Clusteromics III: Acid Synergy in Sulfuric Acid–Methanesulfonic Acid–Base Cluster Formation

Acid–base molecular clusters are an important stage in atmospheric new particle formation. While such clusters are most likely multicomponent in nature, there are very few reports on clusters consisting of multiple acid molecules and multiple base molecules. By applying state-of-the-art quantum chemical methods, we herein study electrically neutral (SA)1(MSA)1(base)0–2 clusters with base = ammonia (A), methylamine (MA), dimethylamine (DMA), trimethylamine (TMA) and ethylenediamine (EDA). The cluster structures are obtained using a funneling approach employing the ABCluster program, semiempirical PM7 calculations and ωB97X-D/6-31++G(d,p) calculations. The final binding free energies are calculated at the DLPNO-CCSD(T0)/aug-cc-pVTZ//ωB97X-D/6-31++G(d,p) level of theory using the quasi-harmonic approximation. Based on the calculated cluster geometries and thermochemistry (at 298.15 K and 1 atm), we find that the mixed (SA)1(MSA)1(base)1–2 clusters more resemble the (SA)2(base)1–2 clusters compared to the (MSA)2(base)1–2 clusters. Hence, some of the steric hindrance and lack of hydrogen bond capacity previously observed in the (MSA)2(base)1–2 clusters is diminished in the corresponding (SA)1(MSA)1(base)1–2 clusters. Cluster kinetics simulations reveal that the presence of an MSA molecule in the clusters enhances the cluster formation potential by up to a factor of 20. We find that the SA–MSA–DMA clusters have the highest cluster formation potential, and thus, this system should be further extended to larger sizes in future studies.


INTRODUCTION
Aerosol particles are important for our global climate due to their direct interaction with solar radiation 1 and their potential to act as a nucleus for cloud droplet formation. 2 Clustering of low volatile acid molecules with atmospheric base molecules is the prime driver of atmospheric new particle formation (NPF). Newly formed atmospheric particles provide the required surface to initiate cloud droplet formation, and modeling studies have shown that NPF can explain roughly half the global number concentration of cloud condensation nuclei (CCN). 3 However, the compounds involved in the formation and growth of atmospheric aerosols are highly uncertain, leading to a large uncertainty in global climate estimation. 4 Over the open oceans and at coastal regions, the emission of dimethyl sulfide (DMS) is believed to be an important source of atmospheric aerosol particles. 5 DMS reacts with oxidants in the atmosphere via long oxidation chains, and over time, DMS is transformed into the low volatile acids sulfuric acid (SA) and methanesulfonic acid (MSA). 6 SA clustering with atmospheric base molecules is wellestablished as a main driver for inland NPF. 7−10 In contrast, the role of MSA in NPF is much more uncertain. Recent measurements have been performed in marine environments across the globe 11−13 identifying typical concentrations of SA and MSA in the range of 10 5 −10 7 molecules cm −3 depending on location and season. However, simultaneous gas-phase measurements of SA and MSA remain scarce, leading to limited information about the combined role of the two compounds in NPF.
Quantum chemical calculations of thermochemical parameters can be used as input to cluster kinetics modeling, 14 yielding detailed insight into the exact role of various chemical species. Both SA−base 15−27 and MSA−-base 28−39 clusters have extensively been studied using quantum chemical methods. However, studies involving clusters containing both SA and MSA remain extremely scarce. Bork et al. 40 studied SA−MSA− DMA clusters using quantum chemical methods. It was found that in marine environments MSA could enhance cluster formation between SA and dimethylamine up to a factor of 3 at 258.15 K. Applying a combination of flowtube experiments and quantum chemical calculations, Wen et al. 41 demonstrated that adding MSA to newly formed SA -water particles led to a dual particle distribution, while adding SA to newly formed MSA−water particles did not show this behavior. In both cases, mixed SA−MSA−water particles emerged, but with highly different number concentrations and size distributions.
Recently, an increased interest has also led to investigation of the potential synergistic effect between two different base molecules such as ammonia and dimethylamine 42,43 as well as different amines such as mono-/di-/trimethylamine. 44 This concept was recently extended to tribase synergy between three base molecules in (SA) 3 (base) 3 clusters. 45 However, genuine multicomponent clusters simultaneously consisting of multiple acid molecules and multiple base molecules have not yet been studied.
Studying acid−base clusters using quantum chemical methods is extremely time-consuming. We recently introduced the clusteromics approach, 46 which involves the comprehensive screening of small multicomponent molecular clusters, thereby providing direct insight into which chemical species are potentially involved in the initial cluster formation and growth. While giving insight into the species involved in cluster formation, the clusteromics approach also aids in constructing high-quality thermochemical data sets that can be applied to train quantum machine learning (QML) models. As a proof-ofconcept, we recently reported the application of a kernel ridge regression ML model with the FCHL representation 47,48 for studying sulfuric acid−water cluster formation. 49 It was shown that it was possible to train an ML model to accurately predict the binding energies of sulfuric acid−water clusters with mean absolute errors below 0.5 kcal mol −1 .
In our first two clusteromics papers, we studied SA−base 50 and MSA−base 51 clustering. Depending on the basicity of the clustering base, SA−base clusters can rapidly form and grow. On the contrary, MSA−base clusters where unable to form in any appreciably amounts by themselves, thereby requiring an additional clustering species. This is caused by the lack of hydrogen bond donors available in the MSA molecule, which hinders the growth beyond the (acid) 2 (base) 2 cluster systems. Exchanging one MSA molecule with an SA molecule in the clusters will increase the hydrogen-bonding capacity, thereby potentially alleviating this deficiency. This work is the third installment in the clusteromics series of papers that sets out to study the thermochemistry and cluster kinetics of mixed (SA) 1 (MSA) 1 (base) 0−2 clusters with the bases ammonia (A), methylamine (MA), dimethylamine (DMA), trimethylamine (TMA), and ethylenediamine (EDA). To the best of our knowledge, this is the first study that investigates SA−MSA− base clusters with two different base molecules.

COMPUTATIONAL DETAILS
Density functional theory and semiempirical PM7 52 geometry optimizations and vibrational frequency calculations were carried out with Gaussian 16. 53 The Gaussian 09 default convergence criteria were used to allow comparison with the data in the Atmospheric Cluster DataBase (ACDB). 54 We used the ORCA 4.2.1 program 55,56 to carry out the Domain based Local Pair Natural Orbital DLPNO−CCSD(T 0 ) 57,58 singlepoint energy calculations using an aug-cc-pVTZ basis set. We will only briefly outline the computational methodology and refer to our two previous studies in the clusteromis series 50,51 and our recent review 59 for full details. Based on numerous benchmarks of the binding energies of atmospherically relevant clusters, 60−62 we employed the ωB97X-D 63 functional with the 6-31++G(d,p) basis set. 64,65 Vibrational frequencies below 100 cm −1 were treated by applying Grimme's quasi-harmonic approximation 66 using the Goodvibes 67 code. The cluster structures were sampled using a funneling workflow: 44 Here, the calculations using the ABCluster program 70,71 followed the recommended settings by Kubecǩa et al. 68 using 3000 as the population size (SN = 3000), a maximum of 200 generations (g max = 200), and a maximum of 4 scout bees (g limit = 4). A total of 1000 local minima were saved for each cluster protonation state. The sorting was based on root-mean-square deviations (RMSD) between the atomic positions using the ArbAlign program 72 and used to identify and remove identical cluster configurations. On the basis of previous studies involving sulfuric acid/organic acid hydrate clusters, 73,74 we applied a 0.38 Å RMSD cutoff value to judge when two clusters were identical.
It was recently pointed out by Kurfman et al. 75 that introducing cutoff values in the PM7 energy could lead to important configurations being filtered out in the process. Hence, all of the unique PM7 structures were used as a starting point for the DFT calculations. The DFT calculations were restarted once as some cluster structures did not converge due to an unfavorable starting geometry from the former PM7 optimization. Finally, for the five cluster structures lowest in free energy at the DFT level, we carried out DLPNO-CCSD(T 0 )/aug-cc-pVTZ calculations on top of the DFT geometries.

Synergistic Effects.
We have previously defined the synergistic effect between two cluster components j and k with the synergy factor Γ j,k : 50,51 Herein, we also study clusters that consist of two different acids and thereby extend the concept of base synergy to the acids SA and MSA via the acid synergy factor Γ SA,MSA : This formulation will allow us to easily identify for which systems it is favorable to exchange a SA molecule with a MSA molecule.
2.2. ACDC. The calculated thermochemical parameters (ΔH and ΔS) are used as input for cluster kinetics simulations using the Atmospheric Cluster Dynamics Code (ACDC) 14,76 to simulate the cluster formation potentials (J potential ). The original ACDC code was downloaded from the ACDC repository 76−78 and modified. We used default values for coagulation losses corresponding to typical values in the boundary layer (cs_exp = −1.6 and cs_ref = 1 × 10 −3 ). The simulations were performed at 278.15 K as this corresponds to conditions where nucleation bursts are frequently observed in pristine environments. Similar to our previous studies, 50, 51 clusters consisting of (acid) 3 (base) 2−3 were allowed to leave the simulation box and contribute to the cluster formation potential. The (acid) 2 (base) 3 base clusters were not allowed to contribute to the J potential value, as clusters that contain more bases than acids are usually unstable in electrically neutral acid−base cluster systems. 25 54 The identified lowest free energy clusters are displayed in Figure 1, presenting the studied largest (SA) 1 (MSA) 1 (base) 2 clusters that contain two different base molecules. The cluster structures were calculated at the DLPNO−CCSD(T 0 )/aug-cc-pVTZ//ωB97X-D/6-31++G-(d,p) level of theory using the quasi-harmonic approximation and at 298.15K, 1 atm.
The identified cluster structures bear high resemblance to the previously studied corresponding SA−base cluster structures. 50 While the MSA−base clusters, 51 for most systems, adopt a "symmetric" shape similar to the (SA) 1 (MSA) 1  Previously, we identified that the SA−TMA system had a high cluster formation potential 50 while the corresponding MSA− TMA system effectively formed zero clusters. 51 This effect was attributed to the emergence of weak SO···H−C noncovalent interactions due to MSA and TMA only having one donor− acceptor pair available for hydrogen bonding. However, the observed interactions between the SA and MSA molecules in the SA−MSA−base clusters in Figure 1 will likely mitigate the low cluster formation potential observed in the MSA−TMA system.
3.2. Thermochemistry. The calculated free energies (at 298.15K and 1 atm) of the studied SA−MSA−base clusters are presented in Table 1. The calculations are performed at the DLPNO−CCSD(T 0 )/aug-cc-pVTZ//ωB97X-D/6-31++G-  (d,p) level of theory using the quasi-harmonic approximation. The corresponding data for the SA−base 50 and MSA−base 51 systems are presented as a comparison. On the basis of the gasphase basicity of the base molecules, 79 they are divided into classifications (weak, medium, strong). The acid homo-and heterodimers show very similar thermochemistry with values of −5.5, −5.4, and −5.1 kcal/ mol for the (SA) 2 , (MSA) 2 , and (SA) 1 (MSA) 1 dimer clusters, respectively. It has previously been shown that for weakly bound cluster systems, such as the sulfuric acid−ammonia system, 76 the acid dimer can be an important initial step in cluster formation. The formation of these dimer clusters will depend on the concentrations of SA and MSA. Because of their similar thermochemistry, having one acid in high excess will perturb the equilibrium concentration of each of the acid dimers. For instance, in the case where MSA is in high excess, the (MSA) 2 and (SA) 1 (MSA) 1 dimer clusters will be formed predominantly.
The (SA) 1 (MSA) 1 (base) 1 clusters show the following trend in stability (in kcal mol −1 ), with more negative free energies representing more stable clusters: (A) 1  . This is consistent with the previously observed trend in the corresponding (SA) 2 (base) 1 clusters. 50 In case of the (MSA) 2 (base) 1 , the stability ranking is slightly different, with the DMA-and TMA-containing clusters being less stable than the EDA-containing clusters. This is caused by the bulky methyl substituents having unfavorable interactions with the methyl group in MSA. Hence, exchanging one MSA molecule with an SA molecule alleviates some of the steric hindrance.
For the (SA) 1 (MSA) 1 (base) 2 clusters, with a single base type, we observe the following stability ranking (in kcal mol −1 ), with more negative free energies representing more stable clusters: . Again, this implies that exchanging one MSA molecule with one SA molecule will relieve some of the deficiencies observed in the MSA-TMA cluster system. In contrast, for the (SA) 2 (base) 2 clusters, the stability of the (SA) 2 (TMA) 2 clusters is significantly higher than the stability of the (SA) 2 (MA) 2 clusters.
For the (SA) 1 (MSA) 1 (base) 2 clusters with two different bases, we observe a w,m/s < m,s < s,s pattern based on the base classifications. Hence, the cluster stability to some extent follows the basicity of the base molecules. The only exception is the (SA) 1 (MSA) 1 (TMA) 1 (EDA) 1 cluster, which ranks lower in stability than the m,s clusters. This pattern can be understood from the number of bulky methyl group substituents in the (SA) 1 (MSA) 1 (TMA) 1 (EDA) 1 cluster. This trend is quite similar to the (SA) 2 (base) 2 clusters with two different bases. However, this differs from the (MSA) 2 (base) 2 clusters, where clusters containing MA rank significantly higher despite their lower basicity. This is consistent with previous studies on MSA− base clusters 33,37 that have demonstrated that this is caused by an intricate combination of hydrogen bond capacity, basicity of the base, and sterical hindrance.
Overall, the stability of the clusters follows (MSA) 2 (base) 1−2 < (SA) 1 (MSA) 1 (base) 1−2 < (SA) 2 (base) 1−2 . Hence, the stability of the mixed (SA) 1 (MSA) 1 (base) 1−2 clusters is seen to be in between that of the (SA) 2 (base) 1−2 and (MSA) 2 (base) 1−2 clusters. However, inspecting the thermochemistry in Table 1, it is clear that the thermochemistry of the mixed clusters more closely resembles that of the corresponding SA−base clusters, especially for the larger clusters. To look further into this trend we can inspect the cluster synergy factors.
3.3. Synergy Factors. The synergy factors, as defined in section 2.1, correspond to the binding free energy difference between a cluster that consists of the components j,k and the average of the corresponding clusters that consist of j,j and k,k. Hence, a negative synergy factor indicates a synergistic effect between the components j,k corresponding to a lowering of the average binding free energy. On the contrary, a positive synergy factor corresponds to an increase in the average binding free energy leading to a dyssynergy between the components. Table  2 presents the calculated base synergy factors at the DLPNO-CCSD(T 0 )/aug-cc-pVTZ//ωB97X-D/6-31++G(d,p) level of theory using the quasi-harmonic approximation at 298.15 K and 1 atm.
In all cases, we observe a slight base synergy, as all the calculated synergy factors are negative. This implies that the mixed base system is more thermodynamically stable compared to the average of the two isolated base systems. We observe large negative values of −1.9, −2.8, and −1.7 kcal/mol for Γ A,TMA , Γ MA,TMA , and Γ DMA,TMA , respectively. This is caused by the fact that the MSA-TMA clusters are quite unstable, and thus, the exchange of one TMA molecule with either A, MA, or DMA leads to a large increase in stability. From the discussion of the cluster structures in section 3.1 and the calculated thermochemistry in Table 1, it is clear that there is some synergy between the two acids SA and MSA in the SA−MSA−base clusters. Table 3 presents the calculated acid synergy factors (Γ SA,MSA ) at the DLPNO-CCSD(T 0 )/aug-cc-pVTZ//ωB97X-D/6-31++G-(d,p) level of theory using the quasi-harmonic approximation at 298.15 K and 1 atm.
For the clusters with two identical bases, the acid synergy factors (Γ SA,MSA ) are favorable for the (SA) 1   3.4. Cluster Formation Potential. The previous sections have presented the calculated cluster thermochemistry, which is essential for the stability of the clusters and, hence, their ability to grow into larger sizes. However, the abundance of each of the clustering species is also important to consider. We have simulated the cluster formation potential (J potential ) of the studied systems using ACDC. We kept the SA concentration fixed at 1 × 10 6 molecules cm −3 and studied MSA concentrations of 1 × 10 5 , 1 × 10 6 , and 1 × 10 7 molecules cm −3 . This allows us to investigate three different MSA:SA concentration ratios which correspond to the scenarios where MSA is limited (1:10), MSA is equal to SA (1:1), and MSA is in excess (10:1). We studied the following atmospherically relevant ranges of mixing ratios of the bases: ammonia (10 ppt to 10 ppb), methylamine (1−100 ppt), dimethylamine (1−10 ppt), trimethylamine (1−10 ppt), and ethylenediamine (1−10 ppt). Table 4 presents the simulated cluster formation potentials in the studied lower and upper limits of the bases.
Unsurprisingly, it is observed that the cluster formation potential for each of the studied systems increases with increasing MSA concentration. This is simply caused by the fact that increased concentrations of clustering acids are available. Hence, even though MSA is a worse clustering species than SA, bases are generally in excess, and thus, increased concentration of the acids will increase the cluster formation potential.
The simulated cluster formation potential of the SA−MSA−A clusters is quite low. Even when considering a high load of up to 10 ppb of ammonia and [MSA] = 10 7 molecules cm −3 , the cluster formation potential remains 1.48 × 10 −3 clusters cm −3 s −1 or below. The clusters are growing out exclusively via collisions with the (SA) 2 (A) 2 clusters even when considering [MSA] up to 10 7 molecules cm −3 . This is caused by the fact that both the MSA−A and SA−MSA−A cluster systems have significantly higher binding free energies than the corresponding SA−A cluster systems.
The cluster formation potential of the SA−MSA−MA cluster system is also observed to be low, with a maximum cluster formation potential of 0.345 clusters cm The SA−MSA−TMA cluster system is also observed to have a high cluster formation potential. However, the clusters exclusively grow out as clusters that contain SA and TMA. This is caused by the high instability of the MSA−TMA clusters. The SA−MSA−TMA cluster formation potential appears to be less sensitive to the MSA concentration compared to the SA− MSA−DMA system. In contrast, the SA−MSA−TMA system is seen to be very dependent on the TMA concentration. This is because the (SA) 1 (TMA) 1 dimer cluster is important for the cluster formation pathways. For instance, at 1 ppt of TMA and [MSA] = 10 5 molecules cm −3 , 9% of the collisions out of the system is due to collisions with the (SA) 1 (TMA) 1 dimer cluster. At 10 ppt of TMA and [MSA] = 10 5 molecules cm −3 this is increased to 26%.    Table 5 presents the calculated enhancement in cluster formation potentials of the studied clusters. At [MSA] = 1 × 10 5 molecules cm −3 , the enhancement is relatively low with a maximum enhancement of 1.14 for the SA− MSA−DMA system. Interestingly, for the SA−MSA−A cluster system there is observed an inhibiting effect for MSA concentrations of 1 × 10 6 molecules cm −3 or below. This is most likely caused by the fact that the SA−A, SA−MSA−A, and MSA−A cluster systems all bind very weakly. Hence, there will be a build-up of smaller clusters distributed over more systems that cannot grow. We see that the enhancement in cluster formation potential is quite limited for the SA−MSA−TMA system and not very sensitive to the MSA concentration, with a maximum enhancement of a factor of 2.98. This is caused by the fact that the MSA-TMA clusters bind very weakly. The SA− MSA−MA/DMA/EDA cluster systems show similar R MSAvalues with enhancements up to a factor of around 20 at [MSA] = 1 × 10 7 molecules cm −3 . It should be mentioned that in the high MSA concentration limit more collisions with MSA molecules will lead out of the system. This also implies that we are intrinsically assuming tha t the f ormed (SA) 1 (MSA) 2 (base) 2 clusters can also be considered stable, which presently remains unknown. Thus, the best estimate of the enhancing potential of having MSA present in the clusters is the situation when [SA] = [MSA] = 10 6 molecules cm −3 . However, this still implies that having MSA present can lead to an enhancement in cluster formation potential around a factor of 2. This clearly demonstrates that MSA shows great synergy in SA−MSA−base cluster systems, and in marine environments where both MSA and SA are present they will most likely both contribute to the formation of new particles. It should be noted that the increase in cluster formation potential is also a consequence of the increased available acid vapor concentration. As the atmosphere is generally limited by strongly nucleating acids such as SA an increase in available clustering material such as MSA will inevitably increase the cluster formation potential.
Out of the systems studied herein, the SA−MSA−DMA clusters show the highest cluster formation potential and thus should be extended to larger system sizes in the future to fully explore cluster formation involving strong bases in marine environments. The cluster thermochemistry has been calculated at the DLPNO-CCSD-(T 0 )/aug-cc-pVTZ//ωB97X-D/6-31++G(d,p) level of theory using the quasi-harmonic approximation. We find that the mixed SA−MSA−base clusters more closely resemble the structures and thermochemistry of the SA−base clusters as opposed to the MSA−base clusters. We find that the inability of the MSA− TMA system in forming clusters is alleviated by exchanging one of the MSA molecules with an SA molecule. Cluster kinetics simulations reveal that the cluster formation potential of the mixed SA−MSA−base clusters are enhanced by up to a factor of 20 compared to the corresponding SA−base clusters. Studying the cluster formation potential, we find that the SA−MSA− DMA clusters have the highest cluster formation potential of the studied systems. Hence, these clusters should be extended to larger sizes in future work.

CONCLUSIONS
As there is a clear positive interaction between the acid components in the clusters, we will in the following manuscripts in the series look into other, more abundant acid molecules that might be relevant for stabilizing the initial cluster formation. For instance, nitric acid has recently been demonstrated to be important in the initial steps of SA−DMA cluster formation 80 as well as for the particle growth 81 in polluted regions. In a similar manner, because of its high abundance, formic acid was recently shown to be the most efficient organic acid in enhancing MSA− MA cluster formation. 82 Furthermore, by studying small clusters consisting of sulfuric acid, formic acid, ammonia, and water, Harold et al. 83 recently showed that formic acid is just as effective as ammonia in stabilizing the clusters. Hence, further studies on the role of nitric acid and formic acid in cluster formation is warranted.
xyz files of the five lowest free energy cluster structures for each studied system at the ωB97X-D/6-31++G(d,p) levels of theory (ZIP)