Density Functional Theory Study of Mechanism of Reduction of N₂O by CO over Fe-ZSM-5 Zeolites

Abstract

Nitrous oxide (N₂O) is an industrial waste gas (e.g., from the production of adipic acid), which damages the ozone layer and causes the greenhouse effect. Density functional theory calculations were employed to investigate the mechanism of direct catalytic decomposition of N₂O and selective catalytic reduction (SCR) of N₂O by CO over Fe-ZSM-5 zeolites. Two stable Fe-active sites with six-membered ring structures on Fe-ZSM-5 were considered. The calculations indicate that the decomposition of N₂O is affected by the coordination environment around Fe and can occur through two reaction pathways. However, there is invariably a more considerable energy hurdle for the initiation of the second stage of N₂O decomposition. When CO participated in the reaction, it showed good reactivity and stability, the reaction energy barriers of the rate-limiting step were reduced by roughly 20.57 kcal/mol compared to the direct catalytic decomposition of N₂O. CO exhibited a superior electron-donating ability and orbital hybridization performance during the reaction, which enhanced the cyclicity of the N₂O reduction catalytic process. Our calculations confirmed the significant role of CO in N₂O reduction over Fe-ZSM-5 observed in previous studies. This study provides a valuable theoretical reference for exploring CO-SCR methods for N₂O reduction over Fe-based zeolite catalysts.

1. Introduction

Nitrogen oxides are currently the main atmospheric pollutants, among which nitrous oxide (N₂O) is a N₂-containing pollutant released by chemical production, crop fertilization, and other activities [1,2,3,4]. N₂O is stable in the atmosphere, with an average lifetime of approximately 110–150 years. This depletes ozone, causing the ozone hole problem [5,6]. The global warming potential of N₂O per molecule is 300 and 21 times higher than those of carbon dioxide (CO₂) and methane (CH₄), respectively [7,8].

Currently, the primary approaches for N₂O treatment include high-temperature thermal decomposition [9], direct catalytic decomposition, and selective catalytic reduction (SCR) [10]. However, high-temperature thermal decomposition has limitations owing to its high temperature requirements, excessive energy consumption, and insufficient conversion rate. The direct catalytic decomposition of N₂O using metal catalysts has become a highly efficient method for industrial applications because of its straightforward process and high energy efficiency. Therefore, this method has attracted considerable attention from researchers [11,12].

The reaction equation for N₂O decomposition is:

$$2{\mathrm{N}}_2\mathrm{O} \stackrel{\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{y}\mathrm{s}\mathrm{t}}{\to }2{\mathrm{N}}_2+{\mathrm{O}}_2$$

(1)

Thermodynamically, this reaction can occur spontaneously at room temperature and atmospheric pressure; however, it is hindered from a kinetic perspective [13].

Therefore, the addition of catalysts to the reaction system to reduce the activation energy is crucial for promoting the industrial application of this process. Precious-metal catalysts, such as Pt and Rh, have high catalytic activity at room temperature and even lower temperatures. However, the preparation costs of such catalysts are high, which is not conducive to the large-scale industrial production of N₂O [14]. As non-precious-metal catalysts, transition-metal-exchanged high-silica zeolites exhibit good reaction activity at high temperatures and have a wide activity temperature range and low preparation costs; therefore, they have broad application prospects in industry [15,16]. Iron-based catalysts are inexpensive and have the advantages of simple preparation and a wide range of application conditions [17,18,19]. The excellent SCR performance of Fe-based catalysts has recently received considerable attention from researchers.

With the development of the smelting industry, gas emissions from industrial production have increased, and components such as CO and H₂ in gas have become effective reducing agents [20,21]. Research on the N₂O decomposition reaction has focused on the SCR route of N₂O using transition-metal-exchanged high-silica zeolites, such as Cu and Fe. The use of CO as a reducing agent during this reaction remains under investigation [22,23]. Wannakao et al. investigated, with experiments, the reaction mechanism of N₂O SCR on Fe-embedded graphene using CO as the reductant. They found that the charge transfer between the Fe atoms in the structure and the reacting molecules significantly affected the reaction process [24]. You et al. observed a decrease in the reaction temperature by more than 100 °C in an SCR reaction experiment that involved catalyzing N₂O on Fe-ZSM-5 using CO as the reductant and found that Fe-ZSM-5 can exhibit good activity and oxygen resistance at relatively low temperatures [25], which provides experimental support for the feasibility of the SCR of N₂O on Fe-ZSM-5. Dai et al. also achieved good reaction results in their experimental and computational studies on the SCR catalysis of N₂O over Fe-BEA and Cu-BEA using CO as a reductant and reported that Fe-BEA exhibited better reaction performance than Cu-BEA [26]. However, Dai et al. only used the 5T model for theoretical research, and the stability of extra-framework iron-containing complexes in ZSM-5 zeolites was not considered; the reaction mechanism of this process was affected by the ligand structure of the active sites. The electron-donating ability and orbital hybridization during the reaction remain unclear. Moreover, issues related to the Fe-active site on the ZSM-5 and its mode of action, as well as the position of the rate-limiting step in the N₂O decomposition process, remain controversial [27,28,29]. Further exploration of the catalytic mechanism of this reaction at the Fe-active sites of the Fe-ZSM-5 is of considerable significance.

In this study, we investigated the mechanism of the catalytic reduction of N₂O by CO over Fe-ZSM-5. The stable mononuclear active sites on Fe-ZSM-5 were screened. On the basis of the calculated model, we proposed a mechanism for the N₂O dissociation and CO participation processes and compared the energy barriers of these two reaction paths. Furthermore, the natural charge and orbital populations of this process were fully analyzed to gain a deeper insight into the catalytic reaction mechanism.

The direct catalytic decomposition of N₂O and the SCR of N₂O, with the participation of CO, were based on Equations (1) and (2):

$${\mathrm{N}}_2\mathrm{O}+\mathrm{CO} \stackrel{\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{y}\mathrm{s}\mathrm{t}}{\to }{\mathrm{N}}_2+{\mathrm{CO}}_2$$

(2)

2. Results and Discussion

2.1. Location and Bonding Energy of Mononuclear Fe Species in Fe-ZSM-5

2.1.1. Optimization Configuration of Fe-ZSM-5

It has been reported that the mononuclear sites in ZSM-5 were more commonly found in straight channels or at the intersection of straight and sinusoidal channels than in the double five-membered rings of the zeolite wall and larger eight-membered rings in the sinusoidal channel [30]. To determine the most stable position of the catalytically active mononuclear Fe site of the Fe-ZSM-5 framework, we examined the 6MR situated in a straight channel (called the a-structure) and the 6MR situated at the intersection of the straight and sinusoidal channels (called the b-structure). The b-structure exhibits a wholly symmetrical layout for the T-sites, which is different from that of the a-structure. Various structural substitutions were conducted by selecting T1 and T7 for the a-structure and the two symmetric T11s for the b-structure, which were the most stable T-sites in the structure [31].

The binding energy of the doped Fe for these various structures can be calculated using the following equation [31,32]:

∆E = E₂ − E₁ − E_Fe

(3)

Here, E₁ refers to the geometrically optimized energy of the framework structure alone; E₂ refers to the geometrically optimized energy of Fe attached to the framework structure; and E_Fe refers to the energy of the Fe atom. Thus, ∆E represents the binding energy of the doped Fe on the Fe-active site structure. It is hypothesized that structures are easier to form and more stable when the generation energy is more negative.

Table 1. Calculation of the Fe-O bond lengths and relative stability of the different configurations of Fe-ZSM-5.

Configuration		Fe-O Bond Length				Fe-O (avg.)	Binding Energy of Doped Fe (kcal/mol)
Structure	T-Site of Al/Si
a-Site
a-1	T1	1.957	1.972			1.965	−142.72
a-2	T7	1.974	1.960			1.967	−151.07
a-3	T1, T7	1.979	1.966	1.986	2.003	1.984	−271.15
b-Site
b-1	T11	2.049	2.005			2.027	−173.01
b-2	T11, T11	1.936	1.925	1.981	1.966	1.952	−272.26

Note: Interatomic distances (<2.5 Å) are given in angstroms, and relative stabilities are in kcal/mol.

presents the geometrically optimized configurations and their corresponding doped Fe-binding energies. The optimized structural model is shown in Figure 1. The details of E1, E2, etc., are given in the Supporting Materials Table S1.

The Fe site on the b-structure with Al atoms substituted at the two T11 positions had the lowest binding energy of doped Fe, and Fe was bonded to the four O atoms attached to the two Al atoms in the framework, forming the most stable configuration of symmetrically distributed charges on the 6MR. The second-most stable site is the Fe site on the a-structure, with the Al atoms substituted at positions T1 and T7. The ring structure below the 6MR of the a-structure has lower symmetry than the b-structure. This results in a less flexible framework and facilitates additional interactions between Fe and O behind the a-structured channel. In a structure in which one Al atom is substituted in the framework, Fe interacts with [AlO₂]⁻ in a triangular manner. This structure exhibits a much lower binding energy than that formed by the substitution of two Al atoms in the framework. Consequently, it is more vulnerable to structural transformation during the reaction process when it interacts with O atoms outside the framework to form Fe-O species—particularly considering the self-organizing nature of Fe. Therefore, the position of the most stable mononuclear Fe site in ZSM-5 first considers the symmetric configuration formed by Fe²⁺ with two [AlO₂]⁻ units at both T11 positions on the b-structure. Then, the Fe²⁺ with two [AlO₂]⁻ units at T1 and T7 formed on the a-structure was considered. The structural screening thought and results are consistent with previous reports on the stability of Cu⁺/Fe²⁺ in ZSM-5 and Fe²⁺ in ferrite [31,33,34].

The spin multiplicity affects the total energy and geometrical structure. To make a choice for the spin multiplicity, in the previous studies, Bell et al. [35], in their study on N₂O decomposition over Fe- and Co-ZSM-5, compared the energies of the 5T model with one Al atom at different spin states and performed their systematic study at the lowest energy obtained for SM = 6. Heyden et al. [36] selected SM = 4 or 6 for systematic calculations and analysis of the N₂O decomposition process on the 5T model with one Al atom. It performed with SM = 6 in the N₂O decomposition process, and the spin changes with SM = 4 occurred only in the part containing recombinant O₂. For two Al structures, previous studies on similar structures in the Fe-ZSM-5 system were consulted [37,38], and it can be determined that the Z(Fe) and Z(FeO*) structures with two Al atoms in this study were stabilized with SM = 1, 3, 5, or 7. So, we optimized each two-Al-atom structure with different spin multiplicities (1, 3, 5, and 7) and chose the one that gives the minimal total energy [35,37]. The lowest energy-stabilized structure was obtained when SM = 5, as shown in

Table 2. Relative stability of Fe-ZSM-5 with different SMs.

Configuration		SM	Relative Stability (kcal/mol)
Structure	T-Site of Al/Si
a-Site
a-3	T1, T7	1	40
		3	15
		5	0
		7	111
b-Site
b-2	T11, T11	1	79
		3	31
		5	0
		7	122

. Therefore, we chosen to use SM = 5 for our calculations and analyzed solely the relative trend of the overall reaction process.

2.1.2. Prediction of Reactive Active Sites on Fe-ZSM-5

To increase the precision of deducing the reaction mechanism path and analyzing the reaction process, the molecular surface ESP and LEAE of the reactant structure and catalyst active sites in the system were computed. These were obtained from the calculation of the wavefunction resulting from geometric optimization.

Figure 2 shows the distributions of the ESP on the molecular surfaces of N₂O and CO. Both ends of the N₂O molecule are shown at the ESP minima, with the O-end concentrated on most of the ESP minima. This is consistent with the current theoretical and experimental N₂O charge distributions, which exhibit a certain polarity. The O-termina carries more electrons than the N-terminal in N₂O, whereas the intermediate N atoms are positively charged [39]. The N-N bond order is higher than that of N-O. The CO molecule exhibits ESP minima at both ends of the molecule, with the C-terminus being the smallest and showing a weak dipole moment. The C-O bond levels are high and strong and are less likely to break.

Figure 3 presents the molecular surface ESP distributions of Fe and Fe-O on the a- and b-structures. There is only one ESP maximum point above Fe on the surface of the a-structure where Fe is located, and it is the maximum value of 64.8 kcal/mol in the structure, showing a concentrated positive ESP interaction. Therefore, when N₂O is close to Fe in the a-structure, the negatively charged O-end of N₂O forms the most substantial ESP interaction with Fe and approaches the O-end of Fe. Iron species are the most probable reaction sites. In the b-structure, the Fe atoms face the O atoms in the back-channel structure of the 6MR, whereas in the a-structure, the Fe atoms face the Si atoms in the back-channel structure of the 6MR. The O atoms exhibit stronger negative electronegativity, which affects the distribution of charges in the b-structure, causing the ESP distribution on the surface of the Fe atom in the b-structure to exhibit a different state from that of the a-structure.

The b-structure has one ESP extreme-value point above the surface Fe atom but exhibits a positive value, which is attributed to the collaborative interaction between Fe and O atoms beneath Fe. In the four regions where Fe was bonded to four O atoms in the framework, four surface ESP extreme-value points were uniformly distributed near Fe. These were the larger ESP extreme-value points on the surface of the structure, and a strong positive ESP was evident near Fe. When the N₂O molecule is close to the Fe site of the b-structure, the O-terminus of N₂O remains near the surface where the Fe site is situated, owing to the strong ESP interaction. Consequently, Fe is the most likely site for the reaction. The diverse ESP distributions on the surfaces of the a- and b-structures indicate how the channel structure behind the Fe framework affects the Fe-coordination environment, which may explain the differences in the results of the reaction energy barrier calculations.

When the first step of N₂O dissociation was completed, Fe-O-active sites were formed on the a- and b-structures. After the extra-framework O was attached to Fe, electrons were obtained from the Fe atoms, and a small amount of negative charge was carried on the extra-framework O. The ESP distributions on the a- and b-structures were in similar states owing to the influence of the extra-framework O on the Fe charge distribution. Above the position of the O atoms have the maximum value of the ESP and is negative, where the O atom is negatively charged. In the four regions where Fe is bonded to the four O atoms in the framework, four uniformly distributed ESP maxima are generated by Fe. These are the largest maxima in the positively charged structure. The O-terminus of N₂O and the C-terminus of CO are prone to ESP interactions with these four positions to facilitate the adsorption of N₂O or CO, and these are possible locations where a transition state can easily occur. This speculation is in perfect agreement with the states searched for in the transition state in the calculations described later. However, because there are other pole sites for judging the interference near the Fe-O site, and both Fe and O can interact with N₂O, the actual electron distribution may change when N₂O is sufficiently close to Fe-O. Consequently, we calculated the LEAE of the Fe-O sites in the a- and b-structures to further analyze the reaction sites. The calculations revealed that the minimum value of the LEAE above the extra-framework O on the surface of the a-structure is –99.04 kcal/mol, and that for the b-structure it is more negative (–104.70 kcal/mol). Thus, the extra-framework O behaves as the most probable reaction site for both the a- and b-structure Fe-O sites. In addition, the reactivity of the b-structure is superior to that of the a-structure. These observations fully align with the transition-state outcomes obtained from the calculations of the reaction mechanism.

2.2. Proposed Catalytic Paths over Fe-ZSM-5

By examining the fixed characteristics of the reactant and reaction intermediate structures present in the system, we identified potential reaction paths through direct intermolecular interactions. The proposed reaction mechanism is expressed as follows:

Part 1:
	Step 1	Z-Fe + N2O→ Z-Fe-N2O
	Step 2	Z-Fe-N2O → Z-Fe-N2O-TS
	Step 3	Z-Fe-N2O-TS → Z-Fe-O-N2
	Step 4	Z-Fe-O-N2 → Z-Fe-O + N2
Part 2-1:
	Step 5	Z-Fe-O + N2O → Z-Fe-O-N2O
	Step 6	Z-Fe-O-N2O → Z-Fe-O-N2O-TS
	Step 7	Z-Fe-O-N2O-TS → Z-Fe-O-O-N2
	Step 8	Z-Fe-O-O-N2 → Z-Fe-O-O + N2
	Step 9	Z-Fe-O-O → Z-Fe-O2
	Step 10	Z-Fe-O2 → Z-Fe + O2
Part 2-2:
	Step 11	Z-Fe-O + CO → Z-Fe-O-CO
	Step 12	Z-Fe-O-CO → Z-Fe-O-CO-TS
	Step 13	Z-Fe-O-CO-TS → Z-Fe-CO2
	Step 14	Z-Fe-CO2 → Z-Fe + CO2

A schematic of the reaction mechanism is shown in Figure 4. Regardless of whether N₂O is decomposed alone or with the involvement of CO, the active site of Fe on the zeolite structure initially adsorbs N₂O by interacting with its O-terminus. In N₂O, the N-O bonds are weaker than the N-N bonds [31]. After addition of the catalyst, it mainly supplies electrons to its anti-bonding orbitals, further weakening the N-O bonds and promoting the preferential breakage of the N-O bonds to achieve N₂O dissociation. Both Fe-O and N₂ are formed, followed by the desorption of N₂. N₂O continues to be adsorbed on the Fe-O site and dissociates to form Fe-O-O and N₂, which then desorbs of N₂ and O₂, completing a catalytic cycle. Alternatively, CO can be adsorbed on the Fe-O site to promote the breaking of Fe-O bonding and directly restore the Fe site.

Dynamic reaction mechanism calculations were performed to determine the energy changes and rate-limiting steps of the reaction.

2.3. Reaction Mechanism of N₂O Decomposition over Fe-ZSM-5

The mechanism of the direct decomposition of N₂O at the Fe sites of the a- and b-structures is shown in Figure 5. On the a-structure, the Fe-active site facilitates the favorable adsorption of N₂O with an adsorption energy of –9.70 kcal/mol, resulting in a certain exothermic reaction. Subsequently, in the adsorption intermediate structure, O activation of N₂O (indicated as O*) continues to approach the Fe site. The interaction of Fe with the extra-framework O* breaks the N-O* bond of N₂O. This leads to the formation of Fe-O* species sites (a-TS1) and N₂, resulting in the transition state TS1. The activation energy barrier for this process is 26.85 kcal/mol, with a vibration frequency of –789.25 Hz, to form the Fe-O* site and N₂.

The occurrence of the transition state aligns perfectly with the ESP distribution analyzed in Section 2.2. Compared with the adsorbed state, transition state TS1 exhibits several notable changes: the N-O* bond length increases from 1.19 to 1.48 Å, the Fe-O* bond length decreases from 2.17 to 1.80 Å, and the N-N-O* bond angle decreases from 179° to 139.02°. The bond between N and O* is broken, and the formed N₂ molecule interacts weakly with the Fe-O*, desorbing from the structure with a lower desorption energy of 3.39 kcal/mol, while the Fe-O* bond is shortened again from 1.80 to 1.60 Å, stabilizing the bond. The reaction energy for this process is –6.11 kcal/mol, resulting in a stable coordination environment with a square cone shape. Iron is connected to four O atoms within the framework, whereas O* is connected to the external bonds of Fe.

In the b-structure, the interaction mechanism with N₂O on the Fe-active site closely resembles that of the a-structure. The adsorption energy of N₂O on the Fe-active site on the b-structure is –11.64 kcal/mol, which is slightly higher than that on the a-structure. Transition state b-TS1 is achieved with an activation energy barrier of 24.36 kcal/mol. The N-O* bond is lengthened from 1.19 to 1.47 Å, while the Fe-O* bond is shortened from 2.18 to 1.80 Å. Additionally, the N-N-O* bond angle decreases from 180° to 139.06°, and the vibrational frequency is –774.15 Hz, resulting in the formation of a transition-state structure that is similar to the a-structure. The desorption energy of N₂ is 3.29 kcal/mol. Moreover, the Fe-O* bond is further shortened from 1.80 to 1.60 Å, resulting in a total reaction energy of −9.80 kcal/mol.

2.4. Reaction Mechanism of N₂O Decomposition over Z(Fe-O*)

After the initial dissociation of N₂O, the Fe-O* site created by the Fe-active site and the extra-framework O* may interact with N₂O to separate the second N₂O molecule, releasing the Fe-active site and producing N₂ and O₂. Through the calculations, the potential creation of species when N₂O dissociated on Fe-O* was analyzed. This analysis led to the identification of two transition states (TS2) that aligned with theoretical simulations and exhibited varying energy barriers. It is highly probable that the adsorption and dissociation of N₂O will predominantly occur at the terminal O atoms of Fe-O*, leading to the definition of the transition state TS2-I. The absorption and dissociation of N₂O may occur close to the Fe atoms in Fe-O*. This interaction can occur with both Fe and the extra-framework O*, leading to the creation of the transition state TS2-II. To verify the plausibility of the existence of the two transition states, detailed reaction process calculations were performed for both the a- and b-structures at the active site.

The mechanism of the TS2-I process on the Fe-O* site of the a-structure is described as follows and the results are shown in Figure 6. The adsorption of N₂O onto the Fe-O* surface occurs with an adsorption energy of –3.65 kcal/mol. The N₂O molecule is adsorbed near the top of Fe-O*, forming a position 81° relative to the horizontal plane. This indicates a direct interaction between the framework’s outer O* and N₂O. In the intersectional area of the 6MR of the framework with Fe-O*, N₂O’s O-terminus approaches Fe-O* and is adsorbed in the vicinity of O*, achieving the TS2-I transition state with an activation energy barrier of 36.46 kcal/mol. The TS2-I vibrational frequency is –708.76 Hz, and the Fe-O* bond is extended from 1.60 to 1.79 Å relative to the adsorbed state. Furthermore, the extra-framework O* and N₂O’s O-terminus approaches 1.56 Å, and the N-O bond is lengthened from 1.19 to 1.33 Å. Within a certain range, the N-N-O bond angle deviates from 180° to 136.22°, rendering the N-O bond vulnerable to breakage. An approximately linear structure of [Fe-O*-O] is formed through the interaction between the Fe-O*-terminal O* and the detached O of N₂O. The N₂ molecule interacts weakly with [Fe-O*-O], resulting in desorption with a lower energy of 0.67 kcal/mol. After desorption, O₂ is formed with an energy of 12.98 kcal/mol, and, subsequently, O₂ is removed from the Fe site with an energy of –11.86 kcal/mol, leading to the reduction of the Fe-active center. Technical abbreviations are introduced upon first use. The total energy of this reaction is –31.86 kcal/mol, making it exothermic.

The mechanism of the TS2-II process on the Fe-O* site of the a-structure is described as follows and shown in Figure 6. The adsorption of N₂O on the Fe-O* sites is similar to that on the TS2-I transition state. On the a-structured Fe-O*, N₂O molecules are adsorbed close to the top of Fe-O* and form a nearly horizontal relative position of approximately 85°, with an adsorption energy of –3.49 kcal/mol, indicating a stable adsorption state. In the region of the intersection of the framework 6MR ring with Fe-O, the O-end of N₂O approaches Fe-O* and is adsorbed close to Fe, and the TS2-II transition state is achieved with an activation energy barrier of 49.71 kcal/mol. The TS2-II vibrational frequency is –863. 89 Hz, and compared with the adsorbed state, at this time, under the relative effect of the O of the N₂O approach, the Fe-O* undergoes an angular deflection, and the Fe-O bond is extended from 1.60 to 1.71 Å. The distance of the O end of N₂O from the Fe site of Fe-O* is 2.03 Å, and that from the terminal O* of Fe-O is 1.91 Å. The N-O bond is stretched from 1.18 to 1.57 Å, and the angle of the N-N-O bond is reduced from 180° to 153.00°. The N-O chemical bond is cleaved, creating a N₂ molecule. The Fe sites engage with the dissociated O obtained from N₂O to form [O-Fe-O*]. The bond lengths of the two extreme O atoms and Fe are 1.86 and 1.93 Å, respectively, with a gap of 1.31 Å between the O atoms. The N₂ is detached from the [O-Fe-O*] site with a desorption energy of –2.67 kcal/mol. Following detachment of the N₂ molecule, O and O* rapidly recombine into ligand-saturated O₂, which is subsequently desorbed from Fe with an energy of –11.92 kcal/mol. This achieves the reduction of the Fe-active sites, completing the catalytic process. The activation energy barrier for the transition state in this process is far higher than that in TS2-I, making it more challenging from a practical standpoint. However, O₂ easily recombines and desorbs. The overall reaction energy is –31.86 kcal/mol, indicating an exothermic reaction.

The mechanism of the TS2-I process on the Fe-O* site of the b-structure is described as follows and shown in Figure 7. N₂O is adsorbed above Fe-O* with an adsorption energy of –6.71 kcal/mol. The O-terminal end of N₂O approaches Fe-O* at the intersection of the framework 6MR with Fe-O* and is adsorbed near O*. It reaches the transition state with an activation energy barrier of 35.46 kcal/mol and a vibrational frequency of –702.74 Hz. N₂ undergoes adsorption and desorption at an energy of 0.92 kcal/mol. Following the formation of O₂ on Fe with an energy of 12.38 kcal/mol, it then desorbs at an energy of –11.71 kcal/mol. The total energy of the reaction is –34.59 kcal/mol.

The mechanism of the TS2-II process on the Fe-O* site of the b-structure is described as follows and shown in Figure 7. On the b-structured Fe-O*, N₂O is adsorbed above Fe-O* with an adsorption energy of –7.01 kcal/mol. It subsequently approaches the Fe-O* site through the O-terminus of N₂O. However, it requires a high activation energy barrier of 50.86 kcal/mol to reach the transition state, with a vibrational frequency of –854.69 Hz. Eventually, N₂ is desorbed at an energy of 2.81 kcal/mol. The oxygen produced through swift recombination on Fe can be rapidly desorbed with an energy of –11.48 kcal/mol, whereas the overall reaction energy is approximately –34.59 kcal/mol.

The overall efficacy of the reaction in the b-structure is superior to that in the a-structure. Although there is little difference in the structural alterations of the active sites during N₂O adsorption and dissociation in structures a and b, there are differences in energy, indicating that the dissociation of N₂O relies on the ligand atmosphere surrounding the Fe-active site. Furthermore, Fe is influenced by the ring structure in which it is positioned on the skeleton of the molecular sieve and by the area behind the channel in the 6MR.

2.5. Reaction Mechanism of CO Participation over Z(Fe-O*)

Comparing the initial dissociation process of N₂O with the second dissociation during the catalytic cycle revealed that the second N₂O dissociation occurs with significantly higher energy barriers on Fe-O* than the first step of the N₂O dissociation process on Fe. This makes the reaction more difficult. When CO is introduced into the N₂O decomposition reaction system, it primarily participates in the reaction at the Fe-O* site that is formed after the dissociation of the first N₂O, as it exhibits better reducibility. Compared with the dissociation process of N₂O on Fe-O*, it is more probable that CO will bind with extra-framework O and cause the reduction of Fe-active sites.

The mechanism of the TS2-CO process on the Fe-O* site of the a-structure is described as follows and shown in Figure 8. On the a-structured Fe-O*, CO is adsorbed onto Fe-O* with an adsorption energy of –3.06 kcal/mol. Subsequently, the C-terminal of CO approaches Fe-O* in the adsorbed state. When the Fe-O* bond is re-stretched from 1.60 to 1.70 Å, and the C moves closer to Fe, resulting in a C-Fe distance of 2.16 Å. During this reaction, the angle of the Fe-O* bond changes. When the C and Fe-O terminal O* distance remains at 2.09 Å, the bond between Fe and O* breaks, allowing rapid interaction between O* and C of CO and forming a new bond. Thus, the transition state TS2-CO is achieved, requiring an activation energy barrier of 15.89 kcal/mol and a vibrational frequency of –805.62 Hz. This bond formation is followed by the formation of CO₂, which binds with a large amount of exothermic heat. The next step involves the desorption of CO₂, which requires an adsorption heat energy of 10.07 kcal/mol, reducing the Fe-active sites and, ultimately, leading to the shutdown of the catalytic process. The overall energy released by this process is –80.6 kcal/mol, indicating a stronger exothermic reaction and a reduced energy barrier in the transition state.

The mechanism of the TS2-CO process on the Fe-O* site of the b-structure is described as follows and shown in Figure 8. On the Fe-O* b-structure, the mechanism of CO’s involvement in the reaction is identical to that for the a-structure. CO is adsorbed onto the Fe-O* surface with an adsorption energy of –2.94 kcal/mol. The close proximity of the CO to Fe-O* allows for it to attain the transition state TS2, which has an activation energy barrier of 15.97 kcal/mol and a vibrational frequency of –920.24 Hz. Subsequently, the easy formation of CO₂ bonds and their desorption at an energy of 8.93 kcal/mol causes the reduction of Fe, completing the catalytic process. The total energy change in the reaction is –80.08 kcal/mol. The difference between the reaction effects of CO on the a- and b-structures is very small.

2.6. Discussion

As shown in Figure 9 and Figure 10, the reaction-mechanism calculations for both the a- and b-structures exhibit consistent findings, with close agreement in the structure and bond lengths of the intermediates during the reactions. This confirms the plausibility of the reaction mechanism and that the appearance of the transition states is not a coincidental outcome. The energy barriers for the reaction of the b-structure were higher than those for the a-structure. This reflects the typicality of the reaction occurring at the Fe-active sites of Fe-ZSM-5 and the influence of the back channel of the structure, where Fe is located, on the catalytic effect.

To confirm the computational results for weak interactions in the system, intermediate structures with weak interaction processes on the a-structure were selected for BSSE calculation tests. The detailed results have been added to Table S6 in the Supporting Materials. The results of the BSSE calculations indicate a mostly consistent trend of corrections. Some of the corrections have less impact compared to the results without BSSE calculations [34,40,41]. In addition, based on the results of the previous research and precalculated tests of the computational basis group, we conclude that selecting the basis group and dispersion function in the present computational method can provide a more accurate description of the system.

We compared the reaction processes occurring in the two transition states of N₂O decomposition on Fe-O*, and there appeared to be no significant difference in the total reaction energy. The adsorption of N₂O and desorption of N₂ on Fe-O* exhibited comparable patterns. The main difference was that the activation energy barrier for the reaction in transition state TS2-II was notably higher than that in transition state TS2-I. Furthermore, the different bond arrangements of Fe-O* and O led to distinct energy barriers for O₂ recombination and desorption.

Previous studies on the N₂O decomposition reaction with zeolite catalysts have provided varying views on whether N₂O dissociation occurs on Fe or on the extra-framework O*. Additionally, there is controversy regarding whether the rate-limiting step in the N₂O decomposition process is N₂O decomposition or O₂ desorption. The study of Heyden et al. [36] earlier proposed two possible pathways for N₂O decomposition on the 5T model and analyzed them in detail; the calculated pathways and energy structure of N₂O decomposition at the [FeO]⁺ site of the 5T model on Fe-ZSM-5 by Bell et al. [35] are consistent with TS2-II in this study; the study of N₂O decomposition on Fe-ZSM-5 by Ganna li et al. [37] obtained the reaction pathways and energy trends consistent with TS2-I.

Because the N₂O decomposition reaction depends on the coordination environment around the active site of Fe, the preparation of zeolite skeletons with varying Si/Al ratios under distinct conditions leads to Fe with different coordination environments. Thus, based on the atomic structure and charge properties of the Fe atom and terminal O* atom, Fe plays different roles in N₂O decomposition and preferentially undergoes TS2-I or TS2-II. In the structure selected in this study, after the first step of the decomposition of N₂O at the Fe-active site, Fe forms a stable coordination environment of the square-cone type with the extra-framework O* and the zeolite framework. This impedes interactions between Fe and N₂O. Thus, once N₂O is adsorbed in close proximity under intermolecular interactions, bond breaking and bond formation are more likely to occur directly on the terminal O* of Fe-O* than on Fe. This situation is also explained by the ESP and LEAE calculations presented in Section 2.2.

Compared with the result of N₂O direct decomposition, the reaction effect of CO on different structures is more stable and less affected by the structure of the zeolites. The involvement of CO in the reaction reduces the transition-state energy barrier by approximately 20 kcal/mol and reduces the overall reaction energy by approximately 40 kcal/mol. The incorporation of CO creates a lower energy barrier for the N₂O decomposition reaction to be replaced with the CO reduction of Fe-O* to produce CO₂. This promotes the recycling of the catalytic reaction and the direct reduction of Fe-active sites, facilitating the subsequent dissociation of the N₂O molecule.

Dai et al. [26] conducted two reaction mechanisms for the reduction of N₂O with CO on the basic 5T model in which the associative mechanism was less effective than the redox mechanism. Our study fully considered the framework structure of ZSM-5 in order to better analyze the influence of the coordination environment of the active site on the zeolite toward the reaction process. And the natures of atomic orbital hybridization and charge transfer were further analyzed on this basis. We concluded that the initiation of the reaction mechanism depends on the adsorption state of the molecules at the active sites. The results indicate that the simultaneous adsorption of N₂O and CO on Fe²⁺ is unlikely to occur, and O* is more active than Fe at the [FeO*]²⁺ site and easily reacts directly with CO, making the associative reactions unlikely to occur. Thus, we have thoroughly examined the redox mechanism and obtained good results. The influence of the Fe-coordination environment on the catalytic reduction process and the mechanism of CO reduction are more clearly defined through a comparision with Dai’s study.

2.7. Electronic Analysis

2.7.1. Analysis of Interatomic Interactions

According to the dynamic reaction process calculations, a static analysis was performed on the reaction process intermediates. Because the reaction processes of the a- and b-structures are similar, the a-structure was selected as an example to clarify the bond formations and bond breaks during the reaction, as well as the reduction process of the Fe-O* species to Fe.

The interatomic interactions of the reaction process on the a-structure were analyzed using an independent gradient model based on the IGMH method. The interaction isosurfaces at δg_inter = 0.006 a.u. are shown in Figure 11, illustrating the atomic contribution to fragment bonding. The blue sections of the isosurface in the figure indicate the prominent attractive weak interactions and bonds with non-negligible covalency. The red parts indicate prominent repulsive interactions, and the green areas indicate relatively weak van der Waals interactions.

The adsorption of N₂O on the Fe sites of the a-structure exhibits blue and green, indicating favorable attractive interactions. During the transition state of N₂O dissociation, the blue regions among Fe-O* bonds increases, and a few red regions emerge, indicating the charge-transfer-induced strengthening and weakening of bonds. Stable interactions occurred between Fe and the activated O*, facilitating bonding. When the second step of the reaction occurred at the Fe-O* site of the a-structure, comparing the TS2-I and TS2-II with the TS2-CO process, the adsorption process exhibited similar interfragment interactions. The transition states exhibited a significant difference in interactions owing to the difference in the main action site and the mode of charge transfer, and it can form products with different structures. Figure 11 indicates that during the TS2-I process of N₂O dissociation, the O-terminus of N₂O has an attractive interaction with O* on Fe-O* but does not directly interact with Fe. In TS2-II, the O-terminus of N₂O interacts with both Fe and O* in Fe-O*. In the TS2-CO process involving CO on Fe-O*, the C-terminus exhibits conspicuous attractive interactions with Fe and O*. The red and blue regions between Fe and O* show the conspicuous strengthening and weakening of the bond order, respectively, induced by charge transfer. The size of the green region between the small molecules and active site during each desorption process indicates the strength of the van der Waals interactions, suggesting the difficulty of desorption. These results are consistent with the energy calculations.

Visual analysis of the interatomic interactions within the system revealed the similar adsorption effects of N₂O and CO on the active sites. However, differences were observed in the reactive transition state and molecular desorption process at the Fe-O* site. These findings are consistent with the results for the bond length and angle variations, as well as the energy calculations for the intermediate structures in Section 2.3.

The PDOS of the transition states during N₂O decomposition and CO participation in the reaction were calculated to further investigate the interactions between Fe-O* and N₂O/CO [42], as shown in Figure 12. When the decomposition of N₂O on Fe-O* occurs in the TS2-I path, the 2p orbital of O is significantly hybridized with the 2p orbital of O*, indicating a strong interaction and generation of O-O bonds. When N₂O interacts with Fe-O* in the TS2-II path, the 2p orbital of O perturbs both the 3d orbital of Fe and the 2p orbital of O*. In particular, the 3d orbital of Fe is significantly perturbed, suggesting that the decomposition of N₂O produces a significant change in the interaction between Fe and O*.

When CO is adsorbed onto Fe-O*, it exhibits O*-2p orbital characteristics similar to the TS2-I process of N₂O, and Fe-3d orbitals akin to the TS2-II process of N₂O. This indicates that the interaction of CO with Fe-O* leads to charge transfer, which results in significant changes in the orbital characteristics of the original Fe and O*, suggesting that the co-adsorption of C with Fe and O* configurations is favorable and can lead to the reduction of Fe-O* to Fe.

2.7.2. Analysis of Hirshfeld Charge

The Hirshfeld charges of the reaction systems were also calculated. The laws governing the changes in the interatomic bond order of the reaction intermediates and transition-state structures were determined for the entire IRC process of the diverse reactions that occur at the Fe-O* site, as shown in Figure 13 and

Table 3. Charge distribution of reaction intermediates and transition states during TS2-I of N₂O decomposition at the Fe-O* site of the a-structure.

Number	Process	State	Atom
			Fe	O*	O	N	N
5		a-O*	0.4985	–0.1733	-	-	-
6	TS2-I	a-O*-N2O	0.5016	–0.1842	–0.1349	0.2349	–0.0819
7		a-O*-N2O-TS	0.5163	–0.2105	0.0046	0.1182	–0.0161
8		a-O*-O-N2	0.4587	0.0120	0.0168	0.0133	0.0354
9		a-O*-O	0.4602	0.0143	0.0201	-	-
10		a-O2	0.2676	0.0742	0.0491	-	-

,

Table 4. Charge distribution of reaction intermediates and transition states during TS2-II of N₂O decomposition at the Fe-O* site of the a-structure.

Number	Process	State	Atom
			Fe	O*	O	N	N
5		a-O*	0.4985	–0.1733	-	-	-
11	TS2-II	a-O*-N2O	0.5372	–0.1653	–0.1475	0.2291	–0.0874
12		a-O*-N2O-TS	0.4882	–0.1423	–0.1225	0.1747	0.0670
13		a-O*-O-N2	0.4848	–0.0396	–0.0314	0.0064	0.0032
14		a-O*-O	0.4848	–0.0403	–0.0420	-	-
15		a-O2	0.2676	0.0491	0.0742	-	-

and

Table 5. Charge distribution of reaction intermediates and transition states during TS2-CO at the Fe-O* site of the a-structure.

Number	Process	State	Atom
			Fe	O*	C	O
5		a-O*	0.4985	–0.1733	-	-
16	TS2-CO	a-O*-CO	0.5033	–0.1788	0.0936	–0.0839
17		a-O*-CO-TS	0.4826	–0.1821	0.2270	–0.0266
18		a-CO2	0.3790	–0.0731	0.3869	–0.1100

.

When N₂O decomposes at the Fe-O* site in the TS2-I pathway, the O-terminus of N₂O is adsorbed onto the O* of Fe-O* and N₂O approaches O* through the O-terminus, triggering the transfer of electrons from O to N. The N-O bond order decreases and continues to decrease as adsorption occurs. The interaction between O and O* is enhanced, increasing the bond order. When O and O* approach a certain distance, the N-O bond electrons are transferred to a certain level, leading to the breaking of the bond and initiation of TS2-I. The interaction between activated O and O* is reinforced, and the charge on O* is transferred to Fe, resulting in stabilization of the bonding once the electrons between O* and O reach equilibrium. This completes the process of N₂O decomposition.

During N₂O decomposition at the Fe-O* site in the TS2-II pathway, the O-terminus of N₂O is adsorbed on the Fe-O* site in almost equal proximity to Fe and O*. Analyzing the atomic charges between the adsorbed and transition states and the bond-level changes during the reaction reveals that during adsorption, electrons are transferred from the O-terminus to the N-terminus in N₂O, and the N-O bond order decreases. N₂O is adsorbed and approaches the Fe-O* sites through the O-terminus. The transfer of electrons from the O-terminus of N₂O to Fe subsequently occurs. Consequently, the Fe-O bond order increased significantly, whereas the Fe-O* bond order decreases. Once the transfer of electrons from the O-terminus to the N-terminus in N₂O reaches a certain level, the N-O bond begins to break, and the bond order decreases rapidly. At this point, the transfer of electrons from O and O* to Fe is nearly saturated. The transfer of electrons from O to O* and the subsequent enhancement of O-O* bonding order. Electron enrichment of O* allows for the continued Fe electron transfer, which briefly increases the Fe-O* bond order. When the level of O-O* bonding surpasses that of Fe-O, O attains a certain level of bonding with both Fe and O*, triggering TS2-II. The enhanced O-O* bonding causes the Fe-O* bond order to be affected and reduced. Subsequently, the N-O bond breaks, and the O*-O bond stabilizes as the electrons reach equilibrium. Iron forms bonds with two extra-framework O at a bond order of approximately one.

By analyzing the detailed charge transfer of the two reaction processes of N₂O decomposition on the Fe-O* sites, we obtained the two processes of N₂O action on the Fe-O* sites. Evidently, the charge of Fe is pivotal in the charge transfer of the reaction process and serves as the main reason for the variance between the two transition-state occurrences and the energy barriers. When TS2-II occurs on the Fe-O* site, the Fe of the resultant O-Fe-O* structure has higher positivity, and O*-O has a high electron-donating capacity, facilitating the formation and desorption of O₂.

When the reductant CO is introduced, the C-terminal end of CO is adsorbed by Fe-O*. This leads to the transfer of the C-terminal electrons to Fe, resulting in a decrease in the C-O bond order and an increase in the C-Fe bond order. As the distance between C and Fe-O* decreases to a certain point, the charge on Fe tends to be saturated, and the C-terminal electrons start to be transferred to O* to stimulate the onset of TS2-CO. The Fe-O* bond begins to break, and the C-O* bond is enhanced. The Fe-C interaction is weakened, the bond order changes significantly, and finally a CO₂ stable bond is formed. Compared with the N₂O decomposition process, CO exhibits a better electron-donating ability and establishes superior charge transfer interactions with both Fe and O*. This results in the direct completion of the Fe-O* bond breaking and the reduction of Fe species.

3. Computational Details

The cluster model was based on an inherent molecular sieve framework 1 (MFI) structure, using Material Studio 8.0 software to intercept clusters of appropriate size from the periodic structure of ZSM-5 in the database. The research on similar structures by Ganna Li et al. [30,37,43] found that the position of Fe²⁺ strongly depends on the possibility of forming direct bonds between Fe²⁺ and the O atoms on the oxygen tetrahedron occupied by Al, the distribution of [FeO]²⁺ species also only slightly depends on the specific local zeolite environment. The six-membered ring (6MR) in the straight channel (called the a-structure) and the 6MR at the intersection of the straight and sinusoidal channels (called the b-structure) [31,36,44,45,46] were selected as structural models, as shown in Figure 14. One or two Al atoms were inserted into the 6MR to create structures with Fe-active sites. The dangling bonds at the Si and Al ends are terminated by H, and the H-bond direction is fixed along the subsequent Si direction to form neutral clusters. The Si and O atoms behind the channel and the structural end H are fixed to preserve the structure of the ZSM-5 framework, whereas the remaining atoms are kept in a relaxed state to simulate the limited rigidity of the framework. The Si–H bond length is set to 1.487 Å [47,48,49]. Both reactant and product molecules are in a relaxed state.

All calculations were performed using density functional theory (DFT) and implemented using the Gaussian 09 package [50]. Becke’s three-parameter exchange with the correlation functional of Lee, Yang, and Parr (B3LYP) was used for the calculations [51,52,53]. The 6-311++G(d, p) basis set was used for H, C, N, O, Si, and Al atoms [54], whereas the relativistic SDD effective core potential was combined with the 3-ζ cc-pVTZ basis set for Fe [55,56]. The zeolite cluster structures and adsorbed molecules were fully geometrically optimized, and spin multiplicity (SM) calculations were performed. The synchronous quasi-Newton method was used to optimize the transition state (TS). Frequency analysis was performed to ensure that all of the transition states had only one imaginary frequency. The relationship between the two local minima and the TS was confirmed by intrinsic reaction coordinate (IRC) calculations at the same energy level [57]. The calculations and mapping of the surface electrostatic potential (ESP) distribution, local electron attachment energy (LEAE), atomic charges, and projected density of states (PDOS) of the structures in the system were performed using Multiwfn and VMD software [58,59]. The Hirshfeld partition (IGMH) method [60] was used to analyze weak interactions in the system. All geometric structures were visualized using Materials Studio 8.0, CYLview, and ChemDraw software [61,62].

4. Conclusions

The stability of mononuclear Fe species in Fe-ZSM-5 and the catalytic cycle for the direct decomposition of N₂O/reduction of N₂O by CO over two stable Fe-active sites in ZSM-5 were investigated using DFT. The stability of the mononuclear Fe species depends on the local configuration of the zeolitic site. The preferred location of the Fe species involves a symmetrical configuration formed by Fe²⁺ with two [AlO₂]⁻ units at T11 of the b-structure and Fe²⁺ with two [AlO₂]⁻ units at T1 and T7 of the a-structure. The N₂O decomposition on [FeO]⁺ is influenced by the coordination environment around Fe and can occur through two reaction pathways, but there is always the problem that the second step of N₂O decomposition is more challenging. In the presence of CO, N₂O conversion is significantly improved over Fe-ZSM-5. The reaction energy barrier of the rate-limiting step was 15.89 kcal/mol; it was reduced by roughly 20.57 kcal/mol compared with N₂O decomposition on [FeO]⁺. This is consistent with the results of previous experimental studies. Moreover, CO exhibited superior electron-donating ability and orbital hybridization during the reaction, and the stability of its participation in the reaction is little affected by the structure of the active sites on the zeolites, which is conducive to maintaining the catalyst structure and activity. This research provides a reliable theoretical reference for exploring CO-SCR methods for N₂O reduction over Fe-based zeolite catalysts.