Pyruvic acid, an efficient catalyst in SO3 hydrolysis and effective clustering agent in sulfuric acid-based new particle formation

The role of pyruvic acid (PA), one of the most abundant α-keto carboxylic acids in the atmosphere, was investigated both in the SO3 hydrolysis reaction to form sulfuric acid (SA) and in SA-based aerosol particle formation using quantum chemical calculations and a cluster dynamics model. We found that the PA-catalyzed SO3 hydrolysis is a thermodynamically 10 driven transformation process, proceeding with a negative Gibbs free energy barrier, ca. -1 kcal mol at 298 K, ~ 6.50 kcal mol lower than that in the water-catalyzed SO3 hydrolysis. Results indicated that the PA-catalyzed reaction can potentially compete with the water-catalyzed SO3 reaction in SA production, especially in dry and polluted areas, where it is found to be ~two orders of magnitude more efficient that the water-catalyzed reaction. Given the effective stabilization of the PA-catalyzed SO3 hydrolysis product as SA•PA cluster, we proceeded to examine the PA clustering efficiency in sulfuric acid-pyruvic acid15 ammonia (SA-PA-NH3) system. Our thermodynamic data used in the Atmospheric Cluster Dynamics Code indicated that under relevant tropospheric temperatures and concentrations of SA (10 cm), PA (10 cm) and NH3 (10 and 5×10 cm), of the PA-containing clusters, only clusters with one PA molecule, namely (SA)2•PA•(NH3)2, can participate to the particle formation, contributing by ~100% to the net flux to aerosol particle formation at 238 K, exclusively. At higher temperatures (258K and 278 K), however, the net flux to the particle formation is dominated by pure SA-NH3 clusters, while PA would 20 rather evaporate from the clusters at high temperatures and not contribute to the particle formation. The enhancing effect of PA of examined by evaluating the ratio of the ternary SA-PA-NH3 cluster formation rate to binary SA-NH3 cluster formation rate. Our results show that while the enhancement factor of PA to the particle formation rate is almost insensitive to investigated temperatures and concentrations, it can be as high as 4.7×10 at 238 K and [NH3] = 1.3×10 molecule cm. This indicates that PA may actively participate in aerosol formation, only in cold regions of the troposphere and highly NH3-polluted 25 environments. The inclusion of this mechanism in aerosol models may definitely reduce uncertainties that prevail in modeling the aerosol impact on climate.

affecting climate by altering cloud properties and influencing the balance of solar radiation (Stocker et al., 2013). Sulfuric acid (H2SO4, SA) that is believed to be the key species driving aerosol formation in the atmosphere Kulmala, 2003;Sipila et al., 2010;Sihto et al., 2006;Kuang et al., 2008), is primarily formed from the hydrolysis of sulfur trioxide (SO3). Main sources of atmospheric SO3 include electrically neutral SO2 oxidation by OH radicals and stabilized Criegee intermediates (Mauldin III et al., 2012;Welz et al., 2012), whereas ion-induced oxidation constitutes a complementary source 35 (Bork et al., 2013;Tsona et al., 2016;Tsona et al., 2015;Tsona and Du, 2019). The sinks of SO3 include its reaction with water to produce sulfuric acid and acid rain, as well as reactions with other organic and inorganic species including ammonia and methanol (Li et al., 2018;Liu et al., 2019).
The general mechanism for SO3 hydration to form sulfuric acid is a hydrogen atom transfer between H2O and SO3 within the SO3•(H2O)n>=2 cluster, assisted by a second water molecule (Hofmann-Sievert and Castleman, 1984;Holland and Castleman, 40 1978), according to the following reaction: SO3 + n H2O → SO3•(H2O)n≥2 → H2SO4•(H2O)n-1 (R1) In the presence of a single water molecule, the above reaction was found to be prevented by a high energy barrier, around 30 45 kcal mol -1 , whereas the barrier height gradually decreases to ca. ~0 kcal mol -1 as the number of water molecules increases to 4 or more (Hofmann and Schleyer, 1994;Morokuma and Muguruma, 1994;Larson et al., 2000;Loerting and Liedl, 2000). In reaction (R1), the second water molecule acting as a catalyst forms a bridge for the hydrogen atom to transfer from H2O to SO3. This reaction is considered as the major loss pathway for SO3 in the atmosphere. Beside a second water molecule, a number of studies have shown that the SO3 + H2O → H2SO4 reaction can be facilitated by organic and inorganic species 50 including sulfuric acid, formic acid, nitric acid and oxalic acid (Torrent-Sucarrat et al., 2012;Hazra and Sinha, 2011;Daub et al., 2020;Long et al., 2013;Lv et al., 2019). In the presence of these species, the SO3 + H2O reaction can effectively proceed in a near barrierless mechanism, where they also act as bridge for hydrogen atom transfer. However, due to the low concentration of each of these catalysts, their overall effect on the rate of sulfuric acid formation from the SO3 + H2O reaction is not strong enough that they cannot effectively compete with the water-catalyzed reaction, giving the relatively high 55 concentration of water. An efficient catalyst would not only promote a fast hydrogen transfer between SO3 + H2O, but also have a high enough concentration to induce a net higher reaction rate than the water.
Pyruvic acid (CH3C(O)COOH, PA), the simplest and one of the most abundant α-keto acid in the troposphere, is highly present in plants and in tropospheric air (Eisenreich et al., 2001;Jardine et al., 2010;Magel et al., 2006;Eger et al., 2020). Sources of PA in tropospheric air include photo-oxidation of isoprene, photolysis of methyglyoxal, reactions of peroxy radicals formed 60 during the oxidation of propane, the photooxidation of aromatic compounds in the presence of NOx, as well as vegetation (Paulot et al., 2009;Jenkin et al., 1993;Warneck, 2005;Praplan et al., 2014;Talbot et al., 1990;Jardine et al., 2010). PA mixing ratios of up to 15, 25 and 96 ppt were reported in the free troposphere and forest canopy over central Amazonia, and in a Finnish boreal forest, respectively (Talbot et al., 1990;Eger et al., 2020). In a rural continental mountain top site over the https://doi.org/10.5194/acp-2021-784 Preprint. Discussion started: 8 November 2021 c Author(s) 2021. CC BY 4.0 License. above the equatorial African rainforest (Helas et al., 1992). In regions highly affected by anthropogenic activities, PA levels of up to 500 ppt were observed, whereas significantly low levels were observed in the marine boundary layer over the Atlantic Ocean (63 o N to 39 o S) (Baboukas et al., 2000;Mattila et al., 2018). PA is expected to be removed from the atmosphere through photolysis and oxidation by OH radicals (Mellouki and Mu, 2003;Reed Harris et al., 2017b;Reed Harris et al., 2017a;Reed Harris et al., 2016;Church et al., 2020). 70 The detection of PA in various media, including gas-phase, aerosol and aqueous-phase (Andreae et al., 1987;Talbot et al., 1990;Bardouki et al., 2003;Baboukas et al., 2000;Chebbi and Carlier, 1996;Kawamura et al., 1996;Kawamura et al., 2013;Kawamura and Bikkina, 2016) makes it a good candidate for atmospheric processes. Moreover, through its carboxyl and carbonyl functions, PA cannot only partake in hydrogen atom transfer reactions but also in molecular clustering owing to its ability to form hydrogen bonds. In this study, we examine the catalytic effect of PA on the SO3 hydration to form SA, assess 75 the subsequent clustering of the reaction products (PA•SA) with additional SA and ammonia molecules. The kinetics of the SO3 hydrolysis are determined and the fate of the product cluster in atmospheric particle formation is evaluated from clusters dynamic simulations.

Quantum chemical calculations 80
The calculations in this study were divided into reaction mechanism and cluster formation parts, and all geometry optimizations were performed using the Gaussian 09 package (Frisch et al., 2013). In the reaction mechanism part, the configurations of different states of the scanned reaction pathways were initially optimized with the M06-2X density functional (Zhao and Truhlar, 2008) used in conjunction with the 6-31+G(d,p) basis set. Identified M06-2X/6-31+G(d,p) structures within 3 kcal mol -1 of the lowest energy structure were re-optimized and their frequencies as well as the zero-point energies were calculated 85 at the M06-2X/6-311++G(3df,3pd) level of theory. It should be noted that frequencies calculations were performed under the harmonic oscillator-rigid rotor approximation at 298 K and 1 atm. Transition states configurations were determined using the synchronous transit quasi-Newton method (Peng et al., 1996), and confirmed by internal reaction coordinate calculations (Fukui, 1981) to ensure they connected the reactants to desired products. Electronic energies of all M06-2X/6-311++G(3df,3pd) optimized structures were corrected by the DLPNO-CCSD(T)/aug-cc-pVTZ method using Orca version 4.2.1 (Riplinger et al., 90 2013;.

Kinetics
The kinetic analysis of the studied reactions was performed following the conventional transition state theory (Duchovic et al., 1996;Truhlar et al., 1996) with the Wigner tunneling correction, and executed with the KiSThelP program (Canneaux et al., two separate reactants to form a binary complex that further interact with the third species to form the pre-reactive intermediate, the evaporation of the pre-reactive intermediate to initial reactants and its forward reaction to form the products, according to the following reaction: Reactions (R2a) and (R2b) are representative examples of processes taking place in the SO3 hydrolysis with X as catalyst, where X is H2O or PA. It should be noted that the pre-reactive intermediate can also form from the formation of the binary complex between the catalyst and water, followed by its interaction with SO3. Recent studies showed that no matter the order 105 in which the binary complex and the pre-reactive intermediate are formed and regardless of the specific reactants involved in the formation of the binary complex, the interactions between SO3, H2O and the catalyst lead to the formation of sulfuric acid plus catalyst (Weber et al., 2001;Jayne et al., 1997;Torrent-Sucarrat et al., 2012;Hazra and Sinha, 2011;Lv et al., 2019).
Assuming equilibrium between the reactants and the complex, and steady-state approximation of the pre-reactive intermediate, the overall rate of reaction (R2) with catalyst X is 110 (1) Where k1 is the collision frequency of SO3 and H2O to form the SO3•••H2O binary complex, k-1 is the evaporation rate constant 115 of SO3•••H2O back to initial reactants, k2 is the collision frequency of SO3•••H2O and the catalyst to form the pre-reactive catalyst (H2O or PA). The determination of equilibrium constants, collision frequencies and unimolecular rate constants was executed using the KiSThelP program.

Cluster formation and dynamic simulations
As reaction (R2) results into the formation of sulfuric acid complexed to the catalyst, we explored the thermodynamics of further clustering with more PA, sulfuric acid (SA) and ammonia (NH3) molecules. To elucidate the role of PA in atmospheric 125 particle formation, the influence of varying temperatures and monomer concentrations on SA-PA-NH3 clustering was (SA)s•(PA)p•(NH3)n (0 ≤ n ≤ s+p ≤ 3). The simulation box was set to 3 × 2, where "3" stands for the total number of acids (SA and PA) and "2" stands for the total number of NH3 molecules. The ACDC model, taking as input the thermodynamic data obtained from quantum chemical calculations, generates the time derivatives of all clusters concentrations and solve for the 130 steady state cluster distribution, using the Matlab ode 15s routine for differential equations (Shampine and Reichelt, 1997).
The time derivatives of clusters concentrations, also called birth-death equations, can be expressed as follows: Where Ci is the concentration of cluster i, βi,j is the collision coefficient of clusters i and j, → , is the rate coefficient of cluster k evaporating into smaller clusters i and j.
For two neutral clusters i and j, the collision coefficient under the assumption of hard-sphere and sticking collision was calculated according to the kinetic gas theory as Where mi and Vi are respective mass and volume of cluster i, kB is Boltzmann constant and T is the absolute temperature. The volume is calculated from atomic masses and densities of the compounds in the cluster.
The rate coefficient of i+j cluster evaporating to i and j clusters was derived as: 145 Where Pref is the reference pressure at which Gibbs free energies are calculated, ΔGi is the Gibbs free energy of formation of cluster i from monomers. Further details on collision rate coefficients and evaporation rate coefficients evaluation as well as 150 on ACDC simulations can be obtained from previous studies Ortega et al., 2012;Olenius et al., 2013b;Olenius et al., 2013a).

Water-catalyzed SO3 hydrolysis
A number of studies have been dedicated to the SO3 + H2O → H2SO4 reaction, which was shown to be prevented by an 155 electronic energy barrier as high as ~30 kcal mol -1 under relevant atmospheric conditions. The presence of a second molecule in this reaction lowers the energy barrier by favoring the formation of two kind of binary hydrogen-bonded complexes,  Hazra and Sinha, 2011;Long et al., 2013;Lv et al., 2019). The underlying mechanism is similar to those previously reported for the same reaction, and is characterized by two hydrogen atom transfers to and from the second water molecule that acts as 165 the catalyst.

Pyruvic acid-catalyzed SO3 hydrolysis
Despite the demonstrated catalytic effect of water on SO3 hydrolysis, comparison of previous results studies demonstrate that as much as four water molecules could be needed to achieve similar results to those obtained when a single molecule of other species is used as catalyst (Hazra and Sinha, 2011;Torrent-Sucarrat et al., 2012;Long et al., 2013;Lv et al., 2019;Daub et al., 2020;Larson et al., 2000). Some of these species include carboxylic acids, sulfuric acid, and nitric acid. From these studies, 175 while the electronic energy barrier could be reduced to ~5.5 kcal mol -1 with water as the catalyst, it could be reduced to 3.7, 1.4, 0.6 and around 1 kcal mol -1 respectively with HNO3, H2SO4, HCOOH and HOOC-COOH as catalysts. These results highlight the catalytic strength of carboxylic acids over other catalysts, and further suggest that a second carboxyl function can have additional catalytic effects on the energy barrier.
In addition to the carboxyl group, PA possesses a ketone function at the α-position. Church et al. have identified four stable 180 conformational structures for PA that mainly differ by the orientation of the methyl group relative to the acidic OH group and that of the hydroxyl H-atom relative to the ketone group, leading to trans-cis (Tc), trans-trans (Tt), cis-trans (Ct) and cis-cis (Cc) conformers, denoted as PATc, PATt, PACt and PACc conformers, respectively. These structures are shown in Fig. S1 in the Supplement, along with their energies given relati to the energy of the most stable conformer, PATc(Church et al., 2020). Only three of these PA conformations were able to form complexes with water: PATc, PATt and PACt. We also note that in during 185 geometry optimization, PATc could interact with H2O and be converted into PATt, forming the binary PATt•••H2O complex.
Similar to the SO3 hydrolysis where water acts as the catalyst, the reaction with PA acting as catalyst proceeds by formation of SO3•••H2O and PA•••H2O complexes prior to the formation of the PA•••H2O•••SO3 pre-reactive intermediate (see Fig. 2).
While the pre-reactive intermediates formed with PATt and PACt conformers have almost equal electronic energy of formation, the PATt conformer is 0.23 kcal mol -1 more stable that the PACt conformer with respect to the Gibbs free energy at ambient conditions. Regardless of the PA conformation, the transformation of the pre-reactive intermediate to form PA•••SA follows hydrogen transfers mechanism where the hydrogen atom transfers from water to PA and then from PA to SO3, releasing the PA•••SA complex, similar to the mechanisms where water, formic acid and oxalic acid act as catalysts. PATt and PACt conformers exhibit comparable binding strength with water at 1 atm and 298 K, with 2.75 and 2.29 kcal mol -1 Gibbs free 195 energy changes, respectively. This is a somewhat more favorable binding than the SO3 binding with water whose Gibbs free energy change is 3.37 kcal mol -1 at similar conditions. It is obvious that the formation of PA intermediates were determined to be 9.03×10 11 s -1 and 1.80×10 12 s -1 , respectively, at 298 K. Corresponding overall rate constants for PA-catalyzed SO3 + H2O reaction, calculated according to Eq. (1) are 2.95×10 -27 cm 6 molecule -2 s -1 and 3.52×10 -215 hydrolysis, not only should the catalyst be efficient in facilitating the hydrogen transfer between H2O and SO3, but its 225 concentration must be high enough to cause a higher SA formation rate than the water-catalyzed reaction.
Comparing the rate constant of the PA-catalyzed reaction the rate constants with the rate constants of reactions with other catalysts, it is obvious that PA is a more efficient catalyst than most organic and inorganic acids in SO3 hydrolysis and, consequently, may be an efficient partaker in SO3 hydrolysis in the atmosphere. To effectively compare the different catalytic effects of PA and water on the SO3 + H2O reaction, it is important to compare the overall rates of SA formation (given in Eq. 230 (1)) that take into account the concentrations of the catalysts. From Eq. (1), the ratio of the rates of SO3 hydrolysis reactions catalyzed by PA and water can be expressed as where α is a measure of the relative efficiency of different catalysts, kx is the overall rate constant of the X-catalyzed SO3 hydrolysis (X = PA, H2O), given in Eq. (1). Assuming water concentrations within 10 15 -10 17 molecule cm -3 that cover dry and humid conditions, and PA concentrations in the range 10 9 -10 11 cm -3 that cover clean and polluted environments, our results show that the efficiency of PA as a catalyst lies in the range ~10 -2 -10 2 relative to water. The H2O-catalyzed SO3 hydrolysis remains the main SO3 loss pathway under humid conditions, whereas the PA-catalyzed SO3 hydrolysis would be 240 the dominant path at dry conditions and polluted areas where PA concentrations can reach the ppb levels. It is estimated that under such conditions, the PA-catalyzed reaction can be around two orders of magnitude more efficient that the H2O-catalyzed SO3 hydrolysis to form sulfuric acid. This shows, in regard of the relatively high PA concentration and the high rate constant of the PA-catalyzed SO3 hydrolysis, that this reaction is more effective for SA production than reactions catalyzed by formic acid, sulfuric acid and oxalic acid. Giving the renowned role of sulfuric acid in aerosol particle formation, the PA-catalyzed 245 SO3 hydrolysis, stabilized as the PA•••SA complex product, might provide an additional pathway for incorporating organic matter into aerosol particles.

Clusters thermodynamics
The thermodynamics of further SA-PA clustering, with and without ammonia (NH3), was examined. In general, the clusters 250 formation is thermodynamically favorable at various tropospheric temperatures as can be seen in Table S1. The binding of PA to SA exhibits similar strength within 1 kcal mol -1 to the binding between two SA molecules, though this binding is weakened in the presence of NH3, likely as a result of the weaker acid nature of PA than SA. mol -1 , respectively, while NH3 additions to (PA)2•NH3 and SA•(PA)2•(NH3)2 are hindered by 0.76 and 0.37 kcal mol -1 thermodynamic barriers, respectively. Similar additions to clusters containing SA instead of PA are much more exergonic and this is as expected given the strong binding between SA and NH3, as compared with the binding between PA and NH3. The cluster formation depicted in the energy diagram of Fig. 3 is based on direct quantum chemical data at 298 K and 1 atm and 260 do not take into account the actual concentrations of monomers. However, such processes in the real atmosphere depend on actual atmospheric conditions such as temperature and the concentrations of monomers participating in the process
Clusters equilibrium concentrations at selected representative conditions are shown in Fig. 4. Previous studies also found that in methane sulfonic acid (MSA)-and trifluoroacetic acid (TFA)-enhanced sulfuric acid-based particle formation, the main cluster contributing to particle formation would bind a single molecule of MSA or TFA (Bork et al., 2014;Lu et al., 2020). 270 This is due to the particular binding strength between the base molecule and SA, as compared to the binding with other acids.
The difficulty to form large clusters containing PA likely result from the low concentration of heterotrimers and tetramers containing PA. For example, it is seen from can reach 10 5 cm -3 . These heterodimers likely undergo faster evaporation than e.g., SA•SA and SA•NH3, hence not effectively 275 contributing to further growth. Highest concentrations of PA-containing clusters are found at low temperatures, exclusively, where the evaporation rates are reduced.
The contribution of PA to the particle formation was estimated by calculating the enhancement factor as r = where J is the cluster formation rate, SA concentration is fixed to 10 6 cm -3 , x = 10 7 -10 10 cm -3 , y = 10 10 -10 12 cm -3 . Fig. 5 shows the enhancement factor as a function of [PA] and [NH3]. At a fixed NH3 concentration of 10 10 cm -3 , the enhancement factor weakly increases with PA concentration within the temperature range considered. The trend was observed to be similar at lower and higher PA and NH3 concentrations, even when SA concentration increased to reach 10 8 cm -3 . The only condition 285 that could lead to significant PA enhancements was observed for [NH3] > 10 11 cm -3 and 238 K. Fig. 5 shows that for 10 11 cm -based particles formation in NH3-polluted and cold environments. This is as expected since the promotion of new particle formation at cold temperatures has previously been evidenced (Lu et al., 2020;Liu et al., 2021). The implication of PA as 290 participating agent in aerosol formation models would definitely reduce the errors existing in current aerosol models.

Clusters formation pathways
Gibbs free energies in Fig. 3 give information on whether the cluster formation is thermodynamically favorable at the reference pressure (1 tam), however, not taking into account the concentrations of the clustering species participating in the process. The actual molecular clustering at given vapor concentrations and temperatures can be determined by performing ACDC 295 simulations Olenius et al., 2013b). This is achieved by calculating the actual Gibbs free energies, that is, the vapor concentration-dependent Gibbs free energies of clusters formation, that are used to track the actual clusters formation pathways at given conditions. The temperatures considered in this study are: 238 K, 258 K and 278 K that span most regions of the troposphere. Monomers concentrations were chosen to be [SA] = 10 6 cm -3 , [PA] = 10 10 cm -3 , and [NH3] = 10 11 and 5 ×10 11 cm -3 (Eger et al., 2020;Nair and Yu, 2020;Yao and Zhang, 2019;Zhang et al., 2021). As our simulation box size 300 was set to 3 × 2, only clusters containing more than three acid molecules (SA and/or PA) with more than two NH3 molecules were allowed to grow out of the system and contribute to particle formation.
Clusters containing more than one PA molecule were found not to contribute to particle formation. While the clusters contribution to the growth is found to weakly depend on monomer concentrations, their temperature-dependency is relatively stronger. Depending on the temperature, the clusters grew through the system via two main paths: one path involving pure SA-305 NH3 clusters and another one where PA also participates (See Fig. 6 and Fig. S2). Cluster formation starts by SA collision with SA or NH3, forming (SA)2 or SA•NH3, followed by NH3/SA addition to form (SA)2•(NH3). While PA can participate in the clusters formation either as (PA)2 or SA•PA cluster, it can effectively contribute in the cluster growth at low temperature (238 K), exclusively. At higher temperatures (258 K and 278 K), however, PA mainly evaporates from the clusters. At these temperatures, only (SA)3•(NH3)2 clusters will grow out of the system by clustering with SA and contribute to particle growth 310 (See Fig. 6(b) and Fig. S2). At 238 K, the largest pure SA-NH3 clusters formed within the system are (SA)2•(NH3)2 and (SA)3•(NH3)2, and they grow out the system by consecutive uptake of PA monomers. The main interactions that contribute to particle formation with the participation of PA are (SA)3•(NH3)2 + PA and (SA)2•(PA)(NH3)2 + PA (See Fig. 6(a)).
We observed that with [SA] = 10 6 cm -3 , [PA] = 10 10 cm -3 , and [NH3] = 10 11 cm -3 , PA-containing clusters do not contribute to the particle formation at 258 K and 278 K, whereas they predominantly contribute to the particle formation at 238 K, with 315 ~100 % of clusters growing out of the simulation box. It follows that under investigated monomers concentrations conditions, PA-containing clusters would completely dominate the particle formation at cold temperatures while pure SA-NH3 clusters will dominate at high temperatures.

Conclusion
The catalytic effect of pyruvic acid (PA) in SO3 hydrolysis to form sulfuric acid (SA) and its possible enhancement in 320 atmospheric particle formation have been highlighted. Using quantum chemical calculations, we found that with PA as a catalyst, the SO3 hydrolysis occurs with negative Gibbs free energy barrier at 298 K and 1 atm, indicating a thermodynamically driven transformation process. Evaluation of the kinetics show that the rate constant of PA-catalyzed SO3 hydrolysis at 298 K is ~3×10 5 times higher than that of water-catalyzed SO3 hydrolysis and 10 1 -10 4 times higher than those of previously investigated SO3 hydrolysis processes with nitric acid, sulfuric acid, oxalic acid and formic acid acting as catalysts, hence, 325 highlighting the effective role of PA in the atmospheric chemistry of SO3. Overall, the determination of the reaction rates, taking into account the catalysts concentrations, indicates that water-catalyzed SO3 hydrolysis would be the main SO3 loss pathway to form sulfuric acid under humid conditions and clear areas, whereas PA-catalyzed SO3 hydrolysis would dominate the process in dry conditions and polluted areas.
As the PA-catalyzed SO3 hydrolysis is highly stabilized by the formation of the SA•PA cluster, we further investigated the 330 role of PA in the formation of SA-based molecular clusters. Using the quantum chemical data from our calculations and an Atmospheric Cluster Dynamics Code, we found that though PA is a weaker clustering agent to SA than SA itself, it effectively contributes to particle formation. Two main pathways were found to drive the cluster formation (one path forming pure SA-NH3 clusters and another one forming PA-containing clusters). Under [SA] = 10 6 cm -3 , [PA] = 10 10 cm -3 , and [NH3] = 10 11 cm -3 conditions, clusters containing more than one PA molecule were observed not to contribute to particle formation, and the 335 main PA-containing cluster to contribute to particle formation is (SA)2•PA•(NH3)2 with the highest enhancement effect, 4.7×10 2 , observed at 238 K and [NH3] = 1.3×10 11 molecule cm -3 . This indicates that PA may actively participate in aerosol formation, especially in cold regions of the troposphere and highly NH3-polluted environments, and may readily be included in aerosol models.

Data availability. 340
All data from this research can be obtained upon request by contacting the corresponding author.

Author contributions.
NTT designed the work and performed all quantum chemical calculations. LL performed the dynamic simulations. NTT and analyzed the data with contributions from all co-authors. NTT wrote the paper with contributions from all co-authors.

Competing interests. 345
The authors declare that they have no conflict of interest.