Theoretical Study on the Gas-Phase and Aqueous Interface Reaction Mechanism of Criegee Intermediates with 2-Methylglyceric Acid and the Nucleation of Products

Criegee intermediates (CIs) are important in the sink of many atmospheric substances, including alcohols, organic acids, amines, etc. In this work, the density functional theory (DFT) method was used to calculate the energy barriers for the reactions of CH3CHOO with 2-methyl glyceric acid (MGA) and to evaluate the interaction of the three functional groups of MGA. The results show that the reactions involving the COOH group of MGA are negligibly affected, and that hydrogen bonding can affect the reactions involving α-OH and β-OH groups. The water molecule has a negative effect on the reactions of the COOH group. It decreases the energy barriers of reactions involving the α-OH and β-OH groups as a catalyst. The Born-Oppenheimer molecular dynamic (BOMD) was applied to simulate the reactions of CH3CHOO with MGA at the gas-liquid interface. Water molecule plays the role of proton transfer in the reaction. Gas-phase calculations and gas-liquid interface simulations demonstrate that the reaction of CH3CHOO with the COOH group is the main pathway in the atmosphere. The molecular dynamic (MD) simulations suggest that the reaction products can form clusters in the atmosphere to participate in the formation of particles.


Introduction
Plants can produce large amounts of volatile organic compounds (VOCs), and alkenes are an important component of VOCs [1]. The ozonolysis of alkenes is the main source of Criegee intermediates (CIs) in the atmosphere [2]. The first step of this process is the opening of the double bond of the alkene, where the oxygens at the ends of the ozone molecule combine with the carbons on either side of the double bond to form the primary ozonide (POZ), which decomposes into a carbonyl compound and an excited CI [3]. The excited CIs can be decomposed into OH radicals [4]. The unimolecular reaction of CIs is an important pathway for generating OH radicals in the atmosphere. Although CI decomposition contributes only about 24% of the OH production during the daytime, it is responsible for most OH formation at night [5]. Atmospheric tropospheric organic chemistry experiments conducted near London, UK, in 2003 showed that alkene ozonolysis accounted for about one-third of the atmospheric source of OH radicals during the day, and at night the average concentration of OH radical was about 2.6 × 10 5 molecule cm −3 , with almost all OH radicals coming from alkene ozonolysis [6,7]. In the Chilean observations, olefin ozonolysis contributed about a quarter of the OH radicals in the atmosphere, with internal alkenes contributing 86%. The OH radical yield of internal alkenes was much higher than that of terminal alkenes [8]. The box modeling showed that the decomposition of CI is the main source of OH in the summer and winter PUMA (Pollution of the Urban Midlands Atmosphere) campaign [9]. Therefore, the decomposition of CI has a profound effect on the oxidation capacity of the troposphere.

Results and Discussion
The lowest energy configuration of MGA is shown in Figure 1. The hydrogen of the beta-hydroxyl group (β-OH) forms a hydrogen bond (2.26 Å) with the oxygen of the alpha-hydroxyl group (α-OH), and the hydrogen on the α-OH forms a hydrogen bond (2.08 Å) with the carbonyl oxygen of the carboxyl group. The hydrogen bonds contribute to the stability of the MGA molecule.

Results and Discussion
The lowest energy configuration of MGA is shown in Figure beta-hydroxyl group (β-OH) forms a hydrogen bond (2.26 Å) alpha-hydroxyl group (α-OH), and the hydrogen on the α-OH (2.08 Å) with the carbonyl oxygen of the carboxyl group. The hyd to the stability of the MGA molecule.

Bimolecular Reactions
In the reactions of syn-and anti-CH3CHOO with the three fun the reaction transition state of anti-CH3CHOO with the COOH g As shown in Figure 2, the energy of the reaction complexes is c The reaction of anti-CH3CHOO with the COOH group is barrierl CH3CHOO with the COOH group is almost barrierless (0.52 k consistent with previous studies that the reactions of C1 and C2 C acids are barrierless pathways [39,40]. The reaction energy barrier α-OH and β-OH groups are 17.30 and 16.67 kcal/mol, respectivel energy barrier of anti-CH3CHOO + α-OH (8.53 kcal/mol) is slightl CH3CHOO + β-OH (6.74 kcal/mol). This suggests that the energetically favorable to react with CH3CHOO than the α-OH g COOH, α-OH and β-OH groups of MGA, the energy barriers o 8.53, 6.74 kcal/mol) are lower than that of syn-CH3CHOO (0.52 indicating that the reactivity of anti-CH3CHOO is higher than tha COOH group of MGA prefers to react with CH3CHOO compa functional groups in the atmosphere. The structures of all reactio  In the reactions of synand anti-CH 3 CHOO with the three functional groups of MGA, the reaction transition state of anti-CH 3 CHOO with the COOH group was not observed. As shown in Figure 2, the energy of the reaction complexes is considered a benchmark. The reaction of anti-CH 3 CHOO with the COOH group is barrierless. The reaction of syn-CH 3 CHOO with the COOH group is almost barrierless (0.52 kcal/mol). This result is consistent with previous studies that the reactions of C1 and C2 CIs with formic and acetic acids are barrierless pathways [39,40]. The reaction energy barriers of syn-CH 3 CHOO with α-OH and β-OH groups are 17.30 and 16.67 kcal/mol, respectively. Similarly, the reaction energy barrier of anti-CH 3 CHOO + α-OH (8.53 kcal/mol) is slightly larger than that of anti-CH 3 CHOO + β-OH (6.74 kcal/mol). This suggests that the β-OH group is more energetically favorable to react with CH 3 CHOO than the α-OH group. In the reactions of COOH, α-OH and β-OH groups of MGA, the energy barriers of anti-CH 3 CHOO (0.00, 8.53, 6.74 kcal/mol) are lower than that of syn-CH 3 CHOO (0. 52, 17.30, 16.67 kcal/mol), indicating that the reactivity of anti-CH 3 CHOO is higher than that of syn-CH 3 CHOO. The COOH group of MGA prefers to react with CH 3 CHOO compared with the other two functional groups in the atmosphere. The structures of all reaction complexes, transition states and products are displayed in Figure S2. To explore the effect of functional groups on the reaction energy barrier, one or t functional groups in MGA are replaced by H atoms. Then the energy barriers for reactions of CH3CHOO with these reactants were calculated. The structures of th reactants and reaction energy barriers are given in Table 1. In all the reactions of t COOH group, the reaction energy barriers are zero or nearly zero kcal/mol, wh indicates that α-OH and β-OH groups do not affect the reaction energy barriers of COOH group and the reactions of CIs with the COOH group are very active. For reactions of the α-OH group, the energy barrier of the syn-CH3CHOO reaction decrea by 0.47 kcal/mol as the β-OH group of MGA is replaced by an H atom. And the ener barriers of the R4 and R5 reactions decrease by 3.63 and 3.93 kcal/mol as the COOH gro of MGA is replaced by the H atom. For anti-CH3CHOO reactions, the energy barr lowered in the R2 reaction (0.07 kcal/mol) is also smaller than that of the R4 and reactions (0.69 and 0.54 kcal/mol), indicating that the COOH group inhibited the reactio of the α-OH group more strongly than the β-OH group. The loss of hydrogen bo between the α-OH and the COOH group makes it easier for the H of the α-OH group transfer to the terminal oxygen of CH3CHOO. For the reactions of syn-CH3CHOO w the β-OH group, due to the long distance of the COOH group from the β-OH group, reaction energy barrier is reduced by 1.37 kcal/mol as the H atom replaces the COO group. The reaction energy barriers are reduced by 3.00 and 4.02 kcal/mol (R1 and reactions) as the α-OH group is replaced by an H atom. The hydrogen bond between α-OH and β-OH group also increases the reaction energy barriers of the β-OH grou However, in the reaction of anti-CH3CHOO, the energy barriers of the R1 and R4 reactio are increased. This may be due to the increased distance between the H of the β-OH gro and the O of the α-OH group (2.46 Å) when anti-CH3CHOO forms a complex with MG ( Figure S2), and it is easier for the addition of the β-OH to anti-CH3CHOO. To explore the effect of functional groups on the reaction energy barrier, one or two functional groups in MGA are replaced by H atoms. Then the energy barriers for the reactions of CH 3 CHOO with these reactants were calculated. The structures of these reactants and reaction energy barriers are given in Table 1. In all the reactions of the COOH group, the reaction energy barriers are zero or nearly zero kcal/mol, which indicates that α-OH and β-OH groups do not affect the reaction energy barriers of the COOH group and the reactions of CIs with the COOH group are very active. For the reactions of the α-OH group, the energy barrier of the syn-CH 3 CHOO reaction decreases by 0.47 kcal/mol as the β-OH group of MGA is replaced by an H atom. And the energy barriers of the R4 and R5 reactions decrease by 3.63 and 3.93 kcal/mol as the COOH group of MGA is replaced by the H atom. For anti-CH 3 CHOO reactions, the energy barrier lowered in the R2 reaction (0.07 kcal/mol) is also smaller than that of the R4 and R5 reactions (0.69 and 0.54 kcal/mol), indicating that the COOH group inhibited the reactions of the α-OH group more strongly than the β-OH group. The loss of hydrogen bond between the α-OH and the COOH group makes it easier for the H of the α-OH group to transfer to the terminal oxygen of CH 3 CHOO. For the reactions of syn-CH 3 CHOO with the β-OH group, due to the long distance of the COOH group from the β-OH group, the reaction energy barrier is reduced by 1.37 kcal/mol as the H atom replaces the COOH group. The reaction energy barriers are reduced by 3.00 and 4.02 kcal/mol (R1 and R6 reactions) as the α-OH group is replaced by an H atom. The hydrogen bond between the α-OH and β-OH group also increases the reaction energy barriers of the β-OH group. However, in the reaction of anti-CH 3 CHOO, the energy barriers of the R1 and R4 reactions are increased. This may be due to the increased distance between the H of the β-OH group and the O of the α-OH group (2.46 Å) when anti-CH 3 CHOO forms a complex with MGA ( Figure S2), and it is easier for the addition of the β-OH to anti-CH 3 CHOO.  The minimum energy pathway for the water-mediated reactions of CH3CHOO with MGA is presented in Figure 3. For the reactions involving the COOH group, the participation of the water molecule increases the reaction energy barriers. The energy  The minimum energy pathway for the water-mediated reactions of CH3CHOO with MGA is presented in Figure 3. For the reactions involving the COOH group, the participation of the water molecule increases the reaction energy barriers. The energy

. Water-Mediated Reactions
The minimum energy pathway for the water-mediated reactions of CH3CHOO with MGA is presented in Figure 3. For the reactions involving the COOH group, the participation of the water molecule increases the reaction energy barriers. The energy 0.00 0.00 The minimum energy pathway for the water-mediated reactions of CH3CHOO with MGA is presented in Figure 3. For the reactions involving the COOH group, the participation of the water molecule increases the reaction energy barriers. The energy 13 The minimum energy pathway for the water-mediated reactions of CH3CHOO with MGA is presented in Figure 3. For the reactions involving the COOH group, the participation of the water molecule increases the reaction energy barriers. The energy 16

. Water-Mediated Reactions
The minimum energy pathway for the water-mediated reactions of CH3CHOO with MGA is presented in Figure 3. For the reactions involving the COOH group, the participation of the water molecule increases the reaction energy barriers. The energy 13

. Water-Mediated Reactions
The minimum energy pathway for the water-mediated reactions of CH3CHOO with MGA is presented in Figure 3. For the reactions involving the COOH group, the participation of the water molecule increases the reaction energy barriers. The energy 15 The minimum energy pathway for the water-mediated reactions of CH3CHOO with MGA is presented in Figure 3. For the reactions involving the COOH group, the participation of the water molecule increases the reaction energy barriers. The energy 13 The minimum energy pathway for the water-mediated reactions of CH3CHOO with MGA is presented in Figure 3. For the reactions involving the COOH group, the participation of the water molecule increases the reaction energy barriers. The energy 12.65 5.90

Water-Mediated Reactions
The minimum energy pathway for the water-mediated reactions of CH 3 CHOO with MGA is presented in Figure 3. For the reactions involving the COOH group, the participation of the water molecule increases the reaction energy barriers. The energy barriers of reactions involving synand anti-CH 3 CHOO are increased by 0.63 and 0.77 kcal/mol, respectively. In contrast, the water molecule decreases the energy barriers of the reactions of α-OH and β-OH groups, which acts as a catalyst. The reaction energy barriers are decreased by 8.66 and 9.99 kcal/mol for the cases of syn-CH 3 CHOO with α-OH and β-OH groups, respectively. The energy barriers of anti-CH 3 CHOO interacting with α-OH and β-OH groups are decreased by 1.79 and 1.96 kcal/mol, respectively. The promoting effect of the water molecule for reactions of syn-CH 3 CHOO is stronger than that for anti-CH 3 CHOO. The water-mediated reactions also suggested that the reactivity of anti-CH 3 CHOO is greater than that of syn-CH 3 CHOO. The structures of all water-mediated reaction complexes, transition states and products are shown in Figure S3.
are decreased by 8.66 and 9.99 kcal/mol for the cases of syn-CH3CHOO with α-OH and β-OH groups, respectively. The energy barriers of anti-CH3CHOO interacting with α-OH and β-OH groups are decreased by 1.79 and 1.96 kcal/mol, respectively. The promoting effect of the water molecule for reactions of syn-CH3CHOO is stronger than that for anti-CH3CHOO. The water-mediated reactions also suggested that the reactivity of anti-CH3CHOO is greater than that of syn-CH3CHOO. The structures of all water-mediated reaction complexes, transition states and products are shown in Figure S3.

Gas-Liquid Interface Reactions
The gas-liquid interface significantly impacts the chemical reactions in the atmosphere [41][42][43]. In this study, CH3CHOO and MGA molecules were placed on a droplet composed of thirty water molecules to explore the effect of the gas-liquid interface on the reactions. To eliminate the impact of droplet position on the reactions, the simulations of reactions involving syn-and anti-CH3CHOO were performed thirty times, each at different positions.

Gas-Liquid Interface Reactions
The gas-liquid interface significantly impacts the chemical reactions in the atmosphere [41][42][43]. In this study, CH 3 CHOO and MGA molecules were placed on a droplet composed of thirty water molecules to explore the effect of the gas-liquid interface on the reactions. To eliminate the impact of droplet position on the reactions, the simulations of reactions involving synand anti-CH 3 CHOO were performed thirty times, each at different positions. Figure 4 shows the key bond length variation and snapshots of the reaction between the anti-CH 3 CHOO and COOH group of MGA at the gas-liquid interface. As presented in Figure 4a, the distances of H-O1, C-O and H-O2 are 0.97, 3.07 and 3.07 Å, respectively, at 0 ps. Subsequently, the H of the COOH group gradually approaches the terminal oxygen of anti-CH 3 CHOO and the distance of C-O decreases at 0.55 ps. At 0.82 ps, a transition-statelike structure is formed between the two molecules. The distances of H-O1, C-O and H-O2 are 1.20, 2.50 and 1.23 Å, respectively. At 0.93 ps, the C-O and O-H2 bonds are formed and stabilized, indicating the formation of the product. The water-mediated reaction process is shown in Figure 4b. At 0 ps, the distances of H2-O3, H1-O3, H2-O2, H1-O1 and C-O1 are 1.00, 2.08, 2.29, 0.97 and 4.12 Å, respectively. The transition-state-like structure appears at 6.99 ps. The water molecule is located between H1 and O2 to transfer the proton. And the distances of H2-O3, H1-O3, H2-O2, H1-O1 and C-O1 are 1.22, 1.03, 1.22, 1.74 and 2.68 Å, respectively. At 7.13 ps, the proton transfer is completed, and the additional product is generated. The distances of H2-O3, H1-O3, H2-O2, H1-O1 and C-O1 are 1.49, 1.02, 1.01, 2.48 and 1.56 Å, respectively. The water molecule becomes the bridge for proton transfer during the reaction. The direct reaction of the COOH group was completed within 1 ps, and the water-mediated reaction was completed at about 7 ps, with a time difference of about 6 ps between the two reactions. In previous studies, the direct reactions of CH 2 OO and CH 3 CHOO with formic and acetic acids were extremely fast, with rate constants greater than 1 × 10 −10 cm 3 molecule −1 s −1 and reaction rates close to the collision limit [40]. Moreover, the reaction of CH 2 OO with formic acid has been shown to be a barrierless process [44]. In the present study, the direct reaction of the COOH group in the gas phase is also barrierless, and the energy barrier rises after adding water molecules, which are unfavorable to the reaction. Based on the above description, it is highly likely that the direct reaction of the COOH group is faster than the water-mediated reaction. The key bond length variations and snapshots of the gas-liquid interfacial reaction of syn-CH 3 CHOO with the COOH group of MGA are depicted in Figure S4. The reactions of CH 3 CHOO with the α-OH and β-OH groups of MGA and the water-mediated reaction of syn-CH 3 CHOO with the COOH group of MGA were not observed in the simulations. fast, with rate constants greater than 1 × 10 cm molecule s and reaction rates close to the collision limit [40]. Moreover, the reaction of CH2OO with formic acid has been shown to be a barrierless process [44]. In the present study, the direct reaction of the COOH group in the gas phase is also barrierless, and the energy barrier rises after adding water molecules, which are unfavorable to the reaction. Based on the above description, it is highly likely that the direct reaction of the COOH group is faster than the water-mediated reaction. The key bond length variations and snapshots of the gas-liquid interfacial reaction of syn-CH3CHOO with the COOH group of MGA are depicted in Figure S4. The reactions of CH3CHOO with the α-OH and β-OH groups of MGA and the water-mediated reaction of syn-CH3CHOO with the COOH group of MGA were not observed in the simulations. The gas-phase reaction and the BOMD simulation results are in good agreement, with the reactions of the COOH group, which has a lower energy barrier, occurring more easily in the BOMD simulations. On the other hand, the reactions of the OH group have high energy barriers that are difficult to observe in the simulations.

MGA-Mediated Hydration of Anti-CH3CHOO
The reaction of CIs with water is the most important sink pathway in the atmosphere [45][46][47]. In the simulations, MGA-mediated hydration of anti-CH3CHOO as a catalyst was observed. As shown in Figure 5, the initial distances of the H4-O4, H4-O5, C-O3 and H1-O6 are 2.70, 0.97, 8.52 and 3.61 Å, respectively. The transition-state-like structure appears at 3.08 ps, where anti-CH3CHOO, MGA and three water molecules form a ring structure. The H4-O4, H4-O5, C-O3 and H1-O6 distances are 1.03, 1.44, 1.46 and 1.41 Å, respectively. The proton transfer of the three water molecules and the COOH group occur almost simultaneously. At 3.13 ps, the distances of H4-O4, C-O3 and H1-O6 are stable at 1.00, 1.38 and 1.00 Å, indicating the formation of the product. The gas-phase reaction and the BOMD simulation results are in good agreement, with the reactions of the COOH group, which has a lower energy barrier, occurring more easily in the BOMD simulations. On the other hand, the reactions of the OH group have high energy barriers that are difficult to observe in the simulations.

MGA-Mediated Hydration of Anti-CH 3 CHOO
The reaction of CIs with water is the most important sink pathway in the atmosphere [45][46][47]. In the simulations, MGA-mediated hydration of anti-CH 3 CHOO as a catalyst was observed. As shown in Figure 5, the initial distances of the H4-O4, H4-O5, C-O3 and H1-O6 are 2.70, 0.97, 8.52 and 3.61 Å, respectively. The transition-state-like structure appears at 3.08 ps, where anti-CH 3 CHOO, MGA and three water molecules form a ring structure. The H4-O4, H4-O5, C-O3 and H1-O6 distances are 1.03, 1.44, 1.46 and 1.41 Å, respectively. The proton transfer of the three water molecules and the COOH group occur almost simultaneously. At 3.13 ps, the distances of H4-O4, C-O3 and H1-O6 are stable at 1.00, 1.38 and 1.00 Å, indicating the formation of the product.

Nucleation of Products
It is reported that the CI reactions are likely to generate low volatile products, which can participate in the nucleation process and form SOA in the atmosphere. The reaction product of CIs and peroxyl radicals is an oligomer, one of the chemical compositions of SOA [48]. In the gas phase, the continuous insertion of CIs into the hydroperoxide esters leads to the formation of oligomers that make an important contribution to the generation of SOA [49]. This study simulated the nucleations of CH 3 CHOO + MGA reaction products (P) with NH 3 , sulfuric acids (SA) and H 2 O. Initially, five products, ten NH 3 , five SA, twenty H 2 O, one hundred and fifty-four N 2 and forty-one O 2, were randomly put into the supercell. The nucleation simulation for the reaction product of anti-CH 3 CHOO + MGA-COOH is shown in Figure 6. At 1.5 ns, there are three clusters in the system, which are (P)(SA)(H 2 O) 2 , (P) 2 (SA)(H 2 O) 4 and (P)(H 2 O) 2 . The NH 3 is not adsorbed into the clusters. The three clusters grow into two larger clusters at 5 ns. Afterwards, there are always two clusters in the system whose composition changes continuously. However, the number of P and SA remained constant, indicating that P binds more strongly to SA than NH 3

Nucleation of Products
It is reported that the CI reactions are likely to generate low volatile products, w can participate in the nucleation process and form SOA in the atmosphere. The rea product of CIs and peroxyl radicals is an oligomer, one of the chemical compositio SOA [48]. In the gas phase, the continuous insertion of CIs into the hydroperoxide e (P)(SA)(H2O)2, (P)2(SA)(H2O)4 and (P)(H2O)2. The NH3 is not adsorbed into the clusters. The three clusters grow into two larger clusters at 5 ns. Afterwards, there are always two clusters in the system whose composition changes continuously. However, the number of P and SA remained constant, indicating that P binds more strongly to SA than NH3 and H2O during nucleation. At 20 ns, the (P)5(SA)5(NH3)4(H2O)20 cluster is formed in the system. The nucleation simulations of the other five products are depicted in Figures S5-S9.

Methods and Materials
Twelve different structures of MGA molecules were optimized, and six different configurations of MGA molecules were obtained ( Figure S1). The MGA molecule with the lowest energy was selected as the reactant (MGA-6). The structural optimization of the reactants, reaction complexes, transition states, and products and the transition state searching was conducted using the M06-2X functional [50] in combination with the 6-31+G(d,p) basis set. The intrinsic reaction coordinates (IRC) calculation was used to confirm that the transition states were connected to the correct reaction complexes and products [51,52]. The single-point energies of all structures were performed at the M06-2X/6-311++G(3df,3pd) level. Gaussian 09 software was used to calculate the electronic structures of all gas-phase reactions [53]. All gas-phase reaction calculations are based on the DFT method. DFT is based on the Hohenberg-Kohn theorem, which describes and determines a system's ground state energy and other physical quantities by electron density and applies the Kohn-Sham equation to calculate real molecular systems. DFT is based on the Hohenberg-Kohn theorem, which describes and determines a system's ground state energy and other physical quantities by electron density and applies the Kohn-Sham equation to calculate real molecular systems. DFT simplifies the Schördinger wave function solution process and solves the 3N-dimensional wave function problem with a three-dimensional electron density problem. The equation for the total energy is:

Methods and Materials
Twelve different structures of MGA molecules were optimized, and six different configurations of MGA molecules were obtained ( Figure S1). The MGA molecule with the lowest energy was selected as the reactant (MGA-6). The structural optimization of the reactants, reaction complexes, transition states, and products and the transition state searching was conducted using the M06-2X functional [50] in combination with the 6-31+G(d,p) basis set. The intrinsic reaction coordinates (IRC) calculation was used to confirm that the transition states were connected to the correct reaction complexes and products [51,52]. The single-point energies of all structures were performed at the M06-2X/6-311++G(3df,3pd) level. Gaussian 09 software was used to calculate the electronic structures of all gas-phase reactions [53]. All gas-phase reaction calculations are based on the DFT method. DFT is based on the Hohenberg-Kohn theorem, which describes and determines a system's ground state energy and other physical quantities by electron density and applies the Kohn-Sham equation to calculate real molecular systems. DFT is based on the Hohenberg-Kohn theorem, which describes and determines a system's ground state energy and other physical quantities by electron density and applies the Kohn-Sham equation to calculate real molecular systems. DFT simplifies the Schördinger wave function solution process and solves the 3N-dimensional wave function problem with a three-dimensional electron density problem. The equation for the total energy is: The items on the right side of the equation are the electron kinetic energy of the system, the attraction potential between the nucleus and the electron, the Coulomb interaction between the charges and the exchange-interaction energy. The electron density equation is: All gas-liquid interface reactions were performed with Born-Oppenheimer molecular dynamics (BOMD) using CP2K software based on the DFT method [54]. The simulations were carried out in supercell with a side length of 35 Å and containing thirty water molecules. The electronic exchange interaction was treated by the Becke-Lee-Yang-Parr (BLYP) functional [55,56]. The valence electron was treated by a double-ζ Gaussian basis set (DZVP) [57]. The core electron was treated by Goedecker-Teter-Hutter (GTH) normconserved pseudopotentials [58,59]. The integration step is set to 1 fs. The simulations were all performed using a constant volume and temperature (NVT) ensemble. The Nose-Hoover chain method was used to maintain the system temperature at 298 K. The ab initio method used in the simulations performs the all-electron system Schördinger equation for the studied system to solve the energy and wave functions. The Schördinger equation was proposed by the Austrian physicist Schrödinger in 1926. The equation is: The nucleation process was calculated using the GROMACS 5.1.0 [60] program. MD simulation was performed in a 200 × 200 × 200 Å 3 supercell. The electrostatic potentials of all substances in the supercell were calculated at the M06-2X/6-31+G(d,p) level. The first step was energy minimization. Then, the NVT ensemble was carried out for 100 ps, and constant pressure and temperature (NPT) were carried out for 20 ns. Berendsen pressure coupling was employed on the pressure coupling [61]. The velocity rescaling thermostat was employed on the temperature coupling [62]. The step size of the dynamic's simulation was set to 1 fs. Particle-mesh Ewald (PME) algorithm was performed to handle long-range electrostatic interactions [63]. The bonding length constraint was handled using the LINCS algorithm [64].

Conclusions
Based on reaction energy barriers calculated in the present work, the reactions with the MGA COOH group are the dominant pathways for CH 3 CHOO interactions in the gas phase. The energy barriers of the reaction involving the α-OH group are higher than that of the β-OH group due to the binding of the two hydrogen bonds. And the reactions of anti-CH 3 CHOO are more favorable than that of syn-CH 3 CHOO. For the effect of functional groups, the α-OH and β-OH groups have almost no impact on the reaction of the MGA COOH group, which is the most active functional group in the reactions with CH 3 COOH. Either the α-OH or β-OH group is affected by the other two functional groups. The presence of the other functional groups almost always inhibits the reactions of the α-OH or β-OH group. The water molecule inhibits the reactions of the MGA COOH group but promotes the reactions of the α-OH and β-OH groups. At the gas-liquid interface, the reactions of the COOH group are also the most dominant pathways, and the water molecule is the bridge for proton transfer. The MGA COOH group can play the role of water molecule involved in the hydration of CH 3 CHOO. Since the direct reaction of CIs with the MGA COOH group is the dominant pathway, dry atmospheric environments are more favorable for the reaction of CIs with MGA. In humid and CI-rich atmospheres (e.g., tropical rainforest regions), water-mediated reactions with MGA-COOH and MGA-mediated hydration are also sinks for CIs. The reaction products of CH 3 CHOO and MGA can form clusters with ammonia, sulfuric acids, and water molecules, which is a significant step in the formation of new particles in the atmosphere. Both the MGA and the reaction products contribute to SOA pollution.