Clusteromics II: Methanesulfonic Acid-Base Cluster Formation.

The role of methanesulfonic acid (MSA) in atmospheric new particle formation remains highly uncertain. Using state-of-the-art computational methods, we study the electrically neutral (MSA)0-2(base)0-2 clusters, with base = ammonia (A), methylamine (MA), dimethylamine (DMA), trimethylamine (TMA), and ethylenediamine (EDA). The cluster configurations are obtained using the ABCluster program and the number of initial cluster configurations is reduced based on PM7 calculations. Thermochemical parameters are calculated using the quasi-harmonic approximation based on the ωB97X-D/6-31++G(d,p) cluster structures and vibrational frequencies. The single point energies are calculated at the DLPNO-CCSD(T0)/aug-cc-pVTZ level of theory. We find that MSA shows a different interaction pattern with the bases compared to sulfuric acid and does not simply follow the basicity of the bases for these small clusters. In all cases, we find that the MSA-base clusters show very low cluster formation potential, indicating that electrically neutral clusters consisting solely of MSA as the clustering acid are most likely not capable of forming and growing under realistic atmospheric conditions.

Introduction

Atmospheric cluster formation is believed to be an important initial stage of new particle formation (NPF). Sulfuric acid (SA) is regarded as one of the principal components driving NPF and SA-base clusters are acknowledged to be important for new particle formation over continental regions. We refer to our first paper in this series (Clusteromics I) for further details on the SA-base cluster formation.[1]

Over the oceans, the emission of dimethylsulfide (DMS) by phytoplankton[2] is believed to be a potent source of new particles, leading to the formation of clouds.[3] DMS reacts with oxidants in the atmosphere (OH, NO3, Cl, and BrO) to yield a broad spectrum of intermediate reaction products such as methane sulfinic acid (MSIA), dimethyl sulfoxide (DMSO), and dimethyl sulfone (DMSO2). Veres et al.[4] recently discovered a new oxidation product, hydroperoxymethyl thioformate (HPMTF), which originates from the autoxidation of DMS, acting as a gas-phase sulfur reservoir in the marine atmosphere.[5] Eventually, these intermediate products are oxidized to yield either sulfuric acid (SA) or methanesulfonic acid (MSA).[6,7] The product distribution is highly complex, depending on several environmental factors such as the temperature, pressure, NO level, and oxidant.[6] MSA has been shown to lie in the concentration range of 105–107 molecules cm–3, hence being close to the concentration of sulfuric acid.[8−14] As more stringent regulations of anthropogenically emitted SO2 are being implemented,[15−19] the anthropogenic contribution to the ambient concentration of SA is expected to decrease. Consequently, the relative global contribution of MSA to new particle formation has been hypothesized to become more important in the future.[17] While SA-base cluster formation has received immense attention in the literature,[20−30] the molecular-level understanding of the potential involvement of MSA is currently lacking.[31] The Finlayson–Pitts group has studied MSA-base nucleation using a combination of quantum chemical (QC) calculations and an experimental flow tube setup. Primarily, amines coupled with ammonia (A), oxalic acid, and water have been studied.[32−38] In all cases, methylamine (MA), dimethylamine (DMA), and trimethylamine (TMA) were shown to enhance MSA-base nucleation. In contrast to SA-base NPF, it was found that MA enhances NPF more than DMA despite having a lower base strength.[34] This effect has been ascribed to the hydrogen-bonding capacity of the base (i.e., the number of hydrogen bond N–H donors) being an important factor in MSA-base new particle formation.[34] The enhancing effect of bases on MSA nucleation is further corroborated by the fact that several field studies have shown increased MSA concentrations in small particles when either ammonia or amines are present.[39,40] However, the modeling study by Hoffmann et al.[41] demonstrated that a significant fraction of particulate MSA (up to 58%) was produced in the aqueous phase. Hence, a considerable portion of particle-phase MSA also originates from multiphase chemistry and not exclusively from gas-phase vapor nucleation or MSA uptake via condensation.

Recently, there has been an increased interest in the quantum chemical (QC) modeling of MSA-base clusters to determine the role of MSA in new particle formation. Chen et al. studied the MSA-ammonia[42] clusters and MSA-MA-water[43] clusters using quantum chemical methods and cluster distribution dynamics modeling. It was found that the bases enhanced MSA-based new particle formation; however, in all cases, the absolute formation rate remained low. Shen et al.[44] studied the MSA-monoethanol amine (MEA) clusters and found that MEA exhibited an even larger enhancing potential than MA. This was ascribed to the additional OH group in MEA that could also participate in hydrogen bonding, thus stabilizing the clusters. Recently, Shen et al.[45] demonstrated that MSA-DMA clusters up to (MSA)1–2(DMA)1–2 cluster sizes were more stable than the corresponding (MSA)1–2(MA)1–2 clusters; however, at larger sizes, steric hindrance of the bulky methyl groups in DMA led to the destabilization of the clusters. This implies that several different amines could synergistically enhance the MSA-driven NPF by maximizing the advantage of the different amine properties in various stages of cluster growth. Using a combination of experiments and QC calculations, Perraud et al.[38] studied the synergistic effect of adding ammonia to MSA-MA and MSA-TMA clusters. In both cases, there was increased production of particles. The effect was most pronounced for the MSA-TMA clusters, as the MSA-MA cluster system is intrinsically very efficient in forming particles by itself. Using the QC methods, Chen et al.[46] studied the synergistic effect between different bases (A, MA, and DMA) in MSA-base trimers. It was found that the thermodynamic stability of the trimers was directly correlated with the basicity of the bases in the trimer clusters. Hence, the role of MSA in new particle formation and especially potential synergistic effects between bases should be investigated in detail and is the focus of the current study.

This work is the second paper in the clusteromics series of papers that set out to map the thermodynamics and kinetics of the initial steps in cluster formation involving potentially important clustering vapors. Here, we report the thermodynamics and cluster growth kinetics of (MSA)0–2(base)0–2 clusters, with base = ammonia (A), methylamine (MA), dimethylamine (DMA), trimethylamine (TMA), and ethylenediamine (EDA). Clusteromics provides guidance on which cluster systems are relevant for extending to larger sizes and yield a systematic approach for constructing thermochemical databases that can be applied to develop Quantum Machine Learning (QML) models. For further information on the clusteromics approach, we refer to our recent perspective.[47]

Computational Details

Semiempirical (PM7[48]) and density functional theory (DFT) (ωB97X-D[49] with a 6-31++G(d,p) basis set) calculations were performed with Gaussian 16 program[50] using the Gaussian 09 default convergence criteria. The single point energies were calculated using the domain-based local pair natural orbital DLPNO-CCSD(T0)[51,52] method using a TightSCF convergence with the ORCA 4.2.1 program.[53,54] The quasi-harmonic approximation[55] was applied using Goodvibes[56] to correct vibrational frequencies below 100 cm–1 by treating them as rotation instead of vibrations when calculating the entropy. It should be noted that the quasi-harmonic approximation slightly increases the free energy of the clusters. For the dimer clusters in the present manuscript, this corresponds to between 0.6 and 1.2 kcal mol–1, thus making them slightly less stable.

The final thermochemical parameters are calculated at the DLPNO-CCSD(T0)/aug-cc-pVTZ//ωB97X-D/6-31++G(d,p) level of theory based on several benchmarks[57−59] and recommendations.[31,60] The DLPNO-CCSD(T0) electronic energies are calculated on top of the DFT geometries (i.e., higher on the CCSD(T) potential energy surface) and also slightly increase the free energy of the clusters. As CCSD(T) geometry optimizations are not possible to carry out for the systems in the present study, it is difficult to directly assess the magnitude of this potential error. However, as the binding energies calculated using DLPNO-CCSD(T0) on top of clusters optimized with different DFT functionals and basis sets do not show large variations,[61] this effect is expected to be minor. Hence, it should be noted that the applied level of theory should correspond to a lower limit of the calculated formation rates.[62]

The sampling procedure of the cluster structures is only mentioned here in brevity. We refer to our first paper in this series[1] for full details on the computational protocol. The structures of the (MSA)2 and (MSA)1(base)1 clusters were taken from ref (59). We studied all combinations of the five bases implying the computational screening of 35 new cluster systems. Schematically, the cluster sampling follows the procedureThis is a well-established protocol based on the previous work by Temelso et al.,[63] Kubečka et al.,[64] and Odbadrakh et al.[65] The PM7 configurations were sorted based on the root mean square deviations (RMSDs) between atomic positions using ArbAlign.[66] Configurations with RMSDs within 0.38 Å or below are treated as identical. Kurfman et al.[67] recently showed that for the (SA)3 cluster system, the introduction cutoff values in the PM7 energy could potentially lead to important configurations being missed. To adequately scan the potential energy surface, all identified PM7 configurations are subsequently optimized at the ωB97X-D/6-31++G(d,p) level of theory. Applying this workflow yielded a total of 5508 unique (MSA)0–2(base)0–2 cluster structures. All of the cluster structures and the calculated thermochemistry have been added to the Atmospheric Cluster DataBase (ACDB).[68]

The synergistic effect between two cluster components j and k is defined by the synergy factor Γ asThus, the synergy factor provides insight into thermodynamics, which leads to a highly nonadditive behavior. The calculated thermochemistry is used as input for the Atmospheric Cluster Dynamics Code (ACDC)[69,70] to study the cluster dynamics. The ACDC code was obtained from the ACDC repository.[70−72]

Results and Discussion

Cluster Structures

We studied (MSA)0–2(base)0–2 clusters, with base = ammonia (A), methylamine (MA), dimethylamine (DMA), trimethylamine (TMA), and ethylenediamine (EDA). The cluster structures have been sampled using the procedure outlined in Section . In the case of the (MSA)1–2(A)1–2, (MSA)1–2(MA)1–2, and (MSA)1–2(DMA)1–2 clusters, we identified structures similar to those recently published by Chen et al.[42,43] and Shen et al.[45]Figure shows the lowest free energy cluster structures consisting of two methanesulfonic acid and two different bases. The calculations are performed at the DLPNO-CCSD(T0)/aug-cc-pVTZ//ωB97X-D/6-31++G(d,p) level of theory with the quasi-harmonic approximation (100 cm–1) at 298.15 K and 1 atm.

Figure 1

Calculated lowest free energy cluster structures at the DLPNO-CCSD(T0)/aug-cc-pVTZ//ωB97X-D/6-31++G(d,p) level of theory. Calculated at 298.15 K, 1 atm with the quasi-harmonic approximation.

(SA)2(base)2 clusters are often held together via direct bisulfate–bisulfate interactions.[1] Compared to SA, an MSA molecule has one of the S–OH groups exchanged with a −CH3 group. After proton transfer from MSA to the bases, the reduced number of S–OH groups implies that direct acid–acid interactions are not possible. This lack of acid–acid interactions means that the cluster structures must be held together by linking the two MSA molecules with the bases. This is one of the reasons that the hydrogen-bonding capacity of the base is quite important for MSA clusters. As seen from Figure , this is illustrated by the clusters containing TMA, where weak S=O···H–C noncovalent interactions begin to emerge. It is seen that the organic −CH3 groups of the MSA molecules orient as far away from each other as possible. Similarly, the base −CH3 groups also point outward, leading to an inner core consisting of the inorganic ions and an outer shell of organic side chains. This emerging core–shell structure might inhibit the further attachment of additional vapor molecules as few vacant hydrogen-bonding sites are available.

Thermochemistry

The thermochemistry of the (MSA)0–2(base)0–2 clusters has been calculated at the DLPNO-CCSD(T0)/aug-cc-pVTZ//ωB97X-D/6-31++G(d,p) level of theory. We applied the quasi-harmonic approximation where the entropy contribution of vibrational frequencies below 100 cm–1 are calculated using the rotational partition function. Table shows the calculated binding free energies at 298.15 K and 1 atm. The classifications, weak (w), medium (m), and strong (s), refer to the gas-phase basicity[73] of the bases in the clusters. The data for the corresponding sulfuric acid–base systems are included for comparison and have been taken from ref (1).

Table 1

Calculated Binding Free Energies (in kcal/mol, at 298.15 K, 1 atm) of the MSA-Base Clusters at the DLPNO-CCSD(T0)/aug-cc-pVTZ//ωB97X-D/6-31++G(d,p) Level of Theory Using the Quasi-harmonic Approximationa

	classification	(SA)1b	(SA)2b	(MSA)1	(MSA)2
(base)0			–5.6		–5.4
(A)1	w	–5.6	–19.4	–3.4	–12.4
(MA)1	m	–7.2	–24.4	–3.9	–17.8
(DMA)1	s	–11.5	–29.4	–7.1	–21.6
(TMA)1	s	–12.6	–27.9	–8.7	–19.1
(EDA)1	s	–10.4	–28.1	–7.1	–22.8
(A)2	w, w	–9.7	–27.0	–2.6	–20.5
(MA)2	m, m	–10.7	–36.6	–7.4	–31.5
(DMA)2	s, s	–14.9	–44.0	–12.0	–36.6
(TMA)2	s, s	–15.3	–41.5	–6.0	–25.6
(EDA)2	s, s	–16.3	–41.8	–12.9	–34.4
(A)1(MA)1	w, m	–10.0	–32.4	–6.7	–26.1
(A)1(DMA)1	w, s	–13.4	–34.7	–5.3	–28.9
(A)1(TMA)1	w, s	–13.6	–32.3	–7.6	–23.1
(A)1(EDA)1	w, s	–12.8	–33.7	–9.1	–27.3
(MA)1(DMA)1	m,s	–14.2	–40.6	–10.7	–33.8
(MA)1(TMA)1	m, s	–13.4	–38.1	–7.4	–28.1
(MA)1(EDA)1	m, s	–13.4	–9.1	–9.7	–32.2
(DMA)1(TMA)1	s, s	–14.8	–42.3	–10.0	–30.7
(DMA)1(EDA)1	s, s	–17.4	–43.4	–10.7	–35.4
(TMA)1(EDA)1	s, s	–15.1	–42.7	–8.3	–29.6

The classifications refer to the base strength, with w = weak, m = medium, and s = strong.

Data taken from ref (1).

In contrast to the SA-base cluster system, the thermochemistry of the (MSA)1(base)1 clusters is not in all cases more favorable than the MSA dimer (ΔG = −5.4). For instance, the clustering of MSA with ammonia or MA is less favorable than the MSA dimer formation. We observe the following pattern in the reaction free energies of the (MSA)1(base)1 clusters (in kcal mol–1): (MSA)1(A)1 (−3.4) < (MSA)1(MA)1 (−3.9) < (MSA)1(EDA)1 (−7.1) ≲ (MSA)1(DMA)1 (−7.1) < (MSA)1(TMA)1 (−8.7). Interestingly, the MSA-base clusters follow the same interaction pattern as the SA-base clusters for the dimers, with the free energy clearly being correlated with the gas-phase basicity of the bases. However, the (MSA)1(base)1 clusters are in all cases drastically higher in free energy than the corresponding (SA)1(base)1 clusters.[1] Logically, this indicates that not only the basicity of the base but also the acidity of the acid is important for the initial cluster formation process. This effect has also recently been demonstrated by Chee et al.,[74] who showed that acid–base heterodimer stabilities were related to the difference between the gas-phase acidity of the acid (HA) and acidity of the conjugate acid of the base (BH+).

Consistent with the SA-base cluster systems, the (MSA)1(base)2 cluster trimers are all significantly less stable than the (MSA)2(base)1 cluster trimers. The binding free energies of the (MSA)2(base)1 clusters follow the pattern (in kcal mol–1): (MSA)2(A)1 (−12.4) < (MSA)2(MA)1 (−17.8) < (MSA)2(TMA)1 (−19.1) < (MSA)2(DMA)1 (−21.6) < (MSA)2(EDA)1 (−22.8). With two MSA molecules in the cluster, the free energy of (MSA)2(TMA)1 becomes less favorable than the corresponding DMA- and EDA-containing clusters. This is clearly illustrated by the hydrogen-bonding capacity of the bases. TMA can only form a single interaction with one of the two MSA molecules, while DMA and EDA can interact with both MSA molecules simultaneously. The issue of hydrogen-bonding capacity of TMA is further illustrated in the (MSA)1(base)2 clusters, which follow the pattern (in kcal mol–1): (A)2 (−2.6) < (TMA)2 (−6.0) < (MA)2 (−7.4) < (DMA)2 (−12.0) < (EDA)2 (−12.9). Here, the TMA-containing cluster has binding free energy less favorable than that of MA. This is caused by the fact that the two TMA molecules each have one hydrogen bond acceptor group, but MSA only has a single hydrogen bond donor group available for cluster formation.

In the case of the (MSA)2(base)2 clusters, the clusters containing DMA and EDA are the most stable. Similar to the SA-base system, the (MSA)2(DMA)2 cluster is the most stable, with a binding free energy of −36.6 kcal mol–1. For the SA-base cluster system, the stability of (SA)2(EDA)2 and (SA)2(TMA)2 clusters were close to each other, with binding free energies of −41.5 and −41.8 kcal mol–1, respectively. This is not the case for the MSA-base clusters, where (MSA)2(EDA)2 and (MSA)2(TMA)2 have binding free energies of −34.4 and −25.6 kcal mol–1, respectively. The low stability of the (MSA)2(TMA)2 cluster is caused by the emergence of weak S=O···H–C noncovalent interactions (see Figure ). Overall, the MSA-base clusters do not simply follow the basicity of the bases in the manner that SA-base clusters do. This is clearly illustrated by the (MSA)2(base)2 clusters containing MA, which in most cases are more stable than the corresponding TMA-containing clusters. As also pointed out by Shen et al.,[45] this is most likely caused by the stability being dependent on an intertwined connection between the hydrogen-bonding capacity, steric hindrance between the bulky −CH3 groups, and base strength.

Combining two different bases in the (MSA)1–2(base)2 clusters leads to very distinctive synergy factors compared to the (SA)1–2(base)2 cluster system. Table presents the calculated synergy factors at the DLPNO-CCSD(T0)/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. The data for the sulfuric acid–base systems are included for comparison and has been taken from ref (1).

Table 2

Calculated Synergy Factors (at 298.15 K, 1 atm) of the Mixed-Base Clusters at the DLPNO-CCSD(T0)/aug-cc-pVTZ//ωB97X-D/6-31++G(d,p) Level of Theory Using the Quasi-Harmonic Approximation

	(SA)1a	(SA)2a	(MSA)1	(MSA)2
ΓA,MA	0.2	–0.6	–1.7	–0.1
ΓA,DMA	–1.1	0.8	2.0	–0.3
ΓA,TMA	–1.1	2	–3.3	–0.1
ΓA,EDA	0.2	0.7	–1.4	0.2
ΓMA,DMA	–1.4	–0.4	–1.0	0.3
ΓMA,TMA	–0.4	0.9	–0.7	0.4
ΓMA,EDA	0.1	0.1	0.4	0.8
ΓDMA,TMA	0.3	0.5	–1.0	0.4
ΓDMA,EDA	–1.8	–0.6	1.7	0.1
ΓTMA,EDA	0.7	–1.1	1.1	0.4

Data taken from ref (1).

For the smaller (MSA)1(base)2 clusters, we observed highly favorable synergy factors up to −3.3 kcal mol–1 in the case of ΓA,TMA. However, as the (MSA)1(base)2 clusters are quite unstable compared to the (MSA)2(base)1 clusters, they are most likely not involved in the cluster formation pathway. For the (MSA)2(base)2, the different bases do not present pronounced synergistic effects, with numerical values below 1 kcal mol–1 in all cases. Hence, we do not observe significant synergy between the bases in the (MSA)1–2(base)2 clusters.

Simulated Cluster Formation Potential

We estimate the cluster formation potential Jpotential as the flux of smaller (MSA)1–2(base)1–2 clusters toward relevant larger clusters at realistic atmospheric conditions and vapor concentrations. Previous studies of atmospherically relevant acid–base clusters have shown that the clusters have the lowest free energy barrier along the diagonal on the acid–base cluster grid, i.e., when the number of acids and bases are approximately equal. This has been demonstrated both for SA-base clusters[70,75] and MSA-base clusters.[42,43] For the (MSA)0–2(base)0–2 cluster systems, this implies that the (MSA)2(base)3, (MSA)3(base)2, and (MSA)3(base)3 clusters are candidates to grow out of the simulation system and contribute to the cluster formation potential Jpotential. From the previous section, it is apparent that the (MSA)1(base)2 clusters are significantly less stable than the (MSA)2(base)1 and (MSA)2(base)2 clusters. Hence, the (MSA)2(base)3 clusters have high evaporation rates and do not contribute to the potential cluster formation. As the (MSA)2(base)1 and (MSA)2(base)2 clusters are the most stable in the system, we investigated whether collisions between them could contribute to the cluster formation potential. It was found that mixing ratios much higher than those present in the atmosphere are required for the (MSA)4(base)2–4 clusters to contribute to the cluster formation pathways. For more information, see the Supporting Information.

When two bases are present in the cluster, it becomes important which compounds are allowed to evaporate when passing the system boundary in a “forbidden” direction. We have assigned the bases that bind most strongly with a higher priority in the simulations, implying that the bases that lead to more weakly bound clusters are removed first from the cluster when passing a “forbidden” growth direction. This assignment does not necessarily follow the gas-phase basicity of the bases as demonstrated with the MSA-MA-TMA system in the Supporting Information. We remind the reader that the flux toward larger clusters is purely a “potential” to form larger clusters and should not be used as an actual cluster formation rate.

To simulate the cluster formation potential of the MSA-base clusters, we chose the following atmospheric relevant mixing ratio ranges 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). The methanesulfonic acid concentration was set to 1 × 106 molecules cm–3. Table presents the cluster formation potential of the MSA-base clusters with a single type of base in the clusters. The upper and lower mixing ratios limits of the studied bases are presented in the table. The corresponding data for the SA-base systems are from ref (1) and included for comparison.

Table 3

Simulated Cluster Formation Potential (Jpotential) for Methanesulfonic Acid Clusters Containing a Single Type of Basea

cluster system	lower limit	upper limit
ammonia (A)	10 ppt	10 ppb
SA-Ab	1.26 × 10–10 cm–3 s–1	1.26 × 10–4 cm–3 s–1
MSA-A	1.69 × 10–15 cm–3 s–1	1.69 × 10–9 cm–3 s–1
methylamine (MA)	1 ppt	100 ppt
SA-MAb	5.49 × 10–6 cm–3 s–1	0.0211 cm–3 s–1
MSA-MA	8.69 × 10–9 cm–3 s–1	8.44 × 10–5 cm–3 s–1
dimethylamine (DMA)	1 ppt	10 ppt
SA-DMAb	0.503 cm–3 s–1	6.69 cm–3 s–1
MSA-DMA	6.76 × 10–5 cm–3 s–1	2.81 × 10–3 cm–3 s–1
trimethylamine (TMA)	1 ppt	10 ppt
SA-TMAb	0.539 cm–3 s–1	21.9 cm–3 s–1
MSA-TMA	141 × 10–11 cm–3 s–1	1.40 × 10–9 cm–3 s–1
ethylenediamine (EDA)	1 ppt	10 ppt
SA-EDAb	0.0428 cm–3 s–1	1.07 cm–3 s–1
MSA-EDA	1.98 × 10–6 cm–3 s–1	1.9 × 10–4 cm–3 s–1

The methanesulfonic acid concentration was fixed at 1 × 106 molecules cm–3. Simulations were performed at 278.15 K.

Data taken from ref (1).

The cluster formation potential of the MSA-base clusters is significantly lower than those of the corresponding SA-base cluster systems.[1] For MSA-A, MSA-MA, and MSA-TMA systems, almost no clusters are formed. It should be mentioned that we only study electrically neutral clusters, and the inclusion of ions might be important for systems that bind weakly.[76] The MSA-DMA system shows the highest cluster formation potential of all of the bases. However, the absolute value remains very low with a formation rate of 2.81 × 10–3 cm–3 s–1. The cluster formation mechanism depends on the base. For the weaker bases (A, MA), the formation of the (MSA)2 dimer serves as the initial step instead of the (MSA)1(base)1 dimer. For MSA-DMA and MSA-EDA, ∼93% of the cluster formation occurs via the (MSA)1(base)1 cluster, with a ∼7% contribution from the (MSA)2 dimer. For the MSA-TMA cluster system, there is a 100% contribution from the (MSA)1(TMA)1 cluster. These trends are well reflected in the calculated thermochemistry of the dimers in the previous section.

Interestingly, a difference of a factor 10 is seen between the cluster formation potentials of MSA-MA and MSA-DMA. This is in sharp contrast to the SA-base system, where there is a difference of a factor of 317.[1] Experimentally, Chen et al.[34] measured the following pattern in the particle number concentrations: A ≪ DMA ≈ TMA ≪ MA. However, these were measurements of particles with diameters of 2.5 nm and above, which implies that nucleation and growth might be difficult to separate. Our findings are consistent with those of Shen et al.,[45] who showed that the MSA-DMA clusters up to (MSA)1–2(DMA)1–2 cluster sizes were more stable than the corresponding (MSA)1–2(MA)1–2 clusters. However, at larger sizes, the MSA-MA clusters become more stable due to too close proximity between the bulky −CH3 groups in DMA and MSA.

While no base synergy was observed in the thermochemistry, there might be synergistic effects on the cluster formation potential simply due to the inclusion of an additional clustering vapor. Figure presents scans of the cluster formation potential as a function of two bases for the clusters containing ammonia. The MSA concentration was fixed at 1 × 106 molecules cm–3 and the simulations were performed at 278.15 K. For each base concentration range, 100 points were simulated, yielding a total of 10 000 ACDC simulations for each system.

Figure 2

Simulated cluster formation potential Jpotential in cm–3 s–1 as a function of base (A, MA, DMA, TMA, and EDA) mixing ratios. The MSA concentration was fixed at 1 × 106 molecules cm–3 and the simulations were performed at 278.15 K. Note the different color scales on the plots.

For the MSA-MA, MSA-DMA, and MSA-EDA systems, ammonia is seen to have little effect and the cluster formation potential is exclusively governed by the stronger bases. Hence, the cluster formation mechanism is due to the (MSA)2(MA)2, (MSA)2(DMA)2, and (MSA)2(EDA)2 clusters colliding with a MSA molecule. For the MSA-A-TMA system, ammonia begins to contribute. This is clearly due to the exceptionally weak cluster formation potential of the MSA-TMA clusters. Inspecting the MSA-A-TMA cluster system and looking at the bottom left corner of the subpart (A = 10 ppt, TMA = 1 ppt), the value of Jpotential has a 97% contribution from the (MSA)2(TMA)1 cluster colliding with the (MSA)1(TMA)1 cluster. Increasing the TMA mixing ratio from 1 to 5 ppt and from 5 to 10 ppt each increases the Jpotential by roughly 1 order of magnitude. However, even at 10 ppt TMA, the absolute Jpotential rate is still negligible with a value of 1.41 × 10–9 cm–3 s–1. Looking at the upper left corner of the figure (A = 10 000 ppt, TMA = 1 ppt), the cluster formation mechanism has a 97% contribution from the (MSA)2(A)2 cluster colliding with MSA. Increasing the TMA mixing ratio (A = 10 000 ppt, TMA = 5 ppt) changes the mechanism, leading to a 77% contribution from (MSA)2(A)2 + MSA, a 16% contribution from (MSA)2(TMA)1 + (MSA)1(TMA)1, and a 5% contribution from the MSA)2(A)1(TMA)1 + MSA. Further increasing the TMA mixing ratio to 10 ppt leads to a 45% contribution from (MSA)2(A)2 + MSA, a 45% contribution from (MSA)2(TMA)1 + (MSA)1(TMA)1, and a 7% contribution from the (MSA)2(A)1(TMA)1 + MSA. This clearly shows the involvement of both A and TMA in the MSA-A-TMA cluster formation.

Figure presents two-dimensional scans for the remaining combinations of bases.

Figure 3

Simulated cluster formation potential Jpotential in cm–3 s–1 as a function of base (A, MA, DMA, TMA, and EDA) mixing ratios. The MSA concentration was fixed at 1 × 106 molecules cm–3, and the simulations were performed at 278.15 K. Note the different color scales on the plots.

MA contributes to the cluster formation potential in all of the mixed-base systems. In the case of the MSA-MA-TMA clusters, it even dominates the cluster formation potential. This behavior is very distinct from the SA-MA-DMA/TMA/EDA systems, where the stronger bases in all cases dominated, with little contribution from MA. For the clusters consisting of two strong bases (DMA/TMA/EDA), TMA makes almost no contribution to the cluster formation potential. However, TMA is still involved in the cluster formation pathway via the formation of mixed-base clusters. For instance, in the mixed MSA-DMA-TMA system at 10 ppt of both DMA and TMA, the cluster formation potential follows the pathway: (MSA)2(DMA)1 → (MSA)2(DMA)2 → flux out. However, the (MSA)2(DMA)1 cluster has a 79% contribution from the (MSA)1(DMA)1 cluster, a 15% contribution from (MSA)2(DMA)1(TMA)1, and 6% contribution from (MSA)2. This implies that the MSA-TMA clusters have a non-negligible contribution to the Jpotential value by feeding into the MSA-DMA pathway via evaporation of a TMA molecule from the mixed (MSA)2(DMA)1(TMA)1 cluster. In the case of the MSA-DMA-EDA clusters, it is seen that both bases contribute to the cluster formation potential, with the largest contribution from DMA. Inspecting the MSA-DMA-EDA system and looking at the bottom left corner of the subpart (DMA = 1 ppt, EDA = 1 ppt), we note that Jpotential has a 89% contribution from the (MSA)2(DMA)2 cluster colliding with MSA and a 9% contribution from the mixed (MSA)2(DMA)1(EDA)1 cluster colliding with MSA. Hence, there is a significant contribution from both bases.

Similar to the SA-base system, the cluster formation potential of the mixed clusters is not a direct sum of the individual cluster systems. In all cases, we see a contribution to the Jpotential value due to the increased available base concentration. However, at the considered conditions, we find that the cluster formation potential of MSA-base clusters is extremely low in all cases. Furthermore, our findings confirm that the MSA-base clusters do not simply follow the basicity of bases but follow a much more intricate connection between the hydrogen-bonding capacity and the basicity of the bases. For instance, the MSA-TMA clusters are clearly limited by the hydrogen-bonding capacity, leading to weakly bound clusters. For these small clusters, steric hindrance should not play a large role, as seen from the well-separated −CH3 groups in Figure . However, for larger clusters, steric effects also contribute. At realistic atmospheric conditions (1 ppt and above depending on the base), the bases are in excess compared to MSA (∼1 × 106 molecules cm–3, ∼0.04 ppt). This implies that the Jpotential value is quite sensitive to the concentration of the acid. Taking the most strongly bound system (the MSA-DMA clusters) as an example, increasing the MSA concentration from 1 × 106 molecules cm–3 to 1 × 107 molecules cm–3 leads to a 233-fold increase in the cluster formation potential, corresponding to an increase from 0.00281 to 0.656 cm–3 s–1. While this is a large enhancement, it remains significantly lower than the corresponding SA-base cluster systems. Based on our findings herein, we advise caution when extending the MSA-base cluster systems to larger sizes. As the calculated new particle formation rates are most likely to be low, we recommend that the absolute new particle formation rates are always included and discussed in MSA-base cluster formation studies.

Conclusions

We have investigated the cluster formation potential of small multicomponent (MSA)0–2(base)0–2 clusters, with the bases ammonia (A), methylamine (MA), dimethylamine (DMA), trimethylamine (TMA), or ethylenediamine (EDA). Contrary to the SA-base cluster systems, we find that the thermochemistry and cluster formation potential do not directly follow the base strength of the bases. In the high concentration limit of the bases, we find the following trend in Jpotential: TMA ≲ A ≪ MA < EDA < DMA. The very low cluster formation potential of TMA is caused by MSA and TMA only having one accessible donor–acceptor pair, leading to a very weak formation of the (MSA)2(TMA)2 cluster. Furthermore, we find that the available acid concentration is a significantly limiting factor for the MSA-base cluster formation. Overall, we recommend caution when the electrically neutral MSA-base cluster systems are extended to larger sizes.

Oxidation of DMS leads to the concurrent formation of MSA and SA. Based on quantum chemical calculations, Rosati et al.[77] recently demonstrated that cluster formation involving (SA)(MSA)(A)1–4 (with x + y ≤ 4) consisted of different mixtures of both SA and MSA molecules. Hence, exchanging one MSA molecule with SA might alleviate the identified deficiencies in the MSA-base system, as this leads to an additional S–OH group, thus increasing the hydrogen-bonding capacity of the clusters. Having both SA and MSA in the clusters will also lead to an increased concentration of acids, which should have a large effect on the cluster formation potential. As only a few studies have considered both SA and MSA in atmospheric molecular clusters, the cluster formation potential of the SA-MSA-base clusters should be further studied.