Theoretical Investigation of the Formation Mechanism of NH3 and HCN during Pyrrole Pyrolysis: The Effect of H2O

Coal is a major contributor to the global emission of nitrogen oxides (NOx). The NOx formation during coal utilization typically derives from the thermal decomposition of N-containing compounds (e.g., pyrrolic groups). NH3 and HCN are common precursors of NOx from the decomposition of N-containing compounds. The existence of H2O has significant influences on the pyrrole decomposition and NOx formation. In this study, the effects of H2O on pyrrole pyrolysis to form NOx precursors HCN and NH3 are investigated using the density functional theory (DFT) method. The calculation results indicate that the presence of H2O can lead to the formation of both NH3 and HCN during pyrrole pyrolysis, while only HCN is formed in the absence of H2O. The initial interaction between pyrrole and H2O determines the N products. NH3 will be formed when H2O attacks the C2 position of pyrrole with its hydroxyl group. On the contrary, HCN will be generated instead of NH3 when H2O attacks the C3 position of pyrrole with its hydroxyl group. In addition, the DFT calculations clearly indicate that the formation of NH3 will be promoted by H2O, whereas the formation of HCN is inhibited.


Introduction
Coal is the major energy source in the modern industrial production process. Coal-mining, coal-burning factories, and other coal-related usage are the dominant sources of NO x emission [1,2]. The harmful atmospheric pollutants of NO x (i.e., NO, NO 2 , N 2 O, etc.) can form acid rain and photochemical smog and endanger human health [3][4][5]. Moreover, the contribution of NO to the greenhouse effect is 260 times higher than that of CO 2 [6].
Nitrogen compounds in coal are primarily pyrrole and pyridine, which have already been widely used in different coal structural models, such as the Given, Wiser, and Shinn models [7][8][9]. The well-known Given model, mainly containing carbon, hydrogen, oxygen, and small amounts of sulfur and nitrogen, was intended to show the types of hydrogen structures in the bituminous coal, and has been widely adopted as a structural representation. The Wiser mode,l along with "structural alternative" carbon skeletal representations, had an increasing scale, representing the rank transition from 76% C to 90% C (wt % basis) [9]. The Shinn model was created at a larger scale (10,000 amu), in which three relatively small unconnected molecular entities were held within a larger molecule [8].
It is notable that around 60% of total coal nitrogen is the pyrrolic nitrogen [10], and this concentration varies slightly with different coal ranks [10,11]. Hence, the thermal decomposition of pyrrolic groups plays a vital role in NO x formation. As a result, pyrrole was commonly employed as the N-containing model compound in coal, and has been extensively studied in recent decades.
Many efforts have been made to characterize the pyrolysis of pyrrole using experimental and theoretical approaches [12][13][14][15][16][17]. Martoprawiro et al. [12] proposed a mechanism for the formation of HCN from pyrrole, which stated that the reaction was initiated by a hydrogen migration to form a cyclic carbene intermediate. Subsequent ring opening and decomposition steps gave rise to HCN and propyne. Moreover, Zhai et al. [18] investigated the mechanisms of pyrrole pyrolysis, outlining the routes for formation of cis-crotonitrile, allyl cyanide, and HCN. Besides HCN, NH 3 is another important precursor of NO x from coal utilization at high temperatures [19][20][21]. Li et al. [20] conducted pyrolysis experiments on coal and concluded that the formation of both HCN and NH 3 was initiated by the N-containing heteroaromatic ring being attacked by radicals. Similarly, Elmer et al. [21] employed a quartz fluidized-bed reactor coupled to a quartz tubular flow reactor for rapid pyrolysis of coal, and suggested that NH 3 might be formed from the interactions of N-containing species with donatable H on the soot surface. However, to date, few theoretical studies have focused on the formation of NH 3 during pyrrole pyrolysis.
During the coal pyrolysis process, H 2 O will play an essential role in the decomposition reactions and formation of various products. Hu et al. [22] investigated the pyrolysis behavior and reaction mechanisms of coal samples containing different moisture contents. They found that the moisture content had a significant influence on the tar yield and light tar content, and H 2 O could upgrade the low-rank coal during pyrolysis [23]. Moreover, Park and co-workers [24] found that studies of coal-N release in the presence of H 2 O were more authentic than those of the only pyrrole, as H 2 O inevitably existed in the coal utilization process. However, there are limited studies focusing on the effect of H 2 O on pyrrole pyrolysis at present. Therefore, in this study, the density functional theory (DFT) method was applied to investigate the detailed pyrolysis mechanism of pyrrole to HCN and NH 3 in the presence of H 2 O, which may help with the development of coal pyrolysis/combustion technologies for NO x control.

Results
Early studies [12,17,25] have already investigated the possible pyrolysis pathways of pure pyrrole using quantum chemistry methods. The obtained activation energies (346 and 316.31 kJ/mol, as shown in Figure 1) are comparable with the activation energy measured from the experimental energy of the overall disappearance of pyrrole between 1300 and 1500 K at 12 atm pressure (310.1 ± 12.5 kJ/mol) [19]. The activation energy difference between the two pathways in Figure 1 is mainly due to the initial H migration to different carbons. In the proposed pathways, the crucial step is the isomerization of pyrrole to the cyclic carbine. Then, the primary N-type product of HCN is formed through a ring opening reaction, as shown in Figure 1. No NH 3 will be formed in this pyrolysis process.
When H 2 O participates in the pyrrole pyrolysis process, it will interact with pyrrole, thus significantly altering the pyrolysis mechanism and pathways. As shown in Figure 2, the possible interactions between pyrrole and H 2 O may occur in four ways, i.e., adj-OH-C 2 -H, adj-OH-N-H, ind-OH-C 1 -H, and ind-OH-C 3 -H (the adjacent position is abbreviated as adj-, the indirect position is abbreviated as ind-), in which H 2 O attacks different positions of pyrrole. In the adj-OH-C 2 -H interaction, H 2 O reacts with pyrrole by simultaneously donating its hydroxyl group to the C 1 position and hydrogen to the C 2 position. The energy barrier of this reaction is 226.4 kJ/mol. In an alternate possible interaction, adj-OH-N-H, H 2 O also donates its hydroxyl group to the C 1 position of pyrrole. Differently, H 2 O provides its hydrogen to the N position, which will result in the opening of the ring. This reaction needs to overcome a higher energy barrier of 297.6 kJ/mol compared to the first reaction (interaction adj-OH-C 2 -H). In the possible ind-OH-C 1 -H interaction, H 2 O also interacts with pyrrole at the C 1 and C 2 position. Different from the first reaction, the hydroxyl group attacks the C 2 position, whereas hydrogen attacks the C 1 position in this reaction. The energy barrier is 235.0 kJ/mol, which is close to that of the first reaction. In the possible ind-OH-C 3 -H interaction, H 2 O reacts with pyrrole at the C 2 and C 3 position with an energy barrier of 293.1 kJ/mol. In summary, based on Figure 2, the initial interaction modes of adj-OH-C 2 -H and ind-OH-C 1 -H are more feasible than the other two interaction modes because of the relatively low energy barriers (226.4 and 235.0 kJ/mol). The possible subsequent pyrolysis pathways based on the four initial interaction ways are presented below to investigate the formation of NH 3 or HCN.

The Effect of H 2 O on Pyrrole Pyrolysis Based on the adj-OH-C 2 -H Interaction
Based on the adj-OH-C 2 -H interaction, five possible pathways might occur and can be classified into two categories according to their products (NH 3 or HCN). NH 3 is the product in three pathways (a-1, a-2, and a-3), as shown in Figure 3, while HCN is the product in the other two pathways (a-4, a-5), as shown in Figure 4.

The Effect of H2O on Pyrrole Pyrolysis Based on the adj-OH-C2-H Interaction
Based on the adj-OH-C2-H interaction, five possible pathways might occur and can be classified into two categories according to their products (NH3 or HCN). NH3 is the product in three pathways (a-1, a-2, and a-3), as shown in Figure 3, while HCN is the product in the other two pathways (a-4, a-5), as shown in Figure 4.  In Figure 3, the concerted interaction adj-OH-C2-H generates a-1-1m, which may undergo three possible subsequent pathways to form NH3. In pathway a-1, intermediate a-1-2t is converted to intermediate a-1-2m, via concerted ring-opening transition state a-1-2t, with an energy barrier of 148.5 kJ/mol. Then intermediate a-1-2m undergoes a hydrogen transfer reaction via three-membered transition state a-1-3t to form products NH3 and a-1-3m, with an energy barrier of 364.3 kJ/mol. In pathway a-2, a-1-2m undergoes another hydrogen transfer reaction via four-membered transition state a-2-1t, transferring H from C3 position to N position, breaking the C-N bond to form products a-2-1m and NH3 with an energy barrier of 458.5 kJ/mol. In pathway a-3, a-1-1m is transformed into intermediate a-3-1m, with an energy barrier of 257.3 kJ/mol. Afterwards, intermediate a-3-1m removes the carbon monoxide through transition state a-3-2t to form the intermediate a-3-2m, with an energy barrier of 62.4 kJ/mol. Finally, a-3-2m decomposes into a-3-3m and NH3 by homolysis of

The Effect of H2O on Pyrrole Pyrolysis Based on the adj-OH-C2-H Interaction
Based on the adj-OH-C2-H interaction, five possible pathways might occur and can be classified into two categories according to their products (NH3 or HCN). NH3 is the product in three pathways (a-1, a-2, and a-3), as shown in Figure 3, while HCN is the product in the other two pathways (a-4, a-5), as shown in Figure 4.  In Figure 3, the concerted interaction adj-OH-C2-H generates a-1-1m, which may undergo three possible subsequent pathways to form NH3. In pathway a-1, intermediate a-1-2t is converted to intermediate a-1-2m, via concerted ring-opening transition state a-1-2t, with an energy barrier of 148.5 kJ/mol. Then intermediate a-1-2m undergoes a hydrogen transfer reaction via three-membered transition state a-1-3t to form products NH3 and a-1-3m, with an energy barrier of 364.3 kJ/mol. In pathway a-2, a-1-2m undergoes another hydrogen transfer reaction via four-membered transition state a-2-1t, transferring H from C3 position to N position, breaking the C-N bond to form products a-2-1m and NH3 with an energy barrier of 458.5 kJ/mol. In pathway a-3, a-1-1m is transformed into intermediate a-3-1m, with an energy barrier of 257.3 kJ/mol. Afterwards, intermediate a-3-1m removes the carbon monoxide through transition state a-3-2t to form the intermediate a-3-2m, with an energy barrier of 62.4 kJ/mol. Finally, a-3-2m decomposes into a-3-3m and NH3 by homolysis of In Figure 3, the concerted interaction adj-OH-C 2 -H generates a-1-1m, which may undergo three possible subsequent pathways to form NH 3 . In pathway a-1, intermediate a-1-2t is converted to intermediate a-1-2m, via concerted ring-opening transition state a-1-2t, with an energy barrier of 148.5 kJ/mol. Then intermediate a-1-2m undergoes a hydrogen transfer reaction via three-membered transition state a-1-3t to form products NH 3 and a-1-3m, with an energy barrier of 364.3 kJ/mol. In pathway a-2, a-1-2m undergoes another hydrogen transfer reaction via four-membered transition state a-2-1t, transferring H from C 3 position to N position, breaking the C-N bond to form products a-2-1m and NH 3 with an energy barrier of 458.5 kJ/mol. In pathway a-3, a-1-1m is transformed into /mol. Finally, a-3-2m decomposes into a-3-3m and NH 3 by homolysis of the C-N bond, with an energy barrier of 76.4 kJ/mol. Based on the above calculation results, pathway a-3 is the most favorable one due to having the lowest overall energy barrier (362.3 kJ/mol). It is notable that previous studies have indicated that only HCN would be formed from pyrolysis of pyrrole or pyroxene-type products in the absence of H 2 O [12,17,18], whereas the participation of H 2 O in pyrrole pyrolysis can provide hydrogen sources leading to the formation of NH 3 , which is consistent with previous experimental results [24].
Based on the adj-OH-C 2 -H interaction, HCN is the only N product formed through the possible pathways a-4 and a-5. As shown in Figure 4 with an energy barrier of 423.6 kJ/mol. The rate-determining step is the reaction to generate HCN (the reaction with the highest energy), and the overall energy barrier of pathway a-5 is 458.0 kJ/mol. It is clear that pathway a-5 is more feasible than pathway a-4 by comparing their whole energy barriers.
According to the above calculation results, H 2 O has a significant effect on the pyrolysis of pyrrole. It results in the formation of NH 3 as a new product, which will not be formed in the absence of H 2 O [12,18,23]. Moreover, H 2 O can also affect the HCN formation. The energy barrier for the generation of HCN in the presence of H 2 O is higher than in the absence of H 2 O [12,17] (details in Figure 1), which indicates that H 2 O can inhibit the formation of HCN during the pyrrole pyrolysis process.

The Effect of H 2 O on Pyrrole Pyrolysis Based on the adj-OH-N-H Interaction
Following the initial adj-OH-N-H interaction, three possible routes might occur, i.e., b-1, b-2, and b-3, as shown in Figure 5. All three pathways result in the formation of NH 3 rather than HCN. the C-N bond, with an energy barrier of 76.4 kJ/mol. Based on the above calculation results, pathway a-3 is the most favorable one due to having the lowest overall energy barrier (362.3 kJ/mol). It is notable that previous studies have indicated that only HCN would be formed from pyrolysis of pyrrole or pyroxene-type products in the absence of H2O [12,17,18], whereas the participation of H2O in pyrrole pyrolysis can provide hydrogen sources leading to the formation of NH3, which is consistent with previous experimental results [24]. Based on the adj-OH-C2-H interaction, HCN is the only N product formed through the possible pathways a-4 and a-5. As shown in Figure 4 According to the above calculation results, H2O has a significant effect on the pyrolysis of pyrrole. It results in the formation of NH3 as a new product, which will not be formed in the absence of H2O [12,18,23]. Moreover, H2O can also affect the HCN formation. The energy barrier for the generation of HCN in the presence of H2O is higher than in the absence of H2O [12,17] (details in Figure 1), which indicates that H2O can inhibit the formation of HCN during the pyrrole pyrolysis process.

The Effect of H2O on Pyrrole Pyrolysis Based on the adj-OH-N-H Interaction
Following the initial adj-OH-N-H interaction, three possible routes might occur, i.e., b-1, b-2, and b-3, as shown in Figure 5. All three pathways result in the formation of NH3 rather than HCN.

The Effect of H 2 O on Pyrrole Pyrolysis Based on the ind-OH-C 1 -H Interaction
Following the initial ind-OH-C 1 -H interaction, four possible pyrolytic pathways, i.e., c-1, c-2, c-3 and, c-4 might take place, as shown in Figure 6. In Figure 6a

The Effect of H2O on Pyrrole Pyrolysis Based on the ind-OH-C1-H Interaction
Following the initial ind-OH-C1-H interaction, four possible pyrolytic pathways, i.e., c-1, c-2, c-3 and, c-4 might take place, as shown in Figure 6. In Figure 6a   It should be pointed out that the activation energy (455.4 kJ/mol) is higher than that of the pyrolysis of hemicellulose, cellulose, or lignin [26]. The main reason can be attributed to the different initial reaction model compounds. The pyrrole structure is highly stable with a five-membered ring, while compounds like hemicellulose and cellulose contain active elements such as oxygen and hydroxyl groups that have promoting effects on the pyrolysis reactions [27]. In summary, the ind-OH-C 1 -H interaction inhibits the formation of HCN, but does not lead to the formation of NH 3 .

The Effect of H 2 O on Pyrrole Pyrolysis Based on the ind-OH-C 3 -H Interaction
As shown in Figure 7, following the ind-OH-C 3 -H interaction, there is only one possible pathway, d-1, which results in the formation of only HCN. It should be pointed out that the activation energy (455.4 kJ/mol) is higher than that of the pyrolysis of hemicellulose, cellulose, or lignin [26]. The main reason can be attributed to the different initial reaction model compounds. The pyrrole structure is highly stable with a five-membered ring, while compounds like hemicellulose and cellulose contain active elements such as oxygen and hydroxyl groups that have promoting effects on the pyrolysis reactions [27]. In summary, the ind-OH-C1-H interaction inhibits the formation of HCN, but does not lead to the formation of NH3.

The Effect of H2O on Pyrrole Pyrolysis Based on the ind-OH-C3-H Interaction
As shown in Figure 7, following the ind-OH-C3-H interaction, there is only one possible pathway, d-1, which results in the formation of only HCN.

Discussion
The above calculation clearly indicates that H2O plays a vital role in the pyrolysis of pyrrole. The type of N products will be determined by the initial interaction of H2O and pyrrole. Based on the calculation results, the optional pathways following each initial interaction of H2O and pyrrole are

Discussion
The above calculation clearly indicates that H 2 O plays a vital role in the pyrolysis of pyrrole. The type of N products will be determined by the initial interaction of H 2 O and pyrrole. Based on the calculation results, the optional pathways following each initial interaction of H 2 O and pyrrole are summarized in Table 1. Following the initial adj-OH-C 2 -H interaction, the optimal pathway is a-3, with an overall energy barrier of 362.3 kJ/mol, and the N product is NH 3 . Within the initial adj-OH-N-H interaction, pathways a-3 and b-1 are the optimal pathways for the formation of NH 3 . The overall energy barriers are 362.2 and 361.4 kJ/mol, respectively. Starting from the initial ind-OH-C 1 -H interaction, the optimal pathway is c-4, with an overall energy barrier of 455.4 kJ/mol, and HCN is the final product. Following the initial ind-OH-C 3 -H interaction, there is only one possible pathway (pathways d-1) for HCN formation, with an overall energy barrier of 413.9 kJ/mol. Compared with the HCN formation from pure pyrrole pyrolysis process (shown in Figure 1), generation of HCN in the presence of H 2 O needs to overcome a higher energy barrier [12,17]. Hence, the presence of H 2 O in pyrrole pyrolysis inhibits the formation of HCN, while promotes the formation of NH 3 . For the two N products of NH 3 and HCN, the formation pathways of NH 3 need to overcome lower overall energy barriers than those of HCN. Therefore, it can be concluded that formation of NH 3 is easier than that of HCN during the pyrrole pyrolysis process in the presence of H 2 O. The research result is consistent with previous experimental results [24], which found that the formation of NH 3 would be promoted by increasing the concentration of H 2 O in the feeding gas. Moreover, Tian et al. [28] proposed that the high NH 3 yield from char-N (pyrrolic-nitrogen) gasification in steam resulted from the increased availability of H radical derived from the steam. According to our calculations, it is the initial interaction of H 2 O and pyrrole that determines the final formation of NH 3 , especially based on the adj-OH-C 2 -H and adj-OH-N-H interactions, since H 2 O will attack the C 2 position of pyrrole with its hydroxyl group in both interactions. The mechanisms discussed in this paper only indicate the thermal decomposition of pyrrole to form HCN and NH 3 . However, according to the previous study [29], N-containing compounds might also undergo polymerization to form solid residues. Therefore, the effects of both solid residues and H 2 O during pyrrole pyrolysis are worthy of investigation in a future work.

Materials
Pyrrole is a heterocyclic organic compound containing a five-membered ring with the formula C 4 H 4 NH. The optimized molecular structure and main parameters (bond length, bond angle) of pyrrole are shown in Figure 8. All carbon atoms are marked with numbers for convenient expression. Due to the symmetrical structure, there is no difference between the C 1 group and C 4 group, or between the C 2 group and C 3 group.

Materials
Pyrrole is a heterocyclic organic compound containing a five-membered ring with the formula C4H4NH. The optimized molecular structure and main parameters (bond length, bond angle) of pyrrole are shown in Figure 8. All carbon atoms are marked with numbers for convenient expression. Due to the symmetrical structure, there is no difference between the C1 group and C4 group, or between the C2 group and C3 group.

Methods
All calculations were carried out using the Gaussian 09 program [30]. The equilibrium geometries of the reactants, intermediates, transition states, and products were optimized by employing B3LYP/6-31G(d,p). DFT is a computational method that derives the properties of a system based on the electron density of the system [31,32]. The B3LYP functional with a 6-31G(d,p) basis set has been proven to be an appropriate choice for modeling organic species [31,33]. Moreover, DFT calculations have been successfully applied to investigate the pyrolysis mechanism of pyrrole model compounds [12,17].
In this work, the optimized structures of the reactants, intermediates, transition states, and products were further evaluated by frequency analysis, adopting the same method and basis set as the structural optimization calculations. The results of a frequency analysis were used to verify the stationary points to be minimal or first-order saddle points and to obtain their thermodynamic parameters. Intrinsic reaction coordinate (IRC) calculations were further performed to ensure the corresponding minimal and first-order saddle point on the same potential energy surface. Enthalpies were used for the discussion on energetics, under the standard conditions of 298.15 K and 1 atm. To evaluate the reliability of the selected calculation method and parameters, the structural parameters of a radical reaction were calculated and confirmed by triple spin multiplicity [31]. The energy barrier was calculated by the difference between the activation energy of reactants and concerted transition states (TS) [34].

Conclusions
In this study, the formation mechanisms of HCN and NH 3 during pyrrole pyrolysis in the presence of H 2 O are investigated by DFT calculation. The results show that H 2 O and pyrrole can interact in four ways, followed by 13 possible pyrolysis pathways. Six pathways will result in the formation of NH 3 (a-1, a-2, a-3, b-1, b-2, b-3), and another six pathways will lead to the HCN (a-4, a-5, c-2, c-3, c-4, d-1), while pathway c-1 does not lead to the formation of either HCN or NH 3 . Among all these pathways, pathways a-3 and b-1 are the most favorable ones, with an overall energy barrier of 362.3 and 361.4 kJ/mol, and both pathways result in the formation of NH 3 .
The formation of NH 3 or HCN is determined by the different initial interactions of H 2 O with pyrrole. When H 2 O attacks the C 2 position of pyrrole, there are two possible interactions (adj-OH-C 2 -H and adj-OH-N-H). In the following pathways based on the two interactions, NH 3 will be formed while the formation of HCN is inhibited. When H 2 O attacks the C 3 position of pyrrole with its hydroxyl group, it leads to another two interactions (ind-OH-C 1 -H and ind-OH-C 3 -H). In the following pathways, HCN will be generated instead of NH 3 . Meanwhile, the formation of HCN is inhibited compared to in reactions without H 2 O.
Author Contributions: J.L. and Q.L. conceived and designed the research; B.H. and X.-y.J. performed the calculations; X.-l.Z. analyzed the data and wrote the paper; C.-q.D. and Y.-p.Y. contributed reagents and analysis tools.

Conflicts of Interest:
The authors declare no conflict of interest and no personal circumstances or interest that may be perceived as inappropriately influencing the representation or interpretation of reported research results. The founding sponsors had roles in the design of the study; in the writing of the manuscript, and in the decision to publish the results.