The Role of Organic Acids in New Particle Formation from Methanesulfonic Acid and Methylamine

Atmospheric organic acids (OAs) are expected to enhance methanesulfonic acid (MSA)-driven new particle formation (NPF). However, the exact role of OAs in MSA-driven NPF remains unclear. Here, we employed a two-step strategy to probe the role of OAs in MSA-methylamine (MA) NPF. Initially, we evaluated the enhancing potential of 12 commonly 10 detected OAs in ternary MA-MSA-OA cluster formation by considering the formation free energies of the (MSA)1(MA)1(OA)1 clusters and the atmospheric concentrations of the OAs. It was found that formic acid (ForA) has the highest potential to stabilize the MA-MSA clusters. The high enhancing potential of ForA results from its acidity, structural factors such as no intramolecular H-bonds and high atmospheric abundance. The second step is to extend the MSA-MA-ForA system to larger cluster sizes. The results indicate that ForA can indeed enhance MSA-MA NPF at atmospheric conditions (the upper limited 15 temperature is 258.15 K), indicating that ForA might have an important role in MSA-driven NPF. The enhancing effect of ForA is mainly caused by an increased formation of the (MSA)2(MA)1 cluster, which is involved in the pathway of binary MSA-MA nucleation. Hence, our results indicate that OAs might be required to facilitate MSA-driven NPF in the atmosphere.

Although nucleation from OAs alone leads to a limited contribution to NPF , previous studies have 45 indicated that OAs might enhance SA-driven nucleation via hydrogen-bond (H-bond) interactions between OAs and SA (Zhang et al., 2004;Zhang et al., 2012;Elm et al., 2020;Wang et al., 2019;Shi et al., 2019). Furthermore, OAs such as lactic-, glyoxylic-, glycolic-and malonic acid have been identified to enhance binary SA-base nucleation, especially at very low temperatures (218 K) Li et al., 2017;Liu et al., 2018;Zhang et al., 2018). Under certain conditions, the ternary SA-base-OA system might present higher nucleation rates compared to the binary systems of SA-base, SA-OA and 50 OA-base. In contrast to SA-driven NPF, MSA-base cluster formation is not very efficient on its own and thereby could be highly dependent on the enhancing effect of other contributing vapors (Dawson et al., 2012;Elm, 2021). While the SA-driven nucleation involving OAs has been extensively studied (Zhang et al., 2004;Elm et al., 2017;Li et al., 2017;Liu et al., 2018;Zhang et al., 2018;Wang et al., 2019;Shi et al., 2019), little is still known about the corresponding MSAdriven nucleation mechanism. 55 The potentially important role of OAs in MSA-driven nucleation has been pointed out by previous studies, which focused on the interaction between MSA and several organic acid monomers or role of oxalic acid in MSA-amine NPF (Zhao et al., 2017;Arquero et al., 2017a;Arquero et al., 2017b;Xu et al., 2017;Sheng et al., 2019). However, to date, the underlying enhancing effects from a broad range of OAs on MSA-amine nucleation have not been examined. Based on our recent work, the enhancing potential of other precursors on MSA-driven nucleation is quite sensitive to the specific molecular structure 60 (Shen et al., 2020;Shen et al., 2019). In addition, there is a large difference in atmospheric abundance of various OAs which also has an influence on the relative importance of different OAs in MSA-amine-OA cluster formation. Therefore, it is desirable to evaluate the role of OAs in MSA-driven NPF by considering the interaction of the different OAs with MSA-amine clusters and the atmospheric abundance of OAs.

Configurational Sampling
A multi-step sampling scheme was used to search for the global minimum structures of the 12 (MA)1(MSA)1(OA)1 clusters, as well as the larger (MSA)x(MA)y(OA)z (0 ≤ y ≤ x+z ≤ 3) clusters. The binary MSA-MA cluster structures were taken from our previous work (Shen et al., 2020). Details of the scheme can be found in our previous studies addressing atmospheric 80 cluster formation (Shen et al., 2019;Shen et al., 2020;Xie et al., 2017;Ma et al., 2019a). Briefly, around 1000-10000 initial configurations for each cluster (fewer initial configurations for clusters with fewer molecules and more initial configurations for clusters with more molecules) were randomly generated, and subsequently underwent a gradual screening process using various theoretical methods, to locate the clusters lowest in free energy. The employed theoretical methods for geometry optimization and single-point energy calculations include PM6, ωB97X-D/6-31+G(d,p), ωB97X-D/6-31++G(d,p), and 85 DLPNO-CCSD(T)/aug-cc-pVTZ. The combination of ωB97X-D/6-31++G(d,p) and DLPNO-CCSD(T)/aug-cc-pVTZ has in several benchmarks shown good performance for studying the formation of atmospheric molecular clusters (Elm et al., 2013;Elm and Kristensen, 2017). All calculations employing semiempirical (PM6) and density functional theory (ωB97X-D functional) methods were performed in the GAUSSIAN 09 program package (Frisch et al., 2009), and DLPNO-CCSD(T)/augcc-pVTZ calculations were performed using the ORCA 4.0.0 program (Neese, 2012). The tight PNO and SCF convergence 90 criteria were used in DLPNO-CCSD(T)/aug-cc-pVTZ calculations by employing keywords tightpno and tightscf. The binding free energy (ΔG) for each cluster was obtained by subtracting the Gibbs free energy of the constituent monomers (MA, MSA, and OA) from that of the cluster at 298.15 K. The ΔG values at other temperatures were also calculated under the assumption that the enthalpy and entropy change (ΔH and ΔS) are constant in the considered tropospheric temperature range (238.15-298.15 K). 95

Estimating the Concentrations of the (MSA)1(MA)1(OA)1 Clusters
The atmospheric relevance of the studied (MSA)1(MA)1(OA)1 clusters is not only determined by the thermodynamics of cluster formation, but also by the atmospheric abundance of the precursor molecules. The concentrations of the The concentrations of precursors used in this study are based on reported values from field campaigns (see Table S1).
Notably, except for ForA and AceA, the concentrations of the OAs were estimated from those measured in the particle phase. 105 Hence, the values in Table S1 may overestimate the gaseous concentrations of the remaining 10 OAs and should be considered as an upper limit. The concentration of the (MSA)2(MA)1 cluster was also calculated as a comparison.
[MA] and [MSA] were set to be 2.5 ×10 8 molecules cm -3 (~10 ppt) and 10 7 molecules cm -3 in the calculations, respectively. It should be noted that the choice of [MA] and [MSA] does not influence the calculated ranking of the OAs.

ACDC Simulations 110
ACDC was employed to study the time evolution of cluster formation rates, steady-state cluster concentrations, and growth pathways for the larger MSA-MA-OA cluster system (Mcgrath et al., 2012). We refer to our previous studies for further details of the theory behind ACDC (Shen et al., 2020;Shen et al., 2019). Briefly, the core of ACDC is to employ the birthdeath equation (Eq. (2)) to describe the time-dependent cluster distributions: where subscripts (i, j, i-j, j-i and i+j) represent different clusters or monomers in the system, ci represents the number concentration of i, βi,j denotes the collision rate coefficient between i and j, γ(i+j) → i denotes the evaporation rate of a cluster i+j into smaller clusters (or monomer) i and j. Qi represents an additional outside source term of i and Si represents other sink terms for i. The collision rate coefficients were calculated by hard sphere kinetic gas theory as: where kb is the Boltzmann constant, T is the temperature, and mi and Vi are the mass and volume of i, respectively. The evaporation rates were calculated using detailed balance as: where ΔG is the formation free energy of the cluster, cref is the reference monomer concentration at 1 atm, which is the pressure at which ΔG was calculated (Mcgrath et al., 2012). Here, the simulated system can be described as a "3×3 box" containing 125 where 3 represents the maximal number of bases (MA) and acids (MSA and OA). We do not consider the MSA-MA-OA clusters that contain more bases than acids, as it has been shown that these usually have high evaporation rates and thereby are of little importance in NPF (Olenius et al., 2013). We used the calculated thermodynamic data of (MSA)x(MA)y(OA)z (0 ≤ y ≤ x+z ≤ 3) clusters as input for ACDC simulations to obtain the cluster formation pathways and new particle formation rates. The selection of boundary clusters was based on the stability of clusters 130 under the studied temperature (see details in the Supplement). As there have not been reported any coagulation coefficient of MSA from field campaigns, we set the coagulation sink to a constant value of 2 ×10 -2 s -1 , corresponding to a typical value in polluted regions (Yao et al., 2018). In addition, the coagulation sink coefficients in the range from 2 × 10 -4 to 2 × 10 -2 s -1 , covering possible values in clean and haze days, were selected to test the effect of coagulation sink coefficients on the main results. The temperature and concentrations of precursor gases (MSA, MA, and OA) were varied in the simulations to probe 135 the effect of various atmospheric conditions. The simulations were performed at 238.15-298.15 K to investigate the effect of temperature. The test ranges for the OA precursor concentrations are 10 8 -10 12 cm -3 .
However, other dicarboxylic acids follow a similar intermolecular interaction pattern as clusters containing monocarboxylic acids. For OxaA, the configuration involving the interaction of two -COOH groups with (MA)1(MSA)1 was not located. This   cluster as a comparison. Generally, the ΔG values of the (MSA)1(MA)1(OA)1 clusters vary from -12.69 to -17.87 kcal mol -1 , and are 2.49-7.67 kcal mol -1 higher (i.e. less negative) than that of the (MSA)2(MA)1 cluster. Based on previous studies, several 170 factors such as the acidity and intramolecular H-bond of OAs can affect their interaction energy with amine or SA . It should be noted that the structures of the simple monocarboxylic acids ForA, AceA, and BenA almost do not change during the interaction with MSA-MA cluster, presenting the intrinsical interacting pattern of the -COOH group with the MSA-MA cluster. Therefore, the MSA-MA-OA systems with the simple monocarboxylic acids were initially selected to analyze which factors that affect the interaction between OAs and MSA-MA cluster. As shown in Fig. 2b,  cluster. Therefore, an energetic penalty should be paid for breaking the original intramolecular H-bonds for these four acids, 190 which should be the main reason that the ΔG values are higher than those evaluated by their pKa values (above the baseline).
A similar phenomenon has previously been observed for -keto carboxylic acids in sulfuric acid-OA dimer clusters . The other three outliers (the dicarboxylic acids MalA, SucA and AdiA) interact with MSA-MA only via one -COOH group, behaving like a simple monocarboxylic acid. It was found that the structure of SucA and AdiA changes slightly during the interaction with MSA-MA cluster compared to their corresponding isolated conformations. The calculated root-195 mean-square-deviation (RMSD) of the OA structure in MSA-MA-OA cluster relative to their corresponding isolated conformers are 0.046 Å and 0.353 Å for SucA and AdiA, respectively. Therefore, the structural change upon cluster formation cannot explain the outliers. The clustering ability of straight-chain dicarboxylic acids has been suggested to follow an alternating even/odd pattern by observing that the dimer formation for GluA (C5) is more efficient than SucA (C4) and AdiA (C6) . Therefore, it was speculated that the alternating even/odd pattern for the clustering ability of the 200 dicarboxylic acids can explain SucA and AdiA as outliers. The structure of MalA changes significantly during the interaction with the MSA-MA cluster with a RMSD of 1.27 Å, which explains the reason for behaving as an outlier. Overall, our results show that the acidity, hydrogen-bond forming capacity, structural deformation energy of OA and even/odd pattern if it is dicarboxylic acid are the main factors determining the formation free energy of MSA-MA-OA cluster.

Analysis of larger MSA-MA-ForA Clusters
The pure (MSA)1-3 and binary (MSA)x(MA)y (1 ≤ y ≤ x ≤ 3) clusters have been discussed in our previous study (Shen et al., 2020;Shen et al., 2019). Here we mainly focus on the ForA-containing clusters.  Based on calculated ΔG values of all considered clusters, the evaporation rates of the clusters were calculated. A previous study established that it is important to consider the concentration of precursor when evaluating the cluster stability (Xie et al., 240 2017). Generally, given higher concentration of precursors, the collision probability for a cluster is increased and the balance between collision and evaporation is shifted forward, resulting in a higher cluster stability. Since the atmospheric concentration of ForA is much higher (about 10 3 ) than that of MA and MSA, an effective evaporation rate was used to evaluate cluster stability of ForA-containing clusters. The effective evaporation rates of the ForA-containing clusters were roughly obtained by scaling the original evaporation rate by 10 -3 , due to the concentration difference. The evaporation rates of binary MSA-MA 245 clusters and effective ones of ForA-containing clusters are presented in Fig. 4. Among the ForA-containing clusters, only the evaporation rates of the (MSA)1(MA)1(ForA)1 and (MSA)1(ForA)1 clusters are lower than those of corresponding binary MSA-MA clusters with equal number of acids and bases. The evaporation rate of the (ForA)2 cluster is found to be comparable to that of (MSA)2. The remaining ForA-containing clusters have much higher evaporation rates compared to the corresponding binary MSA-MA clusters. Therefore, the (MSA)1(MA)1(ForA)1 and (MSA)1(ForA)1 clusters have the highest potential to 250 participate in MSA-MA nucleation, followed by (ForA)2. It deserves mentioning that the evaporation rates of all ForAcontaining clusters are higher than those of corresponding binary MSA-MA clusters if the concentration difference of precursors was not considered. Therefore, it is the high concentration of ForA that drives the stability of the clusters and not the intrinsic evaporation rate.

Enhancing Effect of ForA
Here, we employed the enhancing coefficient R, as the ratio of cluster formation rate (J) for the ternary MSA-MA-ForA cluster system (JMA-MSA-ForA) relative to that of the binary MSA-MA cluster system (JMA-MSA) to present the enhancing effect 260 of ForA. For R above 1, it can be inferred that ForA has an enhancing effect on the binary MSA-MA system. Previous studies have shown that the temperature and concentrations of precursors have a large influence on R of OAs for the ternary SA-base-OA systems Li et al., 2017;Liu et al., 2018;Zhang et al., 2018). Herein, the effects of temperature and precursor concentration on R were examined for the ternary MSA-MA-ForA cluster system. Two steps were employed to investigate the effects of temperature and precursor concentration on the R. First step investigated the variation 265 of R with [ForA] (10 8 -10 12 cm -3 ) at different temperature (238.15-298.15 K). The second step investigated the variation of R with [MA] (1-100 ppt) or [MSA] (10 5 -10 8 cm -3 ) at fixed temperature and [ForA].
The variation of R with [ForA] at 238.15,258.15,278.15 and 298.15 K,[MA]=10 ppt and [MSA] =10 7 molecules cm -3 is presented in Fig. 5a. As seen from Fig. 5a, R almost remains as unity at all considered temperature range when [ForA] is less than 10 9 molecules cm -3 . With increasing [ForA] when [ForA] is more than 10 9 molecules cm -3 , R starts to obviously 270 increase with [ForA] at low temperature (< 258.15 K). However, the effect of [ForA] on R is much less pronounced when temperature is higher than 278.15 K, and the increase of R becomes nonnegligible only at 278.15 K and high [ForA] (>10 11 cm -3 ). Therefore, both temperature and [ForA] can significantly affect R. Similar results were also reported in previous studies on effect of OAs on SA-NH3 nucleation Liu et al., 2018;Zhang et al., 2018). It deserves mentioning that the upper limited temperature that ForA can effectively enhance MSA-MA NPF (258.15K) is about 40 K higher than those of 275 the previously studied OAs enhancing SA-NH3 NPF. In the following part, the condition with a reachable temperature (T = 258.15 K) and [ForA] (10 11 cm -3 (~ 4 ppb)) in the ambient atmosphere (Khwaja, 1995) As can be seen in Fig. 5b, R shows a small but positive dependence on [MA]. However, R has little correlation with [MSA]. The difference between the relationships of R [MA] and R [MSA] can be explained by the difference in cluster stability and 285 relative abundance of the precursors in the system. At [ForA] = 10 11 molecules cm -3 , the abundance of precursors in the system approximately decreases in the order ForA ˃ MA > MSA. Due to the scarcity of MSA in the system, increased MA will prefer to participate in the formation of ForA-containing clusters. Therefore, increased [MA] has a small positive effect on R.
Additionally, since the binding potential of MSA with the MA is much higher than that with MA-ForA clusters, the increased number of MSA molecules will primarily cluster with MA to form binary MSA-MA clusters and consequently the influence 290 on the ternary MSA-MA-ForA pathways is minor. As shown in Fig. S5, when coagulation sink coefficients change from 2 × 10 -4 s -1 to 2 × 10 -2 s -1 , R almost remains constant, indicating the selection of coagulation sink coefficient has no significant effect on R. This is not surprising, as R represents the ratio of the new particle formation rates and thereby the effect of the choice of coagulation sink largely cancels out.

Enhancement Mechanism of ForA 295
The enhancement mechanism of ForA can be disclosed by a comparative analysis on the cluster growth pathway of ternary MSA-MA-ForA and binary MSA-MA cluster system. can continue to grow, consistent with their stability. As ForA-driven catalytic process is the only difference between formation 310 pathway of the ternary MSA-MA-ForA and the binary MSA-MA cluster system, it should be the main reason that the presence of ForA can enhance the nucleation (R = 1.96), compared to the case of binary MSA-MA system. In addition, ForA mainly contributes to the formation of (MSA)2(MA)1 clusters (51%) in the catalytic process. Therefore, ForA enhances the binary MSA-MA nucleation mainly via catalyzing the formation of the (MSA)2(MA)1 cluster. As can be seen from Fig. S6-7, the catalyzed formation of the (MSA)2(MA)1 cluster is the main route for the ForA enhancing binary MSA-MA nucleation when 315 [MA] and [MSA] changes. In addition, as shown in Fig. S8, when coagulation sink coefficients 2 × 10 -4 s -1 and 2 × 10 -3 s -1 were employed, the formation pathway of the ternary MSA-MA-ForA clusters changes slightly compared to the case where a coagulation sink coefficient of 2 × 10 -2 s -1 was used. Therefore, the selection of coagulation sink coefficient has no effect on the predicted catalysis mechanism of ForA.

Atmospheric Implications
In this study, the potential of 12 commonly detected OAs in MSA-MA-OA nucleation has been systematically evaluated by examining the formation of the (MSA)1(MA)1(OA)1 clusters. It was found that ForA has the highest potential to participate 325 in ternary MSA-MA-OA nucleation. This study also suggests that for a given OA to have highest potential in ternary MSA-MA-OA nucleation, the OA should have the following features: high atmospheric abundance, strong acidity, strong H-bond forming capacity, weak or no intramolecular interaction in the monomer, and no/little structural deformation during clustering.
It is noted that besides the simple OAs studied here, there are some complex organics with multi-functional groups including -COOH, e.g. highly oxygenated molecules (HOMs), in the atmosphere. These complex organics also might participate in the 330 MSA-MA nucleation since they could interact with the MSA-MA cluster in a similar fashion as the simple OAs (H-bonds and acid-base reaction). Therefore, studies on the role of the complex organics with multi-functional groups in MSA-MA NPF are warranted to further augment the current understanding of MSA-driven NPF.
This study for the first time reveals that ForA exerts a catalytic enhancing effect on binary MSA-MA nucleation by facilitating the formation of clusters in the initial stage of NPF. Based on reported energetic data of (SA)1(amine)1(OAs)1 335 (amine = MA and DMA, OAs = ForA, AceA, OxaA, PyrA, MalA, MaleA, SucA, GluA, AdiA, BenA and PinA) and eq.(1) , (SA)1(amine)1(ForA)1 is calculated to have the (or second) highest concentration (see Table S3). Therefore, ForA could also have a high enhancing effect on SA-amine nucleation. A study on the enhancing effect of ForA on SA-driven NPF is warranted to further augment the current understanding of the contribution of OAs on NPF. The enhancing effect of ForA on binary MSA-MA nucleation is highly dependent on [ForA] and the temperature. At [ForA] =10 11 molecules cm -3 and 340 258.15 K, a reachable concentration and temperature in ambient atmosphere, ForA can effectively enhance binary MSA-MA nucleation, clarifying its important role in MSA-driven NPF. In addition, the concentration of ForA could be even higher in regions with significant primary emission sources and/or intense chemical production (Franco et al., 2021). Therefore, as a ubiquitous organic acid in the atmosphere, the contribution of ForA to NPF involving MSA and amines deserves more concerns in the future. 345 Data availability. The data in this article are available from the corresponding author upon request (hbxie@dlut.edu.cn).
Author contribution. HBX designed research; RJZ, JWS and HBX performed research; RJZ, JWS and HBX analyzed data; RJZ, JWS, HBX, JWC and JE wrote the paper; and HBX, JWC and JE reviewed and revised the paper.
Competing interests. The authors declare that they have no conflict of interest. 350