Al-Decorated C2N Monolayer as a Potential Catalyst for NO Reduction with CO Molecules: A DFT Investigation

Developing efficient and economical catalysts for NO reduction is of great interest. Herein, the catalytic reduction of NO molecules on an Al-decorated C2N monolayer (Al-C2N) is systematically investigated using density functional theory (DFT) calculations. Our results reveal that the Al-C2N catalyst is highly selective for NO, more so than CO, according to the values of the adsorption energy and charge transfer. The NO reduction reaction more preferably undergoes the (NO)2 dimer reduction process instead of the NO direct decomposition process. For the (NO)2 dimer reduction process, two NO molecules initially co-adsorb to form (NO)2 dimers, followed by decomposition into N2O and Oads species. On this basis, five kinds of (NO)2 dimer structures that initiate four reaction paths are explored on the Al-C2N surface. Particularly, the cis-(NO)2 dimer structures (Dcis-N and Dcis-O) are crucial intermediates for NO reduction, where the max energy barrier along the energetically most favorable pathway (path II) is as low as 3.6 kcal/mol. The remaining Oads species on Al-C2N are then easily reduced with CO molecules, being beneficial for a new catalytic cycle. These results, combined with its low-cost nature, render Al-C2N a promising catalyst for NO reduction under mild conditions.


Introduction
The increasing emission of nitrogen oxides (NO x ) has brought serious harm to the atmospheric environment and human health [1][2][3]. Nitric oxide (NO), which comprises approximately 95% of NO x emissions, is considered a major cause of acid rain and photochemical smog formation [4]. Selective catalytic reduction (SCR) is a promising method that typically selects CO [5][6][7][8][9], H 2 [8][9][10][11], or NH 3 [12] as the reducing agent to eliminate emitted NO. Since CO and NO commonly coexist in exhaust gases, the catalytic reduction of NO with CO as a reducing agent can simultaneously convert CO and NO pollutants into harmless N 2 and acceptable CO 2 . Noble metal catalysts such as Pt, Au, or Pd have been extensively studied; however, there are problems, such as high cost, low abundance, and toxicity [13][14][15][16]. Thus, it is of utmost importance to design high-efficiency and low-cost alternative catalysts to remove or reduce NO molecules.
Reducing the particle size of active metals to a few atoms is a valuable strategy to improve catalytic activity [17][18][19][20]. Compared to traditional catalysts, single-atom catalysts can greatly decrease the amount of metal used, thereby reducing costs. In particular, single-atom catalysts have been proven to efficiently catalyze or adsorb various harmful gas molecules, such as NO [21][22][23][24][25], CO [23,25], H 2 S [26], and SO 2 [27]. Recently, a twodimensional (2D) graphene porous material, a C 2 N monolayer, was successfully prepared via a simple wet chemical reaction [28]. This novel material with a uniform pore distribution has attracted much attention due to its large surface area and good structural stability. Given the uniform cavity structure of C 2 N, it has been demonstrated to be a suitable material for anchoring metal atoms. Previous studies have shown that metal-atom-decorated C 2 N

Computational Methods
All DFT calculations were carried out at the level of the B3LYP exchange-correlation functional with Grimme's DFT-D3 empirical dispersion correction using the Gaussian09 software package [45][46][47][48]. Previous literature confirmed that the B3LYP functional with DFT-D3 is a reasonable condition for calculating intermolecular non-covalent interactions [49]. The 6-31G(d, p) basis set was used to describe all atoms [50]. A pristine C 2 N cluster model in this study contained 37 carbon atoms, 12 nitrogen atoms, and 12 hydrogen atoms. All the energies were corrected with zero-point vibrational energy (ZPE). Vibration frequency calculations were performed to verify the optimized structure, where the minimum structure had no imaginary frequency, and the transition state only had one imaginary frequency. Intrinsic reaction coordinate (IRC) calculations were used to verify the transition states [51][52][53]. Atomic charges were discussed with the natural bond orbital (NBO) analysis [54]. Electron density difference (EDD) plots were obtained with the Multiwfn program [55]. For each adsorption configuration, the EDD plots were calculated as: where ρ A/S , ρ A , and ρ S are the electron density of the total complexes, isolated substrate, and isolated adsorbate, respectively. The adsorption energy (E ads ) of a given adsorbate was defined as: where E total , E A , and E S are the energies of the total adsorbate-substrate systems, isolated adsorbate, and isolated substrate, respectively. The change in Gibbs free energy (∆G) was defined as: where ∆H and ∆S represent the enthalpy with a zero-point energy correction and the entropy change at 298.15 K, respectively.

Geometrical Structures and Stability of Pristine C 2 N and Al-C 2 N Monolayer
Firstly, we examined the geometric structure and stability of the designed Al-C 2 N. The optimized structure of the pristine C 2 N cluster is shown in Figure 1a. The calculated lattice parameter of 8.286 Å was consistent with the experiment result (8.30 Å) [28]. Then, a single Al atom was attached to the C 2 N cluster via two adjacent N atoms (shown in Figure 1b), with both bond lengths being 1.939 Å, in which the Al atom was more preferably anchored at the corners of the six-fold cavity of the C 2 N. The calculated bond length value was in line with the previously periodic system-reported results (1.96 Å) [56]. EDD plots revealed a sizeable interaction area between the Al atom and its two adjacent N atoms. It is worth mentioning that the modification of the Al atoms could effectively change the surface properties of the C 2 N monolayer. As shown in Figure 1c,d, the uniformly distributed charge on the C 2 N monolayer changed to a directional concentrated distribution, which was essential for the subsequent adsorption of gas molecules.

Geometrical Structures and Stability of Pristine C2N and Al-C2N Monolayer
Firstly, we examined the geometric structure and stability of the des The optimized structure of the pristine C2N cluster is shown in Figure 1a. lattice parameter of 8.286 Å was consistent with the experiment result (8.30 a single Al atom was attached to the C2N cluster via two adjacent N ato Figure 1b), with both bond lengths being 1.939 Å, in which the Al atom wa ably anchored at the corners of the six-fold cavity of the C2N. The calculate value was in line with the previously periodic system-reported results (1.9 plots revealed a sizeable interaction area between the Al atom and its two oms. It is worth mentioning that the modification of the Al atoms could effe the surface properties of the C2N monolayer. As shown in Figure 1c,d, the tributed charge on the C2N monolayer changed to a directional concentrate which was essential for the subsequent adsorption of gas molecules. To evaluate the thermal stability of the designed Al-C2N systems, we c simulations at 300 K and 500 K for 8 ps with a time step of 2 fs under the (see Figure S1 in the Supplementary Materials). According to the MD si energies of the Al-C2N system fluctuated gently, suggesting its high therm bility.

Adsorption Behavior of NO and CO Molecules on Al-C2N Surface
The stable configurations of CO and NO adsorbed on the Al-C2N s played in Figure 2. Table 1 summarizes the corresponding adsorption para NO and CO molecules, including the Eads, ΔG, and charge transfer value the calculated ΔG values of the CO or NO molecules adsorbed on the Al-C2 negative, suggesting that the adsorption of these species was thermodynam neous.
The adsorption geometries of the NO, CO, and (NO)2 dimers on Al-C To evaluate the thermal stability of the designed Al-C 2 N systems, we carried out MD simulations at 300 K and 500 K for 8 ps with a time step of 2 fs under the NVT ensemble (see Figure S1 in the Supplementary Materials). According to the MD simulations, the energies of the Al-C 2 N system fluctuated gently, suggesting its high thermodynamic stability.

Adsorption Behavior of NO and CO Molecules on Al-C 2 N Surface
The stable configurations of CO and NO adsorbed on the Al-C 2 N surface are displayed in Figure 2. Table 1 summarizes the corresponding adsorption parameters for the NO and CO molecules, including the E ads , ∆G, and charge transfer values. Note that all the calculated ∆G values of the CO or NO molecules adsorbed on the Al-C 2 N surface were negative, suggesting that the adsorption of these species was thermodynamically spontaneous. which was more negative than the values in Si-doped graphene (−18.4 and −4.4 kcal/mol) [57]. From the viewpoint of adsorption energy, it is clear that the N-end adsorption was energetically more favorable than the O-end. This result was also supported by the NBO charge analysis, in which the N-end mode was accompanied by a larger charge transfer of 0.430 e from the Al-C2N surface to the 2π* orbital of the NO molecule (Table 1). As for the CO molecules, our results demonstrated that CO preferred to adsorb on the Al-C2N surface via its C-end. Figure 2c demonstrates that the C-O bond length of CO was nearly unchanged compared to that of the free CO molecule (1.14 Å), indicating that CO was not activated after being adsorbed on the Al-C2N surface. Based on the Eads value, the adsorption of CO (−21.8 kcal/mol) on Al-C2N was weaker than that of NO (−29.2 kcal/mol). In this case, it was expected that the tendency of the NO molecule to adsorb onto the Al-C2N surface was greater than that of CO. Unlike the NO molecules, CO acted as the electron donor, where the charge value transferred from the CO molecule to the Al-C2N surface was 0.083 e ( Table 1). Table 1. Calculated adsorption energies (Eads, kcal/mol), adsorption free energies (∆G, kcal/mol), and net charge-transfer values (q, e) for different adsorption species on the Al-C2N surface, along with the corresponding energy barriers (Ea, kcal/mol) and reaction energies (ΔEr) for a single NO or (NO)2 dimer reduction on Al-C2N surface.

Adsorbate
Eads Next, we considered the (NO)2 dimer configuration formed by two NO molecules coadsorbed on the Al-C2N surface. The (NO)2 dimer was characterized for the first time by Dinerman and Ewing using infrared spectroscopy [59]. The stable (NO)2 dimer adsorption configurations are illustrated in Figure 2d-h. The IR spectra plots of five (NO)2 dimers on the Al-C2N surface are displayed in Figure S2. As can be seen, five different (NO)2 dimers were obtained on the Al-C2N surface. Figure 2d shows a five-membered ring (NO)2 dimer structure (labeled as Dring), in   The adsorption geometries of the NO, CO, and (NO) 2 dimers on Al-C 2 N are shown in Figure 2. For the NO molecules, two possible adsorption modes (including N-end and Oend) were investigated. From Figure 2a,b, it can be seen that the NO molecules were tilted concerning the Al-C 2 N surface, consistent with previous reports [24,57,58]. As evident, the calculated N-O bond lengths of the NO molecules were elongated to 1.203 Å and 1.213 Å, respectively, when compared with the free NO molecule (1.160 Å). The E ads values for the Nend and O-end adsorption modes were −29.2 and −7.4 kcal/mol, respectively, which was more negative than the values in Si-doped graphene (−18.4 and −4.4 kcal/mol) [57]. From the viewpoint of adsorption energy, it is clear that the N-end adsorption was energetically more favorable than the O-end. This result was also supported by the NBO charge analysis, in which the N-end mode was accompanied by a larger charge transfer of 0.430 e from the Al-C 2 N surface to the 2π* orbital of the NO molecule ( Table 1).
As for the CO molecules, our results demonstrated that CO preferred to adsorb on the Al-C 2 N surface via its C-end. Figure 2c demonstrates that the C-O bond length of CO was nearly unchanged compared to that of the free CO molecule (1.14 Å), indicating that CO was not activated after being adsorbed on the Al-C 2 N surface. Based on the E ads value, the adsorption of CO (−21.8 kcal/mol) on Al-C 2 N was weaker than that of NO (−29.2 kcal/mol). In this case, it was expected that the tendency of the NO molecule to adsorb onto the Al-C 2 N surface was greater than that of CO. Unlike the NO molecules, CO acted as the electron donor, where the charge value transferred from the CO molecule to the Al-C 2 N surface was 0.083 e (Table 1). Next, we considered the (NO) 2 dimer configuration formed by two NO molecules co-adsorbed on the Al-C 2 N surface. The (NO) 2 dimer was characterized for the first time by Dinerman and Ewing using infrared spectroscopy [59]. The stable (NO) 2 dimer adsorption configurations are illustrated in Figure 2d-h. The IR spectra plots of five (NO) 2 dimers on the Al-C 2 N surface are displayed in Figure S2. As can be seen, five different (NO) 2 dimers were obtained on the Al-C 2 N surface. Figure 2d shows a five-membered ring (NO) 2 dimer structure (labeled as D ring ), in which both NO molecules were bound to the Al site through their O-end. The bond lengths of the two formed Al-O bonds and the N 1 -N 2 bond were 1.788, 1.770, and 1.248 Å, respectively. This structure was similar to that of Si-doped graphene (1.783, 1.762, and 1.240 Å for two Si-O bonds and the N 1 -N 2 bond) [60]. Figure 2e,g display the cis-and trans-(NO) 2 dimer structures at the N-end (labeled as D cis-N and D trans-N ), respectively, in which one NO molecule was adsorbed into the Al site via its N-end and two NO molecules were bound through N-N bonds. The calculated bond lengths of the N 1 -N 2 bond were 1.469 and 1.286 Å, respectively. It is noteworthy that two novel (NO) 2 dimer structures were explored in this work, which have not been reported in current catalysts [57,59,[61][62][63][64]. Among the above (NO) 2 dimers, the calculated N 1 -N 2 bond lengths ranged from 1.505 to 1.233 Å, which were much shorter than the value in the gas phase (NO) 2 dimer (1.970 Å). As shown in Table 1, the calculated adsorption energies of the five (NO) 2 dimers on the Al-C 2 N surface were significantly enhanced, with values of −109.7, −53.1, −61.7, −73.8, and −62.0 kcal/mol, respectively, which were larger than twice that of a NO molecule (−29.2 kcal/mol). This indicated that the addition of the second NO molecule was beneficial for strengthening the interaction between the catalyst and NO molecule. Similar results were further verified with the NBO charge analysis, where the considerable charge-transfer values from the Al-C 2 N surface to (NO) 2 dimers were −1.377, −0.672, −0.731, −1.303, and −0697, respectively (Table 1).

NO Reduction Mechanism on Al-C 2 N Surface
Here, the NO reduction mechanism mainly included the direct decomposition process and the (NO) 2 dimer reduction process. For the former, a NO molecule was directly decomposed into O and N atoms. For the latter, two NO molecules were co-adsorbed forming (NO) 2 dimers, followed by their decomposition into N 2 O molecules and O atoms. Subsequently, the N 2 O molecules were desorbed, and the remaining O atoms could be removed with the NO or CO molecules. Figure 3 shows the energy profile of the NO direct decomposition process on Al-C 2 N, where the energy sum of Al-C 2 N and free NO molecules was set as the reference energy. As seen, the reaction began with the NO molecule adsorbed on Al-C 2 N via its N-end. In the TS structure, the calculated O-N bond length of the NO molecule was elongated from 1.215 Å to 2.420 Å. In the FS structure, the O-N bond was broken and the distance between the O and N atoms was 3.292 Å. Our results showed that the NO direct decomposition process was unfavorable both in kinetics and thermodynamics due to the high reaction energy barrier (68.0 kcal/mol) and endothermic nature (41.1 kcal/mol), which agreed withprevious reports, such as Si-doped graphene (39.2 kcal/mol) [24], Si-doped BN nanosheets (57.9 kcal/mol) [60], and Fe-doped graphene (124.1 kcal/mol) [25].

NO Direct Decomposition Process
1.215 Å to 2.420 Å. In the FS structure, the O-N bond was broken and the distance b the O and N atoms was 3.292 Å. Our results showed that the NO direct decomp process was unfavorable both in kinetics and thermodynamics due to the high r energy barrier (68.0 kcal/mol) and endothermic nature (41.1 kcal/mol), which agree previous reports, such as Si-doped graphene (39.2 kcal/mol) [24], Si-doped BN nan (57.9 kcal/mol) [60], and Fe-doped graphene (124.1 kcal/mol) [25].

(NO) 2 Dimer Reduction Process
In this section, we examined the possible reaction pathways of the (NO) 2 dimer reduction process on Al-C 2 N. There were four reaction pathways starting with different (NO) 2 dimer structures described as path I, path II, path III, and path IV, respectively. For simplicity, the remaining oxygen atoms on the Al-C 2 N surface were labeled as O ads .
In path Ia, the five-membered ring (NO) 2 dimer structure (D ring ) was the initial state. The energy profile and corresponding minima state and transition state are displayed in Figure 4a. As can be seen, the D ring structure could be decomposed into the product (N 2 O + O ads ) through the transition state with a high-energy barrier of 33.5 kcal/mol. In the TS structure, the N 2 -O 2 bond broke with the bond length increasing from 1.398 to 2.364 Å, while the N 1 -N 2 bond length decreased from 1.248 to 1.141 Å. The entire process from D ring to the FS structure was endothermic by 23.2 kcal/mol. Given the high reaction barrier and endothermicity, it was expected that the D ring dimer reduction on Al-C 2 N was unfavorable both kinetically and thermodynamically.
In path Ib, a two-step reaction was identified: (i) (NO) 2 → N 2 + 2O ads , followed by (ii) CO + O ads → CO 2 . As shown in Figure 4b, the D ring structure was taken as the initial state and, subsequently, CO was physisorbed over Al-C 2 N to form an intermediate state (the MS1 structure). In the TS1 structure, two N-O bonds broke with the bond lengths increasing to 1.880 and 1.978 Å, respectively, while the N 1 -N 2 bond length was shortened to 1.144 Å. Next, N 2 was completely formed in the MS2 structure. In the next step, CO approached the O 1 atom. The O 1 ···C bond's length reduced from 2.859 to 2.152 Å and, finally, formed the CO 2 molecule. Note that the energy barriers of the first and second steps were 43.1 and 1.6 kcal/mol, respectively, which could be provided by the larger exothermic reaction energy (−67.7 kcal/mol, from D ring to FS).
In path II, the reaction started with the co-adsorption of two NO molecules to generate a cis-(NO) 2 dimer (N-end, D cis-N ) structure, as shown in Figure 5. As seen, this step had a negligible energy barrier and was exothermic by 17.3 kcal/mol. Then, the D cis-N structure could be converted to the more stable cis-(NO) 2 dimer (O-end, D cis-O ) structure by overcoming a small energy barrier of 3.6 kcal/mol, being exothermic by 8.6 kcal/mol. Finally, the D cis-O structure decomposed into the product (N 2 O and O ads species) through TS2 by breaking the N 1 -O1 bond. In the TS2 structure, the N 1 -O 1 distance significantly elongated from 1.469 to 1.659 Å, while the N 1 -N 2 distance decreased from 1.240 to 1.207 Å. We note that there was a negligible energy barrier for this step (2.7 kcal/mol), which was exothermic by 24.8 kcal/mol. Since the entire reaction was a highly exothermic process (−50.7 kcal/mol, from IS to FS), it was thermodynamically feasible under mild conditions. + Oads) through the transition state with a high-energy barrier of 33.5 kcal/mol. In the TS structure, the N2-O2 bond broke with the bond length increasing from 1.398 to 2.364 Å, while the N1-N2 bond length decreased from 1.248 to 1.141 Å. The entire process from Dring to the FS structure was endothermic by 23.2 kcal/mol. Given the high reaction barrier and endothermicity, it was expected that the Dring dimer reduction on Al-C2N was unfavorable both kinetically and thermodynamically. In path Ib, a two-step reaction was identified: (i) (NO)2 → N2 + 2Oads, followed by (ii) CO + Oads → CO2. As shown in Figure 4b, the Dring structure was taken as the initial state and, subsequently, CO was physisorbed over Al-C2N to form an intermediate state (the MS1 structure). In the TS1 structure, two N-O bonds broke with the bond lengths increasing to 1.880 and 1.978 Å, respectively, while the N1-N2 bond length was shortened to 1.144 Å. Next, N2 was completely formed in the MS2 structure. In the next step, CO approached the O1 atom. The O1···C bond's length reduced from 2.859 to 2.152 Å and, finally, formed the CO2 molecule. Note that the energy barriers of the first and second steps were 43.1 and 1.6 kcal/mol, respectively, which could be provided by the larger exothermic reaction energy (−67.7 kcal/mol, from Dring to FS). In path II, the reaction started with the co-adsorption of two NO molecules to generate a cis-(NO)2 dimer (N-end, Dcis-N) structure, as shown in Figure 5. As seen, this step had a negligible energy barrier and was exothermic by 17.3 kcal/mol. Then, the Dcis-N structure could be converted to the more stable cis-(NO)2 dimer (O-end, Dcis-O) structure by overcoming a small energy barrier of 3.6 kcal/mol, being exothermic by 8.6 kcal/mol. Finally, the Dcis-O structure decomposed into the product (N2O and Oads species) through TS2 by breaking the N1-O1 bond. In the TS2 structure, the N1-O1 distance significantly elongated from 1.469 to 1.659 Å, while the N1-N2 distance decreased from 1.240 to 1.207 Å. We note that there was a negligible energy barrier for this step (2.7 kcal/mol), which was exothermic by 24.8 kcal/mol. Since the entire reaction was a highly exothermic process (−50.7 kcal/mol, from IS to FS), it was thermodynamically feasible under mild conditions. In path III, the trans-(NO)2 dimer structure (N-end, Dtrans-N) was considered the starting point for the NO reduction on Al-C2N. From Figure 6a, one could see that the NO molecule bonded with the Al site through the N-end, whereas another NO molecule was weakly physisorbed on the surface, with the distance between the N1 and N2 atoms being 2.445 Å. The co-adsorption energy of 2NO was −35.6 kcal/mol. Next, the Dtrans-N structure In path III, the trans-(NO) 2 dimer structure (N-end, D trans-N ) was considered the starting point for the NO reduction on Al-C 2 N. From Figure 6a, one could see that the NO molecule bonded with the Al site through the N-end, whereas another NO molecule was weakly physisorbed on the surface, with the distance between the N 1 and N 2 atoms being 2.445 Å. The co-adsorption energy of 2NO was −35.6 kcal/mol. Next, the D trans-N structure was formed through a barrierless process. In this structure, the calculated N 1 -N 2 bond was shortened to 1.286 Å, while the N 2 -O 2 bond was extended to 1.451 Å. In the TS structure, the N 2 -O 2 bond was significantly extended from 1.451 to 2.604 Å. Finally, the N 2 -O 2 bond was completely broken, forming N 2 O and O ads moieties. This path revealed a high reaction barrier of 16.5 kcal/mol and was exothermic by 12.7 kcal/mol. Figure 6b exhibits path IV, starting from the trans-(NO) 2 dimer structure (O-end, D trans-O ). In this path, 2NO molecules formed the D trans-O structure through an extremely low-energy barrier (1.6 kcal/mol). Then, the N 1 -O 1 bond length was significantly extended from 1.374 Å in the D trans-O structure to 1.696 Å in the TS2 structure. The energy barrier for this step was 12.7 kcal/mol, which could be provided by the exothermic reaction energy (−24.5 kcal/mol).
Molecules 2022, 27, x 8 → N2O + Oads reaction of only 3.6 kcal/mol, which was even smaller than the valu noble metal catalysts, such as Pd-BNNS (14.9 kcal/mol) [58], Au (8.1 kcal/mol) [65 Ag (6.2 kcal/mol) [66]. These results implied that the Al-C2N catalyst exhibited good lytic activity towards the NO reduction. After the N2O desorption, the remaining Oads atom could be removed with the N CO molecules. In our previous work, we revealed that Al-C2N could serve as a prom catalyst for N2O reduction to environmentally friendly N2 molecules [67]. Figure 7 s the reaction pathways of Oads + NO → NO2 and Oads + CO → CO2 on Al-C2N, respect Our results showed that Oads + NO → NO2 was an endothermic process (7.5 kcal/mol quite a high-energy barrier (15.5 kcal/mol) required to be surmounted. As seen in F 7b, the Oads + CO → CO2 reaction was an exothermic process, and an energy barrier o 6.6 kcal/mol was needed for Al-C2N, which was smaller than the value for Pt-grap (13.4 kcal/mol) [68]. This meant that CO2 molecules were more likely to form on th C2N catalyst in the existence of NO molecules.  According to our results, it was found that the NO reduction preferred to proceed via the (NO) 2 dimer reduction process. First, the E ads values of the (NO) 2 dimers were much larger than that of the single NO molecule. Second, the (NO) 2 dimer reduction process was thermodynamically and kinetically more favorable than the NO direct decomposition process. Based on the energy barriers (E a ) and reaction energies (∆E r ), the NO dimer reduction on the Al-C 2 N surface could occur via path II and path IV (Table 1). Path II was energetically the most favorable pathway with the max energy barrier for the (NO) 2 → N 2 O + O ads reaction of only 3.6 kcal/mol, which was even smaller than the values in noble metal catalysts, such as Pd-BNNS (14.9 kcal/mol) [58], Au (8.1 kcal/mol) [65], and Ag (6.2 kcal/mol) [66]. These results implied that the Al-C 2 N catalyst exhibited good catalytic activity towards the NO reduction.
After the N 2 O desorption, the remaining O ads atom could be removed with the NO or CO molecules. In our previous work, we revealed that Al-C 2 N could serve as a promising catalyst for N 2 O reduction to environmentally friendly N 2 molecules [67]. Figure 7 shows the reaction pathways of O ads + NO → NO 2 and O ads + CO → CO 2 on Al-C 2 N, respectively. Our results showed that O ads + NO → NO 2 was an endothermic process (7.5 kcal/mol), and quite a high-energy barrier (15.5 kcal/mol) required to be surmounted. As seen in Figure 7b, the O ads + CO → CO 2 reaction was an exothermic process, and an energy barrier of only 6.6 kcal/mol was needed for Al-C 2 N, which was smaller than the value for Ptgraphene (13.4 kcal/mol) [68]. This meant that CO 2 molecules were more likely to form on the Al-C 2 N catalyst in the existence of NO molecules.

Conclusions
In this work, we investigated the NO reduction over low-cost Al-C2N catalysts usin DFT calculations in detail. According to the adsorption energy and charge transfer values the adsorption of NO on the catalyst was significantly stronger than that of CO, whic suggested that the Al-C2N catalyst was more selective to NO than CO. For the NO reduc tion mechanism, our results showed that the NO direct decomposition process was barel possible due to the extremely high-energy barrier and endothermicity. In contrast, the ca talysis of the NO reduction via the (NO)2 dimer reduction process was both thermody namically and kinetically favorable. It was found that cis-(NO)2 dimer structures were ke intermediates for the NO reduction, where the calculated max barriers along the mos energetically favorable pathway (path II) was only 3.6 kcal/mol. The remaining Oads spe cies on Al-C2N could be eliminated with CO molecules, which required overcoming th energy barriers of only 6.6 kcal/mol. Overall, Al-C2N is expected to be a promising catalys for NO reduction with CO.
Supplementary Materials: The following supporting information can be downloaded a www.mdpi.com/xxx/s1. Figure S1: molecular dynamics simulation for Al-C2N catalyst at (a) 300 K and (b) 500 K, respectively; Figure S2: IR spectra plots for five kinds of (NO)2 dimers on the Al-C2N surface.

Conclusions
In this work, we investigated the NO reduction over low-cost Al-C 2 N catalysts using DFT calculations in detail. According to the adsorption energy and charge transfer values, the adsorption of NO on the catalyst was significantly stronger than that of CO, which suggested that the Al-C 2 N catalyst was more selective to NO than CO. For the NO reduction mechanism, our results showed that the NO direct decomposition process was barely possible due to the extremely high-energy barrier and endothermicity. In contrast, the catalysis of the NO reduction via the (NO) 2 dimer reduction process was both thermodynamically and kinetically favorable. It was found that cis-(NO) 2 dimer structures were key intermediates for the NO reduction, where the calculated max barriers along the most energetically favorable pathway (path II) was only 3.6 kcal/mol. The remaining O ads species on Al-C 2 N could be eliminated with CO molecules, which required overcoming the energy barriers of only 6.6 kcal/mol. Overall, Al-C 2 N is expected to be a promising catalyst for NO reduction with CO.
Supplementary Materials: The following supporting information can be downloaded at: https:// www.mdpi.com/article/10.3390/molecules27185790/s1. Figure S1: molecular dynamics simulation for Al-C 2 N catalyst at (a) 300 K and (b) 500 K, respectively; Figure S2: IR spectra plots for five kinds of (NO) 2 dimers on the Al-C 2 N surface.
Author Contributions: Conceptualization, methodology, software, and writing original draft, X.L.; investigation, software, and data curation, Y.X.; conceptualization, supervision, and writing-review and editing, L.S. All authors have read and agreed to the published version of the manuscript.