Theoretical Investigations on Mechanisms and Pathways of C2H5O2 with BrO Reaction in the Atmosphere

In this work, feasible mechanisms and pathways of the C2H5O2 + BrO reaction in the atmosphere were investigated using quantum chemistry methods, i.e., QCISD(T)/6-311++G(2df,2p)//B3LYP/6-311++G(2df,2p) levels of theory. Our result indicates that the title reaction occurs on both the singlet and triplet potential energy surfaces (PESs). Kinetically, singlet C2H5O3Br and C2H5O2BrO were dominant products under the atmospheric conditions below 300 K. CH3CHO2 + HOBr, CH3CHO + HOBrO, and CH3CHO + HBrO2 are feasible to a certain extent thermodynamically. Because of high energy barriers, all products formed on the triplet PES are negligible. Moreover, time-dependent density functional theory (TDDFT) calculation implies that C2H5O3Br and C2H5O2BrO will photolyze under the sunlight.


Introduction
With more and more attention paid to atmospheric environments, researchers focused on the reactions that will increase or produce pollution. Observation indicates halogen monoxides, i.e., XO (X = Cl, Br, and I) play important roles in the marine boundary layer (MBL) and lower stratosphere [1,2]. As catalysts in the ozone destruction processes, with higher efficiency than ClO, the reactions of BrO with peroxy radicals RO 2 (R is organic group), such as HO 2 and CH 3 O 2, have been investigated extensively by experimental and theoretical methods [3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Experimentally, the rate constants of BrO reacting with HO 2 [8][9][10], CH 3 O 2 [11,12,15] and C 2 H 5 O 2 [16] radicals were determined by several groups. For the reactions of HO 2 and CH 3 O 2 with BrO, mechanisms and reaction pathways were investigated theoretically [11][12][13][14]16]; however, the products were not confirmed for the C 2 H 5 O 2 + BrO reaction from experiments, and no literature is available from theoretical investigations yet. The following channels were proposed by Sakamoto [ Due to distinct advantages over experimental methodology, quantum chemistry is popular as a useful tool to explore mechanisms and feasible products in many atmospheric reactions [17][18][19][20].
By quantum chemistry methods, the C 2 H 5 O 2 + BrO reaction in the atmosphere was explored at the molecular level to address the mechanisms, channels and products. Moreover, it is expected to provide useful information and new insights into the atmospheric chemistry of C 2 H 5 O 2 with BrO.

Results
Optimized geometries of all reactants, products, intermediates (IM) and transition states (TS) involved in the title reaction were shown in Figure 1. The energetic profiles of the singlet and triplet PESs at the level of QCISD(T)/6-311++G(2df,2p)//B3LYP/6-311++G(2df,2p) was depicted in Figure 2. Moreover, 3 is superscripted to differentiate triplet species from the singlet ones. The reaction enthalpy (∆H) of various channels in the C 2 H 5 O 2 + BrO reaction obtained from the present work and available references are listed in Table 1. The zero-point energy correction (ZPE) and relative energy (∆E) and reaction enthalpy (∆H) at different levels of theory are displayed in Table 2. Before reaction mechanisms and channels are discussed, it is cautious and meaningful to check the validity of the current theoretical level to ensure that our computational result is conceivable and reliable for the title reaction.

Reaction Channels of the C 2 H 5 O 2 + BrO Reaction
In order to give a clear and distinct description of the reaction mechanisms and pathways, we will discuss the formation of intermediates firstly, and the separate reaction channels on the singlet and triplet PESs subsequently.

The Formation of Intermediates in the C 2 H 5 O 2 + BrO Reaction
On the singlet PES with two reactive sites of BrO attacking the reactive O atom in C 2 H 5 O 2 , two initial intermediates, namely C 2 H 5 O 3 Br (IM1) and C 2 H 5 O 2 BrO (IM2), are formed directly without any energy barriers. As shown in Figure 1, the newly formed O-O bond is 1.369 Å in IM1, and O-Br bond is 1.995 Å in IM2. It is worth noting that the singlet and triplet PESs intersection commonly takes place in the radical-radical reactions, especially for barrierless entrances [32,33]. However, the transition probability between the singlet and triplet surfaces was not treated explicitly in the present calculations. Our extensive attempts to calculate the single-triple crossing point for the entrance of the C 2 H 5 O 2 + BrO association have not been successful due to the convergence difficulties of the multireference configuration interactions. The complete active spaces (CAS) calculations with all valence electrons are unaffordable at present. It is noted that the intersystem crossing might be significant in some small organic molecules [34,35], therefore, more rigorous treatment of the singlet-triplet transition has to be reserved for further study.
It is mentioned that several conformers of C 2 H 5 O 3 Br and C 2 H 5 O 2 BrO located according to different dihedral angle of BrOOO (OBrOO) and OOOC (BrOOC) with internal rotations of the relevant O-O and Br-O bonds, and these conformers can interconvert within a few kJ/mol energy barriers; however, the interconversion are out of our focus and not considered in this work.
Energetically, IM1 and IM2 are about 72.3 and 19.1 kJ/mol lower than the initial reactants, respectively. Therefore, C 2 H 5 O 3 Br and C 2 H 5 O 2 BrO should be formed as vibrationally hot molecules: With much internal energy available, the hot molecules of C 2 H 5 O 3 Br ‡ and C 2 H 5 O 2 BrO ‡ may experience further isomerization and dissociation before being quenched by collisions. According to our result, three conceivable isomerization scenarios are located on the singlet PES.
Firstly, IM1 and IM2 interconverts via a triangular transition state TS1. The broken O-O bond is elongated to 2.286 Å in TS1, which is about 67% longer than that in IM1; while the formed Br-O bond is stretched by 0.37 Å from its equilibrium distance in IM2. The energy barrier height for IM1 isomerizing to IM2 is about 106.7 kJ/mol, and IM2 convert to IM1 is around 53.5 kJ/mol. With so high energy barriers the interconversion between IM1 and IM2 is unfeasible in the normal atmospheric conditions with a temperature below 300 K.
Secondly, via a similar triangular structure TS2 with bromine atom migrating from the central oxygen atom to the oxygen atom in C 2 H 5 O group, IM2 (C 2 H 5 O 2 BrO) isomerizes to IM3 (C 2 H 5 OBrO 2 ). Geometrically, the formed Br-O bond is 2.485 Å in TS2, and the broken O-O bond is dramatically stretched by 0.776 Å from that in IM2. While the two non-reactive Br-O bonds (around 1.66 Å) are close to their equilibrium lengths in IM3 (around 1.64 Å). Energetically, IM3 is rather stable on the singlet PES, with its relative energy (∆E) of 83.6 kJ/mol lower than the initial reactants; and 64.5 kJ/mol lower than IM2. However, the energy barrier height for IM2 to IM3 reaches 86.4 kJ/mol; apparently, it is difficult to proceed with low temperature (e.g., T < 300 K), although IM3 is the most stable intermediate on the whole singlet PES. Nevertheless, it might happen in high temperature conditions such as combustion, which is out of consideration in the present work.
From previous studies on the CH 3 O 2 + BrO [14], CF 3 O 2 + IO [36] and CF 3 O 2 + ClO [37] reactions, it is assumed that a high energy barrier for IM3 (ROBrO 2 ) → IM4 (RBrO 3 ) is surmounted. However, IM4 is rather unstable thermodynamically, therefore, it will not play any significant role in the overall reaction in the atmosphere. For completeness, only IM4 was optimized (C 2 H 5 BrO 3 ) without the transition state calculated. As expected, IM4 is unstable, with its relative energy of 97.7 kJ/mol higher than the initial reactants. Based on previous theoretical results and our current calculations [13,14], for all intermediates formed in the RO 2 + BrO (R = H, CH 3 , C 2 H 5 ) reactions, the order of relative stability among the RO 3 Br isomers (i.e., HO 3 Br, CH 3 O 3 Br, and C 2 H 5 O 3 Br) from the most stable to the least stable structure is ROBrO 2 > ROOOBr > ROOBrO > RBrO 3 . This implies that the substitution of alkyl group has no significant effect in RO 3 Br surfaces.
As for the triplet PES, in spite of many attempts, intermediates were not located at the current levels of theory.
To sum up, four intermediates are formed. Several possible dissociation reaction channels are available with abundant internal energy available from intermediates except for IM4. The details will be described in the following section.

The Reaction Pathways on the Singlet PES
According to our result, seven possible products and eight dissociation channels are determined, i.e., four from IM1, two from IM2 and two from IM3, respectively. To give a clear description, we will discuss the formation of products separately.

(b) CH 3 CHO + HOOBr
With migration of H atom in -CH 2 to the O atom in -OOBr, and the relevant O-O bond fission from IM1, HOOBr + CH 3 CHO will be generated via TS4. The barrier energy height takes a value of 120 kJ/mol, while TS4 is 47.7 kJ/mol on the singlet PES. Moreover, the channel of C 2 H 5 O 2 + BrO → CH 3 CHO + HOOBr is highly exothermic by 249 kJ/mol, and the product is rather stable thermodynamically. However, considering the low temperature (T < 300 K) in the atmosphere, especially in higher troposphere and lower stratosphere, CH 3 CHO+HOOBr are unfavorable to form kinetically at the current levels of theory.

CH 3 CHO 2 + HOBr
Similarly, with migration of the H atom in -CH 2 to the O atom in -OBr and the relevant O-O bond fission, 1 CH 3 CHO 2 + HOBr is generated via a five-membered-ring structure TS5 with a barrier height of 123 kJ/mol. Here it is mentioned that HOBr was presumed in the CH 3 O 2 + BrO reaction by Shallcross via a much lower energy barrier (around 62 kJ/mol and the transition state is −3.2 kJ/mol) at the CASPT2-F12/AVDZ//M06-2X/AVDZ levels of theory [15]. In order to check the deviation between our present computational results with Shallcross's, we performed the optimization of several significant intermediates and transition states with M062X functional from DFT methods. The optimized geometrical parameters were listed in Figure 1, from which it could be seen that the bond length and bond angle are close at the B3LYP and M062X methods. Thus, the single point energy deviations come from the employed methods. Regrettably, multiconfigurational methods were not affordable at the moment due to limited computational resource.

(d) CH 3 CHO + HBrO 2
Starting from IM2, CH 3 CHO + HBrO 2 (∆E = −14.8 kJ/mol) is obtained with migration of one H atom from -CH 2 to Br atom and cleavage of the O-O bond simultaneously via TS6 while the relative energy is about 5 kJ/mol lower than that of TS4. Although the relative energy is close (within 8 kJ/mol) among TS4, TS5 and TS6, the energy barrier height of TS6 is 61.9 kJ/mol, which is much lower than that of TS4 (120 kJ/mol) and TS5 (123 kJ/mol). Thus, the channel via C 2 H 5 O 2 + BrO → IM2 → TS6 → CH 3 CHO + HBrO 2 will be more feasible to occur kinetically than the channels via C 2 H 5 O 2 + BrO → IM2 → TS4 → CH 3 CHO + HOOBr or C 2 H 5 O 2 + BrO → IM2 → TS5 → 1 CH 3 CHO 2 + HOBr. However, all the channels are unfavorable at low temperature in the typical atmospheric conditions (T < 300 K).

(e) CH 3 CHO + HOBrO
From IM3, H atom in -CH 2 moves to O atom in OBrO forming a rather stable product CH 3 CHO + HOBrO, and this process is exothermic by 227.8 kJ/mol. Although TS7 (∆E = −17.6 kJ/mol) is the lowest transition state on the singlet PES, the channel via C 2 H 5 O 2 + BrO → IM2 → TS2 → IM3 → TS7 → CH 3 CHO + HOBrO will make a minor contribution to the overall reaction due to the high energy barrier of TS2 (∆E = 67.3 kJ/mol). Besides the elimination channel from IM1, C 2 H 5 OBr + 1 O 2 could be formed via the substitution mechanism as well on the singlet PES, with O atom in BrO attacking the C center in -CH 2 group via a rather high energy barrier of TS8, which relative energy is around 237.6 kJ/mol. Evidently, both channels have no possibility of occurring kinetically in the normal atmospheric conditions, and are negligible to the overall reaction although the formation of the product is exothermic.
In summary, on the singlet PES C 2 H 5 O 3 Br and C 2 H 5 O 2 BrO will be dominant products. Other minor products include CH 3 CHO + HOOBr via IM1 and TS4, CH 3 CHO + HBrO 2 via IM2 and TS6, and 1 CH 3 CHO 2 + HOBr via IM1 and TS5. Considering the typical limitation of 20 kJ/mol for atmospheric reactions, these sub-dominant channels are of no significance kinetically, although their formations should be feasible thermodynamically.

The Substitution and Abstraction Channels on the Triplet PES
On the triplet PES, no intermediate was located with many attempts, thus the channels are much simpler than that on the singlet PES. According to our result, both substitution and direct abstraction mechanisms were determined leading to seven products. As shown in Figure 2, surmounting 3 TS1, 3 TS2, 3 TS3, 3   Here it is mentioned that the formation of HOBr was located via direct hydrogen-abstraction channels with H atom in -CH 3 or -CH 2 group was abstracted. The corresponding transition states are 3 TS6 and 3 TS7, with similar relative energies, i.e., 55.4 and 49.6 kJ/mol, respectively, which are modest to happen in higher temperature conditions. The products in the two channels are 3 CH 2 CH 2 O 2 and 3 CH 3 CHO 2, which are much more unstable than their singlet species. The formations of 3 CH 3 CHO 2 + HOBr and 3 CH 2 CH 2 O 2 + HOBr are endothermic by 17.1 and 21.3 kJ/mol, therefore, the channels are unfavorable thermodynamically.
To sum up, from the above discussions it is concluded that all substitution and abstraction channels on both the singlet and triplet PES are of on significance to the C 2 H 5 O 2 + BrO reaction below 300 K. C 2 H 5 O 3 Br and C 2 H 5 O 2 BrO are dominant to the overall reaction. Thermodynamically, the subsequent dissociation from intermediates leading to CH 3 CHO + HBrO 2 , CH 3 CHO + HOOBr, CH 3 CHO + HOBrO and CH 3 CHOO + HOBr are favorable. However, with high energy barriers involved, these products are difficult to be formed kinetically in the atmospheric conditions below 300 K.

Vertical Excitation Energy T V of C 2 H 5 O 3 Br, C 2 H 5 O 2 BrO and C 2 H 5 OBrO 2
It is known that the photo-oxidation of compounds containing bromine is significant for Br atmospheric chemistry, therefore their photolysis might influence the stratosphere and troposphere. In order to obtain new insights of photolytic information into the Br-containing compounds, the vertical excitation energy (T V ) of the first five excited states for C 2 H 5 O 3 Br, C 2 H 5 O 2 BrO and C 2 H 5 OBrO 2 was calculated by the TDDFT method [38] employing B3LYP/6-311++G(2df,2p), and the results including wavelength (λ), excitation energy (T V ) and oscillator strength (f ) are listed in Table 3.
Known most ultraviolet (UV) light is absorbed and only is 7% left when solar radiation reaches to the surface of Earth, therefore, compounds will be considered to photolyze if the T V value is smaller than 4.13 eV (about 300 nm of threshold in the visible light). From Table 3 it is seen that the T V value of the first two/three excited states of C 2 H 5 O 3 Br and C 2 H 5 O 2 BrO take values smaller than 4.13 eV, and their oscillator strength is not null, implying that the C 2 H 5 O 3 Br and C 2 H 5 O 2 BrO photolyze under the sunlight. Checking the occupied and virtual molecular orbitals it is found that the most contribution comes from HOMO-1 to LUMO with an np O → π* transition associated in both C 2 H 5 O 3 Br and C 2 H 5 O 2 BrO. Therefore, it is speculated that the processes C 2 H 5 O 3 Br → C 2 H 5 O 2 + BrO and C 2 H 5 O 2 BrO → C 2 H 5 O 2 + BrO occur after absorption of sunlight. On the other hand, the T V value of all excited states for C 2 H 5 OBrO 2 is larger than 4.13 eV, thus it will not be the source of reactive bromine species in the troposphere.

Conclusions
Using quantum chemistry methods, the reaction mechanisms and pathways for the atmospheric reaction of C 2 H 5 O 2 + BrO were studied in detail at the QCISD(T)//B3LYP levels of theory. The result indicates that the title reaction occurs on both the singlet and triplet PES, with addition-elimination, substitution and direct H/O-abstraction mechanisms involved. The energy barriers on the singlet PES are lower than that on the triplet PES. C 2 H 5 O 3 Br and C 2 H 5 O 2 BrO is dominant on the singlet PES. Thermodynamically, CH 3 CHO 2 + HOBr, CH 3 CHO + HOBrO, and CH 3 CHO + HBrO 2 are feasible, while they are of no significance due to high energy barriers. Moreover, C 2 H 5 O 3 Br and C 2 H 5 O 2 BrO will photolyze under the sunlight, which might be one source of Br-containing species in the atmosphere.
Author Contributions: C.L. analyzed the data, discussed, wrote and revised the manuscript, Y.T. designed the research, performed the calculations and wrote the manuscript. W.Z. and Z.F. analyzed the data and drawing geometries. X.Q. read and approved the final manuscript.