## 3 Results and Discussion
### Analysis of Hydrogen-Gas and Iron Surface Interactions Based on First Principles
The redistribution of electronic states between the 4s orbitals of iron and the s orbitals of hydrogen atoms on the iron surface results in the formation of new hybrid orbitals at lower energy levels. This formation of new hybrid energy levels signifies the transition of electrons from higher to lower stable energy states, directly reflecting the pairing and  
Figure 4: H’s orbital density of states before and after the reaction. Figure 3: Total density of states before and after the reaction. sharing of electrons during the chemical adsorption process. The formation of new hybrid orbitals further reduces the total energy of the system, demonstrating the stability of the adsorption configuration and providing important theoretical support for understanding the hydrogen adsorption mechanism on the iron surface. Apart from the hybridization of the hydrogen 1s and iron 4s orbitals altering the total density of electronic states, Figures 5-7 indicate that the s, d, and p orbitals of iron contribute to the increase in the total electronic density over the energy range of \(-5\) eV to \(+5\) eV. Based on the analysis above, we can conclude that during the dissociative adsorption process of hydrogen, the interaction between hydrogen and iron atoms leads to the rearrangement of electrons, thereby affecting the distribution of charge density within the system and facilitating new chemical interactions between iron and hydrogen atoms. Furthermore, the electron rearrangement between iron and hydrogen atoms is primarily driven by orbital hybridization (especially the hybridization of hydrogen's 1s orbital with iron's 4s orbital) and interatomic interactions [48; 49]. Through precise calculations of electron difference density, this study delves into the adsorption mechanism of hydrogen on the iron surface. The analysis results reveal changes  
Figure 5: Fe’s orbital density of states before and after the reaction. Figure 6: Fe’d orbital density of states before and after the reaction. in electron density induced by hydrogen adsorption, further deepening our understanding of the dynamics of electron rearrangement between atoms. Figure 8 details the changes in electron difference density during the hydrogen adsorption and dissociation process, clearly displaying the pattern of electron density changes during the dissociative adsorption process of hydrogen molecules on the iron surface. Here, color changes represent trends in electron density increase or decrease. Red areas indicate locations of increased electron density, suggesting electron concentration in these regions. Red areas near the hydrogen molecule suggest that electrons may be transferring from iron atoms to hydrogen atoms, facilitating the formation of Fe-H bonds. Conversely, blue areas show decreased electron density, possibly indicating the migration of electrons originally near iron atoms toward hydrogen atoms, thereby leading to a reduction in electron density around iron atoms. Such changes in electron density not only signify the migration of electrons from iron to hydrogen but are also key steps in the chemical adsorption process [50; 51]. Therefore, electron rearrangement is the fundamental cause of changes in charge density. Charge density difference maps further showcase the redistribution of charge density after electron rearrangement. As shown in Figure 9, red areas indicate increased electron density, while blue areas denote decreased electron density. Especially, significant red areas near hydrogen atoms indicate an increase in electron density, enhancing the interaction between iron and hydrogen atoms and promoting the formation of chemical Fe-H bonds. This is consistent with the results of Figure 9, accurately describing the microscopic mechanism of dissociative adsorption of hydrogen molecules on the iron surface, i.e., the redistribution of charge density through electron migration. The areas with higher charge density exhibit enhanced interatomic interactions, which are key to the formation of chemical bonds.