A potential source of atmospheric sulfate from O2-induced SO2 oxidation by ozone

It was formerly demonstrated that O2SOO forms at collisions rate in the gas-phase as a result of SO2 reaction with O2. Hereby, we present a theoretical investigation of the chemical fate of O2SOO by reaction with O3 in the gas-phase, based on ab initio calculations. Two main mechanisms were found for the title reaction, with fundamentally different products: (i) formation of a van der Waals complex followed by electron transfer and further decomposition to O2 + SO2 + O3 and (ii) formation of a molecular complex from O2 switching by O3, followed by SO2 oxidation to SO3 within the complex. Both 10 reactions are exergonic, but separated by relatively low energy barriers. The products in the former mechanism would likely initiate other SO2 oxidations as shown in previous studies, whereas the latter mechanism closes a path wherein SO2 is oxidized to SO3. The latter reaction is atmospherically relevant since it forms the SO3 ion, hereby closing the SO2 oxidation path initiated by O2. The main atmospheric fate of SO3 is nothing but sulfate formation. Exploration of the reactions kinetics indicates that the path of reaction (ii) is highly facilitated by humidity. For this path, we found an overall rate constant of 15 4.0×10 cm molecule s at 298 K and 50% relative humidity. The title reaction provides a new mechanism for sulfate formation from ion-induced SO2 oxidation in the gas-phase and highlights the importance of including such mechanism in modelling sulfate-based aerosol formation rates. Atmos. Chem. Phys. Discuss., https://doi.org/10.5194/acp-2018-1111 Manuscript under review for journal Atmos. Chem. Phys. Discussion started: 5 November 2018 c © Author(s) 2018. CC BY 4.0 License.

The sulfate radical ion is believed to react with unsaturated compounds to form organosulfates, a major component of secondary organic aerosol (Surratt et al., 2007;Surratt et al., 2008;Schindelka et al., 2013). Using first-principles calculations, it was demonstrated that SO4acts as a catalyst in SO2 oxidation to SO3 by O3 in the gas-phase and hence, plays a role in atmospheric aerosol formation (Tsona et al., 2015;Tsona et al., 2016). The chemistry of O2SOOis largely unknown but, is potentially important for sulfur chemistry and atmospheric aerosol formation. Fehsenfeld and Ferguson found that O2SOO -5 can be decomposed by NO2 into NO3and SO3 (Fehsenfeld and Ferguson, 1974) and it was formerly demonstrated that in the presence of nitrogen oxides (NOx = NO2 + NO), O2SOOcan be converted into sulfates (Tsona et al., 2018). In mildly polluted environments, the concentration of O3 can be few orders of magnitude higher than that of NOx and the chemical fate of O2SOOwould then also greatly depend on collisions with O3. in such environments, O2SOOcould experience much more collisions with O3 than with NOx. 10 Hereby, we investigate the reaction between O2SOO -•••(H2O)0-1 and O3 using ab initio calculations. By determining the reactions thermodynamics and kinetics, we examine the possible pathways for the reaction and propose the most probable outcome of O2SOO -•••(H2O)0-1 based on O3 reaction. Implications of the most relevant pathways in aerosol formation are discussed. 15

Geometry optimizations, thermochemical and charge analysis
All molecules and stationary points in the energy surface were optimized using density functional theory (DFT) based on the M06-2X density functional (Zhao and Truhlar, 2008), and the aug-cc-pVTZ basis set (Dunning Jr et al., 2001). This functional has successfully proven to be adequate for reactions involving transition state (TS) configurations (Elm et al., 2012(Elm et al., , 2013b. 20 Harmonic vibrational frequencies analysis on the optimized structures were performed (at 298 K and 1 atm) using the M06-2X/aug-cc-pVTZ method under the harmonic oscillator-rigid rotor approximation. These calculations ensured that the obtained stationary points were minima or TS and, also, provided the thermal contributions to the Gibbs free energy and the enthalpy.
Transition states structures were initially located by scanning the reactants configurations. The best TS guesses out of the scans 25 were then refined using the synchronous transit quasi Newton method (Peng et al., 1996), and the final TS structures underwent internal reaction coordinate calculations (Fukui, 1981) to ensure they connected the reactants to desired products.
The electronic energies of the M06-2X/aug-cc-pVTZ optimized geometries were corrected with the CCSD(T) method (Purvis and Bartlett, 1982) in conjunction with the aug-cc-pVTZ basis set. The Gibbs free energies, G, of all relevant species were 30 then calculated as Atmos. Chem. Phys. Discuss., https://doi.org/10.5194/acp-2018-1111 Manuscript under review for journal Atmos. Chem. Phys. Discussion started: 5 November 2018 c Author(s) 2018. CC BY 4.0 License.
where ECCSD(T) is the electronic energy calculated with the CCSD(T)/aug-cc-pVTZ method and Gtherm is the thermal contribution to the Gibbs free energy, calculated at the M06-2X/aug-cc-pVTZ level of theory. All geometry optimizations, harmonic vibrational frequencies analysis and electronic energies correction calculations were carried out in the Gaussian 09 5 package (http://gaussian.com/).
To analyse the distribution of the excess electronic charge over different species and fragments in the optimized systems, we used the Atoms-in-Molecules charge partitioning method presented by Bader (Bader, 1998). As input, this method requires electronic density and nuclear coordinates from electronic structure calculations. We used the approach implemented in the algorithm developed by Henkelman and co-workers, which has been shown to work well both for charged and water-containing 10 systems (Tang et al., 2009;Bork et al., 2011;Henkelman et al., 2006).

Reactions kinetics
Regardless of the presence of water, the reaction between O2SOOand O3 begins by forming different van der Waals prereactive intermediates, depending on the orientation of the reactants at impact. The pre-reactive intermediate could either decompose to different species or react further through a transition state configuration to form new products: 15 The traditional approach to determine the rate constant of reaction (R1) relies on the steady-state approximation and leads to the following equation: 20 where kcoll is the collision frequency for O2SOO --O3 collisions, kevap is the rate constant for the evaporation of the pre-reactive intermediate back to initial reactants, and kreac is the unimolecular rate constant for the reaction of the pre-reactive intermediate 25 to the products. Moreover, assuming that kevap >> kreac, the rate constant of reaction (R1) becomes k = Keqkreac over a range of temperatures, with Keq being the equilibrium constant of formation of the pre-reactive intermediate from the reactants. This consideration is, however, not valid for barrierless reactions, since the pre-reactive intermediate seldom thermally equilibrates.
For such reactions, a two-transition state theory has been introduced, treating two distinct transition state bottlenecks that define the net reactive flux (Klippenstein et al., 1988;Georgievskii and Klippenstein, 2005;Greenwald et al., 2005). The first 30 bottleneck, the "outer" transition state, occurs in the association of the initial reactants to form the pre-reactive intermediate, whereas the second bottleneck, the "inner" transition state, occurs in the transformation of the pre-reactive intermediate to the products. Based on this theory, the overall rate constant (k) for a reaction channel is expressed in terms of the outer (kout) and inner (kin) rate constants as: The outer transition state is treated by the long-range transition state theory approach , while the inner transition state is resolved by the transition state theory. It has been demonstrated that for interactions between ions and neutral molecules, due to their long-range attraction, the collision cross section is larger than would be measured from the physical dimensions of the colliding species (Kupiainen-Määttä et al., 2013). To account for this phenomenon, the outer rate constant was determined from the ion-dipole parametrization of Su and Chesnavich who performed trajectory simulations 10 of collisions between a point charge and a rigidly rotating molecule (Su and Chesnavich, 1982). This parametrization is equivalent to a Langevin capture rate constant (kL) scaled by a temperature-dependent term and was found to provide good agreement with experiments (Kupiainen-Määttä et al., 2013). It is given as where kL = qμ −1/2 (πα/ε0) 1/2 , x = μD/(8πε0αkBT) 1/2 , q is the charge of the ion, μ is the reduced mass of the colliding species, ε0 is the vacuum permittivity, α and μD are the polarizability and dipole moment of the neutral molecule, kB is Boltzmann's constant, and T is the absolute temperature. The inner rate constant can be written as: where ΔG # is the Gibbs free energy barrier separating the pre-reactive intermediate and the products, h is the Planck's constant, R is the molar gas constant, and c 0 is the standard gas-phase concentration.
These optimizations led to two main chemical processes, depending on the initial orientation of the reactants, with potentially different outcomes. The first process is the formation of a van der Waals complex followed by its direct decomposition to other 30 Atmos. Chem. Phys. Discuss., https://doi.org /10.5194/acp-2018-1111 Manuscript under review for journal Atmos. Chem. Phys. Discussion started: 5 November 2018 c Author(s) 2018. CC BY 4.0 License.
species. The second process is the barrierless formation of a molecular complex in which the SO2 entity of O2SOO -•••(H2O)0-1 is oxidized to SO3 -.

Cluster formation and decomposition of O2SOO -•••(H2O)0-1
As O3 approaches O2SOO -•••(H2O)0-1 towards the oxygen atoms of the peroxy fragment or the oxygen atom of the SO2 entity, the immediate outcome of O2SOO -•••(H2O)0-1 and O3 collisions is the formation of the van der Waals O3•••O2SOO -•••(H2O)0-1 5 complex in which O3 interacts with O2SOO -. Among the different stable configurations found upon optimizations, we solely report the most stable one with respect to the Gibbs free energy, which is henceforth denoted RC1 and RCW1 for the unhydrated and monohydrated, respectively, shown in Fig. 1. Exploration of RC1 and RCW1 structures reveals that O2SOO -•••(H2O)0-1 basically keeps its configuration upon clustering with O3. Their formations are endergonic at most atmospheric temperature, with Gibbs free energy changes of 4. 5 and 4.7 kcal mol -1 , respectively, at 298 K. These values indicate that, 10 when formed, these complexes would not live long and will rather decompose either to initial reactants or to different species.
Inspecting the vibrational modes of RC1 and RCW1, two vibrations are found that would clearly lead to the dissociation of O2SOOwithin the cluster. The analysis of the charge distribution over O3•••O2SOO -•••(H2O)0-1 shows that the extra electron initially located on O2SOO in the reactants has partially migrated to the O3 molecule in the van der Waals product complex, as can be observed in Fig. S2. This is as expected, given the high electronegativity of O3 relative to those of O2 and SO2 (Rothe 15 et al., 1975). The charge distribution over the different atoms of the optimized complex is weakly affected by the presence of water, as previously demonstrated by Bork and co-workers (Bork et al., 2011).
The most likely fates of RC1 and RCW1 are, therefore, decomposition into O2, SO2 and O3as follows: The numerical values of the formation energies of all intermediate species in reaction (R2) are given in Table 1 and the energy surfaces are plotted in Fig. 2. RC1 and RCW1 decompositions are highly exergonic at 298 K, occurring with -18.1 and -16.7 kcal mol -1 Gibbs free energy changes, respectively. These processes are, therefore, likely to occur in the atmosphere upon The limiting step in reaction (R2) is the formation of RC1 and RCW1, whose formation energies indicated above can then be considered as the only barrier to the formation of O2 + SO2 + O3 -. This leads to overall rate constants (according to Eq. 5) of 1.4×10 -10 and 9.9×10 -11 cm 3 molecule -1 s -1 at 298 K for the unhydrated and monohydrated reaction, respectively. Both reactions are, in principle, collision-limited and the effect of hydration on the kinetics is found to be negligible. The atmospheric 30 relevance of reaction (R2) has been determined earlier (Bork et al., 2012;Bork et al., 2013;Enghoff et al., 2012).

O2SOO -•••(H2O)0-1 reaction with O3
When O3 approaches O2SOO -•••(H2O)0-1 from the sulfur atom side, the formation of a more stable cluster than found above prevails. The incoming O3 molecule strongly interacts with O2SOO -•••(H2O)0-1 by forming a coordination bond with the sulfur atom and hereby, inducing the ejection of the O2 molecule that remains in interaction with the remainder of the system. This process leads to the formation of the O2•••O2S-O3 -•••(H2O)0-1 complex which further transforms, through an intramolecular SO2 5 oxidation, into SO3 -•••(H2O)0-1 + 2O2 according to the following equation: The configurations of the most stable intermediate structures in reaction (R3) are given in Fig. 1. The charge analysis indicated 10 that the oxygen molecules released in the products are in the singlet state. Though the necessity to determine the electronic structure of the O2 molecule in the singlet sate ( 1 Δg) has been demonstrated to be useful (Buttar and Hirst, 1994), obtaining a reliable electronic energy for O2( 1 Δg) is difficult (Drougas and Kosmas, 2005). An alternative approach to determine this energy is to add the experimental energy spacing (22.5 kcal mol -1 ) between triplet and singlet states of O2 to the computed electronic energy of the triplet O2 (Schweitzer and Schmidt, 2003;Drougas and Kosmas, 2005). We used this approach to 15 determine the energies of the products of reaction (R3). The numerical values of the formation energies of all intermediate species in reaction (R3) are thus given in Table 1  The formations of RC2 and RCW2 are highly exergonic, with Gibbs free energy changes at 298 K of -14.7 and -12.4 kcal mol -1 , respectively. These values, with corresponding electronic energies and enthalpies are shown in Table 1. These Gibbs free energy changes for the formation of RC2 and RCW2 are about 19 kcal mol -1 lower than those of RC1 and RCW1 at similar conditions, indicating the higher stability of RC2 and RCW2, and the highly favourable switching reaction at ambient and TSW2 for the unhydrated and monohydrated systems, respectively, and their structures are presented in Fig. 1. While RC2 and RCW2 are formed with similar Gibbs free energies within 2 kcal mol -1 difference, the formation Gibbs free energies of their transition states at similar conditions greatly differ. TS2 is located at 10 kcal mol -1 Gibbs free energy above RC2, while TSW2 is located at -4 kcal mol -1 below RCW2. It is speculated that the low energy barrier in the monohydrated reaction is the result of a strong stabilisation of the transition state due to hydration. The S-O3 bonds in RCW2 and TSW2 are shorter by 5 ~0.03 Å than in RC2 and TS2.
Based on TS2 and TSW2 energies, the unimolecular decomposition of O2•••O2S-O3at 298 K was found to occur at rate constants of 3.1×10 5 s -1 and 6.5×10 15 s -1 , corresponding to atmospheric lifetimes of 3.3×10 3 ns and 1.5×10 -7 ns for the unhydrated and monohydrated systems, respectively. The obtained short lifetimes indicate that O2•••O2S-O3would not live 10 long enough to experience collisions with other atmospheric oxidants. It should be noted that few to no collisions with nitrogen can, however, be achieved. It follows that the most likely outcome of O2•••O2S-O3is decomposition to the products of reaction (R3), which are formed with about -23 kcal mol -1 overall Gibbs free energy at 298 K. The net reaction is an O2 --initiated SO2 oxidation to SO3by O3.

15
The charge analysis clearly indicates that the extra electron, initially confined on the atoms of the O3 fragment of O2•••O2S-O3 (RC2 structure), is partially distributed over other atoms in the transition state (TS2) and is finally located on SO3 in the product (see Fig. 3). Apparent also from Fig. 3 is the antibonding orbital of the singlet O2 molecule.
The overall rate constants of reaction (R3), determined at 298.15 K using Eq. (3), are 1.3×10 -14 and 8.0×10 -10 cm 3 molecule -1 20 s -1 for the unhydrated and monohydrated reactions, respectively. The values of the different components (kout and kin) are listed in Table S1 of the Supplement. It is observed from Table S1 that the inner transition sate provides the dominant bottleneck to the rate constant of the unhydrated reaction, whereas the outer transition state provides the dominated bottleneck to the rate constant of the monohydrated reaction.

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The effective effect of water on the rate constant can be evaluated by taking into account the stability of O2SOO -•••H2O (which is formed at the entrance channel of the reaction in the presence of water before colliding with O3) and the equilibrium vapor pressure of water. Starting from the definition of the reaction rate for the hydrated reaction, At 298 K and 50 % relative humidity, the effective rate constant of the monohydrated reaction is 1.7×10 -10 cm 3 molecule -1 s -1 , 5 four orders of magnitude higher than the rate constant of the unhydrated reaction. Therefore, water plays a catalytic role on the kinetics of reaction (R3). The net rate constant of reaction (R3) can be obtained by weighing the rate constants of the unhydrated and monohydrated reactions to corresponding equilibrium concentrations of O2•••O2S-O3hydrates. Using the law of mass action, we find that O2•••O2S-O3mostly exists as a dry species, constituting 77% of the total population, whereas the monohydrated species is formed at 23%. The net rate constant of reaction (R3) is then determined to be 4.0×10 -11 cm 3 molecule -10 1 s -1 at 298 K.
Considering only the unhydrated process of reaction (R3), the rate constant is 4-5 orders of magnitude lower than the rate constant obtained for the SO2 + O3 -→ SO3 -+ O2 reaction (Fehsenfeld and Ferguson, 1974;Bork et al., 2012). Despite this difference, the oxidation process follows a similar mechanism to the one presented by Bork et al. for the SO2 + O3 -→ SO3 -+ 15 O2 reaction, consisting of the oxygen transfer from O3 to SO2 (Bork et al., 2012). The discrepancy between the two results is associated with the effect of the presence of the O-O fragment initially coordinated to SO2 in the current study, which tends to stabilize the O2•••O2S-O3pre-reactive complex. The presence of the O-O fragment seemingly deactivates SO2 for the upcoming O transfer from O3 to form SO3 -. However, this situation is rapidly reversed with the presence of water as the reaction becomes much faster, proceeding nearly at collision rate. 20

Further chemistry
In real atmospheric and ionized conditions, despite O2 has lower electron affinity than O3, it would likely ionize faster than O3 owing to its much higher concentration. Considering for example chamber experiments, upon interaction of ionizing particles with the gas, electrons can transfer from one species to another and, e.g., O2can form and rapidly hydrate within one 25 nanosecond (Svensmark et al., 2007;Fahey et al., 1982). Furthermore, Fahey et al. showed that O2 -•••(H2O)0-1 association reaction with SO2 is faster than the electron transfer from O2 -•••(H2O)0-1 to O3 (Fahey et al., 1982). This means that in an ionized environment containing O2, O3, and SO2, the formation of O2SOOresulting from SO2 and O2association will happen faster than O3formation. O2SOOwould react thereafter with O3 and the following stepwise process could take place The Gibbs free energy change of this net reaction at 298 K is about -20 kcal mol -1 more negative than that of the SO2 + O3 -→ SO3 -+ O2 reaction at similar conditions. Given that the intermediate steps of reaction (R4) are significantly fast, this reaction 5 is believed to be an important process in most environments of SO2 ion-induced oxidation to SO3or more oxidized species.
The limiting step in the process of reaction (R4) is reaction (R4c) for which an energy barrier has to be overcome before the products are released. SO3is an identified stable ion detected in the atmosphere and in experiments (Ehn et al., 2010;Kirkby et al., 2011;Kirkby et 10 al., 2016). The chemical fate of SO3is fundamentally different from that of SO3 that forms H2SO4 by hydration. Likely outcomes of SO3are hydrolysis, electron transfer by collision with O3, reaction with O2 and H2O and, possibly, radicals, according to the following equations SO3 -+ O2 + H2O → HSO4 -+ HO2 (R7) Fehsenfeld and Ferguson showed that H2SO4 formation could occur in the SO3 -•••H2O cluster, releasing a free electron 20 (Reaction (R5)) (Fehsenfeld and Ferguson, 1974). Owing to the high electron affinity of O3 relative to SO3 (Rothe et al., 1975), the electron can transfer from SO3 to O3 and lead to the formation of SO3, the precursor for sulfuric acid in the atmosphere.
Moreover, the free electron released and the O3formed in reactions (R5) and (R6), respectively, are potential triggers of new SO2 oxidations with implication in aerosol formation (Svensmark et al., 2007;Enghoff and Svensmark, 2008;Bork et al., 2013). Reactions (R7) and (R8) are potential outcomes for SO3as well, forming the highly stable HSO4species that would 25 terminate the oxidation process of SO2 initiated by a free electron. Reactions (R5)-(R8) are likely competitive processes upon SO3formation in the gas-phase, and their different rates would determine the number of SO2 oxidations induced by a free electron. However, they have no other fate than HSO4or H2SO4, the most oxidized forms of sulfur in the atmosphere, which both share many properties and play a central role in atmospheric particle formation.
Experimental studies have shown that in atmospheres heavily enriched in SO2 and O3, a free electron could initiate SO2 30 oxidation and induce the formation of ~10 7 cm -3 sulfates in the absence of UV light, clearly indicating the importance of other ionic SO2 oxidation mechanisms than UV-induced (Enghoff and Svensmark, 2008). To evaluate the importance of the mechanism presented in this study in the formation of sulfates, it is necessary to identify the scavengers that terminate the SO2 oxidation initiated by O2 -. Possible scavengers include radicals, NOx, acids, cations and other particles. The main ones are Atmos. Chem. Phys. Discuss., https://doi.org/10.5194/acp-2018-1111 Manuscript under review for journal Atmos. Chem. Phys. Discussion started: 5 November 2018 c Author(s) 2018. CC BY 4.0 License.
likely NOx and OH, which lead to the formation of the stable NO3and HSO4species. If the ion concentration was known, the contribution of reaction (R4) to H2SO4 formation could be determined by comparing its formation rates from ionic and electrically neutral mechanisms. Alternatively, it can be assumed that reaction (R4) is terminated when the ion cluster hits a scavenger. The free electron which acts as catalyst is then scavenged. The average catalytic turnover number (TON) is defined as (Kozuch and Martin, 2012) The catalytic efficiency of SO2 ion-induced oxidation is then given as 15 Jion = kion × TON (10) Where kion is the ion production rate. Depending on the tropospheric temperature and altitude, measurements at the CLOUD chamber experiments found kion = 2-100 cm -3 s -1 , covering the typical ionization range in the troposphere (Franchin et al., 2015). Assuming nearly pristine conditions with [SO2] = 5 ppb = 1.2 × 10 11 molecule cm -3 , [NOx] = 200 ppt = 4.9 × 10 9 20 molecule cm -3 , and [OH] = 5.0 × 10 5 molecule cm -3 (day and night average), we determine Jion in the range 5.0 × 10 1 -2.5 ×

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With kUV = 1.3 × 10 -12 cm 3 molecule -1 s -1 (Atkinson et al., 2004), JUV = 7.9 × 10 4 molecule cm -3 s -1 , and the proportion of H2SO4 formed from ion-induced oxidation can be estimated from the following equation We find that the contribution of ion-induced SO2 oxidation to H2SO4 formation can range from 0.1 to 3.1% of the total formation rate. This estimate could be improved by considering also the SO2 oxidation by Criegee Intermediates, another important channel for H2SO4 formation.

Conclusions 5
This study highlights the role of the superoxide ions (O2 -) in SO2 oxidation. Our previous study demonstrated that SO2 interacts with O2and forms O2SOOwhose atmospheric fate remains unelucidated (Tsona et al., 2014). In this study, we used ab initio calculations to assess the chemical fate of O2SOOby collisions with O3. Regardless of the presence of water, two main mechanisms are observed, leading to fundamentally different products. The first mechanism is characterized by electron transfer followed by O2SOO decomposition, leading to O3formation and releasing SO2. The chemistry of SO2 + O3has been 10 explored elsewhere. The second mechanism is characterized by SO2 oxidation and proceeds through formation of a pre-reactive complex that subsequently reacts to form the products by overcoming a relatively low energy barrier. The overall reaction, O2 -+ SO2 + O3 → SO3 -+ 2O2, is faster and more energetically favorable than the SO2 + O3 -→ SO3 -+ O2 reaction, thereby highlighting the positive role of O2in SO2 ionic oxidation. Hence, the two reactions may compete in chamber experiments and in the atmosphere. 15 While for the electron transfer and O2SOO decomposition process the reaction is hindered by the presence of water, the oxidation reaction is catalysed instead as the rate constant is increased by 6 orders of magnitude with the presence of water.
Weighing the rate constants of unhydrated and monohydrated reactions to the equilibrium concentrations of hydrates of corresponding pre-reactive complexes leads to the net rate constant of 4.0×10 -11 cm 3 molecule -1 s -1 at 298 K for the oxidation reaction. Hence, this reaction proceeds nearly at collision rate. The main species (SO3 -) in the end products of the studied 20 reaction has been proved to form both in the atmosphere and in experiments, where it definitely plays a role in atmospheric sulfur chemistry and particle formation. The contribution of this mechanism to the total atmospheric sulfuric acid formation is estimated. The studied reaction further deepens the understanding of ion-induced SO2 oxidation, with implications in aerosol formation.

Author contributions 25
NTT and LD designed the work. NTT performed all calculations and wrote the manuscript. LD edited the manuscript.   Atmos. Chem. Phys. Discuss., https://doi.org/10.5194/acp-2018-1111 Manuscript under review for journal Atmos. Chem. Phys. Discussion started: 5 November 2018 c Author(s) 2018. CC BY 4.0 License. Table 1: Electronic energies (ΔE), enthalpies (ΔH298K) and Gibbs free energies (ΔG298K) of the different states in the O2SOO -+ O3 reaction both in the absence and in the presence of water, calculated relative to the energy of initial reactants at the CCSD(T)/augcc-pVTZ//M06-2X/aug-cc-pVTZ level of theory.