4.1.2. Energy-Minimizing Geometrical Configuration and Microcrystalline Structure Parameters

The unoptimized model in Figure 7a was imported into MS for hydrogenation saturation. MM and MD calculations were performed to overcome the molecular structure energy barrier and obtain the minimum energy structure after molecular structural optimization in the Forcite module. The results are shown in Figure 7b. The optimized gas coal molecular model was more compact and had a better stereochemical structure than the models in Figure 7a,b. The optimized molecular energies are shown in Table 6. The calculation and analysis showed that the valence electron energy and the non-bond energy accounted for 39.56% and 60.44% of the total energy, respectively. The total energy of the optimized molecular model was reduced by 91.72%, in which the valence electron energy was reduced by 92.11% and the non-bond energy was reduced by 91.44%. The analyzed results showed that the non-bond energy (hydrogen bond energy, van der Waals energy, and Coulomb energy) plays an important role in the stability of the molecular structure. The van der Waals energy changed the most before and after optimization, which suggests that the π−π interaction between aromatic rings was the main factor in keeping the molecular structure stable. In the valence electron energy (bond stretching energy, bond angle energy, torsion energy, and reversal energy), the descending order was as follows: torsion energy > bond stretching energy > bond angle energy > reversal energy. Therefore, the bond torsion and reversal and the changes in bond angle and length were the basis of the stereoscopic configuration of coal macromolecules. The molecular structure drawn in the Chemdraw software was a planar graph, and the factor of the bond length was ignored. Thus, the bond energy changed the most in the optimized valence energy.

**Figure 7.** Macromolecular structure model of gas coal before and after optimization: (**a**) before optimization; (**b**) after optimization.

**Table 6.** The energies of the gas-coal macromolecular structure before and after optimization.


Note: E—total energy; EV—valence energy; EB—bond energy; EA—angle energy; ET—torsion energy; EI inversion energy; EN—non-bond energy; EH—hydrogen bond energy; Evan—van der Waals energy; EE electrostatic energy.

As shown in Figure 7b, a set of approximately parallel combinations (series 1, 2, and 3) appeared between the aromatic lamellar layers in the structural model formed by a single molecule. However, the spacings (d002) of the two aromatic lamellae were not uniform, which were 3.735 and 3.456 nm, respectively. The maximum values of La and Lc were 12.190 and 7.191 nm, respectively. The spacing of the aromatic layer was 3.575 nm higher than the measured value, which is due to that the bonds connecting the aromatic layers were twisted and inserted in a set of aromatic lamellae 6 and aliphatic carbon structures after optimization. The π−π interaction between aromatic rings played an important role in structural stability, and two sets of vertical structures (aromatic layers 5, 1, and 3 and aromatic layers 10 and 11) appeared at the edge of the model. The reason is that the coal molecule was in a stable state without force [44]. The microcrystalline structural parameters (d002, Lc, and La) of the coal molecular model were slightly different from the experimental values (3.575, 6.62, and 11.77 nm, respectively), which suggests that the short-range order of the high-grade coal structure mainly depends on the directional arrangement of more intermolecular aromatic layers [40].

### *4.2. Density Simulation*

The density of coal is an important physical property, and it was used to verify the reasonability of the model by comparing the value of the constructed model with the experimental value. The Amorphous Cell module in MS software was utilized to add periodic boundary conditions to the model shown in Figure 7b for MM and MD. The constructs of a series of structural models were obtained, and the minimum energy model was selected. The parameters of the density simulation were as follows: the calculation used periodic boundary conditions, the Dreiding force field was used to simulate the field force, and the charge was calculated by the charge balance method (QEq). The number of molecules was 1, the initial density value was 0.7 g/cm3, the final density value was 1.4 g/cm3, and the interval was 0.05 g/cm3 [45]. The geometric configuration with the minimum energy was selected as shown in Figure 8. The relationship between the density and the potential energy of the structural model is shown in Figure 9.

**Figure 8.** Structure of gas coal with a density of 1.0 g/cm3.

**Figure 9.** Relationships between the structural model density and potential energy.

As shown in Figure 9, the total potential energy of the molecular structure decreased gradually first and then increased rapidly with the rise in density. When the density was 1.0 g/cm3, the total potential energy of the molecular structure model was the minimum and the value was 562.944 KJ/mol. At this time, 1.0 g/cm3 was the simulated density of the model, and the parameters of coal molecular crystal cells were a = b=c= 1.6003 nm. Its structural energy is shown in Table 7. When the density was less than 1.0 g/cm3, EV played a dominant role at this stage. When the density was greater than 1.0 g/cm3, the dominant was EN. The density calculated by simulation was smaller than the experimental density of gas coal (1.2564 g/cm3). The reason is that excluding the influence of trace elements and small molecular substances in coal during the density test is difficult under actual conditions [46,47]. Thus, the calculated density was considered reasonable.


**Table 7.** Energy of the coal sample from Huainan.

Comparing Tables 6 and 7 showed that the torsion energy had the largest change among the valence electron energies after periodic boundary conditions were added. The reason is that the energy minimization only was achieved by twisting appropriately when the gas coal molecules under periodic boundary conditions interacted with the surrounding molecules. After periodic boundary conditions were added, the most obvious change in non-bond energy was observed for the van der Waals energy. The major contributor is that the aromatic layers located in parallel were distorted and deformed in the process of the gas coal molecular structure. Thus, they became more compact, which ultimately destroyed π−π interactions between the aromatic layers in the molecule.
