A new insight on the NO–CO reaction at the electronic level: homogeneous, E-R, and L–H mechanisms

Carbonaceous surface, as one of the major carriers in coal combustion, was found to exert great influence on the nitric oxide with carbon monoxide (NO–CO) reaction. Although there have been some studies addressing the NO–CO reaction, the inherent mechanism remains obscure. In this work, some updated mechanisms with details were proposed at the electronic level. Using density functional theory calculations, the preferred pathways were identified with three channels consisting of homogeneous, Eley–Rideal (E-R), and Langmuir–Hinshelwood (L–H) heterogeneous reactions. The reasons for the difference in energy barrier among the three mechanisms were revealed by analyzing the chemical bond and electronic transfer. Results show that among these channels, the NO–CO reaction is more likely to occur along the E-R mechanism, due to its lower energy barrier of the rate-determining step. Compared to the L–H mechanism, there is a higher degree of electronic localization between NO molecules at the initial stage of the E-R mechanism. As a result, the NO dimer formation of the E-R mechanism has a lower energy barrier than that of the L–H mechanism. Meanwhile, a large number of electrons floods into the N–N, N–O, and O–O bonds of NO dimer in the homogeneous reaction, which certainly gets more difficult for the dissociation of O atoms in the gas phase. Accordingly, the following stage of N2 formation in the homogeneous reaction has a higher energy barrier than that in both the E-R and L–H reactions. Compared to the L–H mechanism, the E-R mechanism exhibits a lower degree of electronic localization between N2O and carbonaceous surface, suggesting that the interfacial interaction in the E-R mechanism is weaker. As a result, N2 is easier to remove from the carbonaceous surface in the E-R mechanism than in the L–H mechanism. To sum up, the results deepen the knowledge about the NO–CO reaction, which will help to further develop the oxy-fuel combustion technology.


Introduction
"Carbon capture, utilization, and storage (CCUS)" is one of the most promising ways to reduce anthropogenic CO 2 emissions and meet the climate targets for alleviating global warming [1]. Among optional technologies, oxy-fuel combustion is attracting more and more attention due to its special advantages of high heat and mass transfer rate, fuel flexibility, and simpler boiler structure [2,3]. However, there is a key issue: the high levels of NO x can decrease the partial pressure of CO 2 in flue gas and thus lower the efficiency of CO 2 capture [4]. In this case, a deep knowledge of NO x reduction is necessary for developing the oxy-fuel combustion technology.
Once formed, each NO x molecule will undergo subsequent reactions by one of two types: (i) homogeneous reaction with reductive radical or gas such as NH i , CH i , and CO; (ii) heterogeneous reaction with functional groups over the carbonaceous surface [5]. At present, some studies have paid attention to the NO reduction through macroscopic experiments in fluidized beds [6], drop-tube furnaces [7], and jetstirred reactors [8], as well as microscopic tests including X-ray photoelectron spectroscopy [9], Fourier-transform infrared spectroscopy [10], and Raman spectra [11]. A common outcome from these studies is the NO reduction by CO. In oxy-fuel combustion, a large amount of CO can be formed by the interaction of CO 2 with the carbonaceous surface.
CO is a very active reductant and helps reduce NO into N 2 or others, thereby reducing NO x emissions. The chemical formula can be expressed as follows [12]: During coal combustion, the NO reduction by CO can occur in the gas phase or on the carbonaceous surface [13]. Compared to the homogeneous reaction, the heterogeneous reaction is more complex in terms of reaction pathways. At present, the widely approved heterogeneous channels include Eley-Rideal (E-R) and Langmuir-Hinshelwood (L-H) mechanisms [14]. More details are described as follows, in which the symbols of C*, C(N), and C(O) are the carbonaceous sites with empty, nitrogen, and oxygen atoms, respectively: (i) E-R mechanism: (ii) L-H mechanism: From the above reactions, it can be found that the most conspicuous difference between them is that the E-R mechanism is the direct interaction of NO with C(N), while the indirect interaction between two C(N) sites is for the L-H mechanism. Up to now, there is no consensus on the heterogeneous mechanism. Chambrion et al. [15] and Glarborg [16] clarified that the N 2 formation can be attributed to the recombination of two C(N) moieties, while the interaction between C(N) with NO is less important. This view was supported by Yang et al. [17], who found that the L-H mechanism plays a more important role from the perspective of kinetics. However, an opposite view was proposed by Yang et al. [18], who noted that the E-R mechanism has lower energy barriers and thus dominates the heterogeneous reduction of NO by CO on the carbonaceous surface. Despite some conclusions that have been drawn by previous studies, there is one fundamental problem that has always been overlooked: what is the primary cause for the difference among homogeneous, E-R, and L-H mechanisms? Knowing that will help solve the above dispute.
Given the rapidity and complexity of chemical reactions, the inherent mechanism of NO-CO reaction is hard to be revealed by experiment. Recently, quantum chemistry calculation with the density functional theory (DFT) method has been rapidly developing and is being used to provide a deeper insight into the chemical reaction at the microcosmic [19,20]. Using DFT calculations, Jiao et al. [21,22] found two primary pathways of NO reduction and noted that NO heterogeneous reduction can be affected by the nature of active sites and the presence of CO. On this basis, Zhang et al. [23] proposed some updated mechanisms and clarified that CO plays an important role in the interaction with the surface oxygen atom. For years, the NO heterogeneous reduction by CO on the carbonaceous surface has been continually explored. Some updated reactants, transition states, intermediates, and products involved in NO-CO reaction were successively proposed in the research of Zhao et al. [24], Chen et al. [25], and Gao et al. [26]. However, there is little work concerning the difference in micro-mechanism among various NO-CO reactions. Therefore, the reaction pathways have been disputed and the inherent mechanism behind this does not know for sure, which is unfavorable for the further development of oxy-fuel combustion technology.
Our previous work reported NO and NO 2 homogeneous and heterogeneous reduction reactions in oxy-fuel combustion [27,28], with an emphasis on the role of CO. As an extension of that work, this paper started from the electronic level and focused on the difference in an energy barrier between various reaction mechanisms, to find out the primary cause for this difference. More specifically, three mechanisms consisting of homogeneous, E-R, and L-H heterogeneous reactions were obtained by using DFT calculations. On this basis, the chemical bond and the electron transfer for main intermediates were analyzed to explain the difference among these mechanisms. The reported results will deepen the knowledge about the NO-CO reaction which is helpful in further developing oxy-fuel combustion technology, and also provides a new idea for exploring chemical reactions.

Char edge model
A reasonable model is crucial for obtaining accurate calculation results and reducing calculation time [29,30]. At present, both zigzag and armchair configurations are reliable carbonaceous substrates for nitrogen chemistry calculation [31,32]. Cui et al. [33] experimentally found that coal char has a high ring condensation degree, and the coronene accounts for a large portion of organic groups in coal char. The coronene edge arranges in zigzag mode. Additionally, Jiao et al. [21] and Zhang et al. [34] theoretically clarified that the zigzag configuration is kinetically and thermodynamically more favorable than the armchair configuration in terms of NO reduction. To sum up, the zigzag edge model seems to be more suitable than the armchair edge model for calculating nitrogen chemistry.
The optimized structure of the zigzag surface is shown in Fig. 1a, in which the gray and white balls represent carbon and hydrogen atoms, respectively. Furthermore, the iso-surface and color-filled maps of π electrons density are drawn in Fig. 1b and c to understand the reactivity of the carbonaceous surface. It can be seen that there is an abundant π electron over the carbonaceous surface, especially around these unsaturated sites on the carbonaceous edge. This creates multiple sites and possible pathways for adsorption and reduction of NO.

Calculation methods
All quantum calculations are based on the DFT framework as implemented in the Gaussian09 package [35]. During the geometry optimization and frequency calculation, the m06-2 × functional with 6-311G(d) basis set is used to optimize the geometric structure, and to calculate the corresponding frequency and energy. Farrokhpour et al. [36] clarified that the m06-2x/6-311G(d) basis set has higher accuracy than others, and it has been widely applied to the DFT calculation of nitrogen chemistry [23,29]. To obtain more accurate results, the def2-TZVPP basis set is used to calculate the single-point energy of all reactants, intermediates, transition states, and products. This has been regarded as a reasonable and reliable method for obtaining the energy of organic compounds. All transition states (TS) have only one imaginary frequency, while all intermediates have no imaginary frequency. Possible reaction routes were ascertained using intrinsic reaction coordinate calculations [37]. Additionally, the wave function of the main intermediates is extracted by the Multiwfn program [38] to analyze the electronic structure. These results were drawn by the Visual Molecular Dynamics software [39].

Homogeneous reaction of NO-CO
The energy profile and optimized structures for NO-CO homogeneous reaction are shown in Fig. 2. Here, the blue and red balls represent nitrogen and oxygen atoms, respectively. The energy of all TS, intermediate, and product (P) is the Gibbs free energy in units of kJ/mol relative to reactant (R).
As shown in Fig. 2, the NO-CO homogeneous reaction consists of three transition states and five intermediates, and can be divided into three stages: (i) NO dimer formation, (ii) N 2 O formation, and (iii) N 2 formation. The reaction process is as follows: two free NO molecules come together to form a NO dimer, as shown by IM2. Then, a free CO molecule interacts with the O atom of the NO dimer, leading to the breakage of the N-O bond so that an N 2 O molecule is formed. After that, another CO molecule takes the residual O atom away from the N 2 O molecule, thereby producing N 2 and CO 2 molecules. In this process, the energy barrier of stage (ii) is the lowest, with only 86.630 kJ/mol. By comparison, the stages of both (i) and (iii) have higher energy barriers than stage (ii) (255.491 kJ/mol and 203.620 kJ/mol). According to the rate-determining step theory, the overall reaction rate depends on the rate of the elementary step with the highest energy barrier. So it can be inferred that the NO-CO homogeneous reaction is largely determined by the initial stage, that is, the elementary reaction of IM1 → IM2. A similar outcome was reported by Gonzalez et al. [40], who clarified that the formation of the N-N bond in NO dimer is the rate-determining step of NO to N 2 O conversion. Additionally, in the NO homogeneous reduction, the stage of N 2 O formation (IM3 → IM4) is likely to occur more quickly than the stage of N 2 formation. Accordingly, it can be inferred (a) molecular structure (b) iso-surface map of π electron density (c) color-filled map of π electron density

Fig. 1
Optimized structure and π electron density distribution of zigzag surface. a Molecular structure, b iso-surface map of π electron density, c color-filled map of π electron density that once formed, the NO dimer can be rapidly transformed to N 2 O, while the N 2 O to N 2 conversion is slow.

Adsorption of NO
In general, the first step of NO-CO heterogeneous reaction belongs to the adsorption of gaseous reactants on a solid surface [41]. All possible adsorption structures are displayed in Fig. 3a, with the corresponding adsorption energy. Here, the adsorption energy refers to the change of Gibbs free energy during NO adsorption. Moreover, the average local ionization energy (ALIE) calculations were performed to predict the active site in the subsequent reaction [42]. Here, the special configuration with the lowest energy (ZN1) is analyzed by ALIE calculation, as shown in Fig. 3b, with the corresponding atomic number. Note that the cyan ball represents the minimum point of ALIE. The smaller the ALIE value is, the easier the electrophile reaction occurs. From Fig. 3a, the NO adsorption on the carbonaceous surface in side-on mode (namely ZN1) is the most stable, due to its largest adsorption energy (− 494.266 kJ/mol). Furthermore, it can be seen in Fig. 3b that the minimum points mainly distribute on the NO moiety, the char edge, and the char surface. By comparison, the minimum points around N(1) and C(6) sites have much lower values of ALIE, with only 8.88 eV and 8.16 eV, respectively. This can be attributed to the unsaturated state of N(1) and C (6) sites. Compared to the saturated site, these unsaturated sites are easier to interact with free gaseous molecules. Accordingly, it can be inferred that as another NO molecule gets close to ZN1, it is more likely to interact with N(1) and C(6) sites to form the configurations ZNN1 and ZNN2, as shown in Fig. 3a. The ZNN1 and ZNN2 are the initial reactants in E-R and L-H reaction channels, respectively. Compared to ZNN1, the adsorption energy of ZNN2 is larger (− 45.515 kJ/mol vs. − 140.906 kJ/mol). Accordingly, the NO adsorption on C(6) site is more stable than that on N(1) site. Although the strong interaction of NO with ZN1 can enhance the stability of the adsorption structure, it also makes the N dissociation more difficult. In the following contents, this point would be discussed in detail.

E-R mechanism
Following the E-R mechanism as shown by Eq. (R2)-Eq. (R4), the feasible pathway and the energy profile are shown in Fig. 4. Similar to the NO-CO homogeneous reaction in Fig. 3, the NO-CO heterogeneous reaction in E-R mechanism can be divided into four stages as follows: (i) NO dimer formation, (ii) N 2 O formation, and (iii) N 2 formation, as well as (iv) N 2 desorption. From Fig. 4, the NO-CO heterogeneous reaction is much more complex than the homogeneous reaction. In the E-R mechanism, there are six transition states and nine intermediates. At the initial stage (IM1 → IM2), the free NO molecule interacts with the N atom of NO moiety to form IM2 in Fig. 3a. Although this process can occur spontaneously, it is required to overcome the energy barrier of 69.984 kJ/mol. The following stage (IM3 → IM5) is called the formation of N 2 O. A free CO molecule interacts with the O atom of the carbonyl group to form CO 2 moiety. And then the distance between CO 2 and carbonaceous edge is strengthened until the C-O bond gets broken, leaving an N 2 O moiety on the carbonaceous surface. By comparison, the elementary reaction of IM3 → IM4 has a higher energy barrier than that of IM4 → IM5 (89.279 kJ/mol vs. 60.504 kJ/mol); thus, it dominates the formation of N 2 O. This may be because the interaction of CO with O site saturates the O site, so CO 2 easily desorbs from the char edge. After that, another CO molecule approaches the O atom of N 2 O moiety in the C-down mode, causing that the N-O bond length extends to 2.629 Å in IM7 from 1.231 Å in IM6. The energy barrier of this process IM6 → IM7 is as high as 115.289 kJ/mol, which is higher than that of IM7 → IM8. The fact indicates that CO adsorption is the rate-determining step in N 2 formation. After that, CO 2 and N 2 moieties desorb one after another from the carbonaceous surface, forming gaseous CO 2 and N 2 molecules. Both the two processes (IM7 → IM8 and IM9 → P) have a lower energy barrier than all others, with only 61.919 kJ/mol and 32.826 kJ/mol, respectively. As a whole, the elementary reaction IM6 → IM7 is the ratedetermining step of the E-R heterogeneous reaction. That is, the E-R mechanism is largely determined by the interaction of CO with N 2 O.

L-H mechanism
According to the L-H mechanism, the NO-CO heterogeneous reduction reaction starts from the adsorption structure ZNN2. The reaction pathway and the energy profile are plotted in Fig. 5. Similar to the above E-R mechanism, the NO-CO heterogeneous reaction in L-H mechanism can be also divided into four stages: (i) NO dimer formation, (ii) N 2 O formation, (iii) N 2 formation, and (iv) N 2 desorption.
From Fig. 5, the elementary reaction of IM1 → IM2 belongs to the formation of NO dimer, with a low exothermic Gibbs free energy of − 28.688 kJ/mol. The two NO moieties come together on the carbonaceous surface, leading to the N-O bond breakage and then the N-N bond formation. In this case, there are a carbonyl group and an N 2 O moiety on the carbonaceous surface, as shown by the IM2. After that, CO molecules successively interact with the O atom of carbonyl group and with N 2 O molecule, thereby forming two CO 2 molecules and one N 2 moiety (IM3 → IM5 and IM6 → IM8). The E-R and L-H mechanisms are similar concerning reaction pathways and Gibbs free energy changes. However, in the following stage of N 2 desorption, the L-H mechanism significantly varies from the E-R mechanism, which can be attributed to the adsorption mode of N 2 O. The N 2 O molecule adsorbs on only one active site in the E-R mechanism, while two sites are occupied in the L-H mechanism. In this case, the intermolecular interaction between N 2 O moiety with carbonaceous surface in the L-H mechanism seems to Fig. 4 Schematic energy profiles for the NO-CO heterogeneous reaction in the E-R mechanism be stronger than that in the E-R mechanism. However, this also poses a problem; that is, the N 2 desorption from the carbonaceous surface becomes more difficult, which manifests itself as a higher Gibbs free energy barrier than other stages. More specifically, it can be seen in Figs. 4 and 5 that the energy barrier of N 2 desorption in the L-H mechanism is as high as 216.419 kJ/mol, while only 32.826 kJ/mol occurs in the E-R mechanism. This result may be related to the bonding form of N 2 with the char edge. In the L-H mechanism, N 2 attaches to the char edge in side-on mode, while in the E-R mechanism, N 2 has only one N atom attached to the char edge. Compared to the E-R mechanism, the N 2 bonds more strongly with the char edge in the L-H mechanism. Accordingly, the N 2 desorption in the L-H mechanism exhibits a higher energy barrier than the E-R mechanism. More details would be further discussed through the analysis of electronic structure in the next section. Moreover, the N 2 desorption in the E-R mechanism is exergonic, while an endergonic process can be found in the L-H mechanism.
Based on the above analysis, it can be found that the presence of carbonaceous surface decreases the energy barrier of the NO-CO reaction, especially at the initial stage of NO dimer formation. Compared to the L-H mechanism, the formation of NO dimer in the E-R mechanism exhibits a lower energy barrier of the rate-determining step. Meanwhile, the N 2 moiety desorbs more easily from the carbonaceous surface in the E-R mechanism, which can be attributed to the weaker interaction of N 2 O with active site. Overall, the NO-CO reaction is more likely to follow the E-R mechanism rather than either the homogeneous or the L-H mechanism. However, the underlying cause for this difference remains unclear and thus needs to be further discussed at a deep level.

Chemical bond analysis
The formation and breakage of chemical bonds are of critical importance in both homogeneous and heterogeneous reactions. Here, the electron localization function (ELF) is combined with the reduced density gradient (RDG) to analyze the properties of the chemical bond and intermolecular interaction. Figure 6 shows the iso-surface map of ELF and RDG for homogeneous, E-R, and L-H heterogeneous reactions. The cyan basin represents the iso-surface of ELF = 0.8, which means that electrons are strongly localized in this area. The bigger the cyan basin is, the higher the electronic localization is, and thus the more likely it is to interact with other molecules. The strong electrostatic attraction, van der Waals, and repulsive forces are obtained by RDG calculations and marked with the blue, green, and red disks, respectively. Additionally, in Fig. 6, the green, red, and blue arrows are used to distinguish NO dimer formation, N 2 O formation, and N 2 formation/desorption stages. Figure 6a shows the change of electronic localization degree with the process of NO-CO homogeneous reaction. For the intermediate IM1, the cyan basins are mainly distributed on the outside of the molecular system. This may be because, in N(1) and N(2) atoms, the electrons with parallel spin move as far away from each other as possible by Pauli repulsion. In this case, there is a region with low spin polarization between N(1) and N(2) atoms, which may be unfavorable for the bonding between NO molecules. By comparison, for the E-R mechanism, the N atom of the free NO molecule in IM1 exhibits a big localization area, as shown in Fig. 6b. Accordingly, the chemical bond of N(1)-N(2) forms more easily in the E-R mechanism than in others. This may be responsible for the lower energy barrier of heterogeneous reaction than homogeneous reaction in the initial stage of NO dimer formation (255.491 kJ/mol vs. 69.984kJmol). In addition, it can be noted that at the initial stage of the NO dimer, the energy barrier of the L-H mechanism is higher than that of the E-R mechanism (see Fig. 4 and Fig. 5), which may be related to the different degree of electronic localization between them. Specifically, there is an area with higher electronic localization between N(1) with N(2) in the E-R mechanism by comparison with the L-H mechanism. This means that the NO moiety on the carbonaceous surface is more likely to interact with a free NO molecule rather than with another NO moiety, resulting in a lower energy barrier of NO dimer formation in the E-R mechanism.
During the N 2 O formation, it can be found that for the IM3 in both homogeneous and heterogeneous reactions, a hemispheric region with higher electron localization distributes around the C side than around the O side in the CO molecule. Moreover, the two reactions are similar concerning the weak interaction of CO and N 2 O in IM3. Accordingly, it can be inferred that as CO adsorbs on the unsaturated O site in C-down mode, the presence of carbonaceous surface has little influence on the elementary step of CO interaction with the O atom. However, it is noteworthy that the presence of carbonaceous surface can weaken the strength of N(1)-N(2) bond in the N 2 O moiety. From Table 1, the Mayer bond order of the N(1)-N(2) bond for IM4 in the homogeneous reaction is 2.225, while 1.592 and 1.130 correspond to E-R and L-H mechanisms, respectively. Accordingly, it can be inferred that the intermolecular stability of N 2 O moiety on the carbonaceous surface is inferior to N 2 O molecule in the gas phase, which helps the subsequent reactions such as the dissociation of O atom and N 2 moiety.
For the final stage of N 2 formation, it can be seen in Fig. 6b that there is a great localization region at the N(2) side and an attractive force between N 2 with CO 2 moieties in the IM7. Therefore, the dissociation of CO 2 is required to overcome a great deal of resistance, which manifests itself as a higher energy barrier of CO 2 desorption in the E-R mechanism than L-H mechanism (61.919 kJ/mol vs. 0.465 kJ/ mol). Nevertheless, the energy barrier of N 2 formation in both E-R and L-H mechanisms is lower than that in the homogeneous mechanism. From Table 1, for the IM5, the N(2)-O(2) bond in the homogeneous reaction has a higher Mayer bond order than the other two (1.570 vs. 1.474 vs. 1.365). Moreover, there is a strong attraction between O(2) with C(6) in the E-R mechanism (see Fig. 6b), and there is an area of electronic localization around both C(4)-N(1) and C(6)-N(2) bonds (see Fig. 6c). Overall, all of these things are responsible for the higher energy barrier of O dissociation at the stage of N 2 formation in homogeneous reactions than in both E-R and L-H heterogeneous reactions.

Electron transfer
Based on the above analysis, the ELF combined with RDG results provides a detailed description on the formation and breakage of chemical bonds in the NO-CO reactions. These chemical bonds act as driving forces for electron transfer, which can be used to reveal the interfacial interactions caused by an electronic redistribution. The electron density difference of key intermediates is displayed in Fig. 7, in which the green solid line and blue dotted line represent the accumulation and depletion of electrons, respectively. Additionally, the electronic transfer number (Δq) is also listed in Fig. 7.
From Fig. 7, it is obvious that the presence of carbonaceous surface makes a significant difference in the intermolecular electron transfer. Taking an example of NO dimer formation, a large number of electrons flow into the N-N and N-O bonds in the homogeneous reaction, while in the L-H mechanism, the carbonaceous surface gets also involved in the electronic transfer. Compared to the heterogeneous reaction, the homogeneous reaction has a lower , suggesting that there is a strong interaction force between NO molecules in the gas phase. In addition, a region of electronic depletion can be observed between carbonaceous surface and N 2 O moiety in the E-R mechanism, as shown in Fig. 7(d). By comparison, it can be seen in Fig. 7(g) that there are a large number of electrons between carbonaceous surface and N atoms in the L-H mechanism. Accordingly, the binding of N 2 O moiety and carbonaceous surface in the E-R mechanism is weaker than that in the L-H mechanism, leading to a higher energy barrier at the stage of N 2 desorption in the E-R mechanism than in the L-H mechanism. During the formation of N 2 O, the attack of CO on the NO dimer makes a large number of electrons flow into CO 2 from N 2 O in the homogeneous reaction, as shown in Fig. 7(b). Either in E-R or L-H mechanism, the electronic transfer has little to do with the N 2 O moiety, but it is affected by the carbonaceous surface. More specifically, it can be seen in Fig. 7(e, h) that some electrons flood into the C(2) site, while the accumulation and depletion of electrons had to find around the N 2 O moiety. This certainly activates the carbonaceous surface, thereby making it easier for CO 2 desorption. Accordingly, the CO 2 dissociation from the carbonaceous surface in both E-R and L-H mechanisms exhibits a low energy barrier (60.504 kJ/mol and 65.852 kJ/mol), as shown by IM4 → IM5 in Figs. 4 and 5. Likewise, there is the region of electronic accumulation around the C(6) site in E-R mechanism and the N(2) site in L-H mechanism. Therefore, the CO 2 dissociation in heterogeneous reaction becomes easier, which manifests itself as lower energy barriers of IM7 → IM8 in both E-R and L-H mechanisms than in homogeneous mechanism (203.620 kJ/mol vs. 61.919 kJ/ mol vs. 0.465 kJ/mol).
Additionally, it can be found that there is a clear linear relationship between the electronic transfer number and the adsorption energy. For example, there is an adsorption energy of 45.515 kJ/mol with a corresponding Δq of 0.017e at the stage of IM1 → IM2 in the E-R mechanism, while 140.906 kJ/mol with 0.383 e is for the stage of IM1 → IM2 in the L-H mechanism, as shown in Fig. 7(d, g). To further understand the mechanism behind this, the bonding properties of IM2 in both E-R and L-H reactions are studied using the partial density of states (PDOS) calculations. The calculation results are plotted in Fig. 8, in which the gray dotted line represents the energy level in the highest occupied molecular orbital (HOMO) of alpha and beta electrons. According to the frontier orbital theory, the regions near the HOMO energy level are critical to the bonding in gaseous adsorption.
From Fig. 7(a), the N(1), N(2), and C(2) peaks overlap each other nearby the HOMO energy level. By comparison, both the valence band (VB) and conduction band (CB) Fig. 7 Iso-line maps of electron density difference in key intermediates for NO-CO reactions Fig. 8 The PDOS for the structure of IM2 in the heterogeneous reactions. a E-R mechanism, b L-H mechanism (a) E-R mechanism (b) L-H mechanism nearby the HOMO energy level are mainly dominated by the N(1) atomic orbitals, as shown in Fig. 8b. These facts indicate that there are more hybrid orbitals in the IM1 in the E-R mechanism than L-H mechanism, leading to greater adsorption energy in the E-R mechanism. To sum up, the interfacial interactions are largely determined by the electronic transfer between the carbonaceous surface with gaseous molecules. Through the analysis of electronic transfer, it is reasonable to explain the difference in the energy barrier among homogeneous, E-R, and L-H mechanisms.

Conclusion
In this paper, the NO-CO reduction was discussed at the electronic level, with an emphasis on the difference in the Gibbs free energy barrier among homogeneous, E-R, and L-H heterogeneous mechanisms. Results showed that the energy barriers of both NO dimer and N 2 formation in the homogeneous reaction are much higher than those in the heterogeneous reaction. At the initial stage of NO dimer formation in the gas phase, there is a region with low spin polarization between NO molecules, which is unfavorable for bonding two NO molecules. In this process, a large number of electrons flood into the N-N, N-O, and O-O bonds of NO dimer, thereby strengthening the intermolecular interaction of NO dimer. This may be one of the main reasons for the higher energy barrier of residual O desorption in the homogeneous reaction than in the heterogeneous reaction. At the following stage of N 2 formation/desorption, a large number of electrons enter between N 2 O and carbonaceous surface in the L-H mechanism, causing that there is a region with higher electronic localization. In this case, the C-N bond is strengthened, thereby making the N 2 desorption more difficult, which manifests itself as a higher energy barrier of N 2 desorption in the L-H mechanism than E-R mechanism. Overall, the theoretical results help to improve the knowledge about the NO-CO reaction and also provide new insights into the analysis of nitrogen chemistry.