The Effect of Nitrogen-and Oxygen-Containing Functional Groups on C 2 H 6 /SO 2 /NO Adsorption: A Density Functional Theory Study

: This paper investigates the mechanism of nitrogen-and oxygen-containing functional groups in the collaborative adsorption of harmful gases by activated carbon through numerical simulation. The aim is to provide theoretical guidance for the industrial production of high-performance and universally applicable activated carbon. By employing density functional theory, we explore the impact of pyridine, pyrrole, carboxyl, and carbonyl groups on the co-adsorption of C 2 H 6 /SO 2 /NO by activated carbon through analyzing surface electrostatic potential (ESP), physical adsorption energy, and non-covalent interaction. The ﬁndings demonstrate that the presence of nitrogen-and oxygen-containing functional groups within activated carbon surfaces enhances their polarity, while simultaneously forming strong non-covalent interactions with C 2 H 6 and SO 2 . The N-atom of NO can form a strong C-N ionic bond with the C-atom of the benzene ring. The adsorption site of NO is inﬂuenced by the nitrogen-and oxygen-containing functional groups. On an activated carbon model containing a pyrrole functional group, NO exhibits meta-adsorption behavior, while on activated carbon with pyridine, carboxyl, and carbonyl groups, it shows ortho-adsorption characteristics. The interaction between C 2 H 6 and SO 2 , as well as NO, primarily involves the H-bond, whereas the interaction between SO 2 and NO is predominantly driven by dipole–dipole interactions. These intermolecular forces signiﬁcantly contribute to the mutual adsorption of these molecules.


Introduction
In the process of industrial production and biomass combustion, large amounts of sulfur-and nitrogen-containing pollutants, hydrocarbons, and CO 2 are discharged, and the emission of these pollutants has a negative impact on the global climate, aggravating the greenhouse effect and climate change [1][2][3].The study of collaborative control systems for pollutants will become a key content in the fight against climate change and the improvement of the ecological environment [4].Collaborative treatment of gaseous pollutants by activated carbon adsorption can better meet the needs and objectives of current waste gas treatment.The advantage of the adsorption method is that it is a simple process to operate, does not require the use of overly complicated devices, is easy to implement for automatic control, does not suffer from secondary contamination, and regenerates the adsorbent [5][6][7][8].
The adsorption properties of activated carbon are determined by its pore structure distribution, chemical composition, and molecular structure.The adsorption process primarily relies on the interaction between the activated carbon surface and the adsorbent.The type and strength of this interaction predominantly hinge upon the microcrystalline structure of the graphite layer present on the activated carbon surface [9].Chemically binding atoms and atomic groups other than carbon, the carbon atoms within this graphite layer form a diverse array of surface functional groups that significantly impact its adsorption performance [10,11].The oxygen-containing functional group of coal-based graphene acts as an electron acceptor and transporter, and plays an important role in enhancing charge transfer and hindering the recombination of electron-hole pairs [12,13].N doping remodels the local electron density of graphene surfaces and greatly promote adsorption with various interactions [9].
According to the interaction between the adsorbent surface and the adsorbate, adsorption can be classified into physical and chemical adsorption.Physical adsorption dominates when activated carbon absorbs small gas molecules [14].The physical adsorption process is primarily governed by noncovalent interaction, encompassing dispersion, H-bonds, π-π interaction, dipole-dipole interaction, and ion-dipole interaction [15].To assess these interactions' properties and their contribution to small molecule adsorption on activated carbon accurately and efficiently, simulation calculations based on density functional theory (DFT) can be conducted due to its advantages of cost-effectiveness, high research productivity, and calculation precision.In recent years, there has been a growing body of research focusing on the adsorption behavior based on DFT [16,17].Numerous research examples demonstrate that DFT is highly reliable and convenient for investigating molecular-level adsorption phenomena.The research methods and contents of activated carbon adsorption are summarized in Table 1.As depicted in Table 1, the current research on adsorption by DFT predominantly concentrates on a singular adsorbate, while the investigation into the interaction between multiple adsorbates remains relatively limited.In addition, the role of carbonyl groups in the adsorption process has not been thoroughly studied.−34.95 [18] The co-adsorption of C 2 H 6 /SO 2 /NO on activated carbon surfaces at the molecular level was investigated through Gaussian numerical simulations.The electron distribution and polarity on graphene surface were modified by doping various nitrogen-and oxygencontaining functional groups (pyridine, pyrrole, carboxyl, and carbonyl group) onto the activated carbon model, demonstrating the action mechanism of these functional groups Energies 2023, 16, 7537 3 of 13 in collaborative adsorption of C 2 H 6 /SO 2 /NO on activated carbon via an independent gradient model based on Hirshfeld partition (IGMH) analysis and adsorption energy calculation.

Calculation Models
Considering the accuracy and efficiency, a clustered graphene structure with five fused rings is employed as a model for activated carbon to discuss the effect of nitrogen and oxygen functional groups on the physical adsorption of C 2 H 6 /NO/SO 2 , as illustrated in Figure 1.For simplicity, we denote the original graphene model as OG, while the models containing pyridine functional group, pyrrole functional group, carboxyl group, and carbonyl group are denoted as PD, PR, CBX, and CBN, respectively.group SO2 Opt:M06-2X/6-31G(d, p) Sp: M06-2X/6-311+G G(d, p) −34.95 [18] The co-adsorption of C2H6/SO2/NO on activated carbon surfaces at the molecul level was investigated through Gaussian numerical simulations.The electron distributio and polarity on graphene surface were modified by doping various nitrogen-and oxyge containing functional groups (pyridine, pyrrole, carboxyl, and carbonyl group) onto t activated carbon model, demonstrating the action mechanism of these functional grou in collaborative adsorption of C2H6/SO2/NO on activated carbon via an independent gr dient model based on Hirshfeld partition (IGMH) analysis and adsorption energy calc lation.

Calculation Models
Considering the accuracy and efficiency, a clustered graphene structure with fi fused rings is employed as a model for activated carbon to discuss the effect of nitrog and oxygen functional groups on the physical adsorption of C2H6/NO/SO2, as illustrat in Figure 1.For simplicity, we denote the original graphene model as OG, while the mo els containing pyridine functional group, pyrrole functional group, carboxyl group, an carbonyl group are denoted as PD, PR, CBX, and CBN, respectively.Gaussian 16 [23] software was used to simulate the adsorption of C2H6, NO and SO Based on DFT, the structure was optimized at the level of B3LYP-D3(BJ) [24,25] /6-311+G [26].To improve the accuracy of the calculations, the single point energy of the optimiz structure was calculated at M062X [27] /jun-cc-pVTZ [28,29], taking into account the DF D3 [30] dispersion correction.The adsorption energy ( ) is defined as:

Calculation Methods
Gaussian 16 [23] software was used to simulate the adsorption of C 2 H 6 , NO and SO 2 .Based on DFT, the structure was optimized at the level of B3LYP-D3(BJ) [24,25] /6-311+G** [26].To improve the accuracy of the calculations, the single point energy of the optimized structure was calculated at M062X [27] /jun-cc-pVTZ [28,29], taking into account the DFT-D3 [30] dispersion correction.The adsorption energy (E ads ) is defined as: where E tot , E AC , and E mol represent the single point energies of physical adsorption products, activated carbon models and adsorbates (such as C 2 H 6 ), respectively.
The VMD [31] software and Multiwfn [32] software were used to display the ESP distribution on the molecular van der Waals (vdW) surface through an isosurface coloring of the electron density to study possible active sites, as shown in Figure 2.
Energies 2023, 16, 7537 4 of 14 where  ,  , and  represent the single point energies of physical adsorption products, activated carbon models and adsorbates (such as C2H6), respectively.
The VMD [31] software and Multiwfn [32] software were used to display the ESP distribution on the molecular van der Waals (vdW) surface through an isosurface coloring of the electron density to study possible active sites, as shown in Figure 2. In the IGMH analysis, Multiwfn software was used to analyze the wave function of the optimized structure, and the value of sign(λ2)ρ was mapped to the vdW surface by VMD software for the study of non-covalent interactions between molecules, as shown in Figure 3. λ2 is the second largest eigenvalue of the electron density (ρ) Hessian matrix, and sign() is the meaning of taking a sign.Meanwhile, the δG atom proposed by Lu et al. [33] was mapped to atoms to measure the contribution of each atom to the intermolecular in- In the IGMH analysis, Multiwfn software was used to analyze the wave function of the optimized structure, and the value of sign(λ 2 )ρ was mapped to the vdW surface by VMD software for the study of non-covalent interactions between molecules, as shown in Figure 3. λ 2 is the second largest eigenvalue of the electron density (ρ) Hessian matrix, and sign() is the meaning of taking a sign.Meanwhile, the δG atom proposed by Lu et al. [33] was mapped to atoms to measure the contribution of each atom to the intermolecular interaction, as shown in Figure 4.In the IGMH analysis, Multiwfn software was used to analyze the wave function of the optimized structure, and the value of sign(λ2)ρ was mapped to the vdW surface by VMD software for the study of non-covalent interactions between molecules, as shown in Figure 3. λ2 is the second largest eigenvalue of the electron density (ρ) Hessian matrix, and sign() is the meaning of taking a sign.Meanwhile, the δG atom proposed by Lu et al. [33] was mapped to atoms to measure the contribution of each atom to the intermolecular interaction, as shown in Figure 4.

ESP Analysis
ESP is crucial for the investigation and prediction of intermolecular interactions, particularly in relation to electrostatic interactions.The effect of N-and O-atom doping on the ESP of the activated carbon model is explored in Figure 5.The ESP exhibits negativity above the benzene ring of OG, positivity at the H-atom edge, and a relatively narrow and uniform range from −14.03 to 17.30 kcal/mol.Doping of the pyridine functional groups and pyrrole functional groups changes the ESP distribution of OG [10,20].After embedding the functional groups containing oxygen and nitrogen, the absolute value of ESP above the benzene ring decreases, except for PR, so it can be speculated that the electrostatic interaction of C2H6/SO2/NO adsorbed on it also decreases. of the electron density to study possible active sites, as shown in Figure 2. In the IGMH analysis, Multiwfn software was used to analyze the wave function of the optimized structure, and the value of sign(λ2)ρ was mapped to the vdW surface by VMD software for the study of non-covalent interactions between molecules, as shown in Figure 3. λ2 is the second largest eigenvalue of the electron density (ρ) Hessian matrix, and sign() is the meaning of taking a sign.Meanwhile, the δG atom proposed by Lu et al. [33] was mapped to atoms to measure the contribution of each atom to the intermolecular interaction, as shown in Figure 4.

ESP Analysis
ESP is crucial for the investigation and prediction of intermolecular interactions, particularly in relation to electrostatic interactions.The effect of N-and O-atom doping on the ESP of the activated carbon model is explored in Figure 5.The ESP exhibits negativity above the benzene ring of OG, positivity at the H-atom edge, and a relatively narrow and uniform range from −14.03 to 17.30 kcal/mol.Doping of the pyridine functional groups and pyrrole functional groups changes the ESP distribution of OG [10,20].After embedding the functional groups containing oxygen and nitrogen, the absolute value of ESP above the benzene ring decreases, except for PR, so it can be speculated that the electrostatic interaction of C2H6/SO2/NO adsorbed on it also decreases.

ESP Analysis
ESP is crucial for the investigation and prediction of intermolecular interactions, particularly in relation to electrostatic interactions.The effect of N-and O-atom doping on the ESP of the activated carbon model is explored in Figure 5.The ESP exhibits negativity above the benzene ring of OG, positivity at the H-atom edge, and a relatively narrow and uniform range from −14.03 to 17.30 kcal/mol.Doping of the pyridine functional groups and pyrrole functional groups changes the ESP distribution of OG [10,20].After embedding the functional groups containing oxygen and nitrogen, the absolute value of ESP above the benzene ring decreases, except for PR, so it can be speculated that the electrostatic interaction of C 2 H 6 /SO 2 /NO adsorbed on it also decreases.
As shown in Figure 5b, the ESP of PD ranges from −35.76 to 19.62 kcal/mol, suggesting that the presence of the pyridine functional group enhances both the range and heterogeneity of ESP distribution.While the ESP is negative near the N-atom, indicating that it is more likely to act as an electron donor, the H-atom of C 2 H 6 and the N-atom of NO as well as the S-atom of SO 2 are predicted to be adsorbed.For PR, a maximum ESP value of 40.47 kcal/mol is located near the H-atom attached to the N-atom of pyrrole, which can act as an electron acceptor to adsorb the C-atom of C 2 H 6 as well as O-atoms in NO and SO 2 .When the carboxyl group is doped in the activated carbon model, the ESP on the vdW surface ranges from −33.94 to 47.97 kcal/mol.The ESP is negative near the two O-atoms of the carboxyl group and positive near the H-atom of the carboxyl group, so that the carboxyl group acts not only as an electron donor, but also as an electron acceptor.For CBN, the ESP varies from −43.49 to 22.49 kcal/mol, with the O-atom in the carbonyl group having the most negative ESP and serving as an electron donor.As shown in Figure 5b, the ESP of PD ranges from −35.76 to 19.62 kcal/mol, suggesting that the presence of the pyridine functional group enhances both the range and heterogeneity of ESP distribution.While the ESP is negative near the N-atom, indicating that it is more likely to act as an electron donor, the H-atom of C2H6 and the N-atom of NO as well as the S-atom of SO2 are predicted to be adsorbed.For PR, a maximum ESP value of 40.47 kcal/mol is located near the H-atom attached to the N-atom of pyrrole, which can act as an electron acceptor to adsorb the C-atom of C2H6 as well as O-atoms in NO and SO2.When the carboxyl group is doped in the activated carbon model, the ESP on the vdW surface ranges from −33.94 to 47.97 kcal/mol.The ESP is negative near the two O-atoms of the carboxyl group and positive near the H-atom of the carboxyl group, so that the carboxyl group acts not only as an electron donor, but also as an electron acceptor.For CBN, the ESP varies from −43.49 to 22.49 kcal/mol, with the O-atom in the carbonyl group having the most negative ESP and serving as an electron donor.

Adsorption Simulation of C2H6
C2H6 and OG form weak C-H…C bonds, shown as green isosurfaces in Figure 6a.When C2H6 is adsorbed at the edge of the PD, the pyridine group acts as an electron donor and forms a weak H-bond with the H-atom of C2H6, which appears as a green isosurface.The H atom is a bright red color, indicating that it plays a dominant role in the interaction.Small green flakes form between the C-atom of C2H6 and the H-atom of PD, indicating a weak H-bond.After the embedding of the pyridine functional group, the region of the green isosurface between C2H6 and the activated carbon model increases, and hence the adsorption energy, as shown in Table 2.A weak H-bond forms between the C-atom of C2H6 and the H-atom of PR, in which the pyrrole group acts as an electron acceptor.From the isosurface area in Figure 6a-c and the adsorption energy in Table 2, it can be judged that the pyrrole functional group is more conductive to the adsorption of C2H6 than the pyridine functional group.

Adsorption Simulation of C 2 H 6
C 2 H 6 and OG form weak C-H. ..C bonds, shown as green isosurfaces in Figure 6a.When C 2 H 6 is adsorbed at the edge of the PD, the pyridine group acts as an electron donor and forms a weak H-bond with the H-atom of C 2 H 6 , which appears as a green isosurface.The H atom is a bright red color, indicating that it plays a dominant role in the interaction.Small green flakes form between the C-atom of C 2 H 6 and the H-atom of PD, indicating a weak H-bond.After the embedding of the pyridine functional group, the region of the green isosurface between C 2 H 6 and the activated carbon model increases, and hence the adsorption energy, as shown in Table 2.A weak H-bond forms between the C-atom of C 2 H 6 and the H-atom of PR, in which the pyrrole group acts as an electron acceptor.From the isosurface area in Figure 6a-c and the adsorption energy in Table 2, it can be judged that the pyrrole functional group is more conductive to the adsorption of C 2 H 6 than the pyridine functional group.As can be seen in Figure 6d, C 2 H 6 and CBX form two green disk-like isosurfaces representing the C-H. ..O and O-H. ..C bonds, respectively.The iso-surface area of the O-H. ..C bond surpasses that of the C-H. ..O bond, and the H-atom of the O-H. ..C bond is brown, indicating that the O-H. ..C bond contributes more than the C-H. ..O bond to the interaction and plays a dominant role.Upon the embedding of the carboxyl group, there is a significant increase in adsorption energy from 19.85 to 24.39 kJ/mol.This is because the carboxyl group can act as both an electron donor and an electron acceptor, and thus can interact with multiple atoms of C 2 H 6 , in agreement with ESP predictions.Figure 6e illustrates the adsorption configuration of C 2 H 6 on CBN.Instead of a non-covalent interaction with the carbonyl group, C 2 H 6 forms a H-bond with the H-atom next to the carbonyl group, so that the adsorption energy of C 2 H 6 on CBX is 0.27 kJ/mol lower than that on the OG.As can be seen in Figure 6d, C2H6 and CBX form two green disk-like isosurfaces representing the C-H…O and O-H…C bonds, respectively.The iso-surface area of the O-H…C bond surpasses that of the C-H…O bond, and the H-atom of the O-H…C bond is brown, indicating that the O-H…C bond contributes more than the C-H…O bond to the interaction and plays a dominant role.Upon the embedding of the carboxyl group, there is a significant increase in adsorption energy from 19.85 to 24.39 kJ/mol.This is because the carboxyl group can act as both an electron donor and an electron acceptor, and thus can interact with multiple atoms of C2H6, in agreement with ESP predictions.Figure 6e illustrates the adsorption configuration of C2H6 on CBN.Instead of a non-covalent interaction with the carbonyl group, C2H6 forms a H-bond with the H-atom next to the carbonyl group, so that the adsorption energy of C2H6 on CBX is 0.27 kJ/mol lower than that on the OG.
In Figure 7, the green isosurfaces formed by the different activated carbon models and C2H6 mainly represent dispersive interactions, and there is no obvious difference between them, as can also be seen from the adsorption energies in Table 2.This is mainly because the adsorption site of C2H6 on the activated carbon plane is far away from the functional group, so the functional group has almost no effect on the adsorption of C2H6 on the activated carbon plane.The isosurface area and adsorption energy of C2H6 on In Figure 7, the green isosurfaces formed by the different activated carbon models and C 2 H 6 mainly represent dispersive interactions, and there is no obvious difference between them, as can also be seen from the adsorption energies in Table 2.This is mainly because the adsorption site of C 2 H 6 on the activated carbon plane is far away from the functional group, so the functional group has almost no effect on the adsorption of C 2 H 6 on the activated carbon plane.The isosurface area and adsorption energy of C 2 H 6 on activated carbon planes are larger than those at activated carbon edges, indicating a higher likelihood for C 2 H 6 to be adsorbed onto activated carbon planes.
Energies 2023, 16, 7537 7 of 14 activated carbon planes are larger than those at activated carbon edges, indicating a higher likelihood for C2H6 to be adsorbed onto activated carbon planes.

Co-Adsorption Simulation of C2H6 and SO2
As shown in Figure 8a, the adsorption sites of C2H6 and SO2 are located on the OG plane.C2H6 and SO2 form continuous large-area green isosurfaces with the activated carbon model, respectively, dominated by dispersive interactions.The isosurface between the S-atom of SO2 and the C-atom of OG appears light blue, which is a dipole-dipole interaction.The dispersion-dominated interaction between the O-atom of SO2 and the Catom of the benzene ring is also clearly shown in Figure 8a.At the same time, there is a bond path between the S-atom of SO2 and the C-and H-atoms of C2H6, forming a weak interaction dominated by dispersion and H-bond.

Co-Adsorption Simulation of C 2 H 6 and SO 2
As shown in Figure 8a, the adsorption sites of C 2 H 6 and SO 2 are located on the OG plane.C 2 H 6 and SO 2 form continuous large-area green isosurfaces with the activated carbon model, respectively, dominated by dispersive interactions.The isosurface between the S-atom of SO 2 and the C-atom of OG appears light blue, which is a dipole-dipole interaction.The dispersion-dominated interaction between the O-atom of SO 2 and the C-atom of the benzene ring is also clearly shown in Figure 8a.At the same time, there is a bond path between the S-atom of SO 2 and the C-and H-atoms of C 2 H 6 , forming a weak interaction dominated by dispersion and H-bond.As shown in Figure 8b, the adsorption site of C2H6 remains positioned above the zene ring, while the adsorption site of SO2 moves from the activated carbon plane to activated carbon edge following the incorporation of the pyridine functional group.is because SO2 is an acidic oxide and pyridine is an alkaline functional group, and tends to interact with the pyridine functional group.The S-atom, being less electron tive than the O-atom in SO2, carries a positive charge and forms a blue-centered isosur with the N-atom through a typical dipole-dipole interaction.Meanwhile, a weak H-b is formed between the O-atom of SO2 and the H-atom of PD.The co-adsorption energ C2H6 and SO2 on the PD is 75.94 kJ/mol, shown in Table 3, is higher than on the OG, to the strong dipole-dipole interaction between SO2 and the pyridine functional grou  As shown in Figure 8b, the adsorption site of C 2 H 6 remains positioned above the benzene ring, while the adsorption site of SO 2 moves from the activated carbon plane to the activated carbon edge following the incorporation of the pyridine functional group.This is because SO 2 is an acidic oxide and pyridine is an alkaline functional group, and SO 2 tends to interact with the pyridine functional group.The S-atom, being less electronegative than the O-atom in SO 2 , carries a positive charge and forms a blue-centered isosurface with the N-atom through a typical dipole-dipole interaction.Meanwhile, a weak H-bond is formed between the O-atom of SO 2 and the H-atom of PD.The co-adsorption energy of C 2 H 6 and SO 2 on the PD is 75.94 kJ/mol, shown in Table 3, is higher than on the OG, due to the strong dipole-dipole interaction between SO 2 and the pyridine functional group.The adsorption site of C 2 H 6 moves from the activated carbon plane to the activated carbon edge after the embedding of the pyrrole functional group, as shown in Figure 8c.C-H. ..C bonds are formed between C 2 H 6 and PR.Due to the high absolute value of ESP, the green isosurface area is large near the H-atom of the pyrrole functional group.The adsorption site of SO 2 occurs on the activated carbon plane.The interaction of SO 2 adsorbed on the PR is similar to that on the OG.The interaction between C 2 H 6 and SO 2 is the C-H. ..C bond, formed by the H-atoms of C 2 H 6 and the O-atoms of SO 2 .As mentioned earlier, the interaction of C 2 H 6 adsorbed at the activated carbon edge is weaker than that on the activated carbon plane, so that the co-adsorption energy of C 2 H 6 and SO 2 on the PR is 59.40 kJ/mol is smaller than that on the OG.
Figure 9a shows that the adsorption site of C 2 H 6 is located on the activated carbon plane, while that of SO 2 is located on the activated carbon edge, with no interaction observed between C 2 H 6 and SO 2 .The S-atom of SO 2 is positively charged and forms a blue-centered isosurface with the O-atom of the carboxyl group, which is a dipole-dipole interaction.There is also a very distinct blue-centered isosurface between the O-atom of SO 2 and the H-atom of the carboxyl group, indicating the formation of a strong O-H. ..O bond.Due to the strong interaction between SO 2 and the carboxyl group, co-adsorption energy for C 2 H 6 and SO 2 on CBX amounts to 71.07 kJ/mol, surpassing that observed on OG.
Energies 2023, 16, 7537 9 o adsorbed on the PR is similar to that on the OG.The interaction between C2H6 and SO the C-H…C bond, formed by the H-atoms of C2H6 and the O-atoms of SO2.As mentio earlier, the interaction of C2H6 adsorbed at the activated carbon edge is weaker than on the activated carbon plane, so that the co-adsorption energy of C2H6 and SO2 on the is 59.40 kJ/mol is smaller than that on the OG. Figure 9a shows that the adsorption site of C2H6 is located on the activated car plane, while that of SO2 is located on the activated carbon edge, with no interaction served between C2H6 and SO2.The S-atom of SO2 is positively charged and forms a b centered isosurface with the O-atom of the carboxyl group, which is a dipole-dipole teraction.There is also a very distinct blue-centered isosurface between the O-atom of and the H-atom of the carboxyl group, indicating the formation of a strong O-H…O bo Due to the strong interaction between SO2 and the carboxyl group, co-adsorption ene for C2H6 and SO2 on CBX amounts to 71.07 kJ/mol, surpassing that observed on OG.As can be seen from Figure 9b, the adsorption site of C2H6 is still located on the a vated carbon plane, and a dispersion-led interaction is formed between C2H6 and the b zene ring.There is a green isosurface between the S-atom of SO2 and the O-atom of carbonyl group, which is a dipole-dipole interaction.The O-atoms of SO2 form dispers and weak H-bonds with the C-and H-atoms in the benzene ring, respectively.The O-a of SO2 and the H-atoms of C2H6 form weak H-bonds with small iso-surface area.Beca of the strong interaction between SO2 and the carbonyl group, co-adsorption energy C2H6 and SO2 on CBN is higher than that on OG, indicating that the carbonyl grou beneficial to the co-adsorption of C2H6 and SO2.

Co-Adsorption Simulation of C2H6 and NO
When C2H6 and NO are co-adsorbed on the OG, both C2H6 and NO adsorption s are located on the activated carbon plane, as shown in Figure 10a.The center of the iso face formed between the N-atom of NO and the C-atom of the benzene ring shows obvious blue color, indicating the formation of a strong C-N ionic bond.The O-atom more electronegative than the N-atom in NO, and the electron pair is biased towards As can be seen from Figure 9b, the adsorption site of C 2 H 6 is still located on the activated carbon plane, and a dispersion-led interaction is formed between C 2 H 6 and the benzene ring.There is a green isosurface between the S-atom of SO 2 and the O-atom of the carbonyl group, which is a dipole-dipole interaction.The O-atoms of SO 2 form dispersion and weak H-bonds with the C-and H-atoms in the benzene ring, respectively.The O-atom of SO 2 and the H-atoms of C 2 H 6 form weak H-bonds with small iso-surface area.Because of the strong interaction between SO 2 and the carbonyl group, co-adsorption energy of C 2 H 6 and SO 2 on CBN is higher than that on OG, indicating that the carbonyl group is beneficial to the co-adsorption of C 2 H 6 and SO 2 .

Co-Adsorption Simulation of C 2 H 6 and NO
When C 2 H 6 and NO are co-adsorbed on the OG, both C 2 H 6 and NO adsorption sites are located on the activated carbon plane, as shown in Figure 10a.The center of the isosurface formed between the N-atom of NO and the C-atom of the benzene ring shows an obvious blue color, indicating the formation of a strong C-N ionic bond.The O-atom is more electronegative than the N-atom in NO, and the electron pair is biased towards the O-atom, which will be repelled by the negative charge accumulated on the activated carbon plane.Simultaneously, after the N-atom acquires electrons from the C-atom, the electron distribution in the outer layer of the C-atom is the same as that of the N-atom, and the two form a stable shared electron pair.So, there is a strong interaction between the N-atom of NO and the C-atom of NO of the benzene ring.The adsorption sites and interactions of C2H6 and NO on the PD are similar to those on the OG.The N-atom is adsorbed on the C-atom adjacent to the pyridine nitrogen.This is because pyridine is an electron-withdrawing and ortho-para-positioning group, and the C-atom directly connected with the pyridine nitrogen loses electrons and interacts with NO.The O-atom of NO and the H-atoms of C2H6 form a small discontinuous green isosurface, indicating a weak H-bond.The co-adsorption energy of C2H6 and SO2 on the PD is lower than that on the OG because the interaction of the NO adsorbed on the PD is less strong than on the OG.
Since pyrrole is an electron-donating group and a meta-directing group, a blue-centered isosurface can be observed between the N-atom of NO and the meta-carbon atom of pyrrole nitrogen in Figure 10c.The adsorption site of C2H6 on the PR is located at the activated carbon edge, and the interaction is mainly weak H-bonds, making the co-adsorption energy small, as shown in Table 3.
The adsorption site of C2H6 is located in the CBX plane in Figure 11a.Similar to the pyridine functional group, the carboxyl group is an electron-withdrawing and ortho-positioning group, and thus the adsorption of NO occurs in the ortho-carbon atom of the carboxyl group.The co-adsorption energy of C2H6 and NO on CBX is the highest, indicating that the carboxyl group is most favorable for their co-adsorption.The adsorption sites and interactions of C 2 H 6 and NO on the PD are similar to those on the OG.The N-atom is adsorbed on the C-atom adjacent to the pyridine nitrogen.This is because pyridine is an electron-withdrawing and ortho-para-positioning group, and the C-atom directly connected with the pyridine nitrogen loses electrons and interacts with NO.The O-atom of NO and the H-atoms of C 2 H 6 form a small discontinuous green isosurface, indicating a weak H-bond.The co-adsorption energy of C 2 H 6 and SO 2 on the PD is lower than that on the OG because the interaction of the NO adsorbed on the PD is less strong than on the OG.
Since pyrrole is an electron-donating group and a meta-directing group, a bluecentered isosurface can be observed between the N-atom of NO and the meta-carbon atom of pyrrole nitrogen in Figure 10c.The adsorption site of C 2 H 6 on the PR is located at the activated carbon edge, and the interaction is mainly weak H-bonds, making the co-adsorption energy small, as shown in Table 3.
The adsorption site of C 2 H 6 is located in the CBX plane in Figure 11a.Similar to the pyridine functional group, the carboxyl group is an electron-withdrawing and orthopositioning group, and thus the adsorption of NO occurs in the ortho-carbon atom of the carboxyl group.The co-adsorption energy of C 2 H 6 and NO on CBX is the highest, indicating that the carboxyl group is most favorable for their co-adsorption.activated carbon edge, and the interaction is mainly weak H-bonds, making the co-adsorption energy small, as shown in Table 3.
The adsorption site of C2H6 is located in the CBX plane in Figure 11a.Similar to the pyridine functional group, the carboxyl group is an electron-withdrawing and ortho-positioning group, and thus the adsorption of NO occurs in the ortho-carbon atom of the carboxyl group.The co-adsorption energy of C2H6 and NO on CBX is the highest, indicating that the carboxyl group is most favorable for their co-adsorption.After the carbonyl group is embedded, the adsorption sites of C 2 H 6 and NO are located on the activated carbon plane.The O-and N-atoms of NO form weak H-bonds with the two H-atoms of C 2 H 6 , respectively, appearing as two connected disk-like isosurfaces.The carbonyl group is an electron-withdrawing and ortho-positioning group, so the dipoledipole interaction is formed by the N-atom of NO and the ortho-carbon atom of the carbonyl group.Compared to other activated carbon models, CBX has the smallest absolute value of ESP, producing a lower strength dipole-dipole interaction with NO rather than a higher strength ionic bond, so C 2 H 6 and NO have the lowest co-adsorption energy on CBX.

Co-Adsorption Simulation of C 2 H 6 , SO 2 and NO
For OG, the co-adsorption site of C 2 H 6 /NO/SO 2 is located on the activated carbon plane.However, the iso-surface area between C 2 H 6 /SO 2 and graphene is small, indicating a weak interaction between them.A non-covalent interaction is observed between C 2 H 6 /NO and SO 2 .The H-atom of C 2 H 6 forms a C-H. ..O bond with the O-atom of SO 2 , while the O-atom of NO engages in a dipole-dipole interaction with the S-atom of SO 2 .The co-adsorption sites and interactions of C 2 H 6 /NO/SO 2 on PD resemble those mentioned above for pairwise adsorption.But the strength of the interaction decreases, as evidenced by the adsorption energy in Table 3 and the iso-surface color in Figure 12b.For PR, the adsorption sites of SO 2 and C 2 H 6 are similar to those in the pairwise adsorption.SO 2 is adsorbed on the activated carbon plane, while C 2 H 6 is adsorbed near the pyrrole functional group.Compared to Figure 8c, the number of H-atoms involved in the formation of the non-covalent interaction between C 2 H 6 and PR increases, and thus the interaction region and strength increases, while the interaction region and strength between SO 2 and PR decreases.In comparison with Figure 10c, the adsorption site of NO is changed and the strength of the interaction between NO and PR is weakened.This is mainly due to the dipole-dipole interaction between the O-atom of SO 2 and the N-atom of NO, which weakens the adsorption strength of SO 2 and NO on the PR.
In Figure 13a, the adsorption site of SO 2 is on the activated carbon plane, and NO is ortho-adsorption, similar to that in Figure 11a.C 2 H 6 is adsorbed at the CBX edge, with its C-and H-atoms forming dispersive interactions with the carboxyl functional group.In contrast to planar adsorption, the area and strength of the interaction are weakened, resulting in a reduction in the adsorption energy.The O-atom of NO forms a dispersiondominated weak interaction with the H-atom of C 2 H 6 and the O-atom of SO 2 , thereby promoting mutual adsorption.Figure 13b shows that the adsorption site of SO 2 is similar to that in Figure 9b.The three H-atoms connected to the same C-atom in C 2 H 6 form a weak H-bond with the activated carbon plane.Unlike previous models, the O-atom of NO forms weak H-bonds with the H-atoms of CBN and C 2 H 6 , while the N-atom engages in a dipole-dipole interaction with the O-atom of SO 2 .Due to the weak strength of the interaction formed by C 2 H 6 and NO with CBN, the adsorption energy is only 75.49kJ/mol, which is almost equal to the co-adsorption energy of C 2 H 6 and SO 2 .tional group.Compared to Figure 8c, the number of H-atoms involved in the formatio of the non-covalent interaction between C2H6 and PR increases, and thus the interactio region and strength increases, while the interaction region and strength between SO2 an PR decreases.In comparison with Figure 10c, the adsorption site of NO is changed an the strength of the interaction between NO and PR is weakened.This is mainly due to th dipole-dipole interaction between the O-atom of SO2 and the N-atom of NO, which weak ens the adsorption strength of SO2 and NO on the PR.In Figure 13a, the adsorption site of SO2 is on the activated carbon plane, and NO ortho-adsorption, similar to that in Figure 11a.C2H6 is adsorbed at the CBX edge, with i C-and H-atoms forming dispersive interactions with the carboxyl functional group.I contrast to planar adsorption, the area and strength of the interaction are weakened, r sulting in a reduction in the adsorption energy.The O-atom of NO forms a dispersion dominated weak interaction with the H-atom of C2H6 and the O-atom of SO2, thereby pro moting mutual adsorption.Figure 13b shows that the adsorption site of SO2 is similar t that in Figure 9b.The three H-atoms connected to the same C-atom in C2H6 form a wea H-bond with the activated carbon plane.Unlike previous models, the O-atom of NO form

Conclusions
The co-adsorption of C2H6/SO2/NO by the activated carbon has been investigated a the molecular level.The presence of nitrogen-containing and oxygen-containing func tional groups alters the ESP distribution of activated carbon models, thereby influencing the adsorption mechanism of activated carbon onto C2H6/SO2/NO.
The adsorption interaction of C2H6 on the activated carbon plane is higher than tha on the activated carbon edge, and the functional group has little effect on the adsorption of C2H6 on the activated carbon plane.The non-covalent interaction of C2H6 adsorption on the activated carbon edge is an H-bond.Except for the carbonyl group, other functiona groups promote the adsorption of C2H6 on the activated carbon edge.C2H6 does not inter act non-covalently with the carbonyl group, but forms an H-bond with the H-atom nex to the carbonyl group, resulting in a slightly low adsorption energy.
The S-atom of SO2 can form dipole-dipole interactions with the N-atom of the pyri dine functional group, as well as the O-atoms of both the carboxyl and carbonyl groups facilitating its adsorption at the activated carbon edge.Additionally, SO2 can also be ad sorbed on the activated carbon plane.For the co-adsorption of C2H6 and NO, the N-atom of NO can form a strong C-N ionic bond with the C-atom of the benzene ring.NO is meta adsorbed on the activated carbon model containing a pyrrole functional group, while or tho-adsorbed on activated carbon models containing other functional groups, but the ad sorption site of NO will change due to the influence of C2H6 and SO2.In particular, for th co-adsorption of C2H6/SO2/NO, the O-atom of NO forms a weak H-bond with the H-atom of the benzene ring on the activated carbon model containing a carbonyl group.The inter action between C2H6 and SO2 is dominated by the H-bond formed by the O-atom of SO and the H-atom of C2H6.Both N-and O-atoms of NO can form weak H-bonds with H atoms of C2H6.Moreover, the S-and O-atoms of SO2 can form a dipole-dipole interaction with the O-and N-atoms of NO, respectively, thereby promoting mutual adsorption.

Conclusions
The co-adsorption of C 2 H 6 /SO 2 /NO by the activated carbon has been investigated at the molecular level.The presence of nitrogen-containing and oxygen-containing functional groups alters the ESP distribution of activated carbon models, thereby influencing the adsorption mechanism of activated carbon onto C 2 H 6 /SO 2 /NO.
The adsorption interaction of C 2 H 6 on the activated carbon plane is higher than that on the activated carbon edge, and the functional group has little effect on the adsorption of C 2 H 6 on the activated carbon plane.The non-covalent interaction of C 2 H 6 adsorption on the activated carbon edge is an H-bond.Except for the carbonyl group, other functional groups promote the adsorption of C 2 H 6 on the activated carbon edge.C 2 H 6 does not interact non-covalently with the carbonyl group, but forms an H-bond with the H-atom next to the carbonyl group, resulting in a slightly low adsorption energy.
The S-atom of SO 2 can form dipole-dipole interactions with the N-atom of the pyridine functional group, as well as the O-atoms of both the carboxyl and carbonyl groups, facilitating its adsorption at the activated carbon edge.Additionally, SO 2 can also be adsorbed on the activated carbon plane.For the co-adsorption of C 2 H 6 and NO, the N-atom of NO can form a strong C-N ionic bond with the C-atom of the benzene ring.NO is meta-adsorbed on the activated carbon model containing a pyrrole functional group, while ortho-adsorbed on activated carbon models containing other functional groups, but the adsorption site of NO will change due to the influence of C 2 H 6 and SO 2 .In particular, for the co-adsorption of

Figure 2 .
Figure 2. Color scale bar of the electron density.

Figure 2 .
Figure 2. Color scale bar of the electron density.

Figure 2 .
Figure 2. Color scale bar of the electron density.

Figure 4 .
Figure 4. Coloring method for mapping δG atom to atoms.

Figure 2 .
Figure 2. Color scale bar of the electron density.

Figure 4 .
Figure 4. Coloring method for mapping δG atom to atoms.

Figure 4 .
Figure 4. Coloring method for mapping δG atom to atoms.

Figure 5 .
Figure 5. ESP distribution of (a) OG, (b) PD, (c) PR, (d) CBX, and (e) CBN.The surface local minima and maxima of the ESP are represented as cyan and orange spheres, respectively.The transparent ones correspond to the extrema on the backside of the graph.

Figure 5 .
Figure 5. ESP distribution of (a) OG, (b) PD, (c) PR, (d) CBX, and (e) CBN.The surface local minima and maxima of the ESP are represented as cyan and orange spheres, respectively.The transparent ones correspond to the extrema on the backside of the graph.

Figure 6 .
Figure 6.Sign(λ2)ρ-colored vdW surface corresponding to IGMH analysis for the adsorption of C2H6 at the edge of (a) OG, (b) PD, (c) PR, (d) CBX, and (e) CBN.Atoms are colored by δG atom to highlight their relative contributions.BCPs (orange spheres) and bond paths (brown lines) are also shown.

Figure 6 .
Figure 6.Sign(λ 2 )ρ-colored vdW surface corresponding to IGMH analysis for the adsorption of C 2 H 6 at the edge of (a) OG, (b) PD, (c) PR, (d) CBX, and (e) CBN.Atoms are colored by δG atom to highlight their relative contributions.BCPs (orange spheres) and bond paths (brown lines) are also shown.

Figure 7 .
Figure 7. Sign(λ2)ρ-colored vdW surface corresponding to IGMH analysis for the adsorption of C2H6 on the plane of (a) OG, (b) PD, (c) PR, (d) CBX, and (e) CBN.Atoms are colored by δG atom to highlight their relative contributions.BCPs (orange spheres) and bond paths (brown lines) are also shown.

Figure 7 .
Figure 7. Sign(λ 2 )ρ-colored vdW surface corresponding to IGMH analysis for the adsorption of C 2 H 6 on the plane of (a) OG, (b) PD, (c) PR, (d) CBX, and (e) CBN.Atoms are colored by δG atom to highlight their relative contributions.BCPs (orange spheres) and bond paths (brown lines) are also shown.

Figure 8 .
Figure 8. Sign(λ 2 )ρ-colored vdW surface corresponding to IGMH analysis for the co-adsorption of C 2 H 6 and SO 2 on (a) OG, (b) PD, and (c) PR.Atoms are colored by δG atom to highlight their relative contributions.Bond paths (brown lines) are also shown.

Figure 9 .
Figure 9. Sign(λ2)ρ-colored vdW surface corresponding to IGMH analysis for the co-adsorptio C2H6 and SO2 on (a) CBX and (b) CBN.Atoms are colored by δG atom to highlight their relative tributions.Bond paths (brown lines) are also shown.

Figure 9 .
Figure 9. Sign(λ 2 )ρ-colored vdW surface corresponding to IGMH analysis for the co-adsorption of C 2 H 6 and SO 2 on (a) CBX and (b) CBN.Atoms are colored by δG atom to highlight their relative contributions.Bond paths (brown lines) are also shown.

Figure 10 .
Figure 10.Sign(λ2)ρ-colored vdW surface corresponding to IGMH analysis for the co-adsorption of C2H6 and NO on (a) OG, (b) PD, and (c) PR.Atoms are colored by δG atom to highlight their relative contributions.Bond paths (brown lines) are also shown.

Figure 11 .
Figure 11.Sign(λ2)ρ-colored vdW surface corresponding to IGMH analysis for the co-adsorption of C2H6 and NO on (a) CBX and (b) CBN.Atoms are colored by δG atom to highlight their relative contributions.Bond paths (brown lines) are also shown.

Figure 10 .
Figure 10.Sign(λ 2 )ρ-colored vdW surface corresponding to IGMH analysis for the co-adsorption of C 2 H 6 and NO on (a) OG, (b) PD, and (c) PR.Atoms are colored by δG atom to highlight their relative contributions.Bond paths (brown lines) are also shown.

Figure 11 .
Figure 11.Sign(λ2)ρ-colored vdW surface corresponding to IGMH analysis for the co-adsorption of C2H6 and NO on (a) CBX and (b) CBN.Atoms are colored by δG atom to highlight their relative contributions.Bond paths (brown lines) are also shown.After the carbonyl group is embedded, the adsorption sites of C2H6 and NO are located on the activated carbon plane.The O-and N-atoms of NO form weak H-bonds with the two H-atoms of C2H6, respectively, appearing as two connected disk-like isosurfaces.

Figure 11 .
Figure 11.Sign(λ 2 )ρ-colored vdW surface corresponding to IGMH analysis for the co-adsorption of C 2 H 6 and NO on (a) CBX and (b) CBN.Atoms are colored by δG atom to highlight their relative contributions.Bond paths (brown lines) are also shown.

Figure 12 .
Figure 12.Sign(λ2)ρ-colored vdW surface corresponding to IGMH analysis for the co-adsorption C2H6, SO2, and NO on (a) OG, (b) PD, and (c) PR.Atoms are colored by δG atom to highlight the relative contributions.Bond paths (brown lines) are also shown.

Figure 12 .
Figure 12.Sign(λ 2 )ρ-colored vdW surface corresponding to IGMH analysis for the co-adsorption of C 2 H 6 , SO 2 , and NO on (a) OG, (b) PD, and (c) PR.Atoms are colored by δG atom to highlight their relative contributions.Bond paths (brown lines) are also shown.

Figure 13 .
Figure 13.Sign(λ2)ρ-colored vdW surface corresponding to IGMH analysis for the co-adsorption o C2H6, SO2, and NO on (a) CBX and (b) CBN.Atoms are colored by δG atom to highlight their relativ contributions.Bond paths (brown lines) are also shown.

Figure 13 .
Figure 13.Sign(λ 2 )ρ-colored vdW surface corresponding to IGMH analysis for the co-adsorption of C 2 H 6 , SO 2 , and NO on (a) CBX and (b) CBN.Atoms are colored by δG atom to highlight their relative contributions.Bond paths (brown lines) are also shown.

Table 1 .
Research methods and contents of activated carbon adsorption by DFT.

Table 2 .
Adsorption energy (kJ/mol) of C 2 H 6 on the plane and edge of the activated carbon model.

Table 2 .
Adsorption energy (kJ/mol) of C2H6 on the plane and edge of the activated carbon model.

Table 3 .
Co-adsorption energy (kJ/mol) of C 2 H 6 /SO 2 /NO on the activated carbon model.