# Estimating the Lower Limit of the Impact of Amines on Nucleation in the Earth’s Atmosphere

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{3}, are important common trace atmospheric species that can enhance new particle formation in the Earth’s atmosphere under favorable conditions. While methylamine (MA), dimethylamine (DMA) and trimethylamine (TMA) all efficiently enhance binary nucleation, MA may represent the lower limit of the enhancing effect of amines on atmospheric nucleation. In the present paper, we report new thermochemical data concerning MA-enhanced nucleation, which were obtained using the DFT PW91PW91/6-311++G (3df, 3pd) method, and investigate the enhancement in production of stable pre-nucleation clusters due to the MA. We found that the MA ternary nucleation begins to dominate over ternary nucleation of sulfuric acid, water and ammonia at [MA]/[NH

_{3}] > ~10

^{−3}. This means that under real atmospheric conditions ([MA] ~ 1 ppt, [NH

_{3}] ~ 1 ppb) the lower limit of the enhancement due to methylamines is either close to or higher than the typical effect of NH

_{3}. A very strong impact of the MA is observed at low RH; however it decreases quickly as the RH grows. Low RH and low ambient temperatures were found to be particularly favorable for the enhancement in production of stable sulfuric acid-water clusters due to the MA.

## 1. Introduction

_{2}SO

_{4}] and are observed only if [H

_{2}SO

_{4}] > 10

^{5}cm

^{−3}[7]. However, binary H

_{2}SO

_{4}-H

_{2}O (BHN) [8,9] nucleation cannot fully explain nucleation events observed in the polluted PBL [1–4,7,10]. While key atmospheric nucleation mechanisms are still a subject of ongoing debates [1–5,7,11–14], it is commonly accepted that trace atmospheric species other than H

_{2}SO

_{4}and H

_{2}O are involved in new particle formation in the Earth’s atmosphere and that neutral H

_{2}SO

_{4}-H

_{2}O clusters must be stabilized with ions [12,13], ammonia [14–19], amines [20–23] or organic acids [24–32] in order to nucleate. Theoretical formalism of nucleation of H

_{2}SO

_{4}, H

_{2}O and NH

_{3}is commonly known as the Ternary Homogeneous Nucleation (THN) theory [11,14–19]. The theory has been developed into a global concept explaining nucleation in the PBL back in the early 2000 s. However, the THN prediction [11,15] of an enhancement of up to ~10

^{30}atmospheric nucleation rates due to a few ppt of NH

_{3}later failed due to mistakes in nucleation thermodynamics and kinetics [16,17] and disagreement with laboratory studies showing much smaller NH

_{3}effects of up to a few orders of magnitude at [NH

_{3}] > 1 ppb [14,18,19].

_{2}SO

_{4}-H

_{2}O clusters and can thus stabilize them [19–22], the recent laboratory studies suggest NH

_{3}< MA < TMA ≲ DMA in stabilizing sulfuric acid clusters [46,50]. This indicates that MA, whose background atmospheric concentrations are estimated to be smaller than those of DMA and TMA [34], can be used to estimate the lower limit of the impact of aliphatic amines on atmospheric nucleation.

_{2}O molecules has been investigated, new thermochemical data have been reported and atmospheric implications of the obtained results have been discussed. We have carried out a detailed thermochemical analysis, the comparison of the enhancement due to MA and ammonia and search for favorable conditions, at which MA could considerably enhance the formation of new particles in the Earth’s atmosphere.

## 2. Methods

_{2}O was not involved in cluster formation to more than 70 in the case when high (k > 3) hydrates are formed. The performance of the PW91PW91/6-311++G (3df, 3pd) method has been systematically validated against experimental Gibbs free energies for clusters relevant to the Earth’s atmosphere [6,22,25,52–54] and has shown a very good agreement with all the currently available experiments and higher level ab initio studies [55–59]. The method has been successfully applied to a wide range of nucleation problems including the classical problem Wilson’s of the sign preference [52], stability and dipole moment of sulfuric acid hydrates, atmospheric nucleation of H

_{2}SO

_{4}-H

_{2}O ions of different sign and composition [53], temperature and concentration dependencies of the H

_{2}O nucleation rates [54], and impact of ammonia and organic acids on the stability of neutral and charged binary H

_{2}SO

_{4}-H

_{2}O clusters. A more detailed comparison of PW91PW91 free energies with other ab initio and experimental data can be found in the Supplementary Information. The calculations of cluster distributions have been carried out using the standard chemical kinetics equations (see references [21,58] for details). The present work extends the recent study of Bustos et al. [58], where (H

_{2}SO

_{4})

_{1}(CH

_{3}NH

_{2})

_{1}(H

_{2}O)

_{0–5}clusters have been studied using RI-MP2/CBS method. Compared to [58], the present study covers much larger range of cluster sizes and compositions. In particular, the present study covers the whole range of (H

_{2}SO

_{4})

_{0–2}(CH

_{3}NH

_{2})

_{0–2}(H

_{2}O)

_{0–5}clusters. Calculations have been carried out using the Gaussian 09 suite of programs [60].

## 3. Results and Discussion

#### 3.1. Equilibrium Geometries and Cluster Properties

_{2}SO

_{4})

_{n}(CH

_{3}NH

_{2})

_{m}(H

_{2}O)

_{k}The formation of (H

_{2}SO

_{4})

_{n}(CH

_{3}NH

_{2})

_{m}(H

_{2}O)

_{k}clusters is often accompanied by proton transfer.

_{2}SO

_{4})

_{1}(CH

_{3}NH

_{2})

_{1}(H

_{2}O)

_{2}and (H

_{2}SO

_{4})

_{2}(CH

_{3}NH

_{2})

_{2}clusters shown in Figure 1, the structural formulas of the most stable isomers of (H

_{2}SO

_{4})

_{1}(CH

_{3}NH

_{2})

_{1}(H

_{2}O)

_{2}and (H

_{2}SO

_{4})

_{2}(CH

_{3}NH

_{2})

_{2}are (HSO

_{4}

^{−})(CH

_{3}NH

_{3})

^{+}(H

_{2}O)

_{2}and (HSO

_{4}

^{−})

_{2}(CH

_{3}NH

_{3}

^{+})

_{2}, respectively. Typically, OH bond lengths and O-O distances in (H

_{2}SO

_{4})

_{n}(CH

_{3}NH

_{2})

_{m}(H

_{2}O)

_{k}are a bit shorter than those in (H

_{2}SO

_{4})

_{n}(NH

_{3})

_{m}(H

_{2}O)

_{k}, being a sign of enhanced thermodynamic stability of (H

_{2}SO

_{4})

_{n}(CH

_{3}NH

_{2})

_{m}(H

_{2}O)

_{k}compared to (H

_{2}SO

_{4})

_{n}(NH

_{3})

_{m}(H

_{2}O)

_{k}. In the Supplementary Materials, an interested reader can find the complete data set (over 180 equilibrium geometries in total) for the Cartesian geometries of global and local minima located within ~3 kcal/mol of global minima, which cover the whole range of (H

_{2}SO

_{4})

_{n}(CH

_{3}NH

_{2})

_{m}(H

_{2}O)

_{k}, from (CH

_{3}NH

_{2}) molecules and (CH

_{3}NH

_{2}) hydrates to (H

_{2}SO

_{4})

_{2}(CH

_{3}NH

_{2})

_{2}(H

_{2}O)

_{5}, respectively. The corresponding data sets for (H

_{2}SO

_{4})

_{n}(NH

_{3})

_{m}(H

_{2}O)

_{k}and (H

_{2}SO

_{4})

_{n}(CH3)

_{2}NH)

_{m}(H

_{2}O)

_{k}are available in [26,61] and [22], respectively. Intrinsic statistical and entropic effects related to the difference between the Boltzmann-Gibbs average over the isomer mixture of a given composition and the energy of the global minimum of the same composition and to the difference in entropies between the global and minima do not exceed 0.1 kcal mol

^{−1}in all the cases studied and can be neglected.

#### 3.2. New Thermochemical Data and Their Analysis

#### 3.2.1. Hydration

_{2}O around (H

_{2}SO

_{4})

_{m}(CH

_{3}NH

_{2})

_{n}core. As seen from Table 1, the hydration of CH

_{3}NH

_{2}is weak and, thus, one cannot expect (CH

_{3}NH

_{2})(H

_{2}O)

_{n}to be stable under atmospheric conditions. The hydration free energies of CH

_{3}NH

_{2}vary from −1.46 to 1.7 kcal mol

^{−1}that gives us a clear indication of instability of (CH

_{3}NH

_{2})(H

_{2}O)

_{n}complexes under atmospheric conditions. Bonding of CH

_{3}NH

_{2}with H

_{2}SO

_{4}significantly increases the hydration strength and leads to the formation of stable hydrated clusters. In particular, hydration of three (H

_{2}SO

_{4})(CH

_{3}NH

_{2}), (H

_{2}SO

_{4})

_{2}(CH

_{3}NH

_{2})

_{1}and (H

_{2}SO

_{4})

_{2}(CH

_{3}NH

_{2})

_{2}out of four (H

_{2}SO

_{4})

_{m}(CH

_{3}NH

_{2})

_{n}cores investigated in the present study is strong.

_{2}SO

_{4})(CH

_{3}NH

_{2})

_{2}is much weaker than that of ((H

_{2}SO

_{4})(CH

_{3}NH

_{2}), (H

_{2}SO

_{4})

_{2}(CH

_{3}NH

_{2})

_{1}and (H

_{2}SO

_{4})

_{2}(CH

_{3}NH

_{2})

_{2}; however, it is still strong enough to impact the rates, at which (H

_{2}SO

_{4})(CH

_{3}NH

_{2})

_{2}are formed, especially at high RH. The hydration of (H

_{2}SO

_{4})(CH

_{3}NH

_{2}) and (H

_{2}SO

_{4})(CH

_{3}NH

_{2})(H

_{2}O) obtained in the present study agrees well with the recent the higher level ab initio RI-MP2/CBS study by Bustos et al. [58]

_{2}SO

_{4}and bases such as ammonia, DMA and MA shown in Figure 2 indicates that the hydration of the MA is stronger than that of other common atmospheric bases, NH

_{3}and DMA. These considerations lead us to conclude that rates, at which (H

_{2}SO

_{4})

_{m}(CH

_{3}NH

_{2})

_{n}(H

_{2}O)

_{k}stable pre-nucleation clusters are formed, are definitely RH-dependent.

#### 3.2.2. Affinity of H_{2}SO_{4} to Nucleating (H_{2}SO_{4})_{m}(CH_{3}NH_{2})_{n}(H_{2}O)_{k} Clusters

_{2}SO

_{4}to nucleating (H

_{2}SO

_{4})

_{n}(CH

_{3}NH

_{2})

_{m}(H

_{2}O)

_{k}clusters.

_{2}SO

_{4})

_{n}(NH

_{3})

_{m}(H

_{2}O)

_{k}[47] shows clearly that the (H

_{2}SO

_{4})

_{n}(CH

_{3}NH

_{2})

_{m}(H

_{2}O)

_{k}clusters are much more stable than the corresponding (H

_{2}SO

_{4})

_{n}(NH

_{3})

_{m}(H

_{2}O)

_{k}ones. This is by no means surprising because MA is a much stronger base than NH

_{3}. The H

_{2}SO

_{4}affinity to nucleating (H

_{2}SO

_{4})

_{n}(CH

_{3}NH

_{2})

_{m}(H

_{2}O)

_{k}clusters tends to grow with molar fraction of the base (CH

_{3}NH

_{2}) and varies with the hydration number. This pattern is nearly identical to that of the H

_{2}SO

_{4}affinity to (H

_{2}SO

_{4})

_{n}((CH3)

_{2}NH)

_{m}(H

_{2}O)

_{k}and (H

_{2}SO

_{4})

_{n}(NH

_{3})

_{m}(H

_{2}O)

_{k}.

_{2}SO

_{4}to nucleating (H

_{2}SO

_{4})

_{n}(CH

_{3}NH

_{2})

_{m}(H

_{2}O)

_{k}and (H

_{2}SO

_{4})

_{n}(CH

_{3}NH

_{2})

_{m}(H

_{2}O)

_{k}clusters, the affinities of H

_{2}SO

_{4}, the key atmospheric nucleation precursor to nucleating (H

_{2}SO

_{4})

_{n}(CH

_{3}NH

_{2})

_{m}(H

_{2}O)

_{k}and (H

_{2}SO

_{4})

_{m}((CH3)

_{2}NH)

_{n}(H

_{2}O)

_{k}clusters are quite close. The curves of (1,1), (2,1) for MA and DMA show a similar tendency, in the case of (2,2) at k >2, the affinities of the sulfuric acid to (2,1) MA clusters are higher than those to (2,1) DMA clusters. However, the values of the corresponding affinities to (2,1) DMA- and MA-containing clusters averaged over the hydration number are quite close. This is a clear indication that at identical concentrations of MA and DMA, the impact of MA on formation stable sulfuric acid-water clusters will be quite close to that of the DMA.

#### 3.2.3. Affinity of CH_{3}NH_{2} to Nucleating (H_{2}SO_{4})_{m}(CH_{3}NH_{2})_{n}(H_{2}O)_{k} Clusters

_{2}SO

_{4})

_{n}(CH

_{3}NH

_{2})

_{m}(H

_{2}O)

_{k}clusters via the (H

_{2}SO

_{4})

_{n}(CH

_{3}NH

_{2})

_{m−1}(H

_{2}O)

_{k}+(CH

_{3}NH

_{2}) <=> (H

_{2}SO

_{4})

_{n}(CH

_{3}NH

_{2})

_{m}(H

_{2}O)

_{k}reaction. As seen from Table 3, the MA affinities to nucleating (H

_{2}SO

_{4})

_{n}(CH

_{3}NH

_{2})

_{m}(H

_{2}O)

_{k}strongly depend on the molar fraction of H

_{2}SO

_{4}. In particular, they grow as the molar fraction of H

_{2}SO

_{4}in nucleating cluster increases. The MA affinities to (H

_{2}SO

_{4})

_{n}(CH

_{3}NH

_{2})

_{m}(H

_{2}O)

_{k}are much higher than NH

_{3}affinities to (H

_{2}SO

_{4})

_{n}(NH

_{3})

_{m}(H

_{2}O)

_{k}clusters and are close to the DMA affinities to (H

_{2}SO

_{4})

_{n}((CH

_{3})

_{2}NH)

_{m}(H

_{2}O)

_{k}.

_{3}and DMA. In particular, while the gas-phase MA acts, just like NH

_{3}and DMA, as a highly reactive nucleation agent, the MA clustered with H

_{2}SO

_{4}and H

_{2}O molecules enhances the affinity of the sulfuric acid to (H

_{2}SO

_{4})

_{n}(CH

_{3}NH

_{2})

_{m}(H

_{2}O)

_{k}clusters being formed.

#### 3.3. Impacts of the MA on Formation of Nucleating Clusters under Atmospheric Conditions

_{2}SO

_{4}and H

_{2}O under atmospheric conditions. Figure 4 presents the distributions of hydrated (H

_{2}SO

_{4})

_{m}(CH

_{3}NH

_{2})

_{n}clusters at an ambient temperature of 298.15 K and variable RH. As seen from Figure 4, most of (H

_{2}SO

_{4})

_{1}(CH

_{3}NH

_{2})

_{1}, (H

_{2}SO

_{4})

_{2}(CH

_{3}NH

_{2})

_{1}and (H

_{2}SO

_{4})

_{2}(CH

_{3}NH

_{2})

_{2}clusters are hydrated under typical atmospheric conditions and, hence, the RH dependency of the cluster distributions is obvious. Only < 5% of (H

_{2}SO

_{4})

_{1}(CH

_{3}NH

_{2})

_{1}, < 30% of (H

_{2}SO

_{4})

_{2}(CH

_{3}NH

_{2}) and <10% of (H

_{2}SO

_{4})

_{2}(CH

_{3}NH

_{2})

_{2}remain unhydrated at the relatively low RH = 50%. The fractions of the hydrated (H

_{2}SO

_{4})

_{1}(CH

_{3}NH

_{2})

_{1}, (H

_{2}SO

_{4})

_{2}(CH

_{3}NH

_{2})

_{1}and (H

_{2}SO

_{4})

_{2}(CH

_{3}NH

_{2}) clusters grow quickly with as the RH increases, reaching over 90% at RH = 70%. At RH = 90% almost all the (H

_{2}SO

_{4})

_{1}(CH

_{3}NH

_{2})

_{1}, (H

_{2}SO

_{4}H

_{2}SO

_{4})

_{2}(CH

_{3}NH

_{2})

_{1}and (H

_{2}SO

_{4})

_{2}(CH

_{3}NH

_{2}) clusters are hydrated.

_{2}SO

_{4})

_{1}(CH

_{3}NH

_{2})

_{1}, (H

_{2}SO

_{4})

_{2}(CH

_{3}NH

_{2})

_{1}and (H

_{2}SO

_{4})

_{2}(CH

_{3}NH

_{2})

_{2}have peaks at k = 2, 3, k = 2, 3, 4, and k = 3, 4, respectively. The hydration of less populous (H

_{2}SO

_{4})

_{1}(CH

_{3}NH

_{2})

_{2}is much weaker, however, fractions of hydrated (H

_{2}SO

_{4})

_{1}(CH

_{3}NH

_{2})

_{2}clusters reach ~15%, 25% and 40% at R = 50%, 70% and 90%, respectively. These considerations lead us to conclude that RH is clearly one of the key parameters controlling the (H

_{2}SO

_{4})

_{m}(CH

_{3}NH

_{2})

_{n}(H

_{2}O)

_{k}formation and rates, at which the (H

_{2}SO

_{4})

_{m}(CH

_{3}NH

_{2})

_{n}(H

_{2}O)

_{k}clusters are formed under atmospheric conditions.

_{2}SO

_{4}dimers is a critically important step in the base-enhanced new particle formation. The H

_{2}SO

_{4}dimers consisting of two H

_{2}SO

_{4}, two base molecules and multiple water molecules are assumed to be both large and reactive enough to grow further via collisions with acids other than H

_{2}SO

_{4}[62]. In this case, the production rates of (H

_{2}SO

_{4})

_{2}(amine)n(H

_{2}O)k clusters are comparable to the new particle formation rates and can be used to estimate the maximum new particle production and its sensitivity to the concentration of base concentrations, RH and other relevant parameters.

_{3}) to binary H

_{2}SO

_{4}-H

_{2}O dimers characterizing the impacts of MA and NH

_{3}on the formation of binary sulfuric acid-water clusters.

_{3}is either close to or smaller than that due to MA at ppt level. This is likely to indicate that accounting for the extended range of cluster sizes and compositions increases the difference in the stability of (H

_{2}SO

_{4})

_{m}(CH

_{3}NH

_{2})

_{n}(H

_{2}O)

_{k}and (H

_{2}SO

_{4})

_{m}(NH

_{3})

_{n}(H

_{2}O)

_{k}clusters in the favor of (H

_{2}SO

_{4})

_{m}(CH

_{3}NH

_{2})

_{n}(H

_{2}O)

_{k}and that the difference in the cluster stability between (H

_{2}SO

_{4})

_{m}(CH

_{3}NH

_{2})

_{n}(H

_{2}O)

_{k}and (H

_{2}SO

_{4})

_{m}(NH

_{3})

_{n}(H

_{2}O)

_{k}is likely to be large enough to overcome the very large difference between atmospheric concentrations of [NH

_{3}] ranging from ~1 to 10 ppb and [MA] concentration ranging from a fraction of ppt to several ppt. The relative importance of ternary nucleation of NH

_{3}and MA depends strongly on the atmospheric concentration ratio [MA]/[NH

_{3}]. In particular, the MA ternary nucleation begins to dominate over ternary nucleation of sulfuric acid, water and ammonia at [MA]/[NH

_{3}] > ~10

^{−3}. The conclusion about the relative importance of ternary NH

_{3}and MA nucleation obtained based on extended thermodynamic data sets for MA with accounting for hydration slightly differs from that obtained in the earlier study [20]. Apparently, accounting for the wider range of cluster sizes and compositions leads to a moderate enhancement in the stability of MA-H

_{2}O-H

_{2}SO

_{4}clusters compared to NH

_{3}- H

_{2}O-H

_{2}SO

_{4}ones. Another important detail is that [(H

_{2}SO

_{4})

_{m}(CH

_{3}NH

_{2})

_{n}(H

_{2}O)k] dominate over [(H

_{2}SO

_{4})

_{m}(H

_{2}O)

_{k}] under dry and low RH conditions only. For example, while at RH = 20% [MA] at sub-ppt level is enough to reach [(H

_{2}SO

_{4})

_{m}(CH

_{3}NH

_{2})

_{n}(H

_{2}O)

_{k}]/[(H

_{2}SO

_{4})

_{m}(H

_{2}O)

_{k}] ratio of 10, much higher [MA] exceeding 10 ppt is needed in order to reach the same [(H

_{2}SO

_{4})

_{m}(CH

_{3}NH

_{2})

_{n}(H

_{2}O)

_{k}]/[(H

_{2}SO

_{4})

_{m}(H

_{2}O)

_{k}] at RH = 60%. The impact of the ambient temperature on the enhancement due to the MA is also very strong. In particular, the enhancement due to the MA increases with the decreasing ambient temperature. For example, the [(H

_{2}SO

_{4})

_{m}(CH

_{3}NH

_{2})

_{n}(H

_{2}O)

_{k}]/[(H

_{2}SO

_{4})

_{m}(H

_{2}O)

_{k}] ratios at T = 300 K and T = 270 K differ by more than two orders of magnitude in the favor of the [(H

_{2}SO

_{4})

_{m}(CH

_{3}NH

_{2})

_{n}(H

_{2}O)

_{k}]/[(H

_{2}SO

_{4})

_{m}(H

_{2}O)

_{k}] at T = 270 K. As it may be seen from Figure 5, the equilibrium concentrations of (H

_{2}SO

_{4}) clusters containing MA and strength of the enhancing effect of the MA depends on the RH and the ambient temperature. Low RH and low ambient temperatures are clearly the favorable conditions at which the strongest effect of MA on the formation of stable binary H

_{2}SO

_{4}-H

_{2}O clusters is achieved.

## 4. Conclusions

- (H
_{2}SO_{4})_{m}(CH_{3}NH_{2})_{n}(H_{2}O)_{k}clusters are strongly hydrated under typical atmospheric conditions and, thus, (H_{2}SO_{4})_{m}(CH_{3}NH_{2})_{n}(H_{2}O)_{k}formation rates are RH-dependent. The effect of the MA depends strongly on the RH and the ambient temperature. Low RH and low ambient temperatures are clearly the favorable conditions, at which the strongest effect of MA on the formation of stable binary H_{2}SO_{4}-H_{2}O clusters is achieved. While the enhancing effect is very strong at low RH, it decreases quickly as RH is growing; - At the identical concentrations of MA and DMA, the enhancement in the production of stable (H
_{2}SO_{4})_{m}(H_{2}O)_{k}due to MA is close to that due to DMA; - The MA ternary nucleation begins to dominate over ternary nucleation of sulfuric acid, water and ammonia at [MA]/[NH
_{3}] > ~10^{−3}.

## Supplement

**Supplementary File 1:**

## Acknowledgments

## Author Contributions

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**Figure 1.**Equilibrium geometries of the most stable isomers of (CH

_{3}NH

_{2})(H

_{2}O)

_{2}(

**a**); (H

_{2}SO

_{4}) (CH

_{3}NH

_{2}) (

**b**), (H

_{2}SO

_{4})(CH

_{3}NH

_{2}) H

_{2}O)

_{2}(

**c**), (H

_{2}SO

_{4})

_{2}(CH

_{3}NH

_{2})

_{1}(H

_{2}O)

_{1}(

**d**), (H

_{2}SO

_{4})(CH

_{3}NH

_{2})

_{2}(

**e**) and (H

_{2}SO

_{4})

_{2}(CH

_{3}NH

_{2})

_{2}(

**f**) obtained at PW91PW91/6-311++G(3df,3pd) level of theory.

**Figure 2.**Standard conditions (T = 298 K, P = 1013 KPa) hydration free energies (kcal mol

^{−1}) for (H

_{2}SO

_{4})

_{1}(Base)

_{1}(a) and (H

_{2}SO

_{4})

_{2}(Base)

_{2}(b) clusters. Abbreviations NB, A, DMA and MA refer to no base, ammonia, dimethylamine and methylamine, respectively. The data for ammonia and dimethylamine were adopted from [26,61] and [22], respectively.

**Figure 3.**Standard conditions (T = 298 K, P = 1013KPa) Gibbs free energy changes associated with the formation of thermodynamically stable (H

_{2}SO

_{4})

_{n}(CH

_{3}NH

_{2})

_{m}(H

_{2}O)

_{k}and (H

_{2}SO

_{4})

_{n}((CH

_{3})

_{2}NH)

_{m}(H

_{2}O)

_{k}clusters via the (H

_{2}SO

_{4})

_{n−1}(CH

_{3}NH

_{2})

_{m}(H

_{2}O)

_{k}+ (H

_{2}SO

_{4}) <=> (H

_{2}SO

_{4})

_{n}(CH

_{3}NH

_{2})

_{m}(H

_{2}O)

_{k}and (H

_{2}SO

_{4})

_{n−1}((CH

_{3})

_{2}NH)

_{m}(H

_{2}O)

_{k}+ (H

_{2}SO

_{4}) <=> (H

_{2}SO

_{4})

_{n}((CH

_{3})

_{2}NH)

_{m}(H

_{2}O)

_{k}reactions as functions of the hydration number k. DMA and MA refer to dimethyl- and methylamine, respectively. The data for ammonia and dimethylamine were adopted from [26,61] and [22], respectively.

**Figure 4.**Fraction distribution of (H

_{2}SO

_{4})

_{m}(CH

_{3}NH

_{2})

_{n}(H

_{2}O)

_{k}at ambient temperature (298.15K) and variable RH. The abbreviation mSnMkW denotes (H

_{2}SO

_{4})

_{m}(CH

_{3}NH

_{2})

_{n}(H

_{2}O)

_{k}clusters. Blue, red and yellow bars represent RH of 50%, 70% and 90%, respectively.

**Figure 5.**Concentration ratios of ternary dimers containing MA or NH

_{3}to binary H

_{2}SO

_{4}-H

_{2}O dimers as a function of RH. [NH

_{3}] = 1 ppb is the background concentration of ammoniaMA- and NH

_{3}-enhanced cluster production are considered as simultaneous uncoupled processes. The data for ammonia were adopted from [26,61].

**Table 1.**Changes in enthalpies ΔH (kcal mol

^{−1}), entropies ΔS (cal mol

^{−1}K

^{−1}), and Gibbs free energy ΔG (kcal mol

^{−1}) associated with hydration of nucleating (H

_{2}SO

_{4})

_{n}(CH

_{3}NH

_{2})

_{m}(H

_{2}O)

_{k}clusters at 298.15 K and pressure of 101.3 KPa. Subscript BA refers to the best ab initio RI-MP2/CBS study of Bustos et al. [58].

Reaction | Δ H | Δ S | Δ G | Δ G_{BA} |
---|---|---|---|---|

(CH_{3}NH_{2})+(H_{2}O) <=> (CH_{3}NH_{2})(H_{2}O) | −7.73 | −22.25 | −1.10 | |

(CH_{3}NH_{2})(H_{2}O)+(H_{2}O) <=> (CH_{3}NH_{2})(H_{2}O)_{2} | −8.70 | −34.40 | 1.55 | |

(CH_{3}NH_{2})(H_{2}O)_{2}+(H_{2}O) <=> (CH_{3}NH_{2})(H_{2}O)_{3} | −11.21 | −32.72 | −1.46 | |

(CH3NH)(H_{2}O)_{3}+(H_{2}O) <=> (CH3NH)(H_{2}O)_{4} | −9.10 | −29.31 | −0.36 | |

(CH_{3}NH_{2})(H_{2}O)_{4}+(H_{2}O) <=> (CH_{3}NH_{2})(H_{2}O)_{5} | −7.36 | −30.37 | 1.70 | |

(H_{2}SO_{4})(CH_{3}NH_{2})+(H_{2}O) <=> (H_{2}SO_{4})(CH_{3}NH_{2})(H_{2}O) | −13.02 | −32.49 | −3.33 | −3.53 |

(H_{2}SO_{4})(CH_{3}NH_{2})(H_{2}O)+(H_{2}O) <=> (H_{2}SO_{4})(CH_{3}NH_{2})(H_{2}O)_{2} | −13.85 | −34.66 | −3.52 | −3.95 |

(H_{2}SO_{4})(CH_{3}NH_{2})(H_{2}O)_{2}+(H_{2}O) <=> (H_{2}SO_{4} H_{2}SO_{4})(CH_{3}NH_{2})(H_{2}O)_{3} | −10.97 | −29.73 | −2.11 | |

(H_{2}SO_{4})(CH_{3}NH_{2})(H_{2}O)_{3}+(H_{2}O) <=> (H_{2}SO_{4})(CH_{3}NH_{2})(H_{2}O)_{4} | −10.61 | −31.21 | −1.31 | |

(H_{2}SO_{4})(CH_{3}NH_{2})(H_{2}O)_{4}+(H_{2}O) <=> (H_{2}SO_{4})(CH_{3}NH_{2})(H_{2}O)_{5} | −11.84 | −39.55 | −0.05 | |

(H_{2}SO_{4})(CH_{3}NH_{2})_{2}+(H_{2}O) <=> (H_{2}SO_{4})(CH_{3}NH_{2})_{2}(H_{2}O) | −12.26 | −36.04 | −1.51 | |

(H_{2}SO_{4})(CH_{3}NH_{2})_{2}(H_{2}O)+(H_{2}O) <=> (H_{2}SO_{4})(CH_{3}NH_{2})_{2}(H_{2}O)_{2} | −11.73 | −35.65 | −1.10 | |

(H_{2}SO_{4})(CH_{3}NH_{2})_{2}(H_{2}O)_{2}+(H_{2}O) <=> (H_{2}SO_{4})(CH_{3}NH_{2})_{2}(H_{2}O)_{3} | −13.30 | −35.31 | −2.77 | |

(H_{2}SO_{4})(CH_{3}NH_{2})_{2}(H_{2}O)_{3}+(H_{2}O) <=> (H_{2}SO_{4})(CH_{3}NH_{2})_{2}(H_{2}O)_{4} | −11.30 | −33.74 | −1.24 | |

(H_{2}SO_{4})_{2}(CH_{3}NH_{2})+(H_{2}O) <=> (H_{2}SO_{4})_{2}(CH_{3}NH_{2})(H_{2}O) | −11.26 | −31.27 | −1.94 | |

(H_{2}SO_{4})_{2}(CH_{3}NH_{2})(H_{2}O)+(H_{2}O) <=> (H_{2}SO_{4})_{2}(CH_{3}NH_{2})(H_{2}O)_{2} | −13.49 | −34.61 | −3.17 | |

(H_{2}SO_{4})_{2}(CH_{3}NH_{2})(H_{2}O)_{2}+(H_{2}O) <=> (H_{2}SO_{4})_{2}(CH_{3}NH_{2})(H_{2}O)_{3} | −11.99 | −31.32 | −2.65 | |

(H_{2}SO_{4})_{2}(CH_{3}NH_{2})(H_{2}O)_{3}+(H_{2}O) <=> (H_{2}SO_{4})_{2}(CH_{3}NH_{2})(H_{2}O)_{4} | −12.33 | −35.18 | −1.84 | |

(H_{2}SO_{4})_{2}(CH_{3}NH_{2})(H_{2}O)_{4}+(H_{2}O) <=> (H_{2}SO_{4})_{2}(CH_{3}NH_{2})(H_{2}O)_{5} | −10.82 | −30.46 | −1.74 | |

(H_{2}SO_{4})_{2}(CH_{3}NH_{2})_{2}+(H_{2}O) <=> (H_{2}SO_{4})_{2}(CH_{3}NH_{2})_{2}(H_{2}O) | −12.07 | −36.10 | −1.31 | |

(H_{2}SO_{4})_{2}(CH_{3}NH_{2})_{2}(H_{2}O)+(H_{2}O) <=> (H_{2}SO_{4})_{2}(CH_{3}NH_{2})_{2} (H_{2}O)_{2} | −11.62 | −29.53 | −2.82 | |

(H_{2}SO_{4})_{2}(CH_{3}NH_{2})_{2}(H_{2}O)_{2}+(H_{2}O) <=> (H_{2}SO_{4})_{2}(CH_{3}NH_{2})_{2}(H_{2}O)_{3} | −14.55 | −32.83 | −4.76 | |

(H_{2}SO_{4})_{2}(CH_{3}NH_{2})_{2} (H_{2}O)_{3}+(H_{2}O) <=> (H_{2}SO_{4})_{2}(CH_{3}NH_{2})_{2} (H_{2}O)_{4} | −11.09 | −31.28 | −1.77 | |

(H_{2}SO_{4})_{2}(CH_{3}NH_{2})_{2} (H_{2}O)4+(H_{2}O) <=> (H_{2}SO_{4})_{2}(CH_{3}NH_{2})_{2} (H_{2}O)_{5} | −11.25 | −33.56 | −1.24 |

**Table 2.**Changes in enthalpies ΔH (kcal mol

^{−1}), entropies ΔS cal mol

^{−1}K

^{−1}), and Gibbs free energy ΔG (kcal mol

^{−1}) describing the affinity of H

_{2}SO

_{4}to nucleating (H

_{2}SO

_{4})

_{n}(CH

_{3}NH

_{2})

_{m}(H

_{2}O)

_{k}clusters at 298.15 K and pressure of 101.3 KPa. Subscript BA refers to the best ab initio RI-MP2/CBS study by Bustos et al. [58].

Reaction | Δ H | Δ S | Δ G |
---|---|---|---|

(CH_{3}NH_{2})+(H_{2}SO_{4}) <=> (H_{2}SO_{4})(CH_{3}NH_{2}) | −20.40 | −31.42 | −11.03 (−11.61)_{BA} |

(CH_{3}NH_{2})(H_{2}O)+(H_{2}SO_{4}) <=> (H_{2}SO_{4})(CH_{3}NH_{2})(H_{2}O) | −25.69 | −41.67 | −13.26 |

(CH_{3}NH_{2})(H_{2}O)_{2}+(H_{2}SO_{4}) <=> (H_{2}SO_{4})(CH_{3}NH_{2})(H_{2}O)_{2} | −30.83 | −41.93 | −18.33 |

(CH_{3}NH_{2})(H_{2}O)_{3}+(H_{2}SO_{4}) <=> (H_{2}SO_{4})(CH_{3}NH_{2})(H_{2}O)_{3} | −30.59 | −38.95 | −18.98 |

(CH_{3}NH_{2})(H_{2}O)_{4}+(H_{2}SO_{4}) <=> (H_{2}SO_{4})(CH_{3}NH_{2})(H_{2}O)_{4} | −32.11 | −40.85 | −19.93 |

(CH_{3}NH_{2})(H_{2}O)_{5}+(H_{2}SO_{4}) <=> (H_{2}SO_{4})(CH_{3}NH_{2})(H_{2}O)_{5} | −36.60 | −50.04 | −21.68 |

(H_{2}SO_{4})(CH_{3}NH_{2})+(H_{2}SO_{4}) <=> (H_{2}SO_{4})_{2}(CH_{3}NH_{2}) | −27.42 | −44.17 | −14.25 |

(H_{2}SO_{4})(CH_{3}NH_{2})(H_{2}O)+(H_{2}SO_{4}) <=> (H_{2}SO_{4})_{2}(CH_{3}NH_{2})(H_{2}O) | −25.66 | −42.94 | −12.86 |

(H_{2}SO_{4})(CH_{3}NH_{2})(H_{2}O)_{2}+(H_{2}SO_{4}) <=> (H_{2}SO_{4})_{2}(CH_{3}NH_{2})(H_{2}O)_{2} | −25.30 | −42.90 | −12.51 |

(H_{2}SO_{4})(CH_{3}NH_{2})(H_{2}O)_{3}+(H_{2}SO_{4}) <=> (H_{2}SO_{4})_{2}(CH_{3}NH_{2})(H_{2}O)_{3} | −26.31 | −44.49 | −13.05 |

(H_{2}SO_{4})(CH_{3}NH_{2})(H_{2}O)_{4}+(H_{2}SO_{4}) <=> (H_{2}SO_{4})_{2}(CH_{3}NH_{2})(H_{2}O)_{4} | −28.03 | −48.46 | −13.58 |

(CH_{3}NH_{2})_{2}+(H_{2}SO_{4}) <=> (H_{2}SO_{4})(CH_{3}NH_{2})_{2} | −31.93 | −42.75 | −19.18 |

(CH_{3}NH_{2})_{2}(H_{2}O)+(H_{2}SO_{4}) <=> (H_{2}SO_{4})(CH_{3}NH_{2})_{2}(H_{2}O) | −33.74 | −45.36 | −20.22 |

(CH_{3}NH_{2})_{2}(H_{2}O)_{2}+(H_{2}SO_{4}) <=> (H_{2}SO_{4})(CH_{3}NH_{2})_{2}(H_{2}O)_{2} | −33.81 | −49.43 | −19.07 |

(CH_{3}NH_{2})_{2}(H_{2}O)_{3}+(H_{2}SO_{4}) <=> (H_{2}SO_{4})(CH_{3}NH_{2})_{2}(H_{2}O)_{3} | −38.21 | −54.86 | −21.85 |

(CH_{3}NH_{2})_{2}(H_{2}O)_{4}+(H_{2}SO_{4}) <=> (H_{2}SO_{4})(CH_{3}NH_{2})_{2}(H_{2}O)_{4} | −42.26 | −60.50 | −24.22 |

(H_{2}SO_{4})(CH_{3}NH_{2})_{2}+(H_{2}SO_{4}) <=> (H_{2}SO_{4})_{2}(CH_{3}NH_{2})_{2} | −31.08 | −40.62 | −18.97 |

(H_{2}SO_{4})(CH_{3}NH_{2})_{2}(H_{2}O)+(H_{2}SO_{4}) <=> (H_{2}SO_{4})_{2}(CH_{3}NH_{2})_{2}(H_{2}O) | −30.89 | −40.68 | −18.76 |

(H_{2}SO_{4})(CH_{3}NH_{2})2(H_{2}O)_{2}+(H_{2}SO_{4}) <=> (H_{2}SO_{4})_{2}(CH_{3}NH_{2})_{2}(H_{2}O)_{2} | −30.78 | −34.57 | −20.48 |

(H_{2}SO_{4})(CH_{3}NH_{2})_{2}(H_{2}O)_{3}+(H_{2}SO_{4}) <=> (H_{2}SO_{4})_{2}(CH_{3}NH_{2})_{2}(H_{2}O)_{3} | −32.03 | −32.09 | −22.46 |

(H_{2}SO_{4})(CH_{3}NH_{2})_{2}(H_{2}O)_{4}+(H_{2}SO_{4}) <=> (H_{2}SO_{4})_{2}(CH_{3}NH_{2})_{2}(H_{2}O)_{4} | −31.83 | −29.62 | −22.99 |

**Table 3.**Changes in enthalpies ΔH (kcal mol

^{−1}), entropies ΔS (cal mol

^{−1}K

^{−1}), and Gibbs free energy ΔG (kcal mol

^{−1}) describing the affinity of CH

_{3}NH

_{2}to nucleating (H

_{2}SO

_{4})

_{n}(CH

_{3}NH

_{2})

_{m}(H

_{2}O)

_{k}clusters at 298.15 K and pressure of 101.3 KPa.

Reaction | Δ H | Δ S | Δ G |
---|---|---|---|

(CH_{3}NH_{2}) +(CH_{3}NH_{2}) <=> (CH_{3}NH_{2})_{2} | −4.93 | −21.07 | 1.35 |

(CH_{3}NH_{2})_{2} +(CH_{3}NH_{2}) <=> (CH_{3}NH_{2})_{3} | −3.17 | −24.5 | 4.13 |

(H_{2}SO_{4}) +(CH_{3}NH_{2}) <=> (H_{2}SO_{4})(CH_{3}NH_{2}) | −20.4 | −31.42 | −11.03 |

(H_{2}SO_{4})(H_{2}O)+(CH_{3}NH_{2}) <=> (H_{2}SO_{4})(CH_{3}NH_{2})(H_{2}O) | −21.65 | −32.11 | −12.08 |

(H_{2}SO_{4})(H_{2}O)_{2}+(CH_{3}NH_{2}) <=> (H_{2}SO_{4})(CH_{3}NH_{2})(H_{2}O)_{2} | −22.94 | −34.69 | −12.59 |

(H_{2}SO_{4})(H_{2}O)_{3}+(CH_{3}NH_{2}) <=> (H_{2}SO_{4})(CH_{3}NH_{2})(H_{2}O)_{3} | −21.96 | −32.17 | −12.37 |

(H_{2}SO_{4})(H_{2}O)_{4}+(CH_{3}NH_{2}) <=> (H_{2}SO_{4})(CH_{3}NH_{2})(H_{2}O)_{4} | −18.76 | −28.24 | −10.34 |

(H_{2}SO_{4})(H_{2}O)_{5}+(CH_{3}NH_{2}) <=> (H_{2}SO_{4})(CH_{3}NH_{2})(H_{2}O)_{5} | −20.54 | −36.92 | −9.53 |

(H_{2}SO_{4})(CH_{3}NH_{2}) +(CH_{3}NH_{2}) <=> (H_{2}SO_{4})(CH_{3}NH_{2})_{2} | −16.47 | −32.40 | −6.80 |

(H_{2}SO_{4}) (CH_{3}NH_{2})(H_{2}O)+(CH_{3}NH_{2}) <=> (H_{2}SO_{4})(CH_{3}NH_{2})_{2}(H_{2}O) | −15.70 | −35.95 | −4.98 |

(H_{2}SO_{4})(CH_{3}NH_{2})(H_{2}O)_{2}+(CH_{3}NH_{2}) <=> (H_{2}SO_{4})(CH_{3}NH_{2})_{2}(H_{2}O)_{2} | −13.58 | −36.94 | −2.57 |

(H_{2}SO_{4})(CH_{3}NH_{2})(H_{2}O)_{3}+(CH_{3}NH_{2}) <=> (H_{2}SO_{4})(CH_{3}NH_{2})_{2}(H_{2}O)_{3} | −15.91 | −42.52 | −3.24 |

(H_{2}SO_{4})(CH_{3}NH_{2})(H_{2}O)4+(CH_{3}NH_{2}) <=> (H_{2}SO_{4})(CH_{3}NH_{2})_{2}(H_{2}O)_{4} | −16.60 | −45.06 | −3.17 |

(H_{2}SO_{4})_{2}+(CH_{3}NH_{2}) <=> (H_{2}SO_{4})_{2}(CH_{3}NH_{2}) | −31.65 | −40.13 | −19.69 |

(H_{2}SO_{4})_{2}(H_{2}O)+(CH_{3}NH_{2}) <=> (H_{2}SO_{4})_{2}(CH_{3}NH_{2})(H_{2}O) | −28.47 | −34.41 | −18.21 |

(H_{2}SO_{4})_{2}(H_{2}O)_{2}+(CH_{3}NH_{2}) <=> (H_{2}SO_{4})_{2}(CH_{3}NH_{2})(H_{2}O)_{2} | −29.11 | −35.91 | −18.41 |

(H_{2}SO_{4})_{2}(H_{2}O)_{3}+(CH_{3}NH_{2}) <=> (H_{2}SO_{4})_{2}(CH_{3}NH_{2})(H_{2}O)_{3} | −26.53 | −29.64 | −17.70 |

(H_{2}SO_{4})_{2}(H_{2}O)_{4}+(CH_{3}NH_{2}) <=> (H_{2}SO_{4})_{2}(CH_{3}NH_{2})(H_{2}O)_{4} | −24.05 | −27.87 | −15.74 |

(H_{2}SO_{4})_{2}(CH_{3}NH_{2})+(CH_{3}NH_{2}) <=> (H_{2}SO_{4})_{2}(CH_{3}NH_{2})_{2} | −20.13 | −28.86 | −11.52 |

(H_{2}SO_{4})_{2}(CH_{3}NH_{2})(H_{2}O)+(CH_{3}NH_{2}) <=> (H_{2}SO_{4})_{2}(CH_{3}NH_{2})_{2}(H_{2}O) | −20.94 | −33.69 | −10.89 |

(H_{2}SO_{4})_{2}(CH_{3}NH_{2})(H_{2}O)_{2}+(CH_{3}NH_{2}) <=> (H_{2}SO_{4})_{2}(CH_{3}NH_{2})_{2}(H_{2}O)_{2} | −19.07 | −28.61 | −10.54 |

(H_{2}SO_{4})_{2}(CH_{3}NH_{2})(H_{2}O)_{3}+(CH_{3}NH_{2}) <=> (H_{2}SO_{4})_{2}(CH_{3}NH_{2})_{2}(H_{2}O)_{3} | −21.63 | −30.12 | −12.65 |

(H_{2}SO_{4})_{2}(CH_{3}NH_{2})(H_{2}O)_{4}+(CH_{3}NH_{2}) <=> (H_{2}SO_{4})_{2}(CH_{3}NH_{2})_{2}(H_{2}O)_{4} | −20.4 | −26.21 | −12.58 |

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**MDPI and ACS Style**

Nadykto, A.B.; Herb, J.; Yu, F.; Xu, Y.; Nazarenko, E.S. Estimating the Lower Limit of the Impact of Amines on Nucleation in the Earth’s Atmosphere. *Entropy* **2015**, *17*, 2764-2780.
https://doi.org/10.3390/e17052764

**AMA Style**

Nadykto AB, Herb J, Yu F, Xu Y, Nazarenko ES. Estimating the Lower Limit of the Impact of Amines on Nucleation in the Earth’s Atmosphere. *Entropy*. 2015; 17(5):2764-2780.
https://doi.org/10.3390/e17052764

**Chicago/Turabian Style**

Nadykto, Alexey B., Jason Herb, Fangqun Yu, Yisheng Xu, and Ekaterina S. Nazarenko. 2015. "Estimating the Lower Limit of the Impact of Amines on Nucleation in the Earth’s Atmosphere" *Entropy* 17, no. 5: 2764-2780.
https://doi.org/10.3390/e17052764