Theoretical Study on the Gas Phase and Gas–Liquid Interface Reaction Mechanism of Criegee Intermediates with Glycolic Acid Sulfate

Criegee intermediates (CIs) are important zwitterionic oxidants in the atmosphere, which affect the budget of OH radicals, amines, alcohols, organic/inorganic acids, etc. In this study, quantum chemical calculation and Born–Oppenheimer molecular dynamic (BOMD) simulation were performed to show the reaction mechanisms of C2 CIs with glycolic acid sulfate (GAS) at the gas-phase and gas–liquid interface, respectively. The results indicate that CIs can react with COOH and OSO3H groups of GAS and generate hydroperoxide products. Intramolecular proton transfer reactions occurred in the simulations. Moreover, GAS acts as a proton donor and participates in the hydration of CIs, during which the intramolecular proton transfer also occurs. As GAS widely exists in atmospheric particulate matter, the reaction with GAS is one of the sink pathways of CIs in areas polluted by particulate matter.


Introduction
The reactions of ozone with unsaturated hydrocarbons are important sources of free radicals and particulate matter in the atmosphere [1]. Criegee intermediates (CIs) are tropospheric biradical/zwitterionic species that are derived from the ozonolysis of alkenes [2]. Ozone undergoes 1,3-cycloaddition with a double bond of alkene to form a primary ozonide that subsequently decomposes into a carbonyl oxide (also called Criegee intermediate) and a carbonyl compound [3]. The energized Criegee intermediate, which is produced by exothermic decomposition and contains vibrational excitation, undergoes unimolecular decay or forms a stable Criegee intermediate via collisional quenching [4]. In addition to the above reaction, the contribution that formed through other reactions to the total CIs is inappreciable. The reaction of CH 3 O 2 with OH radicals, affecting the concentrations of HO 2 and O 3 in the oceanic boundary layer, has been determined to produce trace amounts of CH 2 OO (yield of CH 2 OO < 5%) [5]. The oxidation of dimethyl sulfoxide forms CH 2 OO at low temperatures, but the yield is too low to be a pivotal source of CIs [6].
The unimolecular decomposition of CIs, which occurs via the vinyl hydroperoxide pathway or the ester pathway, plays a significant role in the production of atmospheric OH radicals [7,8]. Elshorbany et al. [9] reported that the decomposition of CIs has a 24% contribution to the daytime OH radical formation. In addition, CI decomposition is a steady and dominant source of OH radicals at nighttime [10]. The PUMA campaign (a project that measured pollution of the urban midlands atmosphere in the UK) showed that ozonolysis of alkenes dominates the OH production in winter and accounts for more than 50% of the production in summer [11].
Even if most CIs decay through unimolecular pathways, a fraction of CIs survives for long enough to react with other substances. The reaction with water vapor is the

Results and Discussion
The most stable configuration of GAS is shown in Figure 1. A seven-membered ring structure is formed in the molecule. The hydrogen bond interaction was observed between the terminal hydrogen of the OSO 3 H group and the carbonyl oxygen of the COOH group.

Gas-Phase Reactions
The values of relative Gibbs free energy (CCSD/6-311++G(2d,2p)) of the reactions between CH 3 CHOO and GAS are displayed in Figure 2. The configurations of reaction complexes, transition states, and products are depicted in Figure S1. The reaction energy barriers of syn-CH 3 CHOO with OSO 3 H and COOH groups are 1.00 and 2.87 kcal/mol, respectively. The reactions of anti-CH 3 CHOO with OSO 3 H and COOH groups need to cross energy barriers of 3.30 and 4.09 kcal/mol, respectively. The low energy barriers suggest that these reactions are feasible in the atmosphere. Previous studies have shown that most reactions of CIs with carboxylic acids follow a barrierless pathway [31,32]. However, we observed that the reactions of the COOH group with CH 3 CHOO require overcoming the energy barrier, which may be due to the formation of a six-membered ring that increases the stability of GAS.

Results and Discussion
The most stable configuration of GAS is shown in Figure 1. A seven-membered ring structure is formed in the molecule. The hydrogen bond interaction was observed between the terminal hydrogen of the OSO3H group and the carbonyl oxygen of the COOH group.

Gas-Phase Reactions
The values of relative Gibbs free energy (CCSD/6-311++G(2d,2p)) of the reactions between CH3CHOO and GAS are displayed in Figure 2. The configurations of reaction complexes, transition states, and products are depicted in Figure S1. The reaction energy barriers of syn-CH3CHOO with OSO3H and COOH groups are 1.00 and 2.87 kcal/mol, respectively. The reactions of anti-CH3CHOO with OSO3H and COOH groups need to cross energy barriers of 3.30 and 4.09 kcal/mol, respectively. The low energy barriers suggest that these reactions are feasible in the atmosphere. Previous studies have shown that most reactions of CIs with carboxylic acids follow a barrierless pathway [31,32]. However, we observed that the reactions of the COOH group with CH3CHOO require overcoming the energy barrier, which may be due to the formation of a six-membered ring that increases the stability of GAS. Water molecules are one of the most abundant species in the atmosphere and have a significant impact on atmospheric chemical processes [33]. Therefore, the relative Gibbs

Gas-Phase Reactions
The values of relative Gibbs free energy (CCSD/6-311++G(2d,2p)) of the reactions between CH3CHOO and GAS are displayed in Figure 2. The configurations of reaction complexes, transition states, and products are depicted in Figure S1. The reaction energy barriers of syn-CH3CHOO with OSO3H and COOH groups are 1.00 and 2.87 kcal/mol, respectively. The reactions of anti-CH3CHOO with OSO3H and COOH groups need to cross energy barriers of 3.30 and 4.09 kcal/mol, respectively. The low energy barriers suggest that these reactions are feasible in the atmosphere. Previous studies have shown that most reactions of CIs with carboxylic acids follow a barrierless pathway [31,32]. However, we observed that the reactions of the COOH group with CH3CHOO require overcoming the energy barrier, which may be due to the formation of a six-membered ring that increases the stability of GAS. Water molecules are one of the most abundant species in the atmosphere and have a significant impact on atmospheric chemical processes [33]. Therefore, the relative Gibbs Water molecules are one of the most abundant species in the atmosphere and have a significant impact on atmospheric chemical processes [33]. Therefore, the relative Gibbs free energy (CCSD/6-311++G(2d,2p)) of the water-mediated reactions between CH 3 CHOO and GAS was calculated ( Figure 3). The two lowest energy barriers are 0.78 and 2.55 kcal/mol, which are determined for the water-mediated reaction of syn-CH 3 CHOO with the OSO 3 H group and the reaction of syn-CH 3 CHOO with the COOH group, respectively. Compared with the direct reactions of syn-CH 3 CHOO, the water molecule lowers the energy barrier of the reaction with the OSO 3 H group but increases the energy barrier of the reaction with the COOH group. In contrast, the water-mediated reaction barrier of anti-CH 3 CHOO with OSO 3 H group is increased to 6.11 kcal/mol, and that of anti-CH 3 CHOO with COOH group is decreased to 3.43 kcal/mol. The participation of water molecules leads to the change of the reaction energy barrier to be less than 3 kcal/mol, indicating that the effect of water molecules on the reaction of CH 3 CHOO with GAS is weak. The configurations of the water-mediated reaction stages are presented in Figure S2. reaction with the COOH group. In contrast, the water-mediated reaction barrier of anti-CH3CHOO with OSO3H group is increased to 6.11 kcal/mol, and that of anti-CH3CHOO with COOH group is decreased to 3.43 kcal/mol. The participation of water molecules leads to the change of the reaction energy barrier to be less than 3 kcal/mol, indicating that the effect of water molecules on the reaction of CH3CHOO with GAS is weak. The configurations of the water-mediated reaction stages are presented in Figure S2.

Gas-Liquid Interface Reactions
The gas-liquid interface plays a pivotal and ubiquitous role in atmospheric chemistry, including absorbing various pollutants and changing chemical reaction mechanisms. For example, Shang et al. [34] reported the interfacial reaction of SO2 with oleic acid, which is a new pathway to form organosulfur in the atmosphere. In this study, the gas-liquid interface reaction mechanism of anti-CH3CHOO with GAS was explored at the molecular level. In order to eliminate the effect of reaction location, thirty simulations were performed at different locations of the droplet. The reactions of anti-CH3CHOO with GAS occurred in 16 simulations. The direct and water-mediated reactions of anti-CH3CHOO with the COOH group occurred six and two times, respectively. The direct and watermediated reactions of anti-CH3CHOO with the OSO3H group both occurred four times. The hydration reactions of anti-CH3CHOO occurred 11 times.

Gas-Liquid Interface Reactions
The gas-liquid interface plays a pivotal and ubiquitous role in atmospheric chemistry, including absorbing various pollutants and changing chemical reaction mechanisms. For example, Shang et al. [34] reported the interfacial reaction of SO 2 with oleic acid, which is a new pathway to form organosulfur in the atmosphere. In this study, the gas-liquid interface reaction mechanism of anti-CH 3 CHOO with GAS was explored at the molecular level. In order to eliminate the effect of reaction location, thirty simulations were performed at different locations of the droplet. The reactions of anti-CH 3 CHOO with GAS occurred in 16 simulations. The direct and water-mediated reactions of anti-CH 3 CHOO with the COOH group occurred six and two times, respectively. The direct and water-mediated reactions of anti-CH 3 CHOO with the OSO 3 H group both occurred four times. The hydration reactions of anti-CH 3 CHOO occurred 11 times.
2.2.1. Reaction of Anti-CH 3 CHOO with the COOH Group of GAS Figure 4a shows the structure and bond length variations of the direct reaction between anti-CH 3 CHOO and the COOH group of GAS. Based on the properties of hydrophobicity and hydrophilicity, the methyl group of anti-CH 3 CHOO is placed on the side away from the droplet. At 0 ps, the distances of H-O3, C-O1, and H-O2 are 0.97, 2.66, and 2.52 Å, respectively. Subsequently, the H atom of the COOH group gradually approaches the terminal oxygen of anti-CH 3 CHOO, and the carbonyl oxygen of the COOH group approaches the α-carbon atom of anti-CH 3 CHOO. At 0.14 ps, the distances of H-O3, C-O1, and H-O2 are 1.53, 2.13, and 1.00 Å, respectively, where the transition-state-like structure is formed. At 0.20 ps, the H atom on the COOH group binds to the terminal oxygen of anti-CH 3 CHOO, and the C-O1 and H-O2 bonds are formed and remain stable, indicating the formation of the reaction product.
2.52 Å, respectively. Subsequently, the H atom of the COOH group gradually approaches the terminal oxygen of anti-CH3CHOO, and the carbonyl oxygen of the COOH group approaches the α-carbon atom of anti-CH3CHOO. At 0.14 ps, the distances of H-O3, C-O1, and H-O2 are 1.53, 2.13, and 1.00 Å, respectively, where the transition-state-like structure is formed. At 0.20 ps, the H atom on the COOH group binds to the terminal oxygen of anti-CH3CHOO, and the C-O1 and H-O2 bonds are formed and remain stable, indicating the formation of the reaction product. The mechanism of the water-mediated reaction between the anti-CH3CHOO and COOH group of GAS (Figure 4b) is different from that of the direct reaction. At 0 ps, the initial distances of H2-O3, H1-O3, H2-O2, H1-O4, and C-O1 are 0.98, 2.40, 2.05, 0.97, and 3.22 Å, respectively. At 0.12 ps, the structure of the reactants is similar to the transition state; the distances of H2-O3, H1-O3, H2-O2, H1-O4, and C-O1 are 1.05, 1.22, 1.48, 1.24, and 2.66 Å, respectively. At 0.24 ps, H2-O2 and H1-O4 bonds are formed. However, the C-O1 bond (1.56 Å) is formed at 0.57 ps. In water-mediated reactions, the C-O1 bond is formed later than other bonds, and the water molecule is the bridge of proton transfer.

Reaction of Anti-CH3CHOO with the OSO3H Group of GAS
The direct and water-mediated reactions between the anti-CH3CHOO and OSO3H groups of GAS were observed in our simulations ( Figure 5). For the direct reaction, the distances of H-O2, H-O3, and C-O1 are 0.98, 2.48, and 4.04 Å, respectively, at 0 ps. From 0.38 to 0.63 ps, the H atom of the OSO3H group vibrates between O3 and O2 atoms. The length of H-O3 fluctuates around 0.98 Å from 0.63 ps, but the distance of C-O1 is still decreasing. At 0.71ps, the O1 atom of GAS binds to the C atom of anti-CH3CHOO, indicating the formation of a hydroperoxide product.

Reaction of Anti-CH 3 CHOO with the OSO 3 H Group of GAS
The direct and water-mediated reactions between the anti-CH 3 CHOO and OSO 3 H groups of GAS were observed in our simulations ( Figure 5). For the direct reaction, the distances of H-O2, H-O3, and C-O1 are 0.98, 2.48, and 4.04 Å, respectively, at 0 ps. From 0.38 to 0.63 ps, the H atom of the OSO 3 H group vibrates between O3 and O2 atoms. The length of H-O3 fluctuates around 0.98 Å from 0.63 ps, but the distance of C-O1 is still decreasing. At 0.71ps, the O1 atom of GAS binds to the C atom of anti-CH 3 CHOO, indicating the formation of a hydroperoxide product. For the water-mediated reaction (Figure 5b), the initial distances of H2-O2, H1-O3, and C-O1 are 2.30, 2.03, and 3.10 Å, respectively. The transition-state-like structure is observed at 0.26 ps, where the lengths of H2-O2, H1-O3, H1-O1, H2-O3, and C-O1 are 1.41, 1.09, 1.39, 1.10, and 2.43 Å, respectively. The H2-O2 and H1-O3 are formed at 0.30 and 0.27 ps, respectively. The O1 atom binds to the C atom at 0.52 ps, which occurs later than the formation of the H2-O2 bond. This phenomenon is also observed in the water-mediated reaction between the COOH group of anti-CH3CHOO and GAS, suggesting that watermediated proton transfer initiates the reactions and promotes the binding of C and O at- For the water-mediated reaction (Figure 5b), the initial distances of H2-O2, H1-O3, and C-O1 are 2.30, 2.03, and 3.10 Å, respectively. The transition-state-like structure is observed at 0.26 ps, where the lengths of H2-O2, H1-O3, H1-O1, H2-O3, and C-O1 are 1.41, 1.09, 1.39, 1.10, and 2.43 Å, respectively. The H2-O2 and H1-O3 are formed at 0.30 and 0.27 ps, respectively. The O1 atom binds to the C atom at 0.52 ps, which occurs later than the formation of the H2-O2 bond. This phenomenon is also observed in the watermediated reaction between the COOH group of anti-CH 3 CHOO and GAS, suggesting that water-mediated proton transfer initiates the reactions and promotes the binding of C and O atoms.

Intramolecular Proton Transfer Reaction of Anti-CH 3 CHOO with the OSO 3 H Group of GAS
Most of the previous studies have focused on the reaction of CIs with monofunctional species [35][36][37]. Even the study of CIs and multifunctional species is the independent reaction of a single functional group [38]. However, the reaction involving both functional groups of GAS is observed in this study (Figure 6). At 0 ps, the two interface water molecules are far away from anti-CH 3 CHOO and GAS, and the distances of H2-O4 and H3-O2 are 3.68 and 3.92 Å, respectively. The transition-state-like complex of anti-CH 3 CHOO, GAS, and water molecules is formed at 2.09 ps. The proton of the OSO 3 H group is transferred to the carbonyl oxygen of the COOH group at this time; the distances of H1-O1 and H1-O6 are 1.15 and 1.44 Å, respectively. The proton of the COOH group moves to the water molecule, and the distances of H2-O5 and H2-O4 are 1.26 and 1.28 Å, respectively. In this way, proton transfer occurs between the two functional groups of GAS, and the COOH group acts as the shuttle of proton transfer in this reaction. At 2.37 ps, the H3-O2 bond (the length is 0.99 Å) is formed, indicating proton transfer between the four reactant molecules is complete. The C-O1 bond is formed at 2.79 ps, resulting in the formation of new products. During the whole reaction process, both the COOH group of GAS and water molecules act as bridges of proton transfer. Kumar et al. [39] reported BOMD simulations of anti-CH3CHOO reacting with HNO3 at the gas-liquid interface, suggesting that HNO3-mediated anti-CH3CHOO hydration is the most dominant reaction. In this study, the GAS-mediated hydration of anti-CH3CHOO Figure 6. The intramolecular proton transfer reaction between anti-CH 3 CHOO and OSO 3 H group of GAS at gas-liquid interface.

GAS-Mediated Hydration of Anti-CH 3 CHOO
Kumar et al. [39] reported BOMD simulations of anti-CH 3 CHOO reacting with HNO 3 at the gas-liquid interface, suggesting that HNO 3 -mediated anti-CH 3 CHOO hydration is the most dominant reaction. In this study, the GAS-mediated hydration of anti-CH 3 CHOO occurs and generates C 2 H 3 O 6 Sand H 3 O + ions, and the reaction follows an obvious stepwise mechanism. As shown in Figure 7, anti-CH 3 CHOO and GAS are placed on the droplet surface, which is far from the water molecules at 0 ps. For the first step, the proton on the COOH group is transferred to the terminal oxygen of anti-CH 3 CHOO, and the intramolecular proton transfer occurs in GAS. At 1.86 ps, the distances of H1-O1 and H5-O7 are 1.18 and 1.24 Å, respectively. At 2.10 ps, the distances of H1-O1 and H5-O7 are 0.98 and 1.01 Å, respectively, indicating the protonated anti-CH 3 CHOO and C 2 H 3 O 6 S − ion are formed. In the second step, the O atom of the water molecule combines with α-C of the anti-CH 3 CHOO, and the proton is transferred to another water molecule. At 2.52 ps, the distances of C-O2 and H2-O3 are 1.41 and 0.98 Å, respectively. In thise last step, the water molecules transfer protons to each other, and the H 3 O + ion is formed at 4.85 ps. In this pathway, GAS acts as a water molecule to provide protons for the hydration of anti-CH 3 CHOO.

Atmospheric Implications
These results deepen the understanding of CI fate in the atmosphere. GAS is an ab dant nucleation precursor and has an important contribution to the formation of atm

Atmospheric Implications
These results deepen the understanding of CI fate in the atmosphere. GAS is an abundant nucleation precursor and has an important contribution to the formation of atmospheric particulate pollution [40][41][42]. The reaction with GAS is one of the sink pathways for CH 3 CHOO, especially the direct reaction with the COOH group is a nearly barrierless process (1.00 kcal/mol), which may be the dominant reaction in a dry atmosphere. The water-mediated reaction between CH 3 CHOO and OSO 3 H groups is also a nearly barrierless process (0.78 kcal/mol), which may be the dominant reaction in polluted areas with high humidity.
Furthermore, the BOMD simulations reveal the reaction mechanism of anti-CH 3 CHOO with GAS on droplets. Both direct and water-mediated reactions are observed, with the formation of ring structures during the reaction. Among them, the water-mediated reaction follows the proton transfer mechanism, and the water molecule acts as a bridge for proton transfer. Although it has been reported that CH 3 CHOO can exist stably on the droplet surface [30], all the reactions of anti-CH 3 CHOO with GAS on the droplet occur on the ps timescale. The terminal O atom of anti-CH 3 CHOO binding to the H atom of GAS in the reaction occurs slightly later than the α-C atom of anti-CH 3 CHOO binding to the O atom of GAS, suggesting the reactions are initiated by the binding of O and H atoms. Both quantum chemical calculations and molecular simulations indicate that water molecules can participate in the reaction of CH 3 CHOO with GAS. In addition, though the reaction of CIs with various species on droplets is discussed in the literature [43][44][45][46], intramolecular proton transfer was observed in our simulations. The hydrogen bond and six-membered ring structure are formed inside the GAS molecule, resulting in the intramolecular proton transfer. It is believed that similar reactions can occur in some substances with longer carbon chains and multiple functional groups in the atmosphere. GAS-promoted hydration of anti-CH 3 CHOO as a proton donor was also observed in the simulations. Previous studies have pointed out that nitric acid and methanesulfonic acid promote CIs hydration [39,47]; GAS also tends to perform intramolecular proton transfer while donating a proton, which has appeared many times in the simulations.
The product of CH 3 CHOO reacting with GAS is hydroperoxides. Hydroperoxides participate in the formation of new particles, and SOA in the atmosphere [48][49][50], which have toxic effects on human health and plants [51][52][53], and some macromolecular hydroperoxides can act as CCN [39]. The reactions of CH 3 CHOO with GAS increase the carbon chain length and the ability to form hydrogen bonds, which has great potential in particle formation.

Materials and Methods
The 72 configurations of GAS were optimized, and the most stable configuration was selected as the reactant. The configuration optimization and transition state searching were conducted with the M06-2X method [54] in conjunction with the 6-311++G(2d,2p) basis set. The analysis of intrinsic reaction coordinates (IRC) [55,56] was used to verify that all transition states connect to the expected reactants and products. Single point energies of reactants, complexes, transition states, and products were calculated at the CCSD/6-311++G(2d,2p) level. All calculations of electronic structures were performed with Gaussian 09 program [57].
Thirty gas-liquid interface simulations were carried out by BOMD. All simulations were performed by CP2K [58] software based on the DFT method. The droplet consisted of 30 water molecules, and reactants were placed in a cubic box with the side length set as 35 Å. The Becke-Lee-Yang-Parr (BLYP) [59,60] functional, double-ζ Gaussian basis set (DZVP) [61] and Goedecker-Teter-Hutter (GTH) norm-conserved pseudopotentials [62,63] were adopted to handle electronic exchange interaction, valence and core electrons, respectively. All BOMD simulations were performed in the constant volume and temperature (NVT) ensemble with the integration step of 1 fs. The system temperature (300 K) was controlled using the Nose-Hoover chain method.