Identiﬁcation of Main Active Sites and the Role of NO 2 on NO x Reduction with CH 4 over In / BEA Catalyst: A Computational Study

: The main active sites and the catalytic process in selective catalytic reduction of NO x by CH 4 (CH 4 -SCR) on In / BEA catalyst were investigated by density functional theory (DFT) using a periodic model. The [InO] + and [InOH] 2 + moieties were constructed in the channel of periodic BEA zeolite representing the Lewis and Brønsted acid sites. The electronic structures [InO] + and [InOH] 2 + were analyzed, and it was found that the [InO] + group were the main active sites for CH 4 activation and NO / NO 2 adsorption in the CH 4 -SCR process. CH 4 molecules could be activated on the O site of the [InO] + group in In / BEA, which was resulted from the strong interactions between the C-p orbital of the CH 4 molecule and the O-p orbital of the [InO] + group. CH 4 activation was the initial step in CH 4 -SCR on In / BEA catalyst. NO 2 molecules were essential in the SCR process, and they could be produced by NO reacting with gaseous O 2 or the O atom of the [InO] + group. The presence of NO 2 could facilitate the key intermediate nitromethane (CH 3 NO 2 ) formation and lower the reaction barrier in the SCR process.


Introduction
The selective catalytic reduction (SCR) of NO x by hydrocarbons has attracted much interest in the past years [1,2]. The readily available CH 4 serving as the reducing agent is of great significance from an environmental point of view, because boilers and automobiles fueled by natural gas are important NO x emission sources [3][4][5]. A number of zeolite-supported metal oxides (Pt [6], Co [7], Fe [8], Mo [9], In [10][11][12][13][14][15], etc.) catalysts have been explored, among which the indium-containing zeolites were the prominent one with excellent CH 4 -SCR activities. Nevertheless, the main active sites that are responsible for the CH 4 -SCR over In-containing zeolites are still up for debate. Maunula et al. [16] proposed that intrazeolitic [InO] + was the active site on In/ZSM-5 catalyst during the process of SCR. However, Lónyiet et al. [12,17] found that [InOH] 2+ species originated from H 2 O dissociation were responsible for initiating the steps of the SCR process. In our previous work, CH 4 -SCR activities over In/BEA were measured [18]. The [InO] + group was found to play an important role, but the roles of [InOH] 2+ have not been identified, because the experimental characterizations usually only provided us with limited information. In comparison, quantum chemistry calculation based on density functional theory (DFT) has been a powerful tool to elucidate details regarding the geometry and electronic structures of the active sites, which are essential to get a deeper understanding of the active sites and the catalytic process.

The Optimized Structures of BEA Zeolite and In/BEA Model
The chemical formula of the BEA unit cell used in this work was Si 64 O 128 and the calculated dimensions of the unit cell was a = 12.669 Å, b = 12.675 Å, and c = 26.781 Å, which were very close to the experimental values of a = 12.632 Å, b = 12.632 Å, and c = 26.186 Å [24]. The calculated bond length of CH 4 and NO were 1.097 and 1.164Å, respectively. The experiment values were reported to be 1.086 Å of gaseous CH 4 molecule [24] and 1.151 Å of NO molecule [25]. The GGA slightly overestimated the bond lengths as expected, but the errors produced are within the acceptable range. Therefore, we assume that the calculation parameters set above were reasonable for further calculations.
The optimized structures of the In/BEA unit cell are shown in Figure 1, and the corresponding bond length and Mulliken charge population are present in Table 1. The bond length of [InO] + (d In-O ) were slightly elongated after a hydroxyl group was modeled, the value of which increased to 1.954 Å for the B-model, quite longer than that of the L-model (1.872 Å). By contrast, the bond length of In and oxygen atoms coordinated with Al atoms (d In-O1 = 2.072 Å; d In-O2 = 2.106 Å) of the B-model were shortened compared with that of the L-model (d In-O1 = 2.249 Å; d In-O2 = 2.229 Å). It can be seen from the results of Mulliken charge populations that the charge of Al, O 1 , and O 2 are almost the same between the two models, while the charge between In and O were remarkably different. The q In and q O were 0.978 and -0.608 e for the L-model, and 1.273 and −0.553 e for the B-model, respectively. The total charge of the acid sites of the L-model and B-model were 0.300 and 1.049 e, respectively. This result suggests a quantity of electrons were transferred to the BEA substrate from the [InO] + or [InOH] 2+ group, and the electrons redistribution would further influence the interactions between the gas molecules and the acid sites.  In atoms, respectively, and this color scheme will be used throughout.

The Electronic Structure Analysis for In/BEA Model
As shown in Figure 2, the energy gap between the Lowest Unoccupied Molecular Orbital (LUMO) and the Highest Occupied Molecular Orbital (HOMO) was the largest for the CH 4 molecule, indicating its stronger chemical inertness. Furthermore, based on the frontier molecular orbital theory, it was concluded that the electrons density would be transferred from the HOMO of the CH 4 or NO molecule to the LUMO of the [InO] + or [InOH] 2+ group due to their lower energy gaps. The energy levels of both the HOMO and LUMO of the L-model were higher than that of the B-model, which suggests that the [InO] + group might be more reactive than the [InOH] 2+ group for the In/BEA catalyst. The condensed Fukui function was an effective method to elucidate the ability of a specific atom to gain or lose electrons, and it was defined as [26,27]: The atom with the higher f + A value was prone to accept electrons; otherwise, it was prone to donate electrons. As shown in Table 2

Models
In The partial (PDOS) of the In and O atom of the L-model and B-model were calculated to elucidate electronic structure and bonding mechanism. The results are presented in Figure 3. The orbital energy levels were quite different between the [InO] + and [InOH] 2+ group, but the density of states (DOS) of both In and O atom were mainly donated by the p-orbital. The hybridizations between O-p and In-s, p at around -2.5, 0, and 2.0 eV for the L-model were clearly observed, so were the O-p and In-s at around −7.5 and 3.0 eV for the B-model. This suggests that there were strong covalent interactions between the In and O atom for both the [InO] + and [InOH] 2+ groups, in other words, the active site models used in our work were stable and could reasonably represent the active sites. The Fermi level was set to zero and is represented with a dotted line in this work. It can be clearly seen that the PDOS intensities at the Fermi level of [InO] + was greatly stronger than that of [InOH] 2+ , which indicates that the In and O atoms are more active in the L-model compared with that in the B-model. This result corresponds well to the Fukui function calculations that the [InO] + group exhibited greater electrophilic and nucleophilic abilities than [InOH] 2+ group.

CH 4 Adsorption Characteristics
The adsorption characteristics of CH 4 on the In and O site of the L-model and B-model were carefully explored in this section, and the most favorable adsorption configurations are shown in Figure 4. All the four adsorption processes were found to be exothermic, but CH 4 adsorption characteristics varied greatly at different sites. It is interesting to note that the C-H bond was easily cleaved without an energy barrier when it was initially absorbed on the O site of the L-model ( Figure 4A2). One of the H atoms of CH 4 moved to the O site, and a C-O bond formed simultaneously. This result was similar to the findings of Sinev et al. [28] that an H atom abstraction was energetically favorable with an O atom. It means that the CH 4 activation could occur on the O site of [InO] + group in In/BEA catalyst without the assistance of an NO or NO 2 molecule. By contrast, the [InOH] 2+ group had very weak affinity with the CH 4 molecule, whether on the In site or the O site. CH 4 would move away from the active site after geometry optimization with the d In-C and d C-O equaling 2.469 and 4.358 Å, respectively ( Figure 4B1,B2). In addition, the interactions between CH 4 and the In site of the [InO] + group was also very weak, and the corresponding In-C bond length was 3.360 Å ( Figure 4A1). The binding energies were -0.15, -2.98, -0.48, and -0.10 eV for configuration in Figure 4A1, the configuration in Figure 4A2, the configuration in Figure 4B1, and the configuration in Figure 4B2 Figure 4A1, the configuration in Figure 4A2, the configuration in Figure 4A3, and the configuration in Figure 4A4, respectively. The net charge value was the highest when CH 4 was adsorbed on the O site of the L-model, in accordance with its lowest adsorption energy. Furthermore, the projected density of states (PDOS) of C-p and In-s, p was calculated to clarify the bonding mechanism of CH 4 adsorption and dissociation, the results of which are shown in Figure 5.
The PDOS of C-p scarcely overlaps with the orbitals of the In atom (In-s, p), thus a new chemical bond would not be easily formed. However, the PDOS of C-p and O-p are strongly overlapped at around Fermi level, which indicates that the new formed C-O bond was contributed by the interactions between the C-p orbitals of CH 4 and the O-p orbitals of the [InO] + group in this configuration. Moreover, a mass of electron densities was transferred from C-p orbitals of CH 4 to O-p after adsorption, and the C-p moved to lower energy levels accompanied with its PDOS split. Therefore, CH 4 activation resulted from the strong interactions between C-p and O-p orbitals when it was adsorbed on the O site of the L-model. In the case of CH 4 interacting with the B-model, the electron densities of C-p of CH 4 were redistributed owing to the weak interactions between C-p and In-s, and the energy level of C-p also become lower after adsorption. There were only tiny overlapped DOS bands when CH 4 molecule was adsorbed on the B-model, which indicates that CH 4 could not be easily activated on Brønsted acid sites due to their relatively weaker interactions.

NO and NO 2 Adsorption Characteristics
It was reported that NO 2 was more important than NO in the CH 4 -SCR process, because NO 3 − species would be easily produced when an NO 2 molecule was coordinated with the [InO] + group. Some researchers proposed that NO 3 − could facilitate CH 4 activation and active intermediates formation [12,29]. However, it was found that CH 4 molecules can be easily activated on the O site of the InO + group of the In/BEA catalyst in Section 2.2. As key reactants, the adsorption characteristics of NO and NO 2 on the L-model and B-model of In/BEA required further explorations and comparisons. The adsorption configurations of NO and NO 2 coordinated with the In or O sites of the L-model and B-model are displayed in Figure 6. Interestingly, NO was inclined to coordinate with the O atom rather than the In atom of [InO] + . However, NO 2 was inclined to coordinate with the In atom of [InOH] 2+ . Generally, the NO molecule has stronger affinities with the L-model than the B-model, the binding energy of which was −1.84 and −1.07 eV, respectively. This result is in agreement with the Fukui function results that the activity of the [InO] + group is higher than the [InOH] 2+ group. The adsorbed NO 2 * species was produced simultaneously when NO interacts with the L-model regardless of the adsorption sites ( Figure 6A1,B1), and a similar phenomenon was observed by Huang et al. [30]. In the case of NO 2 adsorption, NO 2 molecule also had stronger interactions with the L-model than the B-model (−1.93 eV vs. −0.56 and −0.42 eV). In addition, NO 3 -* species could be produced as the NO 2 molecule interacts with the L-model, and the adsorption energy was similar to that of the NO adsorbed on the L-model. Therefore, it is concluded that [InO] + groups serve as major active sites for CH 4 activation, NO and NO 2 adsorption in the CH 4 -SCR process.  Figure 6B1,D1,D2, respectively. The higher electrons transfer amounts for NO and NO 2 on the L-model corresponded to their lower binding energies.

O 2 , H 2 O and CO 2 Adsorption Characteristics
The detailed adsorption characteristics of O 2 , H 2 O, and CO 2 were also investigated, because O 2 was the reactant and H 2 O and CO 2 were products in the flue gas. Based on the above results, it was concluded that the [InO] + group rather than the [InOH] 2+ group plays the dominant role in CH 4 activation and the NO/NO 2 adsorption process. Therefore, only the adsorption characteristics on the L-model were calculated and discussed. The optimized structures and their corresponding adsorption energies are displayed in Figure 7, and the bond lengths and Mulliken charge population are shown in Table 5. O 2 and CO 2 molecules were more likely to coordinate with the O site, while H 2 O molecule prefers the In site ( Figure 7A2,B2,C1), the corresponding energy was −0.49, −0.86, and −0.29 eV, respectively. Therefore, the O 2 adsorption process would be less favorable on the active sites. Therefore, it is deduced that activation of CH 4 on the O site of [InO] + would be the initial steps on the In/BEA catalyst. Interestingly, the CO 2 molecule has a strong affinity with the O site of the [InO] + group, with a carbonate formed, yielding the adsorption energy of -0.86 eV ( Figure 7B2). Meanwhile, there is a mass of electrons transferred from the CO 2 molecule to the catalyst, the quantity of which is equal to 0.215 e. The adsorption configurations of H 2 O are shown in Figure 7C1,C2. It is noted that the H 2 O molecule interacted weakly with the [InO] + group and the adsorption energy on the In site and O site were -0.29 and -0.05 eV, respectively. The d In-O bond length for H 2 O interacting with the In and O site were 2.430 and 3.430 Å, respectively, and there was only a small quantity of electrons transferred between the H 2 O molecule and the catalyst. This result suggests that the In/BEA catalyst has excellent water vapor durability in the process of CH 4 -SCR.
The PDOS of O 2 , CO 2 , and H 2 O before and after adsorption were also compared to obtain insights into the bonding mechanism ( Figure 8). The distinct bands at the Fermi level could be observed for the free O 2 , CO 2 and H 2 O molecules, and they overlapped with the In-p and O-p orbitals of the [InO] + group. It is noted that the shape and intensity of free O 2 were greatly changed within the range of -8 to 2 eV after adsorption. The electron density depletion indicates that the O 2 molecule donated electrons to the catalyst. As for the CO 2 adsorption on the In site, the PDOS bands shifted to a lower energy level, but the intensity did not change distinctly. This indicates that the adsorption caused CO 2 electron redistribution while only a few electrons were transferred to the catalyst. By contrast, the electron density depletion was obvious as CO 2 was adsorbed on the O site but there were almost no PDOS band shifts. The situation was similar for H 2 O adsorption on the In and O sites.

Nitromethanes' Formation and Reaction Enthalpy
It was reported by many researchers that nitromethanes (CH 3 NO and CH 3 NO 2 ) are the key intermediates involved in N 2 formation [22,[31][32][33]. As shown in Section 2.3, CH 3 formation on the O site of the [InO] + species was the initial step. Therefore, the formation process of nitromethanes was considered as the CH 3 group further reacting with gaseous NO or NO 2 molecules. It is interesting to find that the adsorption behaviors of NO and NO 2 on the CH 3 group were entirely different. Figure 9 shows that the NO molecule would move away from the CH 3 group whether the NO molecule was placed on the C site or the O site at the beginning, with the N-C bond length equaling 3.707 Å. This indicates that there was a strong repulsion between the NO molecule and the CH 3 group, and CH 3 NO intermediates were not easily produced on the In/BEA catalyst. In comparison, when the NO 2 molecule was placed near the CH 3 group, the C-O bond broke immediately and CH 3 NO 2 was formed simultaneously. Subsequently, CH 3 NO 2 rotated to a tilted position with the N-C bond and C-O length equaling to 3.707 and 1.498 Å, respectively. As a result, it was concluded that CH 3 NO 2 rather than CH 3 NO species could be formed on the catalyst, and this key intermediate would facilitate the following catalytic process. This result also indicates that NO 2 plays a key role in the CH 4 -SCR process for the In/BEA catalyst, in accordance with previous research [13,34]. There are mainly two reaction pathways in the CH 4 -SCR process: (1) CH 4 +O 2 +2NO→CO 2 +2H 2 O+N 2 ; (2) CH 4 +2NO 2 →CO 2 +2H 2 O+N 2 [34,35]. In this regard, co-adsorption characteristics of multiple species of the reactants (IS1-NO, CH 4 , O 2 ; IS2-2NO 2 , CH 4 ) and products (CO 2 , N 2 , H 2 O) were studied. As shown in Figure 10, it is noted that a NO molecule was inclined to coordinate with an O 2 molecule in IS1, and an NO 2 * was formed. The formed NO 2 * was necessary for the CH 3 NO 2 formation. This result is in line with the findings in Section 2.4 and it also suggests that IS2 might be the subsequent status of IS1 in the SCR process, because CH 3 NO could not be easily produced. Additionally, the two reaction routes occurred using the same catalyst. Thus, it is assumed that the status of transition state was the same for the two reaction pathways. It can be seen that both reaction pathway 1 and 2 were exothermic but the energy of IS1 was 3.03 eV lower than that of IS2, suggesting that the total energy barrier E a2 of reaction 2 should be smaller than E a1 .Therefore, it is concluded that NO 2 molecules were essential in the SCR process, and they could be produced by NO reacting with gaseous O 2 or the O atom of the [InO] + group. In this case, on one hand, the formation of key intermediate CH 3 NO 2 could be facilitated, on the other hand, the reaction rates would be much higher due to the lower reaction barrier in the presence of NO 2 .

Computational Methods
There were several DFT calculations concerning zeolites conducted based on a simplified cluster model in order to save calculation time [8,9,36]; the accuracy of the computational results was therefore usually less accurate. In this regard, all DFT calculations were performed on a periodic boundary BEA zeolite model for the first time to achieve results with higher reliabilities (Figure 11). All calculations were performed based on DMol 3 implemented in Materials Studio 2017R2 [37], in which the Perdew-Burke-Ernzerhoff (PBE) [38] functional in the generalized gradient approximation (GGA) [39] was used to calculate the x change-correlation potential. The following three convergence criteria were used for the geometry optimization and energy calculation: SCF tolerance (1.0 × 10 −6 ), the atomic forces (2.0 × 10 −3 Hartree/Å), maximum displacement (5.0 × 10 −3 Å), and total energy variation (1.0 × 10 −5 Hartree). The molecular orbitals were expanded using a double numerical basis set with polarization functions (DNP), which is equivalent to 6-31 G ** . The range of integration for charge density and functional was confined within a global orbital cutoff value of 3.5 Å. The core electrons were treated using the DFT semicore pseudo pots (DSPP) method. A (3 × 3 × 3) Monkhorst-Pack k-point grid was used for In/BEA unit cell optimization. All the atoms in the model were allowed to be relaxed during the calculation.
The [InO] + and [InOH] 2+ moiety introduced one and two positive charges, respectively, which were compensated by substituting one Si 4+ with Al 3+ to keep the charge balance. In the unit cell of BEA, there are nine distinct Si sites denoted as T sites for Al cation substitution, among which T1 and T9 sites substitution were suggested to be relatively stable [36]. Based on the parameters set in our calculations, we found that the structure of Al 3+ substituting on the T9 site is more energetically favorable, and the energy is 0.08 eV lower than that on T1 site. Similar substitution methods were suggested by Yan [9] and Zhou [19]. For the sake of simplicity, the formed [InO] + /BEA model was denoted as the L-model, and the [InOH] 2+ /BEA model was denoted as the B-model. The [InO] + species was placed in the five-member ring, six-member ring and 12-member ring and optimized at the beginning, among which InO + in the 12-member ring has the lowest energy after geometry optimizations. Therefore, further calculations were performed based on this model. Adsorption energy (E ad ) denotes the interaction between the surface and the adsorbate, which is defined as: where E total is the total energy of the catalyst model and gas molecule; E sub and E x are the energy of catalyst model and gas molecule, respectively. A smaller value indicates a stronger adsorption.

Conclusions
The geometry and electronic structure of the [InO] + and [InOH] 2+ groups were quite different, and the [InO] + group was more reactive and served as the main active site in the In/BEA catalyst. Furthermore, CH 4 could be easily activated on the L-model to form a CH 3 group in the absence of NO or NO 2 , while the B-model was inactive in this process. NO 2 plays a more important role than NO in the SCR process, because it could react with the activated CH 3 to form the key intermediate CH 3 NO 2 and lower the total reaction barrier.