orbital have interacted with the iron surface, leading to the transfer of electrons to the electronic states of iron and the formation of new chemical bonds [47]. This change reveals significant electron interaction between the hydrogen atom and the iron surface, resulting in the transfer of s-orbital electrons of hydrogen to the electronic states of iron and ultimately the formation of new chemical bonds. This phenomenon not only reflects the chemical adsorption process of hydrogen atoms on the iron surface but also demonstrates the process of electron reorganization. The analysis of electron orbital hybridization reveals changes in electron behavior during the hydrogen adsorption process on the iron surface. As illustrated in Figure 3, new, broader peaks observed in the lower energy range (\(-10\) eV to \(-5\) eV) typically signify the formation of new energy levels through the hybridization process. These broader peaks indicate that the distribution of electron states becomes more extensive after hybridization, reflecting an enhancement in electron interactions and the splitting of energy levels. Specifically, as demonstrated in Figure 5, the adsorption of hydrogen introduces a new peak in the density of states (DOS) within the same energy range for iron's s-orbital, signaling the involvement of iron's 4s orbital in the hybridization process. Concurrently, Figure 6 reveals that the DOS for iron's d-orbital remains largely unchanged within the \(-10\) eV to \(-5\) eV energy range. This observation suggests that the hybridization primarily involves iron's 4s orbital within this specified energy interval.