Mechanistic and kinetics investigations of oligomer formation from Criegee intermediate reactions with hydroxyalkyl hydroperoxides

Although secondary organic aerosol (SOA) is a major component of PM2.5 and organic aerosol (OA) particles and therefore profoundly influences air quality, climate forcing, and human health, the mechanism of SOA formation via Criegee chemistry is poorly understood. Herein, we perform high-level theoretical calculations to study the gasphase reaction mechanism and kinetics of four Criegee intermediate (CI) reactions with four hydroxyalkyl hydroperoxides (HHPs) for the first time. The calculated results show that the consecutive reactions of CIs with HHPs are both thermochemically and kinetically favored, and the oligomers contain CIs as chain units. The addition of an −OOH group in HHPs to the central carbon atom of CIs is identified as the most energetically favorable channel, with a barrier height strongly dependent on both CI substituent number (one or two) and position (synor anti-). In particular, the introduction of a methyl group into the anti-position significantly increases the rate coefficient, and a dramatic decrease is observed when the methyl group is introduced into the synposition. These findings are expected to broaden the reactivity profile and deepen our understanding of atmospheric SOA formation processes.

Experimentally, Taatjes et al. (2013) studied the kinetics of CH 3 CHOO reactions with H 2 O, SO 2 , and NO 2 and found that the reactivity of anti-CH 3 CHOO toward water and SO 2 is substantially higher than syn-CH 3 CHOO with an upper limit rate coefficient of (1.0 ± 0.4) × 10 −14 cm 3 molecule −1 s −1 .Also, Smith et al. (2015) obtained a similar conclusions for the UV absorption of the CH 2 OO + H 2 O reaction system with the rate coefficient determined as (7.4 ± 0.6) × 10 −12 cm 3 molecule −1 s −1 at 298 K, and it exhibits a large negative T dependence at temperatures from 283 to 324 K. Winterhalter et al. (2001) studied the mechanisms and products of the gas-phase ozonolysis of β-pinene and found that the main products are the excited C9-CI plus HCHO.Moreover, oligomerization reactions of CIs with typical atmospheric species are identified as one of the dominate pathways leading to the formation of highly oxygenated and high-molecular-weight oligomers that have remarkably low vapor pressure, contributing to SOA formation and growth (Bonn et al., 2008;Heaton et al., 2007;Wang et al., 2016;In-omata et al., 2014). For example, Sakamoto et al. (2013) performed laboratory-scale ethylene ozonolysis in a Teflon bag reactor and revealed that the sequential addition of CH 2 OO to hydroperoxides leads to oligomeric hydroperoxides and finally affords SOA.Sadezky et al. (2008) proposed that SOA formation is initiated by the reaction of SCI with an RO 2 radical, followed by the sequential addition of SCIs, and chain termination by reaction with the HO 2 radical.Zhao et al. (2015) studied the ozonolysis of trans-3-hexene in a flow reactor and static Teflon chambers in the absence and presence of an OH or SCI scavenger at 295 ± 1 K, arriving at the same conclusion as above.In particular, oligomers having SCIs as chain units were identified as one of the dominant components of atmospheric SOA and were produced by the sequential addition of C 2 H 5 CHOO to the RO 2 radical.More recently, Wang et al. (2016) investigated the heterogeneous ozonolysis of oleic acid (OL) using an aerosol flow tube and found that reactions of particulate SCIs generate highmolecular-weight oligomers with low volatility that are preferentially partitioned into the particle phase to promote SOA formation.They confirmed that the SCI-based mechanism is the dominant pathway in the formation of high-molecularweight oligomers.
On the other hand, Ehn et al. (2014) reported a large source of low-volatility SOA generated from the ozonolysis of α-pinene and other endocyclic monoterpenes under atmospheric conditions and proposed that the mechanism of extremely low-volatility organic compound (ELVOC) formation is driven by RO 2 autoxidation.The RO 2 autoxidation pathway mainly includes intramolecular hydrogen shift and the sequential O 2 addition steps (Rissanen et al., 2014).Also, several groups obtained similar conclusions that highly oxygenated molecules (HOMs) are produced via RO 2 autoxidation in cyclohexene and terpene ozonolysis systems (Kirkby et al., 2016;Berndt et al., 2018).Moreover, HOMs are major contributors to aerosol particle formation and growth on a global scale (Tröstl et al., 2016;Stolzenburg et al., 2018).Compared with the RO 2 autoxidation pathways, oligomerization reactions involving CIs as the repeat units preserve carbon oxidation state and increase the number of carbon backbone moieties, therefore leading to a large reduction in volatility (Wang et al., 2016).Moreover, oligomerization reaction proceeds over a shorter period of time during the early stage of biogenic SOA formation and growth (Heaton et al., 2007).Therefore, we think that it is essential to investigate the gas-phase Criegee-chemistry-based mechanism of SOA formation and growth.Aplincourt and Ruiz-López (2000) investigated the mechanism of CH 2 OO reactions with CH 2 O, H 2 O, SO 2 , and CO 2 at the CCSD(T) level of theory and found that the reactions with H 2 O, CH 2 O, and SO 2 are preferable, whereas that with CO 2 is unlikely to occur.Because of the high concentration of H 2 O ([H 2 O] ≈ 7.0 × 10 17 molecules cm −3 ) in the atmosphere (Zhang et al., 2014;T. Zhang et al., 2015), reaction with water vapor is the dominant chemical sink (Aplincourt and Ruiz-López, 2000).Also, Ryzhkov and Ariya (2003, 2004, 2006) obtained a similar conclusion that the most energetically favorable pathway of carbonyl oxide reaction with water vapor is the formation of hydroxyalkyl hydroperoxides (HHPs).Kumar et al. (2014) proposed that the gas-phase decomposition of HHPs has two competitive pathways: (i) HO−CI−H → aldehyde or ketone + H 2 O 2 and (ii) HO−CI−H → carboxylic acid + H 2 O.They found that the barrier of an acid-catalyzed former reaction is dramatically lower than that of water-catalyzed and uncatalyzed systems.Aplincourt and Anglada (2003) investigated the unimolecular decay and water-catalyzed decomposition of HHPs generated from isoprene ozonolysis and found that the main products are methyl vinyl ketone (MVK) or methacrolein (MAC) plus H 2 O 2 .Unfortunately, little is known of the reactivity of SCIs toward HHPs generated from reaction with water vapor.Moreover, the effect of substituents on the reactivity of carbonyl oxides is still poorly understood.
Recently, Zhao et al. (2017a) investigated the mechanisms and kinetics of four SCIs reactions with four RO 2 radicals and found that the addition of terminal oxygen in RO 2 to central carbon in SCI is the most kinetically favorable channel.An analogous conclusion was obtained by investigating the reactions of anti-CH 3 CHOO with HO 2 and H 2 O 2 molecules; i.e., the sequential addition of SCIs is a favorable reaction mode for SOA formation (Chen et al., 2017).Vereecken (2017) also investigated the reactions of CH 2 OO with acids and enols using the CCSD(T)//M06-2X/aug-cc-pVTZ method and found that the 1,4-insertion mechanism is preferable.The above milestone investigations provide fundamental insights and lay solid foundations for further studies of the Criegee-chemistry-based mechanism of SOA formation.
In this study, we mainly focus on the gas-phase oligomerization reaction of carbonyl oxides with HHPs, leading to the formation of high-molecular-weight oligomers under atmospheric conditions.This reaction represents the initial step of oligomer formation and growth during alkene ozonolysis and therefore needs to be extensively characterized to gain deeper insights into the fundamental chemical composition of these oligomers in the atmosphere.Moreover, structure-reactivity relationship plays an important role in determining the rates and outcomes of bimolecular processes.Herein, we employ high-level theoretical calculations in conjunction with kinetics analysis to study the mechanisms and kinetics of the reactions of four carbonyl oxides with four HHPs and describe the effects of carbonyl oxide conformations on reaction rate.The carbonyl oxides considered in this work (CH 2 OO, syn-and anti-CH 3 CHOO, and (CH 3 ) 2 COO) are anticipated upon the ozonolysis of ethylene, propylene, isobutene, and 2,3dimethyl-2-butene, while the investigated HHPs are assumed to arise from bimolecular reactions with water vapor in the troposphere.

Computational details
The geometries of all stationary points on a potential energy surface (PES) are optimized and characterized by the M06-2X functional (Zhao and Truhlar, 2006) in combination with the 6-311+G(2df,2p) basis set (Zheng and Truhlar, 2009), since the M06-2X functional allows one to reliably describe the London dispersion energy (Zhao and Truhlar, 2008b) and can produce excellent results in predicting non-covalent interaction energy involving the main-group elements (Zhao et al., 2017a, b;Zhao and Truhlar, 2008a, b).This functional has the best performance for predicting hydrogen bonding, weak interactions, thermochemistry, and kinetics (Zhao and Truhlar, 2008a;Schenker et al., 2011;Ji et al., 2018).Harmonic vibrational frequencies are performed at the same level of theory to verify that the nature of each structure is either a minimum (NIMAG = 0) or a transition state (NIMAG = 1) and to provide the zero-point vibrational energy (ZPVE) corrections.A scale factor of 0.98 is applied to scale all the M06-2X/6-311+G(2df,2p) frequencies to account for the thermodynamic contribution to Gibbs free energy and enthalpy at 298 K and 1 atm (Zheng and Truhlar, 2009).The reactant-product connectivity on either side is established by intrinsic reaction coordinate (IRC) calculations (Fukui, 1981).Then, the single-point energies are calculated at the M06-2X/def2-TZVP level of theory.The predicted free energies are equal to the thermal correction to Gibbs free energies at the M06-2X/6-311+G(2df,2p) level plus the electronic energies obtained at the M06-2X/def2-TZVP level.In order to obtain a better evaluation of the reliability of the M06-2X functional in computing energies, the single-point energies of species included in some selected elementary reactions (R1a-R1d, R3a-R3d and R5a-R5d) are recalculated at the CCSD(T)/6-311+G(2df,2p) level based on the M06-2X/6-311+G(2df,2p) optimized geometries.Furthermore, the basis set superposition error (BSSE) is calculated using the counterpoise method described by Boys and Bernardi (1970) to estimate the stability of the prereactive complexes.The electronic-energy ( E = a ) and freeenergy ( G = a ) barrier comparisons of both approaches for considering and not considering BSSE correction are listed in Table S1 in the Supplement.As shown in Table S1, the contributions of BSSE corrections to the barriers are ∼ 1.4 (CCSD(T)) and ∼ 0.4 (M06-2X) kcal mol −1 , respectively.The mean absolute deviations (MADs) of both approaches are 0.98 ( E The result shows that the M06-2X method in combination with the BSSE correction affords energies similar to those determined by the accurate and well-recognized CCSD(T)-level calculation.Considering the computational costs, the M06-2X/def2-TZVP method is selected to perform the single-point energy calculation for the title reaction system.Finally, the rate coefficients are calculated using a combination of canonical transition state theory (CTST) and an asymmetric Eckart tunneling correction at temperatures between 273 and 400 K (Zhao et al., 2017a;Chen et al., 2017).
As shown in Fig. 5, the CH 2 OO + HO-CH 2 OO-H (Pa 1 ) reaction proceeds according to a two-step mechanism: (i) a fast thermal equilibrium between the reactants and intermediate IM1a and (ii) the addition of CH 2 OO, leading to the formation of product P1a.The whole reaction process is expressed as follows.
The equilibrium coefficient K eq is expressed as Eq. ( 7): where σ is the reaction symmetry number, Q IM (T ), Q A (T ), and Q B (T ) denote the products of electronic, translational, rotational, torsional, and vibrational canonical partition functions for the intermediate and reactants A and B (Mendes et al., 2014), T is the temperature in Kelvin, and G R and G IM are the total free energies of the reactant and complex, respectively.The quantum chemical calculations are executed using the Gaussian 09 program suite (Frisch et al., 2009).Atoms in molecules (AIM) analysis at the bond-critical point (BCP) for the pre-reactive complex and product is performed by using the AIM2000 software (Biegler-König et al., 2000).
The rate coefficients are calculated by implementing the KiSThelP program (Canneaux et al., 2014) 3 Results and discussion

Bimolecular reaction of SCIs with water vapor
Equations ( 8) and ( 9) represent the two types of bimolecular reactions between carbonyl oxides and water vapor.Previous investigations have shown that some carbonyl oxides are largely removed by their reactions with water dimer (Taatjes et al., 2013;Chen et al., 2016b;Chao et al., 2015;Anglada and Solé, 2016) to generate HHPs (Chen et al., 2016a, b;Anglada et al., 2011), which are important atmospheric oxidants initiating vegetation damage (Becker et al., 1990;Kumar et al., 2014).Further mechanistic details of the above reaction can be found in our previous works (Chen et al., 2016a, b).
Figure 1 presents a simplified scheme for the reactions of several distinct carbonyl oxides (CH 2 OO, synand anti-CH 3 CHOO, (CH 3 ) 2 COO) with water dimer to form HHPs. In all cases, each reaction begins with the formation of a strong pre-reactive complex and then surmounts a small barrier that is still lower in energy than the reactants before product generation.Table 1 lists the relative energies of stationary points and the activation energies of elementary reactions.In Fig. 1 and Table 1, labels A, B, C, and D correspond to the relative energies of the pre-reactive complex (RC), transition state (TS), post-reactive complex (PC), and product (P).R1 and R2 denote the synand anti-positions of the substituents, respectively.These four transition states are located by the rotation of two dihedral angles (DO2H4O4H3, DO4H2O3H1).As shown in Table 1, the barrier differences between the computational and literature values that were derived from the CCSD(T)/aug-cc-pVTZ//B3LYP/6-311+G(2df,2p) method (Anglada and Solé, 2016) are 0.5-1.0kcal mol −1 .Such discrepancies may be attributed to the different theoretical method used in computing energies.The barrier of Entry 4 is 3.3 kcal mol −1 , which is lower than the corresponding CCSD(T)/CBS result by 0.5 kcal mol −1 (Anglada and Solé, 2016).The results show that the M06-2X method provides energies similar to those determined by the CCSD(T)-level calculation.Based on the energies given in Table 1, product HHPs (Pa and Pb) are near-isoenergetic conformers differing only in the orientation of the H1 atom along the C 1 -O 3 bond.As mentioned above, HHPs are key reactive intermediates that possess −OH and −OOH functional groups and can therefore sequentially react with carbonyl oxide to generate oligomers.Considering the fact that Pa and Pb are structurally and energetically similar, the former is judiciously selected for studying oligomerization reactions, whereas the latter is merely listed in Figs.S1-S3.
3.2 PES for the reaction of CH 2 OO with HO−CH 2 OO−H CH 2 OO, the simplest Criegee intermediate, originates from the ozonolysis of all exocyclic alkenes, e.g., isoprene, monoterpenes, and sesquiterpenes (Nguyen et al., 2016), which makes its chemistry particularly important for forest and urban environments.The largest sink of CH 2 OO corresponds to its bimolecular reaction with water dimer in the   troposphere, which generates HO-CH 2 OO-H as the dominant product (Kumar et al., 2014;Lewis et al., 2015).Figure 2 shows the schematic PES for the reaction of CH 2 OO with HO-CH 2 OO-H, with the optimized geometries of all stationary points on this PES given in Fig. S4.
Figure 2 shows that the differences between the relative free energies and the electronic energies for all stationary points are significant (∼ 10-24 kcal mol −1 ), implying that the addition reactions of the parent carbonyl oxide with Pa 1 are characterized by obvious contributions of the entropy effect.Similar behaviors are also observed for oligomerization reactions of other carbonyl oxides with HHPs (see Figs. 3-5).The partition function of every vibrational mode involved in the complex IM1a is listed in Table S2.As shown in Table S2, the partition function of the low-frequency vibrational mode (< 200 cm −1 ) is significantly higher than the highfrequency vibrational mode (> 200 cm −1 ), and their contribution is up to 70.5 %.The result implies that the low-frequency vibrational mode contributes to the entropic factor significantly.A similar conclusion is also obtained from the IM2a case (Table S3).Thus, unless otherwise stated, the discussion in the following sections refers to free-energy barriers ( G = a ).The formation of oligomers P2a, P2b, P2c, and P2d (containing CH 2 OO as the repeating unit) is strongly exothermic (> 81 kcal mol −1 ), and the apparent activation energies E app observed for all elementary reactions are negative values, signifying that these reactions are both thermochemically and dynamically feasible under atmospheric condition.Product Pa 1 (HO−CH 2 OO−H) formed in the reaction of CH 2 OO with water dimer has two functional groups (−OH and −OOH), both of which can be involved in addition reactions.The addition reactions of 2CH 2 OO + Pa 1 begin with the formation of loosely bound pre-reactive complexes IM1a and IM1b, with 3.1 and 2.6 kcal mol −1 stability.They are formed by a hydrogen bond between the terminal CH 2 OO oxygen atom and the hydrogen atom of the −OOH group in Pa 1 and a van der Waals (vdW) bond between the central carbon atom of CH 2 OO and the oxygen atom of the −OH group in Pa 1 .The above complexes are immediately converted into products P1a and P1b via transition states TS1a and TS1b with barriers of 8.4 and 11.7 kcal mol −1 , respectively, while the corresponding reaction exothermicities are estimated as 43.4 and 40.5 kcal mol −1 , respectively.The above result shows that the most favorable channel is the addition of the −OOH group of Pa 1 to the parent carbonyl oxide.The detailed mechanism mainly involves the HO−CH 2 OO moiety released from the breaking O−H bond in Pa 1 binding to the central carbon atom of CH 2 OO, and simultaneously the remnant hydrogen atom transfers to the terminal oxygen, leading to product P1a.The electronic density (ρ), Laplacian (∇ 2 ), and the three eigenvalues of the Hessian of the complexes IM1a and IM1b are displayed in Table S4.As shown in Table S4, the ∇ 2 values of all forming bonds (B1(O 5 −H 4 ), B2(O 3 −C 4 ), B3(O 5 −H 3 ), and B1(O 1 −C 4 )) are negative, indicating that they are covalent bonds.The ρ values of B1 and B3 are significantly higher than those of B2 and B4, showing that the bond strength of the former case is higher than the latter case.
The addition pathway opens the door for other subsequent reactions leading to SOA via Criegee chemistry, which may result in aerosol formation and thus impact climate.As pointed out in previous studies (Chen et al., 2016b;Kumar et al., 2014), the thermal unimolecular decay of Pa 1 can occur via two competitive pathways, namely (i) HO−CH 2 OO−H → CH 2 O + H 2 O 2 and (ii) HO−CH 2 OO−H → HCOOH + H 2 O.The barriers of these two pathways in the absence of water and formic acid molecules are 44.7 and 57.9 kcal mol −1 , respectively (Kumar et al., 2014).The result reveals that the formaldehyde-forming channel is preferable.The G = a of the formaldehyde-forming channel in the presence of a single formic acid molecule is 18.5 kcal mol −1 , which is 12.7 and 26.2 kcal mol −1 lower than the water-catalyzed and uncatalyzed reactions.However, since the corresponding barriers are higher than that of the bimolecular reaction with CH 2 OO, the thermal unimolecular decay of HHPs is not taken into consideration in this work.Moreover, the bimolecular reaction of Pa 1 with the OH radical is investigated at the M06-2X/def2-TZVP//M06-2X/6-311+G(2df,2p) level of theory, and the corresponding PES is shown in Fig. S5.As seen from Fig. S5, the hydrogen abstraction reactions between OH and Pa 1 are strongly exothermic and spontaneous, indicating that the occurrence of these reactions in the atmosphere is thermochemically feasible.One can notice that the exothermic reaction RHγ releasing energy is significantly higher than that of RHα and RHβ.The pre-reactive complexes (IMαHa, βH-a, and γ H-a) are formed in the entrance channel and are followed by direct hydrogen abstraction processes leading to the products PHα, PHβ, and PHγ plus H 2 O.The barriers predict TSHα, TSHβ, and TSHγ to be 6.8, 4.8, and 4.4 kcal mol −1 above the energies of the corresponding prereactive complexes IMαH-a, βH-a, and γ H-a.The result again shows that the reaction RHγ is the most energetically favorable channel.One can notice that the barrier of RHγ is lower than that of the corresponding addition reaction R1a 4.0 kcal mol −1 , indicating that the photochemical oxidation of HHPs is important in the atmosphere.In the present study, we mainly focus on the gas-phase reaction mechanism and kinetics of oligomer formation from carbonyl oxide reactions with HHPs.This is because the type of reaction studied is very important for understanding the first step of new particle formation form alkene ozonolysis, particularly in heavily forested areas.
The secondary addition reaction CH 2 OO + P1a is equivalent to the CH 2 OO + Pa 1 reaction and hence features an analogous pathway, i.e., the formation of pre-reactive complexes IM2a and IM2b in entrance channels, followed by the addition of −OH and −OOH groups of P1a to the CH 2 OO central carbon atom to produce P2a and P2b.The barrier heights predict TS2a and TS2b to be −36.3 and −35.9 kcal mol −1 , respectively, below the energies of the separate reactants and 7.1 and 7.0 kcal mol −1 above the energies of the corresponding pre-reactive complexes IM2a and IM2b.The above result shows that these two addition reactions (R2a and R2b) equally contribute to the title reaction system.Compared to the first CH 2 OO addition reaction, the second one features a lower barrier.Finally, the addition reaction CH 2 OO + P1b proceeds via a mechanism fairly similar to those described above for the CH 2 OO + P1a system and is not discussed in detail to avoid redundancy.side of the terminal oxygen (Long et al., 2016).Numerous theoretical studies have proven that the presence of an intramolecular hydrogen bond in the syn-conformer makes it more stable than the anti-conformer (Anglada et al., 2011;Anglada and Solé 2016).The interconversion of these two conformers via rotation around the C−O bond has a very high barrier (∼ 42 kcal mol −1 ), which implies that one can treat synand anti-CH 3 CHOO as independent species existing in the atmosphere (Yin and Takahashi, 2017).Long et al. (2016) proposed that the predominant pathway of the unimolecular decay of syn-CH 3 CHOO is isomerization to vinyl hydroperoxide (VHP) via hydrogen atom migration from the methyl group to the terminal oxygen atom, then the decomposition of VHP produces the OH radical.Also, Donahue et al. (2011a) obtained a similar conclusion that syn-CI isomerization to VHP is preferable due to the low ring strain of the H-atom transfer transition state.Both the prompt decay and thermal unimolecular decay of the energized VHP may dissociate to the OH radical, and their yields are strongly pressure and temperature dependent (Kroll et al., 2001a, b).The preferable route of unimolecular decay of anti-CH 3 CHOO is ring closure to dioxirane via an oxygen atom transfer (Donahue et al., 2011a;Taatjes et al., 2013;Long et al., 2016).The dioxirane can finally isomerize to acetic acid via the "hot acid" channel (Kroll et al., 2001b).Alternatively, synand anti-CH 3 CHOO may undergo bimolecular reactions with water vapor, leading to the formation of HO−C(CH 3 )HOO−H (Anglada et al., 2011).The energy diagram of addition reactions between CH 3 CHOO and HO−C(CH 3 )HOO−H is given in Fig. 3.The optimized geometries of all stationary points are shown in Figs.S6 and S7.

PES for the reaction of CH
Figure 3a demonstrates that the sequential additions of anti-CH 3 CHOO to Pa 2 are strongly exothermic and spontaneous, indicating that the occurrence of these consecutive reactions in the atmosphere is thermochemically feasible.The addition reactions of 2-anti-CH 3 CHOO + Pa 2 start with the barrierless formation of pre-reactive complexes IM3a and IM3b held together by weak hydrogen bonds and vdW forces.Subsequently, the −OH and −OOH fragments in Pa 2 immediately add to the central carbon atom of anti-CH 3 CHOO to produce P3a and P3b.The barriers of these two addition reactions are 5.8 and 8.3 kcal mol −1 with the concomitant release of 39.5 and 34.1 kcal mol −1 of energy.This result confirms that the most favorable channel, both thermochemically and dynamically, corresponds to the −OOH group addition pathway.Notably, the above reaction barriers are lower than that of the 2CH 2 OO + Pa 1 system by ∼ 3.0 kcal mol −1 , indicating that anti-CH 3 CHOO is significantly more reactive than the parent carbonyl oxide.This finding is further corroborated by the results of Anglada and Solé (2016) and Chen et al. (2017), who found that CH 2 OO is significantly less reactive than anti-CH 3 CHOO towards H 2 O, HCOOH, and CH 3 COOH.
The addition reaction anti-CH 3 CHOO + Pa 2 results in the formation of P3a, which can subsequently react with anti-CH 3 CHOO via channels R4a and R4b.Both of these pathways start with the formation of pre-reactive complexes IM4a and IM4b in entrance channels, followed by the addition of −OH and −OOH groups of P3a to the central carbon atom of anti-CH 3 CHOO to produce P4a and P4b.According to the predicted barrier heights, TS4a and TS4b are 6.8 and 16.0 kcal mol −1 above complexes IM4a and IM4b, re- spectively, which reconfirms that the most favorable reaction channel is the −OOH group addition pathway.
At this point, it is worth noting that the addition reactions in the 2-syn-CH 3 CHOO + Pa 2 system proceed through a similar mechanism and are thus only briefly discussed in the following section.As revealed by Fig. 3b, both R5a and R5b pathways start with the formation of vdW complexes IM5a and IM5b, which are spontaneously converted into products P5a and P5b.The barriers of these two addition reactions are estimated as 12.1 and 11.5 kcal mol −1 , respectively, and are therefore significantly higher than those calculated for the comparable 2-anti-CH 3 CHOO + Pa 2 system.This discrepancy is ascribed to the fact that the steric repulsion between the methyl group and the terminal oxygen in syn-CH 3 CHOO results in decreased hydrogen transfer ability and hinders the formation of pre-reactive complexes.
The above result is further supported by recent reports, which claim the syn-conformer to be substantially less reac-tive than the anti-conformer toward key atmospheric species, such as H 2 O, SO 2 , and NO 2 (Taatjes et al., 2013;Anglada et al., 2011;Sheps et al., 2014).The lowest-energy channel among the P5a-P5b + syn-CH 3 CHOO reaction pathways, TS6a, involves the addition of the −OOH group with a barrier of only 10.1 kcal mol −1 and a large exothermicity of ∼ 40 kcal mol −1 .
3.4 PES for the reaction of (CH 3 ) 2 COO with HO−(CH 3 ) 2 COO−H The dimethyl-substituted Criegee intermediate, (CH 3 ) 2 COO, is generated in the ozonolysis of 2,3-dimethyl-2-butene (Lester and Klippenstein, 2018;Drozd et al., 2017).Long et al. (2018) proposed that the unimolecular decay of (CH 3 ) 2 COO is the predominant pathway above 240 K, whereas it can compete with the reaction (CH 3 ) 2 COO + SO 2 below 240 K. Drozd et al. (2017) elucidated the fact that tunneling for both the thermal and prompt unimolecular decay of (CH 3 ) 2 COO is significant.Also, Lester and Klippenstein (2018) obtained a similar conclusion in the unimolecular decay of (CH 3 ) 2 COO to the OH radical reaction that the contribution of tunneling to unimolecular decay rates is significant.Alternatively, (CH 3 ) 2 COO may react with water vapor, leading to the formation of HO−C(CH 3 ) 2 OO−H (Anglada and Solé, 2016).The PES of addition reactions (CH 3 ) 2 COO + HO−C(CH 3 ) 2 OO−H is given in Fig. 4, and the optimized geometries of all stationary points are shown in Fig. S8.
As shown in Fig. 4, the vdW complexes IM7a and IM7b are 4.6 and 4.5 kcal mol −1 lower in energy than the reactants, while the corresponding transition states TS7a and TS7b leading to products P7a and P7b are 9.9 and 13.6 kcal mol −1 higher in energy than the respective complexes.The formations of P7a and P7b are strongly exothermic, with reaction energies of 31.0 and 25.8 kcal mol −1 .Again, this result shows that the addition of the −OOH group in Pa 3 to the central carbon atom of (CH 3 ) 2 COO is both thermochemically and dynamically favorable.Compared with the barriers of the 2-anti-CH 3 CHOO + Pa 2 system given in Fig. 3a, one can notice that the dimethyl-substituted parent carbonyl oxide leads to the barrier increasing by ∼ 4 kcal mol −1 .The secondary addition reaction (CH 3 ) 2 COO + P7a is found to be similar to that described for the (CH 3 ) 2 COO + Pa 3 system.The prereactive complexes IM8a and IM8b are formed in entrance channels with over 4.5 kcal mol −1 stabilization energies, followed by the addition of −OH and −OOH groups in P7a to the central carbon atom of (CH 3 ) 2 COO to generate P8a and P8b.According to the predicted barrier heights, TS8a and TS8b are 11.5 and 12.5 kcal mol −1 above complexes IM8a and IM8b, respectively, which shows that the second addition reactions R8a and R8b are nearly equally accessible.

PES of distinct SCI reactions with HO−CH 2 OO−H
To gain deeper insights into the substituent-influenced modification of atmospheric oligomer composition, one should elucidate the origin of the substituent influence on the reactivity and kinetics of carbonyl oxides.Therefore, an understanding of structure-reactivity relationships is important for determining bimolecular processes and reaction products.Since the addition of the −OOH group to the central carbon atom of SCIs is shown to be both thermochemically and dynamically preferable, this type of addition reaction is selected to study the effect of substituents on the reactivity of carbonyl oxides.The PES of addition reaction SCIs + HO−CH 2 OO−H is given in Fig. 5, whereas those for bimolecular reactions with other HHPs are displayed in Figs.S9-S11.
As shown in Fig. 5, each reaction begins with the formation of a strong pre-reactive complex and then surmounts a medium barrier that is higher in energy relative to the reactants before forming the corresponding products.The bimolecular reaction of CH 2 OO with HO−CH 2 OO−H to form P1a (HO−(CH 2 OO) 2 −H) is characterized by a barrier of 8.4 kcal mol −1 and an exothermicity of 43.4 kcal mol −1 .Hence, the small barrier and large stability of the hydroperoxide species imply that its formation is both thermochemically and kinetically favored.Notably, the introduction of a methyl group at the anti-position reduces the barrier by ∼ 1.0 kcal mol −1 relative to that of the CH 2 OO + HO−CH 2 OO−H system, whereas the corresponding synand dimethyl substitutions increase the above barrier by 4.2 and 3.2 kcal mol −1 , respectively.These results indicate that the anti-conformer is substantially more reactive toward HO−CH 2 OO−H than syn-, dimethyl, and parent conformers in the atmosphere.A similar conclusion has been obtained by studying the reactions of synand anti-CH 3 CHOO with water and SO 2 ; i.e., the rate coefficient of the anti-CH 3 CHOO reaction was calculated to be 1 to 2 orders of magnitude higher than that of the syn-CH 3 CHOO system (Taatjes et al., 2013;Lin et al., 2016;Huang et al., 2015;Anglada and Solé, 2016).Therefore, it is concluded that the position and number of methyl groups significantly affect barrier heights and reaction rates.On the other hand, the exothermicities of other reaction pathways are lower than that of the parent system, which implies that methyl substitution is thermochemically unfavorable.A similar trend is observed for the bimolecular reactions of SCIs with other HHPs (Figs.S9-S11).In order to avoid redundancy, we do not repeat them here in detail.

Kinetics and implications in atmospheric chemistry
To better understand the effect of substituents on reaction kinetics, the rate coefficients of distinct SCI reactions with HO−CH 2 OO−H (Pa 1 ) are computed using a combination of canonical transition state theory (CTST) and an asymmetric   Eckart tunneling correction based on free energies obtained at the M06-2X level in the temperature range from 273 to 400 K.And the different conformers of stationary points in the kinetics study are taken into account, with the results listed in Tables 2 and S5-S8.In order to assess the reliability of our kinetics study, the rate coefficients of some selected reactions (R1a and R9) are recomputed employing the canonical variational transition state theory (CVTST) with Eckart tunneling correction.The calculated result is listed in Table S9.As shown in Table S9, the difference between k CTST(R1a) and k CVTST(R1a) decreases in the range of 2.3 (273 K) to 1.8 (400 K).Such rate coefficient discrepancies between CTST and CVTST are acceptable.A similar conclusion is also obtained from the rate coefficients between k CTST(R9) and k CVTST(R9) .It is concluded that the CTST-Eckart method allows one to reliably describe the kinetics parameters.Table 2 shows that the predicted rate coefficients for the reaction of CH 2 OO with HO−CH 2 OO−H(R1a) decrease with increasing temperature, with a similar trend observed for the syn-CH 3 CHOO(R9), anti-CH 3 CHOO(R10), and (CH 3 ) 2 COO + HO−CH 2 OO−H(R11) systems.The above behavior is ascribed to the fact that the apparent activation barriers E app of these four addition reactions are significantly negative, as previously observed for the reaction of CH 3 O 2 with BrO (Shallcross et al., 2015).As shown in Table S5, the rate coefficients of CH 2 OO + P1a, CH 2 OO + P1b, CH 2 OO + P1c, and CH 2 OO + P1d reactions decrease with increasing temperature, indicating that oligomer formation from CH 2 OO reactions with HHP is preferable under low temperature conditions.Similar conclusions are also obtained from the anti-CH 3 CHOO + P3x (Table S6), syn-CH 3 CHOO + P5x (Table S7), and (CH 3 ) 2 CHOO + P7x (Table S8) systems.In order to avoid redundancy, we do not repeat them here in detail.Considering the errors of the computed free-energy barriers, the uncertainty in the rate coefficient is estimated within an order of magnitude.
The obtained data show that the rate coefficient depends on the relative position and number of methyl groups in the parent carbonyl oxide; e.g., the rate coefficient increases by 2 orders of magnitude when methyl substitution occurs at the anti-position, whereas a reduction by 4-6 orders of magnitude is observed for methyl substitution at the syn-position.Thus, the relative position of the methyl group plays an important role in determining SCI reactivity; in particular, antisubstitution promotes reaction with HHPs and accelerates the formation of oligomers in the atmosphere.Anglada et al. (2011) and Anglada and Solé (2016) arrived at the same conclusion by studying the reactions of SCIs with water vapor, showing that the anti-conformer is significantly more reactive than the parent carbonyl oxide and the syn-conformer.On the other hand, the introduction of two methyl groups does not result in a marked rate coefficient change compared to the parent system, since the addition reaction R11 is mediated by the pre-reactive hydrogen-bonded complex.
As discussed above, the anti-CH 3 CHOO + HO−CH 2 OO−H (Pa 1 ) reaction (R9) is preferred over the other three pathways (R1a, R10, and R11).Therefore, it would be interesting to investigate whether the anti-CH 3 CHOO + Pa 1 reaction can compete well with the anti-CH 3 CHOO + (H 2 O) 2 (R12) system because the latter reaction is the dominant chemical sink (Taatjes et al., 2013;Anglada and Solé, 2016).The ratio of the reaction rates of R9 and R12 is expressed as follows.
The room temperature rate coefficient k R9 is 1.5 × 10 −9 cm 3 molecule −1 s −1 , assuming that the concentration of Pa 1 is approximately equal to that of SCIs (∼ 5.0 × 10 4 molecules cm −3 , within an order of magnitude uncertainty) in the boreal forest and rural environments of Finland and Germany (Novelli et al., 2017).The atmospheric lifetime of anti-CH 3 CHOO reactivity toward Pa 1 can be estimated as 1.3-13 × 10 3 s.The experimental rate coefficient of reaction R12 approximately equals ∼ 1.0 × 10 −11 cm 3 molecule −1 s −1 at 298 K (Lin et al., 2016).The concentration of water dimer is 5.5 × 10 13 molecules cm −3 at 3 km of altitude (Long et al., 2016).The atmospheric lifetime of anti-CH 3 CHOO reactivity toward water dimer is 1.8 × 10 −3 s.The result implies that the reactions studied are minor loss processes in the atmosphere.However, [(H 2 O) 2 ] decreases significantly with increasing altitude (Long et al., 2016).For example, at 15 km of altitude, [(H 2 O) 2 ] is 2.7 × 10 6 molecules cm −3 , the atmospheric lifetime of anti-CH 3 CHOO is 3.4 × 10 4 s.As discussed above, the anti-CH 3 CHOO + Pa 1 reaction can compete with the anti-CH 3 CHOO + (H 2 O) 2 system in some regions where the altitude is above 15 km.The ν R9 /ν R12 ratio is less than 1.4 % when [(H 2 O) 2 ] is ∼ 10 13 molecules cm −3 , meaning that the anti-CH 3 CHOO + Pa 1 reaction is a minor loss process in the atmosphere.However, [(H 2 O) 2 ] is very low at the altitude above 15 km, and the anti-CH 3 CHOO + Pa 1 reaction can compete well with the anti-CH 3 CHOO + (H 2 O) 2 reaction, thus contributing to the formation and growth of SOA.Kumar et al. (2014)  values in the presence of a single water molecular are 31.2and 47.8 kcal mol −1 , respectively, which are 13.5 and 10.2 kcal mol −1 lower than the uncatalyzed reactions.The result reveals that the formaldehyde-forming channel is preferable in the absence and presence of water molecules, and the role of water catalysis on the gas-phase decomposition of Pa 1 is significant.The G = a of the bimolecular reaction of anti-CH 3 CHOO with Pa 1 is 7.3 kcal mol −1 , which is 23.9 kcal mol −1 lower than the formaldehyde-forming channel.It is concluded that the Pa 1 + H 2 O reaction is less competitive compared to the anti-CH 3 CHOO + Pa 1 system.

Conclusions
The gas-phase reaction mechanism and kinetics of Criegee intermediate reactions with HHPs are studied using quantum chemical methodologies in conjunction with statistical theory calculations.The main conclusions are summarized as follows.
1. Oligomerization reactions of SCIs with HHPs are strongly exothermic and spontaneous, signifying that consecutive reactions are thermochemically feasible in the atmosphere.
2. The addition of the −OOH group in HHPs to the central carbon atom of SCIs is both thermochemically and dynamically preferable compared with the −OH group addition pathway.
3. The reaction barrier and kinetics strongly depend on both the number of substituents in the Criegee intermediate and its position (syn-or anti-).
4. The rate coefficients show a significant increase when adding a methyl group on the anti-position, whereas they display a dramatic decrease on the syn-position.On the other hand, the addition of the dimethyl group does not cause much variation in the rate coefficients.
Data availability.All of the research data have been included in the supplement, which are available on the EGU Publications website at https://doi.org/10.5194/acp-19-1-2019(Fu et al., 2019).Author contributions.LC designed the study.LC and YH wrote the paper.LC performed theoretical calculations.YX, ZS, JC, and WW analyzed the data.All authors reviewed and commented on the paper.
Competing interests.The authors declare that they have no conflict of interest.

Figure 1 .
Figure 1.Schematic PES for the bimolecular reaction of SCIs with water dimer.
proposed that the gas-phase decomposition of Pa 1 has two com-petitive pathways: (i) HO−CH 2 OO−H → CH 2 O + H 2 O 2 and (ii) HO−CH 2 OO−H → HCOOH + H 2 O.The G = a