## 3 Results and Discussions
### Molecular Structure Construction of Low-Rank Coal  
Aromatic, aliphatic, and heteroatomic functional groups are present in the molecular structures of the two coals, LR@1 and LR@2, respectively, where the aromatic carbon structures can be determined based on the bridge-to-surrounding carbon ratio (\(X_{\text{BP}}\)), which is known to be 0 for the benzene ring, 0.25 for the naphthalene, 0.4 for the anthracene, 0.5 for the pyrene, and 0.6 for the pyrene isomers. The \(X_{\text{BP}}\) values for the aromatic carbon structures in LR@1 and LR@2 were calculated and found to be 0.289 and 0.273, respectively, as shown in Table 4. The relative errors were 2.281% and 2.559%, indicating that the  
Figure 3: Fitting of \({}^{13}\)C NMR peak splitting for two coal samples (**a**) \({}^{13}\)C NMR spectrum and bifurcation of LR@1 (**b**) \({}^{13}\)C NMR spectrum and bifurcation of LR@2. \begin{table}
\begin{tabular}{l c c c c c c c c c c c} \hline
**Sample** & \(f_{\text{a}}\)\({}^{\text{B}}\) & \(f_{\text{a}}\)\({}^{\text{H}}\) & \(f_{\text{a}}\)\({}^{\text{P}}\) & \(f_{\text{a}}\)\({}^{\text{S}}\) & \(f_{\text{a}}\)\({}^{\text{N}}\) & \(f_{\text{al}}\)\({}^{\text{N}}\) & \(f_{\text{al}}\)\({}^{\text{H}}\) & \(f_{\text{al}}\)\({}^{\text{O}}\) & \(f_{\text{al}}\) & \(f_{\text{a}}\) & \(f_{\text{a}}\)\({}^{\prime}\) & \(X_{\text{BP}}\) \\ \hline LR@1 & 13.16 & 28.60 & 9.26 & 6.68 & 29.09 & 3.78 & 27.95 & 0.88 & 42.31 & 57.69 & 57.69 & 0.295 \\ LR@2 & 12.75 & 27.91 & 7.69 & 12.34 & 32.77 & 3.72 & 20.04 & 3.85 & 39.32 & 60.68 & 60.68 & 0.266 \\ \hline \end{tabular}
\end{table} 
Table 3: Structural parameters of LR@1 and LR@2 coal samples. determined aromatic carbon structures are consistent with the actual aromatic carbon structures in LR@1 and LR@2. Based on the calculated data, the number of aromatic carbons in the two coal structures was determined to be 125 and 112, respectively. The aliphatic carbons in the coal are primarily linked to aromatic rings in the form of branched chains and exist as fatty rings, side chains, or bridge carbons. The lower the coal rank, the longer the alkyl side chains in the molecular structure. From the number of aromatic carbons and the aromatic carbon ratio, the total number of carbons in the two coal structures was calculated to be 217 and 186, respectively. The number of aliphatic carbons was determined to be 92 and 74, respectively. Additionally, based on the elemental analysis data, the number of hydrogen atoms in the two coal structures was found to be 238 and 173, respectively. In addition to the primary carbon structures, both LR@1 and LR@2 coal structures contain heteroatom structures. Based on the XPS experimental data and elemental analysis results, the number of oxygen atoms in each coal structure is determined to be 22 and 21, respectively. The oxygen atoms in both coal structures mainly exist as oxygen-bound aliphatic carbons and oxygen-substituted aromatic carbons. In the LR@1 coal structure, the relative content of oxygen-bound aliphatic carbons and oxygen-substituted aromatic carbons is 0.88% and 9.26%, respectively. This gives a calculated number of C-O bonds as two and Ar-O bonds as twenty. In LR@2, the relative content of oxygen-bound aliphatic carbons and oxygen-substituted aromatic carbons is 3.85% and 7.69%, respectively. The calculated number of C-O bonds is seven, and the number of Ar-O bonds is fourteen. Based on the XPS analysis results, the nitrogen and sulfur atoms in both coal structures are mainly present in the forms of pyridine, pyrrole, and thiophene. Combining the elemental analysis data, it was determined that LR@1 contains two nitrogen atoms and one sulfur atom, present as one pyridine nitrogen, one pyrrole nitrogen, and one thiophene sulfur LR@2 contains one nitrogen atom and one sulfur atom, present as one pyrrole nitrogen and one thiophene sulfur. Based on the experimental data and calculated results, the molecular formulas for LR@1 and LR@2 were determined to be C\({}_{217}\)H\({}_{238}\)N\({}_{2}\)O\({}_{22}\)S and C\({}_{186}\)H\({}_{173}\)NO\({}_{21}\)S,