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Article Cite This: J. Phys. Chem. A 2018, 122, 1612−1622

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Effect of Mixing Ammonia and Alkylamines on Sulfate Aerosol Formation Berhane Temelso,*,†,‡ Elizabeth F. Morrison,‡ David L. Speer,‡ Bobby C. Cao,‡ Nana Appiah-Padi,‡ Grace Kim,‡ and George C. Shields*,†,‡ †

Provost’s Office and Department of Chemistry, Furman University, Greenville, South Carolina 29613, United States Dean’s Office, College of Arts and Sciences, and Department of Chemistry, Bucknell University, Lewisburg, Pennsylvania 17837, United States

‡

S Supporting Information *

ABSTRACT: Sulfate aerosols’ cooling effect on the global climate has spurred research to understand their mechanisms of formation. Both theoretical and laboratory studies have shown that the formation of sulfate aerosols is enhanced by the presence of a base like ammonia. Stronger alkylamine bases such as monomethylamine (MMA), dimethylamine (DMA), and trimethylamine (TMA) further increase aerosol formation rates by many orders of magnitude relative to that of ammonia. However, recent lab measurements have found that the presence of ammonia and alkylamines together increases nucleation rates by another 1−2 orders of magnitude relative to the stronger alkylamines alone. This work explores that observation by studying the thermodynamic stability of clusters containing up to two sulfuric acids and two bases of the same or different type. Initial configurational sampling is performed using genetic algorithm (GA) interfaced to semiempirical methods to find a large number of low-energy configurations. These structures are then subject to quantum mechanical calculations using PW91, M06-2X, and ωB97X-D functionals and MP2 with large basis sets. The thermodynamics of formation is reviewed to determine if it rationalizes why mixed base systems yield higher rates of aerosol formation than single base ones. The gas phase basicity of the bases in a cluster is the main determinant of binding strength in smaller clusters such as those in the current study while aqueous phase basicity is more important for larger particles. Besides thermodynamic considerations, the differences in aerosol formation mechanisms as a function of size and between the gas and particle phases are discussed.

1. INTRODUCTION Atmospheric aerosols play a significant yet poorly constrained role in the global radiation balance. According to the fifth IPCC report released in 2013,1 aerosols from anthropogenic sources have an average cooling effect of −0.82 W m−2, in contrast to 3.00 W m−2 warming effect that well-mixed greenhouse gases have. The error bars associated with the warming effect of greenhouse gases are small whereas those for the direct and indirect effects of aerosols are very large. As a result, understanding the impact of aerosols on the global climate remains the largest uncertainty in climate change models. Despite that overall uncertainty, the large cooling effect of sulfate aerosols (−0.4 ± 0.2 W m−2) has been known for some time, and that has spurred research efforts to understand their mechanism of formation. In fact, there is a strong correlation between sulfuric acid concentration and new particle formation (NPF) in lab experiments and atmospheric observations.2−7 Sulfate aerosol formation is enhanced substantially by the presence of stabilizing bases like ammonia and amines8−18 as well as organics19−23 and highly oxidized molecules (HOMS).24 The effect of bases on sulfate aerosol formation has been studied both experimentally and computationally. Experiments at the Cosmics Leaving OUtdoor Droplets (CLOUD) chamber © 2018 American Chemical Society

found that ammonia at typical atmospheric concentrations of 100s parts per trillion volume (pptv) or ∼109 cm−3 increased aerosol formation rates by a factor of 100−1000.25 Another experiment using the same CLOUD chamber concluded that dimethylamine concentration of 5 pptv (∼107 cm−3) enhances new particle formation by a factor of more than 1000 relative to 250 pptv of NH3.18,26 The latter experiment also showed that increasing the dimethylamine concentration from 5 pptv up to 140 pptv only yielded a 3-fold increase in nucleation rates, suggesting that new particle formation is saturated with respect to dimethylamine at atmospheric concentrations of sulfuric acid (1 pptv or ∼107 cm−3). In both the case of ammonia and amines, the mechanism by which bases enhance nucleation is called base stabilization where one-to-one acid−base pairs prevent evaporation of monomers and stabilize the clusters.16,18 Other experiments have observed the enhancing effects of bases on aerosol formation, but the degree of the enhancement varies. For example, Yu et al.14 studied the enhancement factor in 2 nm or Received: November 13, 2017 Revised: December 21, 2017 Published: January 5, 2018 1612

DOI: 10.1021/acs.jpca.7b11236 J. Phys. Chem. A 2018, 122, 1612−1622

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The Journal of Physical Chemistry A larger particles, EF2 nm, in the presence of five amines (monomethylamine, dimethylamine, trimethylamine, triethylamine, and tert-butylamine) relative to ammonia. They generally found smaller enhancement factors10,12,13 that correlated strongly with the relative pKb of bases. The pKb, which reflects the strength of the bases in aqueous solution, increases in the order NH3 (pKb = 4.75), TMA (pKb = 4.22), MMA (pKb = 3.35), DMA (pKb = 3.27).14 The correlation between the EF2 nm and pKb suggests that species larger than 2 nm in diameter behave more like particle phase than gas phase entities. A look at the effect of ammonia, MMA, DMA, and TMA on the much smaller sulfuric acid dimer by Jen et al.27 found that the stabilizing effect of the bases increased in the order NH3 < MMA < TMA ≤ DMA, which is largely in line with the order of their gas phase basicity. However, when a 1:2 mixture of ammonia and dimethylamine (DMA) was present, Yu et al.14 found the enhancement factor in 2 nm particles increased by a factor of 101−102 relative to cases where ammonia or DMA was present alone.14 This unusual finding was attributed to synergistic interactions between ammonia and DMA.14 A 2015 work by Glasoe et al.28 likewise showed that at atmospherically relevant concentrations of sulfuric acid and MMA or DMA(∼2 pptv) the mixing of 200−600 pptv of ammonia enhanced nucleation by a factor of 101−102 relative to the case of MMA or DMA alone. Mixing ammonia with MMA and DMA not only increased the number of new particles formed but also decreased the number of MMA and DMA in the critical cluster from 2.7 and 2.0, respectively, in the absence of ammonia to about 1.0 in the presence of ammonia.28 Furthermore, the number of sulfuric acids in the critical cluster decreased from about 4.0 and 2.5 in MMA and DMA alone, respectively, to ∼1.9 and ∼1.6 when NH3 and the amines are mixed. On the basis of these findings, it was suggested that addition of ammonia to a cluster containing a single amine is more stabilizing than the addition of another amine molecule.28 In short, mixing 200 pptv of NH3 to 2 pptv of the MMA or DMA increases new particle formation by a factor of 100 relative to MMA alone and 20 compared to DMA alone. Yu et al.14 similarly found that mixing ∼500−800 pptv of NH3 with 1000−1500 pptv of DMA increased new particle formation by a factor of 10 compared to 1500−1800 pptv of DMA alone. Both Glasoe28 and Yu14 agree that these synergistic interactions between ammonia and amines are relevant at atmospheric concentration of the bases and sulfuric acid. This synergistic effect can explain many experimental observations, such as the lack of DMA concentration dependence past 3 pptv in aerosol formation rates reported by Almeida et al.,18 perhaps due to the presence of NH3. It likely plays a critical role in the atmosphere where the concentration of NH3 is generally 2−3 orders of magnitude larger than of amines. As important as this effect is, it is not well understood at a molecular and mechanistic level. While the aforementioned laboratory studies measured the enhancing effect of mixing ammonia and alkylamines on sulfate aerosol formation, most computational works have focused on the effect of individual bases, particularly ammonia and DMA, on aerosol formation.11,29−35 A few notable exceptions include papers reporting that DMA displaces ammonia in charged sulfuric acid clusters, although it is unclear if similar displacement reactions would occur in neutral clusters.36,37 The first and main goal of this work is to investigate clusters containing ammonia and amines together since such clusters had not been well-studied computationally despite their

important role in sulfate aerosol formation. The secondary goal is to provide physical insight into the experimentally observed synergy between ammonia and amines. To gain that insight, one has to think about the competing processes involved in cluster formation and decay.38 Given a certain small cluster, monomers can condense on it and lead to its growth or monomers can evaporate from it leading to its decay. The competition between collision and evaporation of monomers generally dictates the fate of the cluster. The condensation or collision of a monomer with a cluster is generally considered to lead to the formation of a bigger cluster due to the assumption that the process is collision limited. However, the evaporation rate of a monomer from a cluster depends on how strongly that monomer is bound to the cluster.31 The evaporation rate is related to the binding Gibbs free energy of the cluster. The more strongly bound the cluster is the less likely monomers are to evaporate and lead to its decay. Bases are important in sulfate aerosol formation because they stabilize clusters and decrease the evaporation rate of monomers. This work investigates if a mix of ammonia and amines stabilizes clusters, and hence decreases evaporation rates of monomers and leads to cluster growth, better than ammonia or amines alone. To examine the nature of this synergistic effect, we studied the thermodynamics of formation of clusters containing 1−2 sulfuric acids and 1−2 bases of the same or different type. By comparing the stability of clusters containing a single kind of base with those containing a mix of ammonia and alkylamines, we were able to determine if the synergistic effect is thermodynamic in nature. We also examined if an investigation of larger clusters is necessary to capture the observed synergy.

2. METHODOLOGY One of the biggest challenges in studying molecular clusters is searching the large number of possible configurations and finding the most stable structures. Addressing this challenge requires a knowledge of the potential energy surface for the molecular clusters as well as an efficient algorithm to navigate this surface.39 One of the most successful methods to explore configurational spaces is genetic algorithm (GA),40,41 and it has been extensively applied to perform global optimization on molecular clusters among other problems. GA is implemented in OGOLEM42 and CLUSTER43 packages, and they both interface with a vast array of computational approaches ranging from molecular mechanics force fields to semiempirical methods, density functional theory, and ab initio methods. The most computationally feasible approach in the current case is to perform GA on molecular clusters whose fitness is evaluated on the basis of their energy, calculated, and optimized using PM7,44 self-consistent charge density-functional tightbinding (SCC-DFTB),45 and effective fragment potential (EFP2)46 semiempirical methods. PM7, SCC-DFTB, and EFP2 are implemented in MOPAC,47 DFTB+,48 and libEFP,46 respectively. The methodology employed in this work is summarized in Figure 1. In the GA calculations, 250−1000 initial structures were generated randomly and evolved for 5000−30 000 crossovers followed by optimizations. The final pool of optimized structures was checked for uniqueness, and those structures within 10 kcal mol−1 of the putative global minimum structure were selected for further optimizations using density functional theory (DFT). The performance of different functionals for atmospheric hydrates has been studied extensively by Elm and Mikkelsen.49,50 Their work compared 1613


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due to basis set incompleteness (BSIE) and superposition (BSSE) errors.51−55 To correct BSIE and BSSE, we calculated the explicitly correlated DF-MP2-F1256 energies on the DFMP2/aVDZ optimized geometries. As implemented in Molpro 2015.1,57 the DF-MP2-F12 method employing the 3C(FIX) ansatz58 with cc-pVTZ-F12 (VTZ-F12) orbital basis,59 the recommended VNZ-F12/OPTRI auxiliary basis,60 and VTZ/ MP2FIT density fitting basis yields binding energies that should be close to the MP2 complete basis set (CBS) value.61 For the sake of brevity, the (DF) is removed from DF-MP2 and DFMP2-F12 for the rest of the article. The Gibbs free energies of cluster formation are calculated by combining the DFT/6-311++G(d,p) and MP2-F12/VTZ-F12 electronic energies with DFT/6-311++G(d,p) and MP2/aVDZ thermodynamic corrections, respectively, employing unscaled harmonic vibrational frequencies assuming ideal gas conditions with a rigid-rotor approximation for molecular rotations and a harmonic oscillator model for vibrations. The reported Gibbs free energies at a given temperature correspond to those of the global minimum at that temperature.

3. RESULTS A good way to assess the interaction of sulfuric acid with bases is to compare the binding energy of a sulfuric acid dimer (S1− S1) with that of dimers containing a sulfuric acid and a base (S1−B1). Figure 2 shows the structure and binding energy of

Figure 1. Methodology employed to obtain accurate thermodynamics of cluster formation.

the performance of different functionals against experimental and benchmark computational data. They concluded that it is prudent to use different functionals when evaluating cluster formation free energies because each functional has inherent errors and there are not systematic improvements among the investigated functionals. On the basis of their common use in atmospheric aerosol studies and good performance, we used the PW91, M06-2X, and ωB97X-D functionals in this work. PW91 is a GGA functional that has been applied most extensively to the study of sulfate aerosols, while M06-2X is a general purpose hybrid-meta functional that has been successful in a myriad of applications, and ωB97X-D is a range-separated hybrid functional with an empirical dispersion correction. The set of structures generated using GA on semiempirical (PM7, SCCDFTB, EFP2) potential energy surfaces are initially optimized using PW91/6-31+G* to get reasonably good structures and energies. From the PW91/6-31+G* optimized structures, those whose energy is within 5 kcal mol−1 of the putative global minimum are further optimized using PW91, M06-2X, and ωB97X-D functionals with the 6-311++G(d,p) basis set using ultrafine density grids. Elm and Mikkelsen49,50 have shown that geometry optimizations and frequency calculations using smaller split-valence basis sets like 6-31++G(d,p) and 6-311+ +G(d,p) do not introduce large errors in the computed Gibbs free energy relative to calculations using larger split valence basis sets like 6-311++G(3df,3pd). The final set of isomers calculated using the three functionals with 6-311++G(d,p) are further optimized using density fitting (DF) second-order Møller−Plesset perturbation theory (MP2) with aug-cc-pVDZ (aVDZ) basis sets with the goal of comparing DFT results with ab initio ones. To speed up the MP2 calculations, density fitting of integrals was used both for the reference Hartree−Fock (HF) and MP2 calculations with the appropriate fitting basis sets, namely aVDZ/JKFIT and aVDZ/MP2FIT for the HF and MP2 calculations, respectively. MP2 generally overbinds systems when used with a moderate size basis set like aVDZ

Figure 2. Comparison of the MP2-F12/VTZ-F12//MP2/aVDZ binding energy of sulfuric acid (S) with different bases (A, MMA, DMA, TMA) or another sulfuric acid (S1−S1). The structures correspond to the G°(298 K) global minima. The hydrogen bond distances are in angstroms, and the binding energies are in kcal mol−1 units.

the MP2-F12/VTZ-F12 G°(298 K) global minima. Sulfuric acid clearly binds more strongly to another base (S1−B1) than another acid (S1−S1). With the exception of the complex with ammonia, all the other bases undergo a proton transfer reaction with sulfuric acid, and the resulting electrostatic interactions provide substantial stabilization to the complexes. On top of the electrostatic interaction between the protonated bases and bisulfate ion, the pairs of hydrogen bonds help bind the clusters together. The magnitude of the binding energies correlates very well with the gas phase basicity of the bases. That is true when comparing the MP2-F12/VTZ-F12//MP2/aVDZ results, and also for PW91/6-311++G(d,p), M06-2X/6-311++G(d,p), and ωB97X-D/6-311++G(d,p) predictions, as demonstrated in Figure 3 and enumerated in Table 1. The MP2 and DFT predictions display the same trend even though the extent of their agreement depends on the DFT functional. M06-2X and ωB97X-D tend to overbind the clusters relative to MP2 while PW91 shows no distinct trend relative to MP2. The same conclusions hold for bigger clusters containing two acids and one base (S2−B1), one acid and two bases (S1−B2), and two acids and two bases (S2−B2). Both the MP2 and DFT predictions in Figure 4 and Table 2 suggest that S2−B1 clusters containing bases with higher gas phase basicity are more 1614


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Figure 4. Binding electronic [ΔEe] (a) and 298.15 K Gibbs free energy [ΔG°(298 K)] (b) of clusters containing two sulfuric acid and one base molecule calculated using different methods. The predictions by all four methods exhibit the same correlation between the gas phase basicity and strength of binding.

Figure 3. Binding electronic [ΔEe] (a) and 298.15 K Gibbs free energy [ΔG°(298 K)] (b) of clusters containing one sulfuric acid and one base molecule calculated using different methods. The predictions by all four methods exhibit the same correlation between the gas phase basicity and strength of binding.

Table 2. MP2-F12/VTZ-F12//MP2/aVDZa Binding Energy of Clusters Containing Two Sulfuric Acid (H2SO4, S) Molecules Bound to Ammonia [NH3, A], Monomethylamine [CH3NH2, MMA], Dimethylamine [(CH3)2NH, DMA], or Trimethylamine [(CH3)3N, TMA]b

a

Table 1. MP2-F12/VTZ-F12//MP2/aVDZ Binding Energy of Clusters Containing one Sulfuric Acid (H2SO4, S) Molecule Bound to Ammonia [NH3, A], Monomethylamine [CH3NH2, MMA], Dimethylamine [(CH3)2NH, DMA], or Trimethylamine [(CH3)3N, TMA]b

2S1 + B1 → S2−B1

S1 + B1 → S1−B1

S1A1 S1MMA1 S1DMA1 S1TMA1 S1−S1

ΔEe

ΔEe

ΔE0

ΔG

MP2-F12/VTZF12

0K

216.65 K

273.15 K

298.15 K

−16.9 −21.9 −25.6 −26.4 −18.9

−15.1 −19.7 −23.1 −24.1 −17.4

−9.6 −13.2 −15.9 −17.0 −9.6

−8.0 −11.5 −14.0 −15.2 −7.7

−7.3 −10.7 −13.2 −14.3 −6.8

S2A1 S2MMA1 S2DMA1 S2TMA1 S2

ΔE0

ΔG

MP2-F12/VTZF12

0K

216.65 K

−47.4 −54.0 −58.5 −56.6 −18.9

−42.5 −49.7 −54.0 −51.9 −17.4

−28.3 −34.2 −38.5 −35.9 −9.6

273.15 K 298.15 K −24.4 −30.1 −34.4 −31.7 −7.7

−22.6 −28.2 −32.5 −29.8 −6.8

Both the MP2 and MP2-F12 calculations employed density fitting. Free energies are at a standard state of 1 atm pressure and the given temperature. All energies are in kcal mol−1 units. Please see Table S2 analogous predictions from DFT.

a

Both the MP2 and MP2-F12 calculations employed density fitting. b Free energies are at a standard state of 1 atm pressure and the given temperature. All energies are in kcal mol−1 units. Please see Table S1 analogous predictions from DFT. a

b

strongly bound with the exception of S2−TMA, which is slightly less strongly bound than S2−DMA despite TMA having a larger gas phase basicity. The absence of this anomaly in the S1−B1 system (see Figure 3) suggests that the bulky methyl groups in TMA affect its capacity to bind a second sulfuric acid. The gas phase basicity (GB) increases in the order NH3 < MMA < DMA < TMA. In clusters containing two bases, the choice of having bases of the same or different types allows us to examine the effect of

mixing bases. Figure 5 and Table 3 demonstrate that S1−B2 containing bases of the same type (S1−A2, S1−MMA2, S1− DMA2, S1−TMA2) exhibit the same trend as (S2−B1) systems: the strength of the binding correlates with the gas phase basicity of the bases, with the exception of S1−TMA2 which is less strongly bound than S1−DMA2. S1−B2 containing different bases (S1−A1−MMA1, S1−A1−DMA1, S1−A1−TMA1) also show correlation between the strength of the binding and the bases in the clusters with the exception of S1−A1−TMA1. Clusters containing TMA being less strongly bound than those 1615


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Figure 5. Binding electronic [ΔEe] (a) and 298.15 K Gibbs free energy [ΔG°(298 K)] (b) of clusters containing one sulfuric acid and two base molecules calculated using different methods. The predictions by all four methods exhibit the same correlation between the gas phase basicity and strength of binding. The dashed arrows point the direction of energy change upon going from mixed ammonia-amine to amine-only system.

Figure 6. Binding electronic [ΔEe] (a) and 298.15 K Gibbs free energy [ΔG°(298 K)] (b) of clusters containing two sulfuric acid and two base molecules calculated using different methods. The predictions by all four methods exhibit the same correlation between the gas phase basicity and strength of binding. The dashed arrows point the direction of energy change upon going from mixed ammonia-amine to amine-only system.

Table 3. MP2-F12/VTZ-F12//MP2/aVDZa Binding Energy of Clusters Containing a Sulfuric Acid (H2SO4, S) Molecule Bound to Two Bases, Namely, a Combination of Ammonia [NH3, A], Monomethylamine [CH3NH2, MMA], Dimethylamine [(CH3)2NH, DMA], or Trimethylamine [(CH3)3N, TMA]b

Table 4. MP2-F12/VTZ-F12//MP2/aVDZa Binding Energy of Clusters Containing Two Sulfuric Acid (H2SO4, S) Molecules Bound to Bases, Namely, a Combination of Ammonia [NH3, A], Monomethylamine [CH3NH2, MMA], Dimethylamine [(CH3)2NH, DMA], or Trimethylamine [(CH3)3N, TMA]b 2S1 + 2B1 → S2−B2

S1 + 2B1 → S1−B2 ΔEe

S1A2 S1MMA2 S1DMA2 S1TMA2 S1A1MMA1 S1A1DMA1 S1A1TMA1

ΔE0

ΔG

ΔEe MP2-F12/VTZF12

0K

216.65 K

−18.9 −68.9 −80.6 −89.9 −86.4 −74.7 −79.2 −77.4

−17.4 −61.2 −73.8 −82.7 −77.8 −67.5 −71.5 −68.9

−9.6 −40.2 −51.4 −58.0 −53.0 −45.9 −48.5 −45.9

MP2-F12/VTZF12

0K

216.65 K

273.15 K

298.15 K

−31.7 −38.5 −43.2 −42.0 −37.0 −40.5 −38.9

−27.7 −34.6 −39.8 −38.9 −32.3 −35.9 −34.5

−16.2 −20.1 −24.5 −24.1 −19.2 −22.2 −21.4

−12.9 −16.2 −20.5 −20.2 −15.5 −18.5 −17.9

−11.4 −14.4 −18.6 −18.4 −13.9 −16.8 −16.2

S2 S2A2 S2MMA2 S2DMA2 S2TMA2 S2A1MMA1 S2A1DMA1 S2A1TMA1


a

ΔE0

ΔG 273.15 K 298.15 K −7.7 −34.3 −45.6 −51.5 −46.4 −40.1 −42.3 −39.8

−6.8 −31.7 −42.9 −48.5 −43.4 −37.4 −39.4 −37.1


a

b

b

with DMA further indicates that TMA’s methyl groups are hindering its binding capacity. Lastly, Figure 6 and Table 4 report the binding energies of S2−B2 clusters, and their predictions are in line with those for the S1−B2 system. Aside from the total binding energies of these clusters, it is instructive to look at the reaction energy for adding a sulfuric

acid molecule (S1) to smaller clusters (S1−B1 and S1−B2) to form bigger clusters (S2−B1 and S2−B2). Figure 3 already predicts that S1 + B1 → S1−B1 is a very favorable reaction, with the extent of the forward reaction correlating strongly with the base’s proton affinity or gas phase basicity. Figure 7a 1616


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Figure 7. MP2-F12/VTZ-F12//MP2/aVDZ energy of reaction for adding a sulfuric acid molecule (S1) to a cluster containing (a) one acid and one base (S1B1) or (b) one acid and two bases (S1B2). Both (a) and (b) show that although DMA and TMA have comparable gas phase basicity, sulfuric acid binds more strongly to DMA because it has more favorable steric interactions. The more favorable energy of reaction for adding S1 to S1−MA2, S1−DMA2, and S1−TMA2 over S1− A1−MA1, S1−A1−DMA1, and S1−A1−TMA1 does not support the notion of synergistic interactions in mixed ammonia−amine systems for a cluster this size. Please see Figures S5 and S6 for analogous predictions from DFT. The dashed arrows point the direction of energy change upon going from mixed ammonia-amine to amine-only system.

Figure 8. PW91/6-311++G(d,p), M06-2X/6-311++G(d,p), and ωB97X-D/6-311++G(d,p), electronic [ΔEe] (a) and 298.15 K Gibbs free energy [ΔG°(298 K)] (b) of reaction for adding a sulfuric acid molecule (S1) to a cluster containing two acid and two base (S2−B2) molecules. The addition of S1 to S2−A1−DMA1 and S2−A1−TMA1 being more thermodynamically favorable than addition to S2−DMA2 and S2−TMA2 is the first indication that the strength of the bases is not the only factor determining the growth of these clusters. The dashed arrows point the direction of energy change upon going from mixed ammonia-amine to amine-only system.

demonstrates that S1 + S1−B1 → S2−B1 is also highly favorable in the forward direction, but clusters with TMA deviate from the established correlation between reaction energies and gas phase basicities. The same trends are observed in Figure 7b for S1 + S1−B2 → S2−B2 for reactions involving two bases of the same or different type. All the trends shown in Figures 3−7 suggest that the gas phase basicity of the bases dictates the strength of the binding in these small molecular clusters as long as steric effects do not inhibit optimal binding. While those results do not support improved stabilization in mixed ammonia−amine clusters relative to those containing ammonia or amines alone, preliminary results on the formation of larger clusters (S3−Bm, m = 1−3) provides the first evidence for synergy between ammonia and amines. Figure 8 shows the energy of reaction for the addition of sulfuric acid (S1) to smaller clusters containing a mix of ammonia (A1) and amines (B1) is more favorable than addition to clusters containing amines alone. These results likely preview a synergistic effect between ammonia and amines that would be present to a greater extent in larger clusters.

4.1. Comparison of DFT and MP2 Binding Energies. While the computational cost of DFT methods makes them an attractive option for studying large molecular clusters, it is essential to benchmark them against wave function methods like MP2 which have been shown to perform well for hydrogen-bonded systems. Myllys et al.62 have compared DFT binding energies calculated using 11 different functionals for six clusters of importance to sulfate aerosol formation and found that the predicted binding energies differed by as much as 4 kcal mol−1 even for the small clusters studied. However, obtaining the binding energy by calculating single point energies with the more robust DLPNO−CCSD(T)63,64 or CCSD(T)-F1265 methods removed most of the variation in the binding energies predicted by the different DFT functionals. This realization led to the conclusion that a lot of the scatter in DFT binding energies comes from the DFT electronic energy rather than zero-point or thermodynamic corrections. In our case, both the MP2 and DFT binding energies are calculated at geometries optimized at their respective levels of theory; therefore, our findings cannot be directly compared with those of Myllys et al.62 However, their conclusions generally agree with ours in that the differences between MP2 and DFT ΔG(298 K) values are essentially the same as the ΔEe ones. These differences can be as large as 3 kcal mol−1 for S1−B1 systems (Figure 3), 6 kcal mol−1 for S2−B1 systems (Figure 4), 5 kcal mol−1 for S1−B2 systems (Figure 5), and 13 kcal mol−1

4. DISCUSSION The results outlined above have important implications for methods development as well as our understanding of the role of bases in sulfate aerosol formations. Those points are discussed below. 1617


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The Journal of Physical Chemistry A for S2−B2 systems (Figure 6). While these differences are substantial in absolute terms, they generally do not exceed 10% of the electronic binding energy (ΔEe) or 25% of the binding standard Gibbs free energy[ΔG(298 K)]. Also, MP2 and DFT predict the same trends as far as the effect of bases on sulfate clusters is concerned. Nevertheless, we support the suggestion by Elm and Mikkelsen49,50 that when evaluating cluster formation free energies with DFT, one should use different functionals and ensure that they make similar predictions instead of trusting any individual functional. The inability to improve DFT systematically like in wave function methods is one of the downsides of using DFT.66,67 Of the 22 types of clusters in this work, the 16 clusters containing one kind of base have been previously studied using DFT,31,68 with a much smaller number employing wave function methods like MP255,69−71 for optimizations and frequency calculations or CC2,31 DLPNO-CCSD(T),62 and CCSD(T)-F1262 for final single point energy calculations on structures computed using DFT methods. The most notable of the DFT studies are those of Ortega et al.31 whose B3RICC2 method combines B3LYP/CBSB7 geometries and frequencies with RI-CC2/aug-cc-pV(T+d)Z single point energies and Herb, Nadykto, and Yu,34,68,72 who used PW91/6-311+ +G(3df,3pd) to assess the binding of sulfuric acid with bases. In general, Ortega’s B3RICC2 [RI-CC2/aug-cc-pV(T+d)Z// B3LYP/CBSB7] results overbind clusters while the Herb, Nadykto, and Yu’s34,68,72 PW91/6-311++G(3df,3pd) results show no discernible pattern relative to our MP2 binding energies. However, although those works take very different approaches in terms of configurational sampling and quantum chemical calculations, their overall conclusions regarding the correlation between the strength of a base and the binding energy of the resulting cluster are consistent with ours. The remaining eight clusters we have studied have a mix of ammonia and an amine. To the best of our knowledge, these mixed base clusters have not been studied previously with the exception of S1−A1−DMA1 and S2−A1−DMA1 which were included in Kupiainen et al.’s36 investigation of amine substitution in sulfuric acid−ammonia clusters. Their work employed Ortega et al.’s B3RICC2 [RI-CC2/aug-cc-pV(T +d)Z//B3LYP/CBSB7] method, and it shows similar overbinding relative to our MP2 results. 4.2. Effect of Mixing Ammonia and Amines. The importance of studying mixed base systems cannot be understated given that ammonia and amines are present in the atmosphere with average concentrations of 100s pptv (∼109 cm−3) and 1 pptv (∼107 cm−3), respectively, compared to sulfuric acid concentrations of 1 pptv (∼107 cm−3). The source and abundance of ammonia vary depending on the geography, but Ge, Wexler, and Clegg have estimated the global emission of ammonia, MMA, DMA, and TMA to be 50 000 ± 30 000, 83 ± 26, 33 ± 19, and 169 ± 33 Gg N a−1 (109 g of nitrogen per annum), respectively.73−75 With the ratio of ammonia to amines being roughly 1000:1, it is conceivable that most sulfate aerosols likely contain a lot of ammonia and some amines. Kupiainen et al.’s36 aforementioned work and other studies by DePalma and Bzdek37,76 suggest that collisions between DMA and clusters containing ammonia readily lead to substitution of ammonia with DMA. Their studies show that the growth of clusters by adding ammonia is generally a slow process compared to the substitution reaction of ammonia by DMA. The goal of our study was not to investigate substitution reactions of ammonia by amines, but rather the potential

thermodynamic stability a mixture of ammonia and amines can confer on a given cluster. This hypothesis was devised to explain the increased new sulfate particle formation in experiments where ammonia and amines were present together compared to cases where only ammonia or amines were available.14,27,28 Our results conclusively show that clusters containing ammonia and amines (S1−A1−MMA1, S1−A1− DMA1, S1−A1−TMA1, S2−A1−MMA1, S2−A1−DMA1, S2−A1− TMA1) are thermodynamically less favorable than those containing amines alone (S1−MMA2, S1−DMA2, S1−TMA2, S2−MMA2, S2−DMA2, S2−TMA2). For clusters in this small size regime, the gas phase basicity of bases in the cluster dictates their thermodynamic stability. As noted previously, clusters containing TMA buck this trend because of the steric hindrance of the methyl groups. 4.3. Synergy in Mixed Ammonia−Amine Systems. All our investigations of the total binding energy of Sn−Bm, n, m = 1−2, in Figures 3−6 found no indication of synergistic stabilizations in mixed ammonia−amine clusters relative to amine-only clusters. Moreover, looking at the energy of reaction for the addition of S1 to smaller clusters to form S1−B1, S2−B1, or S2−B2 in Figure 7 found that additions to amine-only clusters were more favorable than to mixed ammonia−amine clusters: S1 + B1 → S1−B1 S1 + S1−B1 → S2 −B1

S1 + S2 −B1 → S2 −B2 A similar look at the energy of reaction for the addition of ammonia (A1) or amines (B1) to smaller clusters to form S2− A1−B1, S2−B1−A1, or S2−B2 likewise finds that addition to S2− B1 to S2−B2 is the most favorable reaction. S2 −A1 + B1 → S2 −A1−B1 S2 −B1 + A1 → S2 −B1−A1

S2 −B1 + B1 → S2 −B2 The base addition reactions are summarized in Supporting Information section S3.2. While all the results reported above for Sn−Bm, n, m = 1−2, provide no evidence to support synergy in mixed ammonia−amine systems, looking at larger clusters might. To test the presence of ammonia−amine synergy in larger clusters, we performed preliminary calculations on the formation of larger clusters (S3−Bm, m = 1−3) following the same rigorous methodology used for the Sn−Bm, n, m = 1−2, clusters but employing the three DFT methods only. The results provide the first evidence for synergy between ammonia and amines. Figure 8 shows the energy of reaction for the addition of sulfuric acid (S1) to smaller clusters containing ammonia (A1) and/or amines (B1) to smaller clusters to form S3−B1−A1, S3−A1−B1, or S3−B2. S1 + S2 −A1−B1 → S3−A1−B1

S1 + S2 −B2 → S3−B2 The addition of S1 to S2−A1−DMA1 and S2−A1−TMA1 is more thermodynamically favorable than addition to S2−DMA2 and S2−TMA2. This is the first indication that the strength of the bases is not the only factor determining the stability of these clusters. Similarly, investigations summarized in Support1618


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The Journal of Physical Chemistry A ing Information section S3.4 found that S3−A1 + B1 → S3−A1− B1 is a more favorable reaction than S3−B1 + B1 → S3−B2.

by Olenius et al.79 examined the enhancement in new particle formation due to MMA, DMA, and TMA by running their cluster population dynamics model incorporating cluster evaporation rates derived from their B3RICC2 calculations. They concluded that DMA and TMA behave similarly in terms of their enhancing potential while MMA was much weaker and significantly more sensitive to changes in temperature and relative humidity. Their predictions largely support the idea that gas phase basicity is a good predictor of a base’s stabilizing potential. Considering their conclusions are based on the concentration of sulfuric acid dimers (∑[(H2SO4)2]) bound to different bases, the correlation between the gas phase basicity and stabilizing potential of the bases makes sense. As the clusters grow and water is included, the new species should behave as if they are in particle phase. A good measure of a base’s strength in solution is its base dissociation constant, kb, or negative log thereof (pKb). The pKb of the bases has a very different order from the gas phase basicity (GB) reported above. The pKb increases from NH3 (pKb = 4.75) to TMA (pKb = 4.22) to MMA (pKb = 3.35) and DMA (pKb = 3.27).14 Therefore, we expect the stabilization effect of bases on larger sulfate aerosols to follow the pKb rather than the GB. In fact, that is precisely what Yu et al.14 observed when measuring the EF2 nm (enhancement factor for particles larger than 2 nm) of ammonia and several amines. Although amines have a much larger gas phase basicity than ammonia, their stabilizing effect becomes less prominent as the clusters grow and become substantially hydrated. A recent study of 10−20 nm nanoparticles composed of sulfuric acid, water, ammonia, and amines in the CLOUD chamber found that the particles mainly contained ammonia even when there was an excess amount of amines.80 Those results suggest that gas phase basicity is not the only determining factor on the stabilizing effect of bases and that the synergistic effects between ammonia and amines must be considered. Kinetic effects like steric hindrance and collision efficiencies also need to be taken into account. Lawler et al.’s work80 is the latest addition to interesting experimental studies highlighting the synergy between ammonia and amines in sulfate aerosol formation.14,28

S3−A1 + B1 → S3−A1−B1 S3−B1 + A1 → S3−B1−A1 S3−B1 + B1 → S3−B2

The results above for S3−Bm, m = 1−3, suggest that an amine prefers binding to S3−A1 over S3−B1. If the strength of the base was the driver for these reactions, we would have seen the opposite to be true. While these results are encouraging, they would need to be reproduced for larger clusters. This is the first case among the reactions studied here where the reaction energy does not correlate with the aqueous phase basicity of the base. The ability of the bases to participate in cluster formation depends on the strength and number of hydrogen bonds they can form. NH3 can form as many as four hydrogen bonds (three as a donor and one as an acceptor) in its neutral form and four hydrogen bonds as a donor in its protonated form (NH4+). The alkylamines are stronger bases than ammonia, and they are present in their protonated form in all the clusters studied here. The protonated MMA, DMA, and TMA can form only three, two, and one hydrogen bond, respectively. The fact that the larger alkylamines can only form a smaller number of hydrogen bonds limits their ability to be involved in cluster formation relative to ammonia, especially as the cluster become larger. This is very likely part of the reason for the somewhat surprising synergy between ammonia and the alkylamines. The extent of the synergy is expected to increase with cluster size. The amines are better able to promote proton transfer and form strongly bound clusters in the small size regime while ammonia is better able to bind multiple molecules together in larger clusters. Smaller amines like MMA are expected to exhibit smaller synergistic interaction while TMA would show larger synergy. 4.4. Gas Phase Basicity versus Aqueous Base Dissociation Constant. In more quantitative terms, the gas phase proton affinities (PAs) and gas-phase basicities (GBs) of a molecule are a good measure of the strength of a base. For a molecule B, the PA and GB values are changes in enthalpy (ΔH) and Gibbs free energies (ΔG), respectively, of the reaction + + BH(g) → B(g) + H(g)

5. CONCLUSIONS Bases like ammonia (A) and alkylamines like monomethylamine (MMA), dimethylamine (DMA), and trimethylamine (TMA) have each been shown to increase sulfate aerosol formation rates by many orders of magnitude compared to binary cases (BHN) where only sulfuric acid (SA) and water (W) are present. Experimental measurements found that ammonia and dimethylamine (DMA) at atmospherically relevant concentrations increased sulfate aerosol formation rates by a factor of 102−103 and 105−106, respectively, compared to BHN cases. However, if both ammonia and alkylamines (MMA, DMA) are present at the same time, the sulfate aerosol formation rates by a factor of another 101−102 compared to the case of MMA or DMA alone. This unexpected phenomenon has been attributed to the synergistic interaction between ammonia and the alkylamines, but its physical basis is not understood. To examine the nature of this synergistic effect, we studied the thermodynamics of formation of clusters containing 1−2 sulfuric acids and 1−2 bases of the same or different type. By comparing the stability of clusters containing a single kind of base with those containing a mix of ammonia and alkylamines, we were able to conclude that the mixed base

(1)

Compared to ammonia, alkylamines where hydrogens are substituted with methyl groups should have higher PAs and GBs with increasing methylation. Indeed, the PAs for ammonia, MMA, DMA, and TMA are 853.6, 899.0, 929.5, and 948.9 kJ mol−1, respectively, while the GBs are 819.0, 864.5, 896.5, and 918.1 kJ mol−1 for the same four bases.77,78 Therefore, one would expect TMA to be the strongest base in gas phase, and our results in Figures 2 and 3 do show that TMA binds more strongly to sulfuric acid than the other bases considered. However, as we try to bind additional sulfuric acid or base molecules, TMA’s bulky methyl groups prevent them from clustering in optimal configurations. Therefore, clusters containing the less bulky DMA are better at binding multiple acids and/or bases (Figures 4−6). The effect of steric hindrance in TMA notwithstanding, we can safely assume that the small clusters in this study can be treated as gas phase clusters whose binding correlates with the GBs of their bases. A recent study 1619


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1662030 as part of MERCURY consortium. This research used National Science Foundation XSEDE resources provided by the Texas Advanced Computing Center (TACC) under Grants TG-CHE090095 and TG-CHE120025 and also used resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract DE-AC02-05CH11231.

systems were no more stable than those containing alkylamines only. The binding energy of these clusters correlated directly with the gas phase basicity (GB) of the bases in all cases except for clusters containing TMA. Our inability to rationalize the experimentally observed synergy between ammonia and alkylamines in mixed base systems prompted us to look at larger clusters where such effects may be more apparent. Preliminary studies on the S3−Bm, m = 1−3, system found that while the stability of those clusters still depends on the relative strength of the bases within, the energy of reaction to form the clusters by the addition of sulfuric acid (S1) or ammonia (A1) or amines (B1) to smaller clusters to form S3−B1−A1, S3−A1− B1 or S3−B2 provides the first hint of synergistic effects. The addition of S1 to S2−A1−DMA1 and S2−A1−TMA1 is more thermodynamically favorable than addition to S2−DMA2 and S2−TMA2. This is the first case among the reactions studied here where the reaction energy does not correlate with the strength of the bases alone. Further studies on larger clusters are needed to confirm that the same synergy drives the enhanced aerosol formation in mixed ammonia−amine systems. The smaller clusters in this study behave much like gas phase clusters while the stabilization effect of bases on bigger particles correlates with the bases’ aqueous dissociation constants (Kb or pKb), which have a different ordering. Therefore, different measures of strength of bases need to be used depending on the size of the clusters or aerosol particles in question. The steric hindrance of the bulky methyl groups in the larger amines limits the number of such amines that can effectively incorporated into aerosol particles. Therefore, aerosol particles are likely to incorporate many small ammonia molecules for every large amine. Future studies of the effect of bases on aerosol formation should factor in the size and steric limitations of bases as well as their stabilizing strength.

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(1) Stocker, T. Climate Change 2013: The Physical Science Basis: Working Group I Contribution to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change; Cambridge University Press: 2014. (2) Kulmala, M.; Vehkamäki, H.; Petäjä, T.; Dal Maso, M.; Lauri, A.; Kerminen, V. M.; Birmili, W.; McMurry, P. H. Formation and Growth Rates of Ultrafine Atmospheric Particles: A Review of Observations. J. Aerosol Sci. 2004, 35, 143−176. (3) Kuang, C.; McMurry, P. H.; McCormick, A. V.; Eisele, F. L. Dependence of Nucleation Rates on Sulfuric Acid Vapor Concentration in Diverse Atmospheric Locations. J. Geophys. Res. 2008, 113, D10209. (4) Kerminen, V. M.; Petäjä, T.; Manninen, H. E.; Paasonen, P.; Nieminen, T.; Sipilä, M.; Junninen, H.; Ehn, M.; Gagné, S.; et al. Atmospheric Nucleation: Highlights of the EUCAARI Project and Future Directions. Atmos. Chem. Phys. Discuss. 2010, 10, 16497− 16549. (5) Sipilä, M.; Berndt, T.; Petäjä, T.; Brus, D.; Vanhanen, J.; Stratmann, F.; Patokoski, J.; Mauldin, R. L.; Hyvarinen, A. P.; et al. The Role of Sulfuric Acid in Atmospheric Nucleation. Science 2010, 327, 1243−1246. (6) Bzdek, B. R.; Zordan, C. A.; Luther, G. W., III; Johnston, M. V. Nanoparticle Chemical Composition During New Particle Formation. Aerosol Sci. Technol. 2011, 45, 1041−1048. (7) Bzdek, B. R.; Johnston, M. V. New Particle Formation and Growth in the Troposphere. Anal. Chem. 2010, 82, 7871−7878. (8) Ball, S. M.; Hanson, D. R.; Eisele, F. L.; McMurry, P. H. Laboratory Studies of Particle Nucleation: Initial Results for H2SO4, H2O, and NH3 Vapors. J. Geophys. Res. 1999, 104, 23709−23718. (9) Zhang, R.; Khalizov, A.; Wang, L.; Hu, M.; Xu, W. Nucleation and Growth of Nanoparticles in the Atmosphere. Chem. Rev. 2012, 112, 1957−2011. (10) Benson, D. R.; Young, L. H.; Kameel, F. R.; Lee, S. H. Laboratory-Measured Nucleation Rates of Sulfuric Acid and Water Binary Homogeneous Nucleation from the SO2 + OH Reaction. Geophys. Res. Lett. 2008, 35, L11801. (11) Kurtén, T.; Loukonen, V.; Vehkamäki, H.; Kulmala, M. Amines Are Likely to Enhance Neutral and Ion-Induced Sulfuric Acid-Water Nucleation in the Atmosphere More Effectively Than Ammonia. Atmos. Chem. Phys. 2008, 8, 4095−4103. (12) Benson, D. R.; Yu, J. H.; Markovich, A.; Lee, S. H. Ternary Homogeneous Nucleation of H2SO4, NH3 , and H2O under Conditions Relevant to the Lower Troposphere. Atmos. Chem. Phys. 2011, 11, 4755−4766. (13) Erupe, M. E.; Viggiano, A. A.; Lee, S. H. The Effect of Trimethylamine on Atmospheric Nucleation Involving H2SO4. Atmos. Chem. Phys. 2011, 11, 4767−4775. (14) Yu, H.; McGraw, R.; Lee, S.-H. Effects of Amines on Formation of Sub-3 nm Particles and Their Subsequent Growth. Geophys. Res. Lett. 2012. (15) Zollner, J. H.; Glasoe, W. A.; Panta, B.; Carlson, K. K.; McMurry, P. H.; Hanson, D. R. Sulfuric Acid Nucleation: Power Dependencies, Variation with Relative Humidity. Atmos. Chem. Phys. 2012, 12, 4399−4411. (16) Kulmala, M.; Kontkanen, J.; Junninen, H.; Lehtipalo, K.; Manninen, H. E.; Nieminen, T.; Petäjä, T.; Sipilä, M.; Schobesberger, S.; et al. Direct Observations of Atmospheric Aerosol Nucleation. Science 2013, 339, 943−946.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.7b11236. Cartesian coordinates and figures of all the clusters within 0.5 kcal mol−1 of the electronic or standard Gibbs free energy global minimum; all DFT binding energies (PDF) Cartesian coordinates and energies, which are also presented in a convenient form at http://www. molecularclusters.xyz (ZIP)

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REFERENCES

AUTHOR INFORMATION

Corresponding Authors

*E-mail [email protected] (B.T.). *E-mail [email protected] (G.C.S.). ORCID

Berhane Temelso: 0000-0002-5286-1983 George C. Shields: 0000-0003-1287-8585 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge NSF, Bucknell University and Furman University for their support of this work. This project was funded by NSF Grants CHE-1213521, CHE-1721511, and DUE-1317446, and NSF Grants CHE-1229354 and CHE1620


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