## 3 Results and Discussion
### DFT Calculated CH\({}_{4}\) and H\({}_{2}\)O Adsorption on Coal
#### 3.1.2 CH\({}_{4}\) and H\({}_{2}\)O Adsorption on Coal Molecules  
We calculated the adsorption of CH\({}_{4}\) and H\({}_{2}\)O on various sites on the three representative coal molecules as described in Section 2. The results suggest that the binding affinity of CH\({}_{4}\) and H\({}_{2}\)O to coal is primarily determined by the local chemical environment, i.e., the functional groups, on the coal molecules. Chemical compositions and structures of the portions on the coal molecules which are greater than 5 A away from the CH\({}_{4}\) or H\({}_{2}\)O molecule have little effect on the binding energy. Table 2 enumerates the binding energies of CH\({}_{4}\) versus the functional groups, beside which CH\({}_{4}\) is adsorbed. For each type of adsorption site, several typical adsorption structures are shown, along with their respective adsorption energies. Table 3 gives the same information for H\({}_{2}\)O adsorption. Several observations can be made based on the results in Tables 2 and 3. 1. The most stable adsorption site for CH\({}_{4}\) is above aromatic planes, especially if a CH\({}_{4}\) molecule interacts with more than one aromatic planes, such as the case in row 1 of Table 2. Polycyclic \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Method**} & \multicolumn{2}{c}{**CH\({}_{4}\)**} & \multicolumn{2}{c}{**H\({}_{2}\)O**} \\ \cline{2-5}  & **E\({}_{\text{ads}}\) (kJ/mol)** & **Distance (Å)** & **E\({}_{\text{ads}}\) (kJ/mol)** & **Distance (Å)** \\ \hline PBE+DFT-D & \(-\)24.90 & 3.22 & \(-\)31.63 & 3.03 \\ PBE (no dispersion) & \(-\)8.24 & 3.58 & \(-\)7.12 & 3.19 \\ BLYP+DFT-D & \(-\)29.24 & 3.19 & \(-\)28.26 & 3.03 \\ BLYP (no dispersion) & \(-\)0.63 & 4.60 & \(-\)12.54 & 3.30 \\ RPBE & \(-\)4.62 & 3.96 & \(-\)6.68 & 3.64 \\ m11-L & \(-\)29.47 & 2.87 & \(-\)29.48 & 3.10 \\ revtpss & \(-\)4.59 & 3.22 & \(-\)11.37 & 3.17 \\ COMPASS forcefield & \(-\)5.38 & 3.47 & \(-\)20.19 & 3.36 \\ Literature (DFT) & \(-\)31.8 [36] & 3.36 [36] & \(-\)17.4 [37] & 3.25 [37] \\ Experimental & \(-\)13.5 [38] & 3.03 [38] & \(-\)19.0 [39] & - \\ \hline \end{tabular}
\end{table} 
Table 1: Binding energies and distances of CH\({}_{4}\) and H\({}_{2}\)O on the graphene predicted by different DFT functionals and the COMPASS forcefield. For Perdew–Burke–Ernzerhof (PBE) and BLYP functionals, we also tested the effect if no dispersion corrections are considered. Binding energy E\({}_{\text{ads}}\) is defined as E\({}_{\text{ads}}\) = E (surface + adsorbate) – E(surface) – E(adsorbate). A more negative E\({}_{\text{ads}}\) value means stronger binding. For comparison, values from previous theoretical and experimental studies are also included. RPBE = revised PBE. aromatic planes, which resemble the graphene plane, have slightly stronger bind affinity with CH\({}_{4}\), than monocyclic aromatic planes. 2. The most stable adsorption site for H\({}_{2}\)O is N atom sites with H\({}_{2}\)O can form strong hydrogen bonds with N. However, considering that the percentage of the N element in coal is rather low, the amount of H\({}_{2}\)O molecule that can be attracted in coal by N atoms by hydrogen bonding is limited. 3. Water can form hydrogen bonds with O atoms or be adsorbed on aromatic planes, both of which have similar adsorption energies (around \(-\)33 kJ/mol). The adsorption of H\({}_{2}\)O on aromatic planes is slightly stronger than CH\({}_{4}\) adsorption, which has E\({}_{\text{ads}}\) values around 20 kJ/mol. However, this difference is not large enough to allow the coal surface to have a strong binding preference with H\({}_{2}\)O. 4. The presence of substituents on the aromatic rings, such as hydroxyl, carbonyl, -O-, -N=, and -S-groups, often have little influence (\(<\)5 kJ/mol) on the adsorption energies of CH\({}_{4}\) and H\({}_{2}\)O. 5. The least favorable adsorption sites for both CH\({}_{4}\) and H\({}_{2}\)O are alkane groups and chains.