Atmospheric oxidation mechanism and kinetics of indole initiated by (cid:113) OH and (cid:113) Cl: a computational study

. The atmospheric chemistry of organic nitrogen compounds (ONCs) is of great importance for understanding the formation of carcinogenic nitrosamines, and ONC oxidation products might inﬂuence atmospheric aerosol particle formation and growth. Indole is a polyfunctional heterocyclic secondary amine with a global emission quantity almost equivalent to that of trimethylamine, the amine with the highest atmospheric emission. However, the atmospheric chemistry of indole remains unclear. Herein, the reactions of indole with (cid:113) OH and (cid:113) Cl, and subsequent reactions of resulting indole radicals with O 2 under 200 ppt NO and 50 ppt HO 2 (cid:113) conditions, were investigated by a combination of quantum chemical calculations and kinetics modeling. The results indicate that (cid:113) OH addition is the dominant pathway for the reaction of (cid:113) OH with indole. However, both (cid:113) Cl addition and H abstraction are feasible for the corresponding reaction with (cid:113) Cl. All favorably formed indole radicals further react with O 2 to produce peroxy radicals, which mainly react with NO and HO 2 (cid:113) to form organonitrates, alkoxy radicals and hydroperoxide products. Therefore, the oxidation mechanism of indole is distinct from that of previously reported amines, which primarily form highly oxidized multifunctional compounds, imines or carcinogenic nitrosamines. In addition, the peroxy radicals from the (cid:113) OH reaction can form N-(2-formylphenyl)formamide (C 8 H 7 NO 2 ), for the ﬁrst time providing evidence for the chemical identity of the C 8 H 7 NO 2 mass peak observed in the (cid:113) OH + indole experiments. More importantly, this study is the ﬁrst to demonstrate that despite forming radicals by abstracting an H atom at the N site, carcinogenic nitrosamines were not produced in the indole oxidation reaction.


Introduction
Volatile organic compounds (VOCs) play a central role in air quality and climate change as their transformations are highly relevant for the formation of secondary organic aerosols (SOA), toxic air pollutants and ozone (O 3 ) (Ehn et al., 2014;Karl et al., 2018;Lewis Alastair, 2018;Khare and Gentner, 2018;Ji et al., 2018). Therefore, an accurate description of the atmospheric transformation mechanism and kinetics of VOCs is essential to fully explore the global impacts of VOCs. Despite massive effort to understand the atmospheric fate of VOCs, current mechanism-based atmospheric models often underestimate SOA and O 3 formation quantity. Therefore, the emission in-ventories or reaction mechanism employed in the models are either missing some vital primary VOCs or there remain an unrevealed reaction mechanism of currently known VOCs. Hence, it is crucial to identify unaccounted reaction pathways of known VOCs or the transformation mechanism of unconsidered VOCs with high concentrations.
Organic nitrogen compounds (ONCs) are a subgroup of VOCs that are widely observed in the atmosphere (Silva et al., 2008). Until now, about 160 ONCs have been detected in the atmosphere, accounting for 10 % of total gas phase nitrogen (excluding N 2 ) (Ge et al., 2011;Silva et al., 2008). Due to the adverse effects of ONCs on air quality (formation of particles via acid-base reactions or generation of toxic ni-trosamines, nitramines, isocyanic acid and low volatile products via gas phase oxidation), the chemistry of ONCs has gained significant attention in recent years (Almeida et al., 2013;Chen et al., 2017;Lin et al., 2019;Nielsen et al., 2012;Zhang et al., 2015;Xie et al., 2014Xie et al., , 2015Xie et al., , 2017F. F. Ma et al., 2018aF. F. Ma et al., , 2021bShen et al., 2019Shen et al., , 2020. Detailed transformation pathways of a series of ONCs, including lowmolecular-weight alkyl amines (Nicovich et al., 2015;Xie et al., 2014Xie et al., , 2015F. F. Ma et al., 2021b), aromatic aniline Shiels et al., 2021), heterocyclic amines (Sen-Gupta et al., 2010;Ma et al., 2018a;Borduas et al., 2016b;Ren and Da Silva, 2019) and amides Borduas et al., 2016aBorduas et al., , 2015Bunkan et al., 2016Bunkan et al., , 2015, have been investigated. These studies have shown that the functional groups connected to the NH x (x = 0, 1, 2) group highly affect the reactivity of ONCs and eventually lead to their different atmospheric impacts. Therefore, the comprehensive understanding the reaction mechanism of ONCs with various functional groups linked to the NH x group is of great significance in assessing the atmospheric impact of ONCs.
Indole is a polyfunctional heterocyclic secondary amine (Laskin et al., 2009). Atmospheric indole has various natural and anthropogenic sources including vegetation, biomass burning, animal husbandry, coal mining, petroleum processing and the tobacco industry (Q. Ma et al., 2021;Cardoza et al., 2003;Yuan et al., 2017;Zito et al., 2015). The global emission of indole is around 0.1 Tg yr −1 (Misztal et al., 2015), which is almost equivalent to that of trimethylamine (∼ 0.17 Tg yr −1 ) (Schade and Crutzen, 1995;Yu and Luo, 2014) which has the highest emission among the identified atmospheric amines. A field measurement study found that the concentration of indole can reach 1-3 ppb in ambient air during a springtime flowering event (Gentner et al., 2014). From a structural point of view, the -NH-group of indole is located at 9-center-10-electron delocalized π bonds, possibly altering its reactivity compared with that of previously well-studied aliphatic amines and aniline. Therefore, considering the large atmospheric emission of indole and its unique structure compared with previously studied amines, the reaction mechanism of indole needs to be further evaluated to assess its atmospheric impacts. Furthermore, elucidating the reaction mechanism of indole will add to the fundamental understanding of the transformation mechanism of ONCs.
Hydroxyl radicals ( q OH) are considered to be the most important atmospheric oxidants governing the fate of most organic compounds (MacLeod et al., 2007). Previous experimental studies have investigated the reaction kinetics and identified the products of the q OH + indole reaction. Atkinson et al. found that the rate constant (k OH ) of the q OH + indole reaction is 1.54 × 10 −10 cm 3 molecule −1 s −1 at 298 K, translating to a 20 min lifetime of indole (Atkinson et al., 1995). Montoya-Aguilera et al. found that isatin and isatoic anhydride are the two dominate monomeric products for q OH initiated reaction of indole. More importantly, they found that the majority of indole oxidation products can contribute to SOA formation with an effective SOA yield of 1.3 ± 0.3 under the indole concentration (200 ppb) employed in their chamber study (Montoya-Aguilera et al., 2017). Although the chemical formulas of some of the indole oxidation products have been detected, detailed mechanistic information, such as the products branching ratio of the q OH initiated reaction of indole, remains unknown. Additionally, the lack of commercially available standards of some products presents a significant obstacle to identify the exact chemical identity of the products. Therefore, to fully understand the role of indole in SOA formation, it is essential to investigate the detailed atmospheric transformation of indole initiated by q OH.
Besides reactions with q OH, reactions with chlorine radicals ( q Cl) have been proposed to be an important removal pathway for ONCs due to the identification of new q Cl continental sources and the high reactivity of q Cl (Wang et al., 2022;Li et al., 2021;Jahn et al., 2021;Xia et al., 2020;Young et al., 2014;Faxon and Allen, 2013;Riedel et al., 2012;Atkinson et al., 1989;Ji et al., 2013;Thornton et al., 2010;Le Breton et al., 2018). q Cl initiated atmospheric oxidation of ONCs can lead to the formation of N-centered radicals, once a strong 2-center-3-electron (2c-3e) bond complex has been formed between q Cl and NH x (x = 1, 2) (Mc-Kee et al., 1996;Xie et al., 2015Xie et al., , 2017Ma et al., 2018a). The formed N-centered radicals can further react with NO to form carcinogenic nitrosamines, increasing the atmospheric impact of ONC emissions (Xie et al., 2014(Xie et al., , 2015Ma et al., 2018aMa et al., , 2021bOnel et al., 2014a, b;Nielsen et al., 2012;Da Silva, 2013). As a secondary amine, indole reaction with q Cl has the possibility of forming N-centered radicals and subsequently forming nitrosamines via the reaction with NO. Since the -NH-group of indole is embedded in a unique chemical environment compared with previously well-studied ONCs, the reaction mechanism of q Cl with indole remains elusive. In addition, there are only a few studies concerning the reactions of polyfunctional heterocyclic ONCs with q Cl.
In this work, we investigated the reaction mechanism and kinetics of indole initiated by q OH and q Cl by employing a combination of quantum chemical calculations and kinetic modeling. The initial reactions of q OH and q Cl with indole and the subsequent reactions with O 2 of resulting intermediates were further investigated.

Ab Initio electronic structure calculations
All the geometry optimizations and harmonic vibrational frequency calculations were performed at the M06-2X/6-31+G(d,p) level of theory (Zhao and Truhlar, 2008). Intrinsic reaction coordinate calculations were performed to confirm the connections of each transition state between the corresponding reactants and products. Single point energy calcu-lations were performed at the CBS-QB3 method based on the geometries at the M06-2X/6-31+G(d,p) level of theory (Montgomery et al., 1999). The combination of the M06-2X functional and CBS-QB3 method has successfully been applied to predict radical-molecule reactions F. F. Ma et al., 2021a;Wang et al., 2018;Wang and Wang, 2016;Wu et al., 2015;Fu et al., 2020). T 1 diagnostic ( Table S2 in the Supplement) values in the CCSD(T) calculations within the CBS-QB3 scheme for the intermediates and transition states involved in the key reaction pathways were checked for multireference character. The T 1 diagnostic values for all checked important species in this work are lower than the threshold value of 0.045, indicating the reliability of applied single reference methods (Rienstra-Kiracofe et al., 2000). In addition, similar to our previous studies, a literature value of 0.8 kcal mol −1 for the isolated q Cl was used to account for the effect of spinorbit coupling in the q Cl + indole reaction (Nicovich et al., 2015;Xie et al., 2017;Ma et al., 2018a). Atomic charges of indole and pre-reactive complexes in the q Cl + indole reaction are obtained by natural bond orbital (NBO) calculations (Reed et al., 1985). All calculations were performed within the Gaussian 09 package (Frisch et al., 2009). Throughout the paper, the symbols "R, RC, PC, TS, IM and P" stand for reactants, pre-reactive complexes, post-reactive complexes, transition states, intermediates and products involved in the reactions, respectively, and their subscripts denote different species. In addition, "A//B" was used to present the computational method, where "A" is the theoretical level for single point energy calculations and "B" is that for geometry optimizations and harmonic frequency calculations.

Kinetics calculations
MultiWell-2014.1 and MESMER 5.0 software were employed to investigate the kinetics for short time and long time reaction, respectively (Barker and Ortiz, 2001;Barker, 2001;Glowacki et al., 2012). For the initial reactions of q OH and q Cl with indole, the reaction kinetics were calculated within the MultiWell-2014.1 program. For the subsequent reactions of resulting primary intermediates, MES-MER 5.0 was selected for simulating the reaction kinetics, since it has good performance for long time runs, especially for simulating the variation of the different intermediates over time. Both the MultiWell and MESMER codes employ the Rice-Ramsperger-Kassel-Marcus (RRKM) theory to calculate the reaction kinetics for reactions with intrinsic energy barriers (Holbrook, 1996;Robinson, 1972). The long-range transition-state theory (LRTST) with a dispersion force potential within the MultiWell-2014.1 program (Barker and Ortiz, 2001) or the inverse Laplace transformation (ILT) method within the MESMER 5.0 program was employed to calculate the reaction rate constants for the barrierless recombination reactions (from R to RC and P to PC) (Rienstra- Kiracofe et al., 2000). Computational details for performing LRTST and ILT calculations were described in our previous studies (F. F. Ma et al., 2021a, b;Guo et al., 2020;Ding et al., 2020). The parameters used in the LRTST calculations and Lennard-Jones parameters of intermediates estimated by the empirical method proposed by Gilbert and Smith (Gilbert and Smith, 1990) are listed in Tables S3 and S4, respectively. N 2 was selected as the buffer gas, and an average transfer energy of E d = 200 cm −1 was used to simulate the collision energy transfer between active intermediates and N 2 . In addition, E d between 50-250 cm −1 were selected to study energy transfer parameters effects. For the reactions involving H abstraction or H shift, tunneling effects were taken into account in all of the reaction rate constants calculations by using a one-dimensional unsymmetrical Eckart barrier (Eckart, 1930), and are discussed in the Supplement. The kinetic calculations were primarily performed at 298 K and 1 atm, with additional ones at 0.1, 0.4 and 0.7 atm in the troposphere relevant range to explore pressure effects. Variation in the energy transfer parameters and pressure resulted in only minor changes (< 0.1 %) in the calculated rate coefficients and branching ratios of the main reaction pathways (see details in the Supplement).

Initial reactions of indole
In principle, q OH and q Cl could add to the unsaturated C=C bonds and benzene ring or directly abstract H atoms connected to either to a C atom or the N atom of indole. Considering the planar C s structure of indole, q OH and q Cl addition to one side of indole was only considered here. However, although numerous attempts were made, we failed to locate the TSs and addition IMs of q Cl addition to the C2, C3, C4, C7, C8 and C9 sites of indole (the numbering of the atoms is given in Fig. 1), suggesting that such additions are in fact unfeasible. Therefore, 7 H-abstraction pathways of q OH and q Cl, respectively, 8 q OH-addition pathways and 2 q Claddition pathways were considered for the q OH and q Cl with indole reactions. The schematic zero-point energy (ZPE) corrected potential energy surfaces of q OH and q Cl with indole reactions are presented in Fig. 1. As can be seen in Fig. 1, each H-abstraction reaction pathway proceeds through an RC and PC, and the addition pathways through an RC for the q OH and q Cl with indole reactions. For the H-abstraction pathways, the activation energy (E a ) for the -NH-group for both reactions are at least 2.0 kcal mol −1 lower than the corresponding E a values for the -CH-groups. This indicates that H abstraction from the -NH-group forming C 8 H 6 N radicals and H 2 O or HCl is the most favorable among all the H-abstraction pathways. In addition, the activation energy for the H abstraction from the -NH-group in the q Cl + indole reaction is much lower than the corresponding q OH + indole reaction. This is consistent with previously reported reactions of other amines with q OH and q Cl (F. F. Ma et al., 2018aMa et al., , 2021bXie et al., 2014Xie et al., , 2015Xie et al., , 2017Tan et al., 2021;Ren and Da Silva, 2019;Borduas et al., 2015).
For the addition reactions, the most favorable reaction site differs for the indole + q OH and indole + q Cl reactions. Among all 8 q OH addition pathways, q OH addition to the C7 site of the C=C bond via TS 1−7 forming IM 1−7 is the most favorable pathway. Different from the reaction with q OH, the additions of q Cl to the C5 and C6 sites to form IM 2−5 and IM 2−6 , respectively, are significantly more favorable. By comparing the E a values of the addition and Habstraction pathways for both q OH and q Cl with indole reactions, it can be concluded that q OH addition to the C7 site is the most favorable for the q OH + indole reaction. All the q OH + indole hydrogen abstraction reactions have high energy barriers. However, the additions of q Cl to the C5 and C6 sites, as well as the -NH-H abstraction, are all favorable due to their very low E a values for the q Cl + indole reaction. Interestingly, we found that all the pathways for the indole + q Cl reaction can proceed via a stable 2c-3e bonded RC, which is different from that of the q OH + indole reaction. Among all 2c-3e bonded RCs, only RC 2−10 from the -NH-abstraction pathway is formed between the N atom and q Cl, while the others are formed between the C atom and q Cl. Note that RC 2−11 , which forms from C atom and q Cl, is the most stable among all the formed RCs in the q Cl + indole reaction. To the best of our knowledge, this is the first time that such a stable 2c-3e bonded RC has been identified between the C atom and q Cl. In addition, the energy of RC 2−10 is higher than that of the traditional 2c-3e bonded RCs formed from alkylamine and q Cl, which would result from the delocalization of lone pair electrons of the N atom. By analyzing the NBO charges of these nine RCs (Table S5), we found that significant charge transfer occurs between q Cl and indole. The charge at the Cl atom for RC 2−5 , RC 2−6 , RC 2−10 , RC 2−11 , RC 2−12 , RC 2−13 , RC 2−14 , RC 2−15 and RC 2−16 are −0.35e, −0.33e, −0.31e, −0.39e, −0.35e, −0.33e, −0.39e, −0.35e and −0.33e, respectively, indicates that all RCs are charge-transfer complexes. Similar chargetransfer complexes were also found in our previous study of the q Cl + piperazine reaction (Ma et al., 2018a). With the master equation theory, the overall rate constants (k OH and k Cl ) and branching ratios ( ) for all H-abstraction and q OH/ q Cl-addition pathways involved in the q OH and q Cl with indole reactions were calculated at 298 K and 1 atm. The calculated k OH and k Cl values of indole are 7.9 × 10 −11 and 2.9×10 −10 cm 3 molecule −1 s −1 , respectively. The calculated k OH value is close to the available experimental value of 1.5×10 −10 cm 3 molecule −1 s −1 (Atkinson et al., 1995), supporting the reliability of employed computational methods. Over the temperature range 230-330 K (Ma et al., 2018b), the calculated k OH and k Cl values have a negative correlation with temperature ( Fig. S1 in the Supplement). Based on the calculated values of the q OH and q Cl with indole reactions (Table 1), it can be concluded that IM 1−7 (77 %) q Cl + indole IM 2−5 31 % IM 2−6 46 % P 2−10 23 % P 2−11 0 P 2−12 0 P 2−13 0 P 2−14 0 P 2−15 0 P 2−16 0 is the main product for q OH + indole reaction, and IM 2−5 (31 %), IM 2−6 (46 %) and P 2−10 (C 8 H 6 N radicals + HCl) (23 %) are the main products for q Cl + indole reaction. In addition, the calculated values of IM 1−7 , IM 2−5 , IM 2−6 and P 2−10 (C 8 H 6 N radicals + HCl) change negligibly with the variation in temperature, pressure and energy transfer parameters (see the Supplement). Therefore, we mainly considered the further transformation of IM 1−7 , IM 2−5 , IM 2−6 and C 8 H 6 N radicals in the following part.

Subsequent reactions of addition intermediates
Similar to other C-centered radicals (Zhang et al., 2012;Guo et al., 2020;F. F. Ma et al., 2021a;Yu et al., 2016Yu et al., , 2017Ji et al., 2017;Ding et al., 2020a), the intermediates IM 1−7 , IM 2−5 and IM 2−6 will subsequently react with O 2 . Two different pathways (Fig. 2) were considered for the reactions of the intermediates IM 1−7 , IM 2−5 and IM 2−6 with O 2 . One pathway is the direct hydrogen abstraction by O 2 from the C site connecting to the -OH or -Cl group forming P 1−7−1 (C 8 H 7 NO + HO 2 q ), P 2−5−1 (C 8 H 6 NCl + HO 2 q ) and P 2−6−1 (C 8 H 6 NCl + HO 2 q ); the other is the O 2 addition to the C sites with high spin density (see spin density distribution in Table S10) of the intermediates IM 1−7 , IM 2−5 and IM 2−6 to form peroxy radicals Q-iOO-a/s, where Q stands for intermediates IM 1−7 , IM 2−5 and IM 2−6 , and i stands for the numbering of the C positions where O 2 is added. The O 2 molecule can be added to the same (-syn, abbreviated as -s) and opposite (-anti, abbreviated as -a) sides of the plane relative to the -OH or -Cl group. The C2, C4, C6 and C8 sites of IM 1−7 , C2, C4, C6 and C8 sites of IM 2−5 and C3, C5, C7 and C9 sites of IM 2−6 are high spin density sites susceptible to O 2 addition. As can be seen from the energetic data shown in Fig. 2, O 2 addition to the C4 site of IM 1−7 to form IM 1−7 -4OO-a/s (−0.6/−0.6 kcal mol −1 ), C6 site of IM 2−5 to form IM 2−5 -6OO-a/s (−0.3/−2.0 kcal mol −1 ) and C5 site of IM 2−6 to form IM 2−6 -5OO-a/s (2.0/1.7 kcal mol −1 ) are the most favorable among all possible entrance pathways for the respective reactions. It deserves mentioning that the formation energy ( E) of IM 2−5 -6OO-a/s and IM 2−6 -5OO-a/s are only about 9.0 kcal mol −1 , which could indicate that they likely re-dissociate back to the reactants IM 2−5 /IM 2−6 and O 2 , if IM 2−5 -6OO-a/s and IM 2−6 -5OO-a/s does not rapidly transform to other species.

Subsequent reactions of C 8 H 6 N radicals from the H-abstraction pathway
Here, the bimolecular reaction with O 2 was mainly considered for C 8 H 6 N radicals as its sole atmospheric fate. It was found that the spin density distribution was mainly centered at the C atoms (C4 (0.662), C6 (0.261), C8 (0.178)) and N atom (0.256), indicating that the C 8 H 6 N radical is delocalized. This is in contrast to previously studied N-centered radicals formed from alkylamine oxidation, which is highly localized (Xie et al., 2015(Xie et al., , 2014Ma et al., 2018a;Tan et al., 2021;Borduas et al., 2015). Therefore, O 2 addition to the C4, C6, C8 and N1 sites (including attack from both sides) is considered for the reaction of the C 8 H 6 N radicals with O 2 . As can be seen in Fig. 4, O 2 additions to the C4 site of the C 8 H 6 N radicals forming C 8 H 6 N-4OO-a/s with E a of −0.3 kcal mol −1 are the most favorable, translating to pseudo-first-order reaction rate constants of 3.0 × 10 7 s −1 .
Such rate constants are about 7 orders of magnitude higher than that of typical N-centered radicals reacting with NO even under very high NO concentration (5 ppb). Therefore, C 8 H 6 N radicals do not react with NO to form carcinogenic nitrosamines in any appreciable amount, which is different from the previously reported reaction mechanism of Ncentered radicals formed from the reactions of alkylamines with q Cl (Xie et al., 2015(Xie et al., , 2014Ma et al., 2018a). To the best of our knowledge, this is the first study to reveal that despite forming radicals by abstracting an H atom at the N site, carcinogenic nitrosamines were not produced in the indole oxidation reaction. For the transformation of the formed C 8 H 6 N-4OO-a/s radicals, the ring closure reaction to form C 8 H 6 N-43OOa/s is the most favorable, but it still needs to overcome a 27.8 kcal mol −1 energy barrier; therefore, the further transformation of the formed C 8 H 6 N-4OO-a/s should proceed very slowly. The C 8 H 6 N-4OO-a/s should mainly react with NO and HO 2 q to form NO-P 6 and HO 2 -P 6 . Detailed kinetics calculations (Fig. 3d) further confirm that the reaction of C 8 H 6 N radicals with O 2 mainly form NO-P 6 and HO 2 -P 6 under 200 ppt NO and 50 ppt HO 2 q conditions.

Comparison with available experimental results and atmospheric implications
This study found that q OH and q Cl initiated reactions of indole mainly form organonitrates, alkoxy radicals and hydroperoxide products with N-(2-formylphenyl)formamide (C 8 H 7 NO 2 ) as a minor product at 200 ppt NO and 50 ppt HO 2 q conditions. The formed closed-shell products have high oxygen-to-carbon ratios compared with indole and therefore are expected to have lower vapor pressures, likely being first generation products that can be further oxidized and contribute to the formation of SOA. With our findings, a comparison was made with the available experimental study on q OH initiated reaction of indole. The calculated k OH value (7.9 × 10 −11 cm 3 molecule −1 s −1 ) of indole is consistent with the experimental value (15 × 10 −11 cm 3 molecule −1 s −1 ) (Atkinson et al., 1995), indicating the reliability of applied theoretical methods. A signal with the molecular formula C 8 H 7 NO 2 has been ob-served in the mass spectrum in an experimental study by Montoya-Aguilera et al. (2017), supporting the formation of the predicted N-(2-formylphenyl)formamide. To the best of our knowledge, our study is the first to reveal the chemical identity of the mass spectrum signal as N-(2formylphenyl)formamide, as opposed to the proposed 3-oxy-2-hydroxy-indole. In addition, monomeric products (isatin and isatoic anhydride) and dimer products have not been observed in our computational study. We speculate that they may be produced from the subsequent conversion of the formed alkoxy radicals, multi-generation reactions of organonitrates and hydroperoxide as well as self-or cross reactions of peroxy radicals (RO 2 + RO 2 ). Therefore, further studies are warranted to investigate the subsequent transformation of the formed alkoxy radicals, organonitrates and hydroperoxide, and the RO 2 + RO 2 reactions, to accurately describe the atmospheric impact of indole.
The calculated k Cl value of the indole + q Cl reaction is a factor of 3.7 higher than that of the indole + q OH reaction, and is close to the k Cl values for the reactions of alkylamines, heterocyclic amines and amides with q Cl (Xie et al., , 2015Ma et al., 2018a;Nicovich et al., 2015). The contribution of q Cl to the transformation of indole is calculated to be 3.6 %-36 % that of q OH, assuming q Cl concentrations equal to 1 %-10 % of that of q OH (Wang and Ruiz, 2017;Nicovich et al., 2015;Xie et al., 2017Xie et al., , 2015Ma et al., 2018a). Therefore, q Cl plays an important role in the overall transformation of indole. More importantly, q Cl initiated reaction of indole does not lead to the formation of carcinogenic nitrosamines although q Cl can favorably abstract the H atom from the N site to form C 8 H 6 N radicals, which is a plausible precursor of carcinogenic nitrosamines. Hence, to the best of our knowledge, this is the first study to reveal that despite forming radicals by abstracting an H atom at the N site, carcinogenic nitrosamines were not produced in the indole oxidation reaction. This is most likely caused by the delocalized character of the formed C 8 H 6 N radicals due to the existence of the adjacent unsaturated bonds. Therefore, this study further confirms that the functional groups connected to the NH x (x = 1, 2) group highly affect the atmospheric fate of ONCs. Further studies should be performed to investigate the structure-activity relationship of q Cl initiated reactions of ONCs to comprehensively evaluate their atmospheric impacts. Data availability. The data in this article are available from the corresponding author upon request (maff@dlut.edu.cn, hbxie@dlut.edu.cn).
Author contributions. FM and HBX designed the research model; JX, FM and HBX performed the research; JX, FM and HBX analyzed the data; JX, FM, JE, HBX and JC wrote the paper; and FM, HBX, JE and JC reviewed and revised the paper.
Competing interests. The contact author has declared that none of the authors has any competing interests.
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Acknowledgements. We thank Struan H. Robertson (Dassault Systèmes) for the discussion on the MESMER simulations. The study was supported by National Natural Science Foundation of China (grant nos. 22176022, 21876024), the LiaoNing Revitalization Talents Program (grant no. XLYC1907194), the Major International (Regional) Joint Research Project (grant no. 21661142001) and the Supercomputing Center of Dalian University of Technology.
Financial support. This research has been supported by the National Natural Science Foundation of China (grant nos. 22176022, 21876024), the LiaoNing Revitalization Talents Program (grant no. XLYC1907194) and the Major International (Regional) Joint Research Project (grant no. 21661142001).
Review statement. This paper was edited by John Liggio and reviewed by two anonymous referees.