It is confirmed that the emission of the organic compounds especially polycyclic aromatic hydrocarbons (PAHs) can lead to photochemical air pollution, acid deposition and ozone depletion after a series of complex chemical and physical transformation  . These toxic air pollutants can also exert some diverse influence on human-beings, such as lung cancer  . The researches show that with the increase of the number of aromatic ring, the carcinogenic will increase too  . The aromatic compounds in polluted atmospheres are aromatic hydrocarbons and their derivatives, such as aromatic aldehydes, phenolic compounds and nitro-polycyclic aromatic hydrocarbons      . Since the last century, there are many parallel experimental studies in laboratory and ambient atmospheric about PAHs and its derivatives    . Recently, there is an increasing interest in the mechanism studies of the gas-phase tropospheric chemistry of PAHs, such as naphthalene  , anthracene  , phenanthrene   , triphenylene  , 9,10-dichlorophenanthrene  , DDT  and benzo[a]pyrene  .
2. Computational Methods
All of the calculations involved in this work were performed by using Gaussin09 package of programs  . M06-2X/aug-cc-pVTZ level of theory was chosen for the stationary point geometry optimization and frequency calculations, which is believed that the extra exchange-correlation functional included for accurate thermochemical and kinetical calculations especially  . This method has been identified by a couple of relevant gas phase radical oxidation reactions   . Furthermore, the intrinsic reaction coordinates (IRC) approach calculations were carried out at the same level in order to verify the designed transition structures connecting to the expected energy minima. The corresponding energy embedded with the reaction scheme were all corrected, where the energy barriers ΔE is corrected by the Zero-Point Energy and reaction enthalpies ΔH is corrected with thermodynamic correction respectively. The z-matrix of optimized geometries for the reactants, intermediates and transition states calculated with M06-2X/aug-cc-pVTZ method are provided in Supplemental Information.
3. Results and Discussion
3.1. OH-Initiated Acenaphthylene Reaction
Due to acenaphthylene is a C2v axial symmetrical molecule, there are totally 6 alternative potential reaction sites. For convenience to discuss the following contents, the C atoms of acenaphthylene are numbered as presented in Figure 1.
3.1.2. Hydroxyl Addition Pathways
Because of the resourceful negative charge on the O atom of OH radical, the OH radical can append to the C1 to C6 reaction sites of acenaphthylene molecule leading to six primary processes to form corresponding OH-initiated acenaphthylene radicals (as shown in Figure 3). Herein, there are six transition state structures identified with the O atom of the OH radical linking to the individual carbon atoms from one side of the aromatic molecular ring plane. The structures of these transition states are similar, the new formed C-O bonds are all perpendicular to the corresponding conjugated ring, respectively.
Figure 1. The structure of acenaphthylene with C-atom labeling.
The reaction scheme embedded with the energy barriers ΔE (kcal/mol) and reaction enthalpies ΔH (kcal/mol) is presented in Figure 3 as well. The calculated results show that C1-site OH radical addition is energetically the most favorable reaction pathway because of the lowest barrier and the strongest exothermicity, which indicates that the dominant reaction site for the OH addition to acenaphthylene is the unsaturated bond in the cyclopenta-fused ring. The potential barrier for P5 formation at the M06- 2X/aug-cc-pVTZ level is 0.25 kcal/mol and the reaction enthalpies is −33.33 kcal/mol. The C6 site reaction is the most impossible way to occur because of the highest reaction barrier (17.35 kcal/mol).
As these two reaction channels show that the reaction activity of the different C sites is anisotropic. Generally, acenaphthylene tends to the hydroxyl addition reaction to form much more stable OH-initiated acenaphthylene radical. Well C1 is the best reaction site for the hydroxyl addition reaction to form the most stable radical isomer P5. C3, C4 and C5 are having the similarity reaction activity in both reaction channels. The
Figure 3. Proposed reaction pathways of OH addition to acenaphthylene at the M06-2X/aug- cc-pVTZ level of theory.
hydroxyl addition reaction is unlikely happened at C6 site. It is supposed that at general condition, the hydroxyl addition reaction is the dominant reaction pathway when the OH radical is provided. So in the next section, we focus on the further reaction possibility of the OH-initiated acenaphthylene radicals.
3.2. Decomposition of the OH-Initiated Acenaphthylene Radical
Because of sterically hindered and energetically unfavorable of the C2 and C6 sites, herein only the further reaction of P5, P7, P8 and P9 radicals will be discussed in this section. There are two possible reaction channels for the H atom decomposition from OH-initiated acenaphthylene radical are proposed theoretically concerning P5 as the reactant described in Figure 4. The crucial difference for the transition states of the reactions is the O or H atom from the C1 site to connect the symmetrical C atom by forming a C-C-H or C-C-O three-member ring structure.
As the hypothetical reaction scheme, the mechanism of P11 formation is a concerted
Figure 4. The OH addition reaction scheme of P5 embedded with energy barriers ΔE (kcal/mol) and reaction enthalpies ΔH (kcal/mol).
reaction with the OH migrates to form a three-member ring and the H-atom of OH is taken away instantaneously. P12 formation is a two-step process, the first step is that the H-atom from the carbon site which connecting the OH radical migrates to the adjacent carbon atom C1’ (C2-site carbon is unallowed because of sterically hindered) to form the intermediate P5-IM1 through a C-C-H triatomic ring transition state P5-TS2, the H atom of OH in P5-IM1 will be away later through a transition state P5-TS3 to form neutral product 1-acenaphthenone (denoted as P12).
By using GC-MS technology, Zhou  has detected 1-acenaphthenone (denoted as P12) in the process of OH-initiated acenaphthylene degradation in their experimental research. The calculated results show that the previous P5 radical can through a stepwise process to form P12 with the H atom migration followed by the H atom elimination from the hydroxyl of C1 site, there are 36.44 kcal/mol and 40.33 kcal/mol potential barriers, respectively, and the rate-determining step is the second process. The other pathway for P5 is crossing 81.88 kcal/mol of potential barrier to form P11 by a concerted reaction. P12 is a more stable isomer with the energy lower about 34.7 kcal/mol than P11. So, forming P12 and H radical is the energetically most favorable channel because of the lower barrier and stable product, which supporting the relevant experimental results perfectly.
Similarly, the decomposition of P7 and P9 both has two channels as well. The schemes of these processes can be identified as Figure 5 and Figure 6. Zhou  and Reisen  have detected P14 and epoxide (denoted as P13) in their experimental research works, respectively. Herein it is predicted theoretically that P7 needs to across 36.81 kcal/mol and 69.55 kcal/mol two barriers to form P14 with the second process acting as the rate-determining step. While the barrier to produce P13 is 101.33 kcal/ mol, and P14 is a more stable isomer with the energy lower about 30.37 kcal/mol than P13. So, the pathway forming P14 is the energetically most favorable channel because of the lower barrier and a more stable product. The mechanisms here are similar compared with the previous discussion.
Due to C6-site carbon sterically hindered and energetically unfavorable, the decom-
Figure 5. The OH addition reaction scheme of P7 embedded with energy barriers ΔE (kcal/mol) and reaction enthalpies ΔH (kcal/mol).
Figure 6. The OH addition reaction scheme of P9 embedded with energy barriers ΔE (kcal/mol) and reaction enthalpies ΔH (kcal/mol).
position of P9 is quite the same with P7. There are two reaction pathways to form the products P15 and P16 with the different reaction mechanism. The barrier to form epoxide P15 is 88.33 kcal/mol, which is about 11.00 kcal/mol lower than P13. There are 44.13 and 50.76 kcal/mol of the reaction barriers to form acenaphthenone P16, P16 is a more stable isomer with the energy lower about 29.65 kcal/mol than P15. So, the pathway forming P16 is the energetically most favorable channel. Comparing the potential barriers of transition state to P16, there is not significant rate determinant reaction in this step-wise reaction pathway because of the comparable reaction barrier heights.
Figure 7. The OH addition reaction scheme of P8 embedded with activation energies ΔE (kcal/mol) and reaction enthalpies ΔH (kcal/mol).
respectively. P18 is the most stable isomer with the energy lower about 51.54, 29.89 and 23.96 kcal/mol than P13, P15 and P17. The pathway of forming P18 is the energetically most favorable channel because of the lowest barrier and the most stable product.
In the earlier experimental research works mentioned above, Zhou  and Reisen  groups both declared that they have detected the OH-initiated acenaphthylene radical decomposition products acenaphthenone and epoxide respectively, and the two products gives the same relative molecular mass (MW = 168) resulting in the configuration isomers. But herein with the DFT calculations, we predicted both reaction channels to produce all the possible product isomers, which results in the channels for the epoxide all having rather higher reaction barrier than for the acenaphthenone ones, which means because of more extra energy needed to overcome the high reaction barrier theoretically, it hardly to produce epoxide at the ordinary experimental condition as the reference works. The calculations suggested the OH-acenaphthylene radical has a priority to form the acenaphthenone rather than epoxide. Certainly, to verify the conclusion we proposed, a series of IR or NMR detection in the process maybe epoxide inquired. In all of the acenaphthenone formed by OH-initial acenaphthylene radical adducts, the most stable isomer is P12, it further illustrate that there is a tendency for the OH addition reaction on C1-site to form the most stable product as well.
3.3. Secondary Reaction Pathways of OH-Acenaphthylene
3.3.1. OH-Acenaphthylene Reactions with O2 or O2/NO
It has been proofed by the Zhou  and Reisen  experimental works, that the predecessor OH-initiated acenaphthylene can take place complex addition reactions with some micro-molecules in air. They detected that adducts of OH-initial acenaphthylene can yield dialdehyde (denoted as P19), naphthalene-1,8-dicarbaldehyde (denoted as P20) and 1,8-naphthalic anhydride (denoted P21) in their experimental works. Herein, we propose the possible reaction pathways through the theoretical calculations to explain the mechanism about these products formation.
A series of mechanisms of P19 formation from the adduct P7 and O2 or O2/NO are demonstrated respectively in Figure 8. There are two spatial position (the trans-posi- tion and cis-position of OH) for the O atom of O2 attacking the C4-site of P7, only the trans-position of OH is taken as the example in this paper because the cis-position has a relatively large sterically hindered as the comparison calculations. There are about 13.4 kcal/mol and 0.43 kcal/mol lower in the energy of trans-P7-IM2 and trans-P7-TS4 than the corresponding cis-position transition state structure and product. The adduct O2-P7 will form through a transition state (denoted as P7-TS4) with the 26.64 kcal/mol potential barrier height and later intermediate P7-IM2 is formed by the C?O interaction enhanced.
There are two pathways can lead the aimed product P19. The first channel is the terminal O atom attacks the other side H atom of OH group to form a hexatomic ring transition state P7-TS5 by overcome 46.55 kcal/mol barrier height, by exothermic 8.16 kcal/mol energy to release the H atom migrate to O2 side (denoted as P7-IM3). The aromatic ring will then experience a ring opening reaction to form P7-IM4 through a transition state (denoted as P7-TS6) with C=O double bond is formed. In the end, the OH radical departures to form the aimed product (denoted as P19). Another pathway is P7 reacts with O2 followed by the reaction with NO and one more O2 also can form
Figure 8. The secondary reaction scheme of P7 embedded with energy barriers ΔE (kcal/mol) and reaction enthalpies ΔH (kcal/mol).
P19. After the formation of P7-IM2, N atom of NO can attack O2 side to form the adduct NO-O2-P7 (denoted as P7-IM5) through a barrierless process. Then NO takes terminal O-atom of O2 away to form NO2 and leaves P7-IM6 with the corresponding aromatic ring opening. Follow on, another O2 can attack the carbon atom which connecting to the OH radical through a transition state to form adduct (denoted as P7- IM7). Later O2 will take H atom originally from OH away to form HO2 radical and then departure to form the aimed product P19.
Similarly, the possible pathways for O2 and O2/NO react with another OH-intitated radical P5 is demonstrated in Figure 9. Due to the energy of trans-P5-TS4 is lower about 22.29 kcal/mol and the energy of trans-P5-IM2 is lower about 3.53 kcal/mol compared with the corresponding cis-position reaction isomers; herein we take trans- position reaction for the example. O2 can attack on C1-site carbon from the trans-posi- tion to form the adduct O2-P5 through a transition state (denoted as P5-TS4) with only 13.76 kcal/mol barrier height. Then one O atom from O2 attacks the other side H atom of OH to form a hexatomic ring, the H atom migrates to O2 side (denoted as P5-IM3) by releasing 23.68 kcal/mol energy, meanwhile C=O double bond formed, later the OH radical departures to form the aimed product (denoted as P20). In another pathway, P5 reacts with O2/NO, N atom of NO can attack on O2 side to form adduct of NO-O2-P5 (denoted as P5-IM4). The calculated results show that to form the adduct process is a barrierless reaction as well. Then NO will take away an O atom of O2 to form NO2 and departure from P5-IM4. Follow on, O2 can attack another side carbon atom which
Figure 9. The secondary reaction scheme of P5 embedded with energy barriers ΔE (kcal/mol) and reaction enthalpies ΔH (kcal/mol).
is connected the OH radical through a transition state to form adduct (denoted as P5-IM6). Later O2 will take H atom originally from OH away to form HO2 radical departure from the aimed product P20.
Compared with the pathways of P7 and P5 reacting with O2 from the thermodynamics point of view, there is not significant energy variation for the reactions, so in the troposphere, both of these two pathways are possible to form dialdehyde. But from the dynamics part, the reaction discussed above will both take place only when the concentration of NO is enough for the second pathway, otherwise, only the first pathway reaction will happen.
By the analyses of 1,8-naphthalic anhydride structure (denoted P21), the further possible reaction mechanism for P21 formation mechanism is proposed by taking P20 as the precursor as Figure 10. Firstly, OH radical attacks the one of the H atoms of aldehyde group in P20 by absorbing about 2.45 kcal/mol energy to form a transition state (denoted as P20-TS1), and then OH radical takes the H atom away to form a water molecule from the complex. Later O2 molecule attacks the C=O bond of the energy-rich intermediate (denoted as P20-IM1) to form P20-IM2 through a transition state. In this process, forming P20-TS2 need absorb about 14.61 kcal/mol energy compared with the reactants. Where after, the terminal O atom attacks another side H atom to form an eight-member ring transition state (denoted as P20-TS3), and then O atom takes the H atom away remaining an aldehyde group radical. Finally, C-O bond formed with OH radical departure to form the aimed product 1, 8-naphthalic anhydride (P21).
3.3.2. OH-Acenaphthylene Reactions with NO2
It is found experimentally that there are two typical nitro-PAHs nitroacenaphthylene and nitroacenaphthylenol could be formed in the process of OH-initialed PAH  . Accordingly, all the precursors P5, P7, P8 and P9 can take place NO2-adduct reactions with NO2 appearance. The mechanism about these nitro-PAHs can be clarified theoretically as Figure 11. There are trans- and the cis-two spatial positions for N atom of
Figure 10. The secondary reaction scheme of P20 embedded with energy barriers ΔE (kcal/mol) and reaction enthalpies ΔH (kcal/mol).
Figure 11. The secondary reaction scheme of P5, P7, P8, P9 and NO2 embedded with energy barriers ΔE (kcal/mol) and reaction enthalpies ΔH (kcal/mol).
NO2 attacking on the adjacent carbon atom bonding the OH group of adduct. Thus, two kinds of products are formed named nitroacenaphthylene and nitroacenaphthylenol through the different reaction pathways. First of all, NO2 attaches to the precursors to form the corresponding adducts with comparable stabilized energy from different sides of the OH group. Later, the H atom of the NO2 reaction site will attach the same side H atom or O atom of OH group to form the typical C-C-H-H or C-C-O-H four-atomic ring transition states with significant difference of the reaction barrier height, after that there are H2 or H2O formed and departed to obtain a series of isomer products.
The calculated results show that it is a barrierless process for NO2 attacking the corresponding precursors to form the relatively stable adducts. The stability is diverse from each other, where adducts derived from P5 and P8 (associated with C5 site) are more stable than the others, while adducts from P7 are the most unstable ones. P5, P7 and P9 are all favor to form adducts from the trans-position of the OH group but P8. All the precursors are favor to form the nitroacenaphthylene isomers from the reaction barriers comparison, where P7 has the relatively lowest reaction barrier. The reaction barriers for the nitroacenaphthylenol formation are relatively higher than the corresponding nitroacenaphthylene ones about 30.0 to 40.0 kcal/mol; again P7 has the comparatively lowest reaction barrier.
It is found that the most stable isomers for both nitroacenaphthylene and nitroacenaphthylenol are from P5 reacting with NO2 by the stability comparison of all the products P22 to P31. When NO2 attacks P5 to form P5-IM7 and P5-IM8, there are 41.04 kcal/mol and 39.11 kcal/mol energy released at the beginning of the reaction. As a trans-position adduct, P5-IM7 will decompose to produce nitroacenaphthylene (denoted as P22) through a 13.74 kcal/mol potential barrier, while the cis-position adduct P5-IM8 needs to across an especially higher potential barrier 46.37 kcal/mol to form nitroacenaphthylenol (denoted as P23). Comparing these two reaction pathways, we draw a prediction that the nitroacenaphthylene is the relatively high abundance of products for PAH reacting with NO2.
The authors thank to the generous computing time supporting from the Supercomputing Center of University of Science and Technology of China.
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