Density Functional Calculation of H2O/CO2/CH4 for Oxygen-Containing Functional Groups in Coal Molecules.

To investigate the adsorption mechanism of H2O, CO2, and CH4 molecules on oxygen-containing functional groups (OFGs) in coal molecules, quantum chemical density functional theory (DFT) simulations were performed to study the partial density of states and Mulliken bond layout of H2O molecules bonded to different OFGs. The adsorption energy and Mulliken charge distribution of the H2O, CO2, and CH4 molecules for each OFG were determined. The results showed that H2O molecules form 2, 1, 1, and 1 hydrogen bonds with -COOH, -OH, -C=O, and -O-R groups, respectively. Double hydrogen bonds connected the H2O molecules to -COOH with the smallest adsorption distances and highest Mulliken bond layout values, resulting in the strongest bonding between the H2O molecules and -COOH. The most stable configuration for the adsorption of these molecules by the -OH group was when the O-H bond in the OFG served as a hydrogen bond donor and the O atom in the H2O molecule served as a hydrogen bond acceptor. The order of the bonding strength between the OFGs and H2O molecules was Ph-COOH > Ph-OH > Ph-C=O > Ph-O-R. The adsorption energy calculation results showed that H2O molecules have a higher adsorption stability than CO2 and CH4 molecules. Compared with the -OH, -C=O, and -O-R groups, the -COOH group had a higher adsorption capacity for H2O, CO2, and CH4 molecules. The adsorption stability of the CO2 molecules for each OFG was higher than that of the CH4 molecules. From the Mulliken charge layout, it was clear that after the adsorption of the H2O molecules onto the OFGs, the O atoms in the OFGs tend to gain electrons, while the H atoms involved in bonding with the H2O molecules tend to lose electrons. The formation of hydrogen bonds weakens the strength of the bonds in the H2O molecule and OFGs, and thus, the bond lengths were elongated.

Introduction

The continuous exploitation of coal, oil, and natural gas could lead to the exhaustion of fossil-based energy sources. Fossil fuel usage is associated with the release of large amounts of greenhouse gases, such as CO2 and CH4, which threaten the ecological environment. Therefore, the development of cleaner, nonconventional energy sources is the way forward. Coal bed methane (CBM) is a gas resource that is associated and symbiotic with coal. It is a clean, high-quality energy source (compared to coal) and a chemical raw material with CH4 as the main component while containing certain amounts of CO2 and N2,[1] with largely no pollutants after combustion (assuming CO2 as a non-pollutant). Hence, CBM can be used as a clean energy source to improve the energy mix.[2−5] The CO2 emitted from the production processes and purified by adsorption, membrane separation, absorption, and low-temperature separation is injected into a coal seam to induce a competitive adsorption between CO2 and CH4, thereby effectively displacing CH4 gas in the coal seam and realizing enhanced coal bed methane (ECBM) recovery. CO2 carbon capture, utilization, and storage (CCUS) and CH4 separation and utilization are feasible and effective ways to reduce the greenhouse effect. Hence, it is important to study the adsorption properties of CO2 on coal surfaces to reduce greenhouse gas emissions.[6]

The adsorption of gases on the surface of coal seams is influenced by the pressure,[7] temperature,[8] moisture content,[9−11] surface functional groups,[12−14] pore structure,[15,16] and degree of coalification of the coal matrix,[17−19] among which the surface functional groups have a particularly important influence in the case of medium and low-rank coals. In recent years, the density functional theory (DFT) and molecular dynamics (MD) simulations, as well as improvements made to computer hardware, have made quantum theory and molecular simulation methods effective theoretical tools for studying the adsorption properties of gases in coal seams and for calculating surface interactions.[20−23] Huo et al. investigated the adsorption strength of different oxygen-containing functional groups (OFGs) for H2O molecules using the DFT, and based on the analysis of the electron density and potential energy density, the order of the capacity of four different OFGs to adsorb H2O molecules was found to be Ph–C–O–OH > Ph–COOH > Ph–OH > Ph–CHO.[24] Wang et al. studied the interaction between H2O molecules and OFGs using the quantum chemical DFT and concluded that the order of influence of the H2O molecules on the adsorption stability of the OFGs was carboxyl group > phenolic hydroxyl group > aldehyde group > ether and that the OFGs could improve the wettability on the surface of coal molecules.[25] Xiang et al. investigated the adsorption behavior of the binary component CH4:CO2 (molar ratio of 1:1) using the grand canonical Monte Carlo (GCMC) method, and the results showed that the adsorption capacity for CO2 was significantly greater than that for CH4 at the same temperature and pressure, the competitive advantage was evident, and CO2 injection could help effectively displace CH4.[26] Xu et al. investigated the adsorption and desorption of CH4 and CO2 on a 4 × 4 carbon model using the DFT, and the results showed that CO2 had a higher adsorption stability than CH4 and that CO2 injection could promote the desorption of CH4.[27] Zhou et al. used the quantum chemical DFT to study the interaction between CH4 and H2O on the surface of different grades of coal and concluded that a coal–H2O system has a greater adsorption energy than a coal–CH4 system for coals of different maturities and that water injection could improve CBM recovery.[28] Yu et al. calculated the competitive adsorption and self-diffusion of CH4, CO2, and H2O on the surface of low-rank coal vitrinite (C214H180O24N2) using GCMC and MD simulations.[29] The results showed that in the CH4/CO2/H2O = 1:1:1 ternary competitive system, the adsorption amount of the mirror mass group at the same temperature and pressure was in the order of H2O > CO2 > CH4, and the value of the self-diffusion coefficient was in the order of DH2O > DCO2 > DCH4 in the saturated adsorption configuration. This shows that the adsorption capacity is highest for H2O molecules and that injecting water into a coal seam can help improve CBM production. The adsorption effect of H2O was better than that of CO2, which could accelerate the recovery of coal seam gas.[29]

Many simulations and calculations have been performed on the adsorption of H2O, CO2, CH4, and other molecules on the surface of coal molecules;[30−33] however, few studies have analyzed the adsorption of small molecules at the atomic and electronic levels. To investigate the adsorption behavior of small molecules of H2O, CO2, and CH4 on different OFGs (−COOH, −OH, —C=O, and −O–R) in the coal molecules, this study analyzed and compared the interactions between these molecules and each OFG on the surface of a coal model based on the DFT. Moreover, the adsorption mechanism was explored to provide a reference for studying the gas adsorption characteristics on the surface of coal molecules containing different OFGs and to provide theoretical support for the application of H2O-ECBM and CO2-ECBM.

Calculation Method

The optimization of the molecular models of OFGs, H2O, CO2, and CH4 and the calculation of the molecular properties in this study were conducted using the DS BIOVIA Materials Studio 2020 software. The geometric optimization of OFGs, H2O, CO2, and CH4 molecules and the calculation of the adsorption energy of small molecules in OFGs were done using the Dmol[3] module. The maximum iteration for the geometric optimization was set to 500 to ensure convergence. The correlation function adopted for the electron exchange was the Perdew–Burke–Ernzerhof (PBE) functional based on generalized gradient approximation (GGA),[34] the Grimme method was used for the DFT-D correction, DFT Semicore Pseudopots and double numeric with polarization basis set (DNP) was employed,[35] the accuracy was set to Fine, unrestricted electron spins were considered, and symmetry was applied. The convergence accuracy of the self-consistent field was set to 1.0 × 10–6,[36] the maximum number of SCF cycles was set to 500, and the smearing value was set to 0.005 Å. An energy value of 1.0 × 10–5 Ha was set as the convergence criterion for the geometric optimization. The maximum force was set to 0.002 Ha/Å, and the maximum displacement was set to 0.005 Å.

The energy of the completely optimized stable adsorption configuration was optimized using the CASTEP module to calculate its partial density of states (PDOS),[37] Mulliken bond layout, and electron density difference. Different stable adsorption configurations were optimized in periodic unit cells of 15 Å × 15 Å × 15 Å. The exchange correlation function and convergence standard were the same as those employed in the Dmol[3] module, and ultra-soft pseudopotentials were used to describe the interaction between the electrons and ions.[38] The smearing value used for the PDOS analysis was 0.2 eV. The electron density difference was calculated by defining the density difference for the H2O, CO2, and CH4 molecules in different adsorption configurations by Edit Sets, and the electron density difference graph was derived using Analysis.

The adsorption stability of the H2O, CO2, and CH4 molecules on different OFG surfaces can be expressed in terms of the adsorption energy. If the adsorption energy is negative, the reaction is exothermic. The lower the value, the stronger and more stable the adsorption, and vice versa. The calculation formula for the adsorption energy is as follows:where E is the adsorption energy of each molecule on different OFG surfaces (kJ/mol); E is the total energy of different OFGs with each small molecule after adsorption (kJ/mol); E is the energy of different OFGs (kJ/mol); and E is the energy of different small molecules (H2O, CO2, and CH4) (kJ/mol).

To comprehensively analyze the effect of the OFGs in the coal molecules on the adsorption of H2O, CO2, and CH4 molecules, 2 × 2 hexacyclic aromatic clusters (C16H10) were selected to simulate the surface of coal molecules during the quantum chemical calculations.[39] The interactions between the OFGs, such as carboxyl (Ph–COOH), phenolic hydroxyl (Ph–OH), carbonyl (Ph—C=O), and ether (Ph–O–R) groups and the different molecules were calculated separately (where Ph– denotes phenyl, and R– denotes alkyl).

Results and Discussion

Hydrogen Bond Analysis

The most stable configuration of H2O molecules for adsorption by different OFGs was used as an example to analyze the bonding properties. Figure shows four adsorption configurations. As shown in Figure , the most stable adsorption positions of the H2O molecules on the different OFGs are all above the OFG, and the initial configurations of the H2O molecules are in the down form, except for the H2O molecules at Ph–O–R, which are in the up form. The H2O molecule forms 2, 1, 1, and 1 hydrogen bonds with −COOH, −OH, —C=O, and −O–R, respectively. The H2O molecule forms a double hydrogen bond when adsorbed by −COOH with the shortest hydrogen bond length of 1.700 Å. In the adsorption by the −OH group, the O–H bond in the OFG as the hydrogen bond donor and the O atom in the H2O molecule as the hydrogen bond acceptor are the most stable adsorption configuration, with a hydrogen bond length of 1.841 Å. In the adsorption by the —C=O and −O–R groups, the hydrogen bond lengths formed are 1.877 and 2.048 Å, respectively. The initial bond length of the H2O molecule is 0.970 Å, and the initial bond angle is 103.749°. Table presents the bond lengths and bond angles of the H2O molecules at different OFG adsorption equilibria. Table presents the bond lengths of the OFGs before and after the adsorption equilibria.

Figure 1

The most stable configurations of H2O molecules for adsorption by different OFGs (white: H atoms; red: O atoms; gray: C atoms). (a) H2O/Ph–COOH, (b) H2O/Ph–OH, (c) H2O/Ph—C=O, and (d) H2O/Ph–O–R.

Table 1

Bond Length and Bond Angle of H2O Molecules for Adsorption by Different OFGs at Adsorption Equilibriuma

adsorption site	d(HW1,OW)/Å	d(OW,HW2)/Å	θ(HW1OWHW2)/(°)
Ph–COOH	0.992	0.971	104.957
Ph–OH	0.975	0.972	104.683
Ph—C=O	0.983	0.969	104.277
Ph–O–R	0.974	0.970	102.946

HW and OW denote the H and O atoms in the H2O molecule, respectively, HW1 is the H atom involved in bonding with the H2O molecule, HW2 is the H atom not involved in bonding with the H2O molecule, and neither H atom is involved in bonding with the H2O molecule and Ph–OH.

Table 2

Bond Length of OFGs before and after Adsorption Equilibriuma

adsorption site	atomic relationship	d(before adsorption)/Å	d(after adsorption)/Å
Ph–COOH	C=OS1	1.223	1.239
	C–OS2	1.369	1.344
	OS2–Hs	0.980	1.012
Ph–OH	C–OS	1.373	1.362
	OS–HS	0.973	0.989
Ph—C=O	C=OS	1.231	1.238
Ph–O–R	Ph(C)–OS	1.368	1.374
	OS–C(R)	1.428	1.435

HS and OS denote the H and O atoms of the OFG, respectively; OS1: the O atom of the C=O bond in −COOH; OS2: the O atom of the O–H bond in −COOH.

The bonding mechanism of the H2O molecules with each OFG was further elucidated by calculating the PDOS. Figure a,b shows the PDOS of the H2O molecule forming two hydrogen bonds with the Ph–COOH surface. Figure a,b shows the hydrogen bonds HW1···OS1 between the H atom of the H2O molecule and the O atom of the C=O bond in −COOH and the hydrogen bonds HS···OW between the H atom of the O–H bond in −COOH and the O atom of the H2O molecule, respectively. The orbitals of OS1 and OW are mainly distributed in the valence band near the Fermi energy level, and the distribution is not evident in the conduction band, which is favorable for bonding. In Figure a,b, the H 1s orbital and O 2p orbital are bonded in the energy range of −9 to −3 eV, and the anti-bonds are bonded in the energy range of 4–13 eV, with evident resonance phenomena, indicating the formation of two hydrogen bonds on the surface of the H2O molecules and Ph–COOH. Hydrogen bonds are formed by the interaction between the H 1s orbital and O 2p orbital. The hydrogen bond HS···OW is stronger than HW1···OS1 owing to the stronger delocalization of H 1s in Figure b than in Figure a. Figure c–e shows that the −9 to −3 eV, H 1s orbital, and O 2p orbital are bonded and that the 4–13 eV, H 1 s orbital, and O 2p orbital are anti-bonded. Corresponding to the hydrogen bond HS···OW between the H atom of the −OH group and the O atom in the H2O molecule, the hydrogen bond HW1···OS between the H atom of the H2O molecule and the O atom in the —C=O group and the hydrogen bond HW1···OS between the H atom of the H2O molecule and the O atom in the −O–R group. From the off-domain nature of H 1s, as shown in Figure , it is clear that the order of the bonding strength between the OFGs and H2O molecules is Ph–COOH > Ph–OH > Ph—C=O > Ph–O–R.

Figure 2

PDOS of hydrogen bond formation between H2O molecules and each OFG. (a) H2O/Ph–COOH, between HW1 and OS1, (b) H2O/Ph–COOH, between HS and OW, (c) H2O/Ph–OH, between HS and OW, (d) H2O/Ph—C=O, between HW1 and OS, and (e) H2O/Ph–O–R, between HW1 and OS.

To quantify the bond strength of the H2O molecules at different OFG sites, the Mulliken bond layout of the H2O molecules adsorbed on the surfaces of different coal models was determined. Table presents the results. Based on the calculation results, the average bond lengths of the H2O molecules forming hydrogen bonds with different OFGs are 1.781, 1.841, 1.877, and 2.048 Å. The adsorption equilibrium distances are significantly lower than 3 Å, which is not near the covalent bond length (van der Waals forces act in the range of 3–5 Å). This shows that the adsorption mechanism of H2O molecules on the OFGs is chemisorption. The Mulliken bond layouts of the H2O molecules adsorbed at different OFG sites are in the order of Ph–COOH > Ph–OH > Ph—C=O > Ph–O–R. The shorter the hydrogen bond length, the greater the Mulliken bond layout value, indicating stronger hydrogen bonds, a result consistent with the PDOS calculations of the hydrogen bond formation.

Table 3

Mulliken Bond Layout of H2O Molecules Adsorbed on the Surface of Different Coal Modelsa

adsorption configuration	H2O/Ph–COOH		H2O/Ph–OH	H2O/Ph—C=O	H2O/Ph–O–R
bond	HW1···OS1	HS···OW	HS···OW	HW1···OS	HW1···OS
distance/Å	1.862	1.700	1.841	1.877	2.048
Mulliken layout	0.08	0.11	0.08	0.07	0.03

HW and OW denote the H and O atoms in the H2O molecule, HS and OS denote the H and O atoms of the OFG, respectively, and ··· represents the existence of hydrogen bonds between the two atoms.

Adsorption Energy Calculation

Figure shows the most stable adsorption configurations of the H2O, CO2, and CH4 molecules for different OFGs. Table shows the adsorption energies of the H2O, CO2, and CH4 molecules for the OFGs. The results showed that the adsorption energies of the H2O molecules for each OFG are significantly lower than those of the CO2 and CH4 molecules. The adsorption capacity is much greater than those of the CO2 and CH4 molecules; this is mainly attributed to the interaction between the H2O molecules and each OFG via hydrogen bonding. The order of the strong and weak adsorption abilities of the H2O molecules for different OFGs is Ph–COOH > Ph–OH > Ph—C=O > Ph–O–R. This order is in full agreement with the Mulliken bond layout order described above and also with the order of strong and weak adsorption capacity in the literature of Xia et al. and Gao et al.[40−42] The adsorption capacity of the H2O molecules for Ph–COOH is much greater than that for the other OFGs because of the formation of double hydrogen bonds during the adsorption of the H2O molecules by Ph–COOH, with an adsorption energy of −70.474 kJ/mol, which is close to the adsorption energy of −69.250 kJ/mol obtained by Xia et al.[40] Gao et al. calculated the adsorption energy between a single H2O molecule and the hydroxyl, carbonyl groups in lignite as −43.140 and – 38.240 kJ/mol, respectively, which is closer to the results calculated in this paper.[41,42]

Figure 3

Most stable adsorption configurations of H2O, CO2, and CH4 molecules for different OFGs (white: H atom; red: O atom; gray: C atom).

Table 4

Adsorption Energies of H2O, CO2, and CH4 Molecules for Different OFGs

	adsorption energy/Eads (kJ·mol–1)
adsorption site	H2O	CO2	CH4
Ph–COOH	–70.474	–13.437	–10.142
Ph–OH	–49.089	–12.259	–8.197
Ph—C=O	–40.997	–12.954	–7.123
Ph–O–R	–32.344	–10.681	–7.391

Both CO2 and CH4 are nonpolar molecules; however, CO2 molecules have a strong polarizability and quadrupole moment, enabling them to easily interact with polar OFGs and exhibit significant electron transfer. The CH4 molecule is an orthotetrahedral structure formed by averaging the energy and spatial orientation of one 2s orbital and three 2p orbitals; this structure is very stable and has less electron transfer when interacting with OFGs. The adsorption energy calculations of CO2 and CH4 molecules for each OFG show that the CO2 molecules have a higher adsorption capacity than the CH4 molecules. The order of the strong and weak adsorption capacities of the CO2 molecules is Ph–COOH > Ph—C=O > Ph–OH > Ph–O–R, and the results are in agreement with those obtained by Cheng et al.[43] The order of the strong and weak adsorption abilities of the CH4 molecules is Ph–COOH > Ph–OH > Ph–O–R > Ph—C=O. Comparing the adsorption energy magnitudes of the different molecules for each OFG, it can be found that the adsorption energy values of H2O, CO2, and CH4 molecules, particularly H2O molecules, for −COOH were lower than those for the other OFGs, indicating that the adsorption ability is stronger on the −COOH group.

Charge Analysis

The variation in the charge between the bonding atoms or interacting atoms when H2O, CO2, and CH4 molecules were adsorbed on different OFG surfaces can be graphically represented by electron density difference diagrams. The charge transfer of different molecules adsorbed on each OFG surface can be represented visually using the Mulliken charge layout. Figure shows the electron density difference diagrams of the H2O, CO2, and CH4 molecules in each OFG adsorption system. In the figure, the negative value (blue area) indicates a decrease in the electron density before relative adsorption, and the darker the color, the greater the decrease in the electron density; the positive value (red area) indicates an increase in the electron density before relative adsorption, and the darker the color, the greater the increase in the electron density. To clearly observe the electron density difference diagrams, the isosurface value for the H2O and CH4 molecules adsorbed on the OFG surface in the stable configuration was taken as 0.20 electron/Å3, and the isosurface value for the CO2 molecules adsorbed on the OFG surface in the stable configuration was taken as 0.05 electron/Å3. Tables –7 present the Mulliken charge layouts of the H2O, CO2, and CH4 molecules adsorbed on different OFG surfaces before and after adsorption equilibrium, respectively.

Figure 4

Electron density difference diagrams of H2O, CO2, and CH4 molecules in different OFG adsorption systems: (a) H2O/Ph–COOH, (b) H2O/Ph–OH, (c) H2O/Ph—C=O, (d) H2O/Ph–O–R, (e) CO2/Ph–COOH, (f) CO2/Ph–OH, (g) CO2/Ph—C=O, (h) CO2/Ph–O–R, (i)CH4/Ph–COOH, (j) CH4/Ph–OH, (k) CH4/Ph—C=O, and (l) CH4/Ph–O–R.

Table 5

Mulliken Charge Layout of H2O Molecules for Different OFGs before and after Adsorption Equilibrium

adsorption site	atom	Mulliken (before adsorption)	Mulliken (after adsorption)	Mulliken (variance)	atom	Mulliken (before adsorption)	Mulliken (after adsorption)	Mulliken (variance)
Ph–COOH	HS	0.274	0.314	0.040	OW	–0.499	–0.538	–0.039
	OS2	–0.434	–0.454	–0.020	HW1	0.249	0.307	0.058
	OS1	–0.427	–0.492	–0.065	HW2	0.249	0.267	0.018
	C	0.474	0.484	0.010
Ph–OH	HS	0.263	0.295	0.032	OW	–0.499	–0.512	–0.013
	OS	–0.441	–0.469	–0.028	HW1	0.249	0.273	0.024
	C	0.287	0.280	–0.007	HW2	0.249	0.277	0.028
Ph—C=O	OS	–0.398	–0.441	–0.043	HW1	0.249	0.292	0.043
	C	0.296	0.309	0.013	OW	–0.499	–0.563	–0.064
	-				HW2	0.249	0.244	–0.005
Ph–O–R	OS	–0.462	–0.493	–0.031	HW1	0.249	0.287	0.038
	Ph(C)	0.295	0.282	–0.013	OW	–0.499	–0.547	–0.048
	R(C)	0.013	–0.001	–0.014	HW2	0.249	0.254	0.005

Table 7

Mulliken Charge Layout of CH4 Molecules for Different OFGs before and after Adsorption Equilibriuma

adsorption site	atom	Mulliken (before adsorption)	Mulliken (after adsorption)	Mulliken (variance)	atom	Mulliken (before adsorption)	Mulliken (after adsorption)	Mulliken (variance)
Ph–COOH	C	0.474	0.467	–0.007	CW1	–0.314	–0.342	–0.028
	OS1	–0.427	–0.428	–0.001	HT	0.316	0.338	0.022
	OS2	–0.434	–0.425	0.009
	HS	0.274	0.274	0
Ph–OH	OS	–0.441	–0.439	0.002	CW1	–0.314	–0.326	–0.012
	HS	0.263	0.262	–0.001	HT	0.316	0.323	0.007
Ph—C=O	OS	–0.398	–0.398	0	CW1	–0.314	–0.323	–0.009
	C	0.296	0.297	0.001	HT	0.316	0.321	0.005
Ph–O–R	OS	–0.462	–0.461	0.001	CW1	–0.314	–0.323	–0.009
	Ph(C)	0.295	0.295	0	HT	0.316	0.327	0.011
	R(C)	0.013	0.004	–0.009

CW1: the C atom in the CH4 molecule; HT: all H atoms in the CH4 molecule.

From Figure a–d and Table , it can be seen that the O–H bond in −COOH acts as a hydrogen bond donor and the O atom in the H2O molecule acts as a hydrogen bond acceptor; after adsorption, the H atom in −COOH loses 0.040 electrons, while the O atom in the H2O molecule gains 0.039 electrons. The O–H bond in the H2O molecule acts as a hydrogen bond donor, and the O atom in the C=O bond of −COOH acts as a hydrogen bond acceptor. After adsorption, the H atom in the H2O molecule loses 0.058 electrons, and the O atom in the C=O bond of −COOH gains 0.065 electrons, consistent with the electron density difference diagrams. In addition to the O atom in the C=O bond of COOH, the O atom in the O–H bond also gains electrons because of the strong electronegativity of the O atom on the OFG, which easily gains electrons, and the H atom in the H2O molecule is the main electron-losing atom. The formation of hydrogen bonds weakens the bonding strength between the H2O molecule and OFG. From Tables and 2, it can be seen that d(C=OS1), d(OS2–Hs), and d(HW1,OW) in the H2O/Ph–COOH stable adsorption configuration elongate by 0.016, 0.032, and 0.022 Å, respectively, similar to the C=O bond and O–H bond elongation distances calculated by Gao et al.,[44] and the action of OS1 on HW1 changes the bond angle of the H2O molecule from 103.749 to 104.957°. At the −OH site, the −OH functional group has an electron conjugation effect, leading to an increase in the density of the Π electron cloud on the benzene ring and a gain of 0.007 electrons. The O–H bond in Ph–OH acts as a hydrogen bond donor, and the O atom in the H2O molecule acts as a hydrogen bond acceptor. After adsorption, the H atom in the O–H bond loses 0.032 electrons, the O atom gains 0.028 electrons, and the O atom in the H2O molecule gains 0.013 electrons. In the H2O/Ph–OH stable adsorption configuration, d(OS,HS) and d(HW1,OW) elongate by 0.016 and 0.005 Å, respectively. The charge of the O atom in the H2O molecule changes less, whereas the charges of the two H atoms in the H2O molecule change significantly, 0.024 and 0.028, which increases the bond angle between the H2O molecules from 103.749 to 104.683°. In both the —C=O and −O–R sites, OS has a high electronegativity and easily gains electrons, and Hw1 involved in the bond formation easily loses electrons, resulting in an increase in the OS charge by 0.043 and 0.031 in —C=O and −O–R, respectively; however, the bond length elongation is not evident in —C=O and −O–R , both being 0.007 Å. The bond angle of the H2O molecule in the H2O/Ph—C=O adsorption configuration changes from 103.749 to 104.277°, whereas in the H2O/Ph–O–R adsorption configuration, the bond angle of the H2O molecule decreases from 103.749 to 102.946° due to the charge attraction of OS to HW2.

As listed in Table , for the CO2 molecule in the Ph–COOH, Ph–OH, Ph—C=O, and Ph–O–R stable adsorption configurations, the O atoms in the OFGs all gain electrons, −0.011, −0.017, −0.01, and −0.01 e, respectively, and the C atoms in CO2 all lose electrons, 0.016, 0.026, 0.02, and 0.02 e, while the two O atoms of CO2 gain −0.012, −0.027, −0.024, and – 0.016 electrons, respectively. Figure e–h shows that the electron density difference diagrams are consistent with the results of the Mulliken atomic charge analysis. As shown in Table , the charge transfer is less when the CH4 molecule is adsorbed by different OFGs, and the center C atoms of the CH4 molecule all gain electrons, −0.028, −0.012, −0.009, and −0.009 e; the H atoms in the CH4 molecule all lose electrons; and the charges of the atoms in the different OFGs do not change significantly. The same consistency can be observed even in Figure i–l.

Table 6

Mulliken Charge Layout of CO2 Molecules for Different OFGs before and after Adsorption Equilibriuma

adsorption site	atom	Mulliken (before adsorption)	Mulliken (after adsorption)	Mulliken (variance)	atom	Mulliken (before adsorption)	Mulliken (after adsorption)	Mulliken (variance)
Ph–COOH	C	0.474	0.473	–0.001	CW	0.553	0.569	0.016
	OS1	–0.427	–0.438	–0.011	OW1	–0.276	–0.267	0.009
	OS2	–0.434	–0.432	0.002	OW2	–0.276	–0.297	–0.021
	HS	0.274	0.274	0
Ph–OH	OS	–0.441	–0.458	–0.017	CW	0.553	0.579	0.026
	HS	0.263	0.269	0.006	OW1	–0.276	–0.290	–0.014
					OW2	–0.276	–0.289	–0.013
Ph—C=O	OS	–0.398	–0.408	–0.010	CW	0.553	0.573	0.020
	C	0.296	0.294	–0.002	OW1	–0.276	–0.276	0
					OW2	–0.276	–0.300	–0.024
Ph–O–R	OS	–0.462	–0.472	–0.010	CW	0.553	0.573	0.020
	Ph(C)	0.295	0.294	–0.001	OW1	–0.276	–0.282	–0.006
	R(C)	0.013	0.001	–0.012	OW2	–0.276	–0.286	–0.010

CW: the C atom in CO2 molecule; OW1, OW2: two O atoms in CO2 molecule.

Combining the adsorption energy and charge analysis of the H2O, CO2, and CH4 molecules on different OFGs, it can be concluded that, the stronger the adsorption stability of different small molecules on the coal model surface for each OFG, the more evident the charge transfer between the group atoms, and the order of the adsorption stability of the small molecules on each OFG is H2O > CO2 > CH4.

Conclusions

The results of the PDOS and Mulliken bond layout analysis showed that H 1s orbitals and O 2p orbitals interact to form hydrogen bonds. The average bond lengths of the H2O molecules forming hydrogen bonds with −COOH, −OH, —C=O, and −O–R groups were 1.781, 1.841, 1.877, and 2.048 Å, respectively. Combining the numerical magnitude of the Mulliken bond layout, the delocalization of H 1s in PDOS, and the adsorption energy between the H2O molecules and different OFGs, the order of the bond strength between the H2O molecules and OFGs was found to be Ph–COOH > Ph–OH > Ph—C=O > Ph–O–R.

The results of the adsorption energy calculations for the different molecules confirmed the interaction between the H2O molecules and different OFGs via hydrogen bonding; hence, the adsorption stability of the H2O molecules for each OFG was higher than those of the CO2 and CH4 molecules. The adsorption stability of the H2O molecules for Ph–COOH was greater than that for the other OFGs because of the formation of two hydrogen bonds between the H2O molecules and −COOH. Similarly, the adsorption stability of the CO2 and CH4 molecules for Ph–COOH was greater than that for the other OFGs.

The results of the Mulliken charge layout and electron density difference analysis of the different molecules showed that after the adsorption of the H2O molecules by the different OFGs, the O atoms in the OFGs easily gain electrons and that the H atoms involved in bonding with the H2O molecules easily lose electrons, resulting in different degrees of elongation of the bond between the OFGs and H2O molecules; the most evident elongation was of the O–H bonds in the −COOH groups at 0.032 Å. The difference in the adsorption configuration led to an increase in the bond angle of the H2O molecule in the −COOH, −OH, and —C=O groups and a decrease in the case of the −O–R group. After the adsorption of the CO2 molecules by different OFGs, all the O atoms in the OFG gained electrons, and all the C atoms in the CO2 molecules lost electrons. After the adsorption of the CH4 molecules by different OFGs, all the C atoms at the center of the CH4 molecules gained electrons, while all the H atoms in the CH4 molecules lost electrons. The electron gained and lost by the different molecules were consistent with the electron density difference diagrams.

OFGs are important factors affecting gas adsorption; the adsorption stability of different small molecules for each OFG was found to be H2O > CO2 > CH4, indicating that H2O molecules have the highest adsorption capacity and that injecting water into the coal seam can improve the CBM yield; the adsorption effect of H2O was better than that of CO2, which can help accelerate the recovery of coal seam gases.