## 3 Results and Discussions
### DFT Calculations  
To further explore the hydrogen adsorption ability of the molecular structures of LR@1 and LR@2, the electrostatic potential [32] and frontier molecular orbitals (FMOs) [33] of the coal structures at the atomic level were analyzed. The electrostatic distribution can reveal the charge distribution on the coal molecular surface and its attraction to H\({}_{2}\). The FMOs can help predict the potential adsorption reaction sites and reactive groups. In FMOs, the Highest Occupied Molecular Orbital (HOMO) reflects the electron density distribution in the molecule and indicates the orbitals most likely to lose electrons. The HOMO energy level determines its electron-donating ability in reactions. The Lowest Unoccupied Molecular Orbital (LUMO) is the orbital in the coal molecule most likely to accept electrons, and the LUMO energy level determines the coal molecule's ability to interact with electron acceptors [34]. DFT calculations were performed to obtain the electrostatic distribution of the two low-rank coal molecular structures and H\({}_{2}\), as shown in Figure 5. In Figure 5, the red regions represent high electron density areas, which are prone to nucleophilic reactions, while the blue regions represent low electron density areas, which are more likely to undergo electrophilic reactions. From the electrostatic distribution of the molecular structures in Figure 5, it can be seen that there is a smooth delocalized electron density distribution on the surfaces of both coal structures and the H\({}_{2}\) molecule. The head of the H\({}_{2}\) molecule exhibits nucleophilic behavior, while the middle region shows low electron density. Compared with functional groups such as pyridine and pyrrole, the positive electrostatic regions in the molecular structure of the two coals are concentrated in the branched H atoms, O-H groups, and part of the surface of the benzene ring, and the negative electrostatic regions are concentrated in the surface of the O-H groups and part of the benzene ring, which indicates that the head region of the H\({}_{2}\) molecule is susceptible to electrophilic and nucleophilic reactions with the oxygen-containing functional groups in the molecular structure of the two coals. This indicates that the head region of the H\({}_{2}\) molecule can easily have electrophilic and nucleophilic reactions with the oxygen-containing functional groups in the molecular structure of the two coals to form a stable adsorption structure. Additionally, the branched structure of the aliphatic carbon and the polyaromatic structure of the aromatic carbon provide more effective adsorption sites, enhancing the adsorption of H\({}_{2}\) by the low-rank coal structures. From the distribution of the FMOs in Figure 5, it can be seen that in LR@1, the HOMO and LUMO orbitals are concentrated on the polyaromatic carbon atoms and some protonated aromatic carbon atoms. In LR@2, the HOMO and LUMO orbitals are concentrated on the carbon atoms of anthracene, pyrene, and some benzene rings. This indicates that in the low-rank coal structures, the polyaromatic structures offer more regions for electron donation/acceptance, which can interact with H\({}_{2}\) molecules, promoting adsorption reactions.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Coal**} & \multicolumn{4}{c}{**Actual Elemental Content (\%)**} & \multicolumn{4}{c}{**Calculated Elemental Content (\%)**} \\ \cline{2-10}  & **C** & **H** & **O** & **N** & **S** & **C** & **H** & **O** & **N** & **S** \\ \hline LR@1 & 79.96 & 7.35 & 10.84 & 0.87 & 0.98 & 78.39 & 8.26 & 11.51 & 0.86 & 0.98 \\ LR@2 & 80.06 & 6.25 & 12.03 & 0.51 & 1.15 & 79.81 & 7.02 & 11.73 & 0.43 & 1.01 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Comparison of experimental and calculated elemental contents.