Methane sulfonic acid enhanced formation of molecular clusters of sulfuric acid and dimethyl amine

In the introduction we have added the following: It is generally accepted that much particulate MSA originate from surface oxidation of dimethyl sulfoxide (DMSO) and methane sulfinic acid (MSIA) (Davis et al., 1998; Barnes et al., 2006). However, in a recent study by Dall'Osto et al. (2012), gaseous MSA concentrations were found to decrease during marine particle formation events, suggesting that MSA may contribute to growth and possibly formation of the initial molecular clusters seeding aerosol formation.


Introduction
One of the least understood micro-physical processes in the atmosphere is the conversion of low volatile gaseous molecules into an aerosol particle.Aerosol particles are a major source of cloud condensation nuclei and aerosol formation represents one of the largest uncertainties in climate and cloud models (Solomon et al., 2007;Kazil et al., 2010;Pierce and Adams, 2009).Despite recent advances in theory and instrumentation, the chemical composition of the molecular clusters forming the seeds for the thermally stable aerosol particles remains highly uncertain in most locations.
The decisive importance of sulfuric acid for atmospheric 35 aerosol formation is well established, but within the last decades it has become evident that at least one, but probably more stabilizing species participate as well (Weber et al., 1996;Almeida et al., 2013).Nitrogenous bases, most efficiently dimethyl amine (DMA), and highly oxidized or-40 ganic compounds are known to enhance sulfuric acid based aerosol formation.However, in locations where these are sparse other species may contribute significantly.
Methane sulfonic acid (MSA) is the simplest organosulfate and is a well known oxidation product of dimethylsulfide.

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Over oceans and in coastal regions, gaseous MSA is present in concentrations of about 10 to 50 % of the gaseous sulfuric acid (H 2 SO 4 ) concentration, (Berresheim et al., 2002;Huebert et al., 1996) although MSA/H 2 SO 4 ratios up to 250 % have been reported (Davis et al., 1998).Similarly, 50 in sub-µm aerosol particles MSA is typically found in concentrations of 5 to 30 % of the sulfate concentrations (Ayers et al., 1991;Huebert et al., 1996;Kerminen et al., 1997) although MSA/sulfate ratios around 100 % have been reported in aerosols smaller than 0.2 µm (Facchini et al., 2008).It 55 is generally accepted that much particulate MSA originate from surface oxidation of dimethyl sulfoxide (DMSO) and methane sulfinic acid (MSIA) (Davis et al., 1998;Barnes et al., 2006).However, in a recent study by Dall'Osto et al. (2012), gaseous MSA concentrations were found to de-60 crease during marine particle formation events, suggesting that MSA may contribute to growth and possibly formation of the initial molecular clusters seeding aerosol formation.
Several laboratory and theoretical studies have attempted to explain these observations and determine at which state 65 MSA enters the aerosol particle.Earlier studies have often used classical nucleation theory to predict or reproduce particle formation rates of various mixtures of H 2 SO 4 , MSA and water, generally finding that MSA is of minor importance (Wyslouzil et al., 1991;Napari et al., 2002;Van Dingenen and Raes, 1993).Later studies by Dawson et al. (2012) andBzdek et al. (2011) combining flow tube experiments and ab initio calculations, found that water and nitrogenous bases enhanced MSA based aerosol formation and that amines are more efficient than ammonia, and recently, Dawson et al. (2014) found that trimethylamine was susceptible for substitution by both methylamine and DMA.Further, Dall'Osto et al. (2012) used quantum chemical calculations, considering the molecular clusters containing up to two acids and one DMA molecule, to support the hypothesis that MSA, H 2 SO 4 and DMA could co-exist in newly formed molecular clusters.
These studies have prompted a more rigorous ab initio based evaluation of whether MSA contributes to aerosol formation or mainly enters the aerosol during growth.This study targets the enhancing effect of MSA on sulfuric acid-DMA based cluster formation.Via systematic conformational searches we have obtained minimum free energy structures of clusters of composition MSA x (H 2 SO 4 ) y DMA z where x + y ≤ 3 and z ≤ 2. The corresponding thermodynamic data is used in the Atmospheric Cluster Dynamics Code (ACDC) (McGrath et al., 2012;Olenius et al., 2013) whereby the enhancing effect of MSA is obtained by comparing ternary MSA-H 2 SO 4 -DMA to binary H 2 SO 4 -DMA based cluster formation rates.
The clusters studied in this work do not contain water molecules due to the considerable additional computational effort required to obtain the necessary thermodynamic data.Hydration can be expected to stabilize weakly bound clusters more than strongly bound clusters and it is therefore conceivable that we will underestimate the contribution from some of the minor growth pathways.However, since DMA is a much stronger base than water, hydration is not likely to have a significant effect on the stability of clusters containing DMA.Therefore, the main growth pathways and growth rates are unlikely to change significantly due to hydration.
2 Computational details

Ab initio calculations
The most critical parameters in cluster growth models are the cluster binding free energies since the evaporation rate depends exponentially on these.At present, density functional theory (DFT) and second order Møller-Plesset perturbation theory (MP2) are the most popular ab initio methods for calculating the thermodynamics of molecular clusters.It is often mentioned that average uncertainties are on the order of 1 kcal mol −1 , but depending on the specific system and method, uncertainties may be significantly larger.Therefore, careful testing and validation should precede each study, which we will discuss in the following.
Since acid-base clustering is considered one of the fundamental processes driving aerosol formation, we have tested the performance of four commonly used DFT functionals and MP2, comparing these to previously published data.Also, the effect of electronic energy corrections from high level 125 coupled cluster calculations is tested.The basis set effects have previously been found to be much less significant, provided that a basis set of at least triple-ζ quality is used (Bork et al., 2014a).In this study we use the 6-311++G(3df,3pd) (Francl et al., 1982;Clark et al., 1983) basis set in all DFT 130 and MP2 calculations.
From the first and second sections of Table 1, we see that the CCSD(T)-F12/VDZ-F12 electronic energy corrections significantly reduce the scatter of the data.This suggest that the thermal and zero-point vibrational terms are well 135 produced by the four DFT functional and MP2, and that the main errors are associated with the electronic energies.Also, the data reveal that amongst the tested methods the M06-2X, ωB97X-D and PW91 density functionals perform well whereas B3LYP performs poorly on systems representative 140 by clustering of H 2 SO 4 and MSA with DMA.
In several recent studies (Bork et al., 2014a,b;Leverentz et al., 2013;Elm et al., 2012Elm et al., , 2013b) the M06-2X functional (Zhao and Truhlar, 2008) has been shown to be amongst the most reliable and accurate density functionals with re-145 spect to binding free energies of molecular clusters.Therefore, its performance for the present systems was investigated in greater detail.Table 2 shows the effect of a CCSD(T)-F12a/VDZ-F12 single point electronic energy correction to the M06-2X Gibbs free energy for six relevant reactions.

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For the formation of the DMA • H 2 SO 4 and DMA • MSA complexes a slight underestimation is observed in agreement with previous studies of similar systems (Bork et al., 2014a;Elm et al., 2012Elm et al., , 2013b)).For the MSA • H 2 SO 4 , (H 2 SO 4 ) 2 and MSA 2 complexes the DFT values are seen 155 to overestimate the Gibbs free energies of formation by up to 2.14 kcal mol −1 .No reliable representative experimental data exist for comparison of acid-acid cluster binding energies.However, the binding energy of (H 2 SO 4 ) 2 has been investigated by Ortega et al. (2012), using MP2 up to pentru-160 ple ζ basis sets including also anharmonic and relativistic effects, arriving at a value of −7.91 kcal mol −1 .This indicates that the apparent overbinding of the M06-2X functional is less severe than 2 kcal mol −1 and that M06-2X based errors in binding energies of molecular clusters with both acid-acid 165 and acid-base bonds will tend to cancel out rather than to accumulate.
Besides an appropriate computational method, a second pre-requisite for obtaining correct cluster binding free energies is to obtain the global minimum energy structures.In this study we employ a systematic sampling technique initiated by 1000 auto generated guess structures, pre-optimized using the PM6 semi-empirical method (Stewart, 2007).The up to 100 best guess structures are further refined using M06-2X/6-311++G(3df,3pd).For full detail of the sampling technique we refer to our previous investigations (Elm et al., 2013c,a).Additionally, guess structures for all cluster compositions were manually constructed based on previously published (H 2 SO 4 ) x DMA y and (H 2 SO 4 ) x (NH 3 ) y structures (Nadykto et al., 2011;Ortega et al., 2012).In several cases this lead to identical structures as the above mentioned systematic sampling, but in no cases did the manual approach lead to improved binding energies compared to the systematic approach.

Cluster growth model
The resulting thermodynamic data was studied with the kinetic model Atmospheric Cluster Dynamics Code (ACDC) (McGrath et al., 2012;Olenius et al., 2013).The code solves the time evolution of molecular cluster concentrations for a given set of clusters and ambient conditions, considering all possible collision and fragmentation processes.In this study, ACDC is used to find the steady-state of the cluster distribution at given concentrations of MSA, H 2 SO 4 and DMA.The collision rate coefficients are calculated as hard-sphere collision rates and the evaporation rate coefficients are calculated from the Gibbs free energies of formation according to detailed balance.
As the vapour-phase concentrations of MSA and H 2 SO 4 generally are measured with chemical ionization mass spectrometry (CIMS), the atmospheric concentrations reported in the literature are likely to include contributions from acid molecules clustered with bases, in addition to the bare acid monomer (Kupiainen-Määttä et al., 2013).Therefore the acid concentrations in ACDC (both MSA and H 2 SO 4 ) are defined as the sum of all clusters consisting of one acid molecule and any number of DMA molecules.An external sink with a loss rate coefficient of 2.6 × 10 −3 s −1 , corresponding to coagulation onto pre-existing larger particles is used for all clusters (Dal Maso et al., 2008).Testing showed that variations in this value between 10 −3 s −1 and 5 × 10 −3 s −1 did not affect the main conclusions of this study (Figure S1).
When a collision leads to a cluster that is larger than the simulated system, the cluster is allowed to grow out if it contains at least three acid and three base molecules since these compositions are assumed to be along the main growth path.
The probability of a three acid-three base cluster to grow further vs. to re-evaporate back into the system was investigated by optimizing also the MSA(H 2 SO 4 ) 2 DMA 3 cluster.At T = 298 K, for example, the reaction

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This reveals that, depending on the conditions, evaporation of 3 acid and 3 based clusters can be significant and that larger clusters than considered in this study should be included for quantitative assessments of formation rates of nanometer sized MSA-H 2 SO 4 -DMA based particles, in 240 particular at higher temperatures.Our analysis is therefore restricted to formation rates of 3 acid-3 base molecular clusters.
Cluster types outside the simulation box not containing at least three acids and at least three base molecules are con-245 sidered unstable and hence much more likely to shrink by evaporations rather than being stabilized by another collision.Therefore these types of clusters are brought back into the simulation by monomer evaporations.In the case that the evaporating molecules are excess acid, the first evaporating 250 molecule is assumed to be MSA since it is a weaker acid than H 2 SO 4 .From these simulations we determine the formation rate of clusters that grow out of the system, and track the main growth routes by following the flux through the system (Olenius et al., 2013).

Structures and thermodynamics
Structures and thermodynamic data for all of the most stable MSA x (H 2 SO 4 ) y DMA z clusters, where x + y ≤ 3 and z ≤ 2, are given as Supplement.These clusters share several 260 structural features.In all cases where the number of base molecules does not exceed the number of acid molecules (MSA or H 2 SO 4 ) the DMA moiety is protonated but in none of the clusters SO 2− 4 is found.In most clusters containing both H 2 SO 4 and MSA, H 2 SO 4 is more acidic than 265 MSA.However, in a few cases including the most stable H 2 SO 4 • MSA • DMA cluster, deprotonated MSA and doubly protonated H 2 SO 4 is seen in the same cluster (Fig. 1a).This is in accordance with the findings of Dall'Osto et al. (2012).Another common feature is the monolayer-like rather than 270 bulk-like structures of even the largest clusters investigated, e.g.MSA(H 2 SO 4 ) 2 DMA 3 (Fig. 1b).This tendency has been seen in other studies of similar systems, e.g.H 2 SO 4 -DMA based clusters (Ortega et al., 2012) and HSO − 4 -H 2 SO 4 -NH 3 based clusters (Herb et al., 2012).This is opposite to clus-275 ters containing several water molecules where bulk-like H 2 O structures tend to be more stable (Bork et al., 2013(Bork et al., , 2011)).
It is well known that strong acids and strong bases tend to form strong hydrogen bonds and more stable clus-ters than weaker acids and bases.Since MSA is a weaker acid than H 2 SO 4 it is expected that the MSA • DMA binding energy is weaker than the H 2 SO 4 • DMA binding energy (Table 2).It is, on the other hand, surprising that the MSA • H 2 SO 4 bond is at least 1.5 kcal mol −1 stronger than the H 2 SO 4 • H 2 SO 4 bond, and that the MSA • MSA bond is at least 0.5 kcal mol −1 stronger than the H 2 SO 4 • H 2 SO 4 bond.In larger clusters, H 2 SO 4 is, however, significantly more stabilized compared to MSA, and, besides the MSA dimer, clusters containing more than one MSA molecule are less stable than their corresponding H 2 SO 4 containing analogues (Table S1).

Clustering enhancements
To analyse the clustering abilities of MSA, a series of ACDC simulations based on these thermodynamics were performed at varying conditions.As a first measure, the binary cluster formation rate of MSA and DMA was compared to those of H 2 SO 4 and DMA at similar conditions, i.e. the ratio where J denotes the cluster formation rate at the indicated conditions.This was calculated for three temperatures (258, 278 and 298 K) spanning the boundary layer to the lower half of the troposphere, and x in the range from 10 5 to 2 × 10 6 molecules cm −3 , corresponding to typical H 2 SO 4 and MSA concentrations as described in the introduction.We used three DMA concentrations spanning most reported marine values (y = 10 7 , 10 8 and 10 9 molecules cm −3 ) (see Gibb et al., 1999 andTable 4 in Ge et al., 2011).Only field data from the boundary layer is available and the results presented here may thus not be representative for the free troposphere, if DMA concentrations turn out to be very different from the boundary layer.The resulting values for r 1 are shown in Fig. S2.In all cases, we find that this ratio is less than 10 −2 and, as expected, we conclude that binary MSA and DMA based cluster formation is of minor importance under normal conditions.
The main objectives of this study is to investigate the errors of neglecting MSA as a source of condensible vapour, as this is the case in most present aerosol formation parametrizations and models.A suitable measure for this is the ratio where J denotes the cluster formation rate at the indicated MSA concentration on top of a representative H 2 SO 4 concentration, here chosen to be 10 6 molecules cm −3 .All other parameters are as defined above.r 2 is shown in Fig. 2 as a function of [MSA].
As expected both temperature and DMA concentrations 330 are important parameters for the ratio, r 2 .At lower temperatures, entropy effects are decreased and all binding free energies are more negative.In this case, the cluster growth becomes increasingly insensitive to the chemical nature of the colliding species and more dependent on the collision fre-335 quency.At high DMA levels, DMA is in large excess compared to H 2 SO 4 and cluster growth is thus limited by acid collisions.In this case, having an extra source of acid has a larger effect than at lower DMA concentrations where the DMA excess is less severe.The approximately linear de-340 pendence of r 2 on the MSA concentration could indicate that only a single MSA molecule participates at these cluster sizes.This will be further investigated in Sect.3.3.Adding a small amount of MSA has a small effect on the cluster formation rate, but in locations where approximately 345 equimolar amounts of MSA and H 2 SO 4 are present, this added MSA increases the cluster formation rate by ca. 15 % at 298 K, by ca. 100 % at 278 K, but by more than 300 % at 258 K in the case of [DMA]=10 9 molecules cm −3 .Recalling the discussion in the Sect.2.1, and taking the latter case 350 as example, this increase may, however, be as small 200 % or as large as 500 % if the binding energies are 1 kcal mol −1 over-or underestimated, respectively (Fig. S3).
We consider a final descriptive ratio, indicating the effects of an unknown concentration of MSA compared to a similar 355 deficiency in the H 2 SO 4 concentration.This is given as the ratio where J represents the cluster formation rate at the given 360 conditions and x represents the added/deficient concentration of MSA or H 2 SO 4 in addition to a fixed H 2 SO 4 concentration, again chosen to be 10 6 molecules cm −3 .This ratio is shown in Fig. 3 for T = 258 K as function of x with the same conditions as above.This figure confirms that MSA is a less 365 efficient clustering agent than H 2 SO 4 , but also that the difference is very concentration dependent.Adding a small extra amount of acid, e.g. up to 2 × 10 5 molecules cm −3 , MSA is ca.60-90 % as efficient as a similar amount of added H 2 SO 4 .However, when the acid concentrations is doubled from the

Growth paths
The ACDC model was used to track the main growth pathways of the clusters growing out of the simulation system.As shown in Fig. 4, the flux through the system proceeds princi-H 2 SO 4 -DMA clusters, and another one where the clusters contain one MSA molecule in addition to H 2 SO 4 and DMA.
Clusters containing more than one MSA molecule were not found to contribute significantly to the growth.The relative contribution of the two growth mechanisms to the flux out of the system depends on the concentrations of the different species; at a higher MSA concentration the contribution of MSA-containing clusters is more prominent, as can be expected.In the case of [DMA]=10 8 molecules cm −3 between 11 and ca.51 % of the clusters growing out of the simulation box contains one MSA at [MSA]=10 5 molecules cm −3 and 10 6 molecules cm −3 (Fig. 4).Since such clusters contain three acid molecules (H 2 SO 4 or MSA), this implies overall MSA/H 2 SO 4 ratios of 3 % and 17 % at these conditions.

Conclusions
Methane sulfonic acid (MSA) is found in considerable quantities in the gas and aerosol phase over oceans and in coastal regions.We have investigated the effect and role of MSA in formation of molecular clusters in atmospheres containing various quantities of MSA, H 2 SO 4 and dimethyl amine (DMA).We use the kinetic model Atmospheric Cluster Dynamics Code and quantum chemical calculations of clusters containing up to three acids (MSA and/or H 2 SO 4 ) and two DMA molecules.
In accordance with numerous previous studies, we confirm that MSA is a less potent clustering agent than H 2 SO 4 , but far from negligible at normal conditions.The effect of MSA depends on both temperature and concentrations of MSA and DMA, but we find that enhancements of binary H 2 SO 4 -DMA based cluster formation between 15 and 300 % are typical in the marine lower to mid-troposphere.
We analyse these findings by tracking the main growth paths.We find that at most a single MSA is present in the growing clusters at the conditions investigated here  1991), Huebert et al. (1996) ) and Kerminen et al. (1997) in small aerosol particles.This strengthen the hypotheses that surface oxidation of DMSO or MSIA is the major source of particulate MSA (Davis et al., 1998;Barnes et al., 2006).However, we have shown that MSA may enter the aerosol 440 particle at the earliest possible stage and significantly assists in cluster formation.This is a consequence of MSA being a strong acid, binding strongly to DMA and H 2 SO 4 , and that DMA in most pristine oceanic locations is in large excess compared to acid.For ac-445 tual predictions of nanometer sized aerosol formation rates, larger clusters than the three acid-two base clusters studied here must be included in the kinetic model.

370[H 2
SO 4 ]=10 6 molecules cm −3 forming the reference conditions, the added MSA yields an increased cluster formation rate of ca.20-60 % compared to the same amount of added H 2 SO 4 .When the acid concentration is tripled the enhancement is ca.10-40 %.See Figs.S4 and S5 for corresponding 375 plots of T = 278 K and T = 298 K.

Fig. 1 .Fig. 2 .
Fig. 1. (A) Most stable configuration of the MSA • H2SO4 • DMA cluster.The lengths of the hydrogen bonds are given in Å.In this cluster, MSA is a stronger acid than H2SO4.(B) Configuration of the MSA • (H2SO4)2• DMA3 cluster.As all investigated clusters, the most stable structure is more monolayer-like than bulk-like.The hydrogen bonds are shown as dashed lines.figure

Fig. 3 .
Fig. 3. Cluster formation rate of added MSA relative to the same amount of added H2SO4 as defined in Eq. (3).

Fig. 4 .
Fig. 4. Main cluster formation pathways at T = 258 K and [H2SO4]=10 6 molecules cm −3 , [DMA]=10 8 molecules cm −3 and two representative MSA concentrations.Dominating growth pathways are represented by thick arrows.Fluxes to clusters formed via several different pathways are indicated in the side table where A, M and D is shorthand for H2SO4, MSA and DMA, respectively.
The growth of pure H 2 SO 4 -DMA clusters begins with the formation of the H 2 SO 4 • DMA heterodimer, whereas the first step on the MSA-H 2 SO 4 -DMA growth route is the MSA • H 2 SO 4 complex or the MSA • H 2 SO 4 • DMA cluster, formed by collision of MSA and H 2 SO 4 • DMA.This is understandable as H 2 SO 4 • DMA and MSA • H 2 SO 4 are the two most stable dimers that can form in the system (Table 2).After the formation of the initial complex, the growth proceeds through subsequent collisions with H 2 SO 4 and DMA molecules, but also H 2 SO 4 • DMA dimers that are bound strongly enough to exist in notable amounts.In the MSA-H 2 SO 4 -DMA system, the H 2 SO 4 • DMA dimers contribute up to approximately 15 % of the H 2 SO 4 concentration measurable by CIMS (i.e.clusters consisting of one H 2 SO 4 and zero or more DMA molecules) in the conditions of Fig. 4, whereas MSA • DMA dimer concentrations, on the other hand, are negligible.
and, typically, MSA/H 2 SO 4 ratios are below ca.15 % at these clus-ter sizes.Using this model, we are thus unable to explain MSA/H 2 SO 4 ratios up to 30 % observed by Ayers et al.