A multistep global minimum sampling scheme, which has previously been applied to study the atmospheric cluster formation (Ma et al., 2019), was employed to search for the global minima of the (GA)x(SA)y(DMA)z, (GAS)x(SA)y(DMA)z and (GASA)x(SA)y(DMA)z (0≤z≤x+y≤3) clusters. The global minimum structures of the GA, GAS and GASA molecules were taken from a previous study (Tan et al., 2022b). To locate the global minimum energy structure, the artificial bee colony algorithm was systematically employed by the ABCluster program to generate 1000 initial random configurations for each cluster (Zhang and Dolg, 2015), and then these configurations were further pre-optimized using the PM7 semi-empirical method implemented in the MOPAC2016 program (Stewart, 2007, 2013, 2016). Second, up to 100 structures with relatively lower energies were selected from the 1000 structures, and a M06-2X/6-31+G* level of theory was applied for subsequent optimization. Finally, further geometry optimization and frequency calculations at the M06-2X/6-311++G(3df,3pd) level of theory were performed to optimize the 10 best of 100 optimized configurations, and then the global minimum structure with the lowest energy was obtained.

All the density functional theory (DFT) calculations were implemented in the GAUSSIAN 09 program package (Frisch et al., 2009). The M06-2X function combined with the 6-311++G(3df,3pd) basis set was chosen as it has been proven to be accurate in estimating the thermodynamic properties of atmospheric clusters, such as organic acid–SA–amine clusters, amide–SA clusters or amino acid–SA clusters (Clark et al., 1983; Elm et al., 2012; Herb et al., 2011; Elm et al., 2015, 2016; Ge et al., 2018a, b). Intrinsic reaction coordinate (IRC) calculations were carried out to verify the connections of the transition states with the reactants and products. Single-point energies were calculated at the DLPNO-CCSD(T)/aug-cc-pVTZ level based on the optimized geometries using the ORCA 4.1.2 package (Riplinger and Neese, 2013; Riplinger et al., 2013; Neese, 2012; Lu, 2022), which has gained popularity in large cluster formation studies (Xie et al., 2017; Chen et al., 2020; Shen et al., 2019). Zero-point energies at the M06-2X/6-311++G(3df,3pd) level were performed to correct for the corresponding single-point energies. The corresponding formation Gibbs free energies of the stable clusters aare summarized in the Supplement.

The formation of GAS and GASA can be described by the following two reactions. (GA+SO3)-OH→GAS (GA+SO3)-COOH→GASA The equilibrium constant K(GA+SO3)-OH for the formation of GAS and K(GA+SO3)-COOH for the formation of GASA are K(GA+SO3)-OH=GASGASO3=e-ΔGRT, K(GA+SO3)-COOH=GASAGASO3=e-ΔGRT, and the equilibrium concentration of GAS and GASA can be roughly estimated theoretically using the following expressions: [GAS]=K(GA+SO3)-OH[GA][SO3], [GASA]=K(GA+SO3)-COOH[GA][SO3], where K(GA+SO3)-OH and K(GA+SO3)-COOH are equal to the equilibrium constants from the formation Gibbs energies of the GAS and GASA, respectively. [GA] and [SO3] are the concentrations of the GA and SO3 monomer, respectively. We use the reactant concentrations of [GA] = 1.11×107–2.72×109 molec. cm-3 according to the values of some field observations (Mochizuki et al., 2019; Miyazaki et al., 2014; Stieger et al., 2021; Mochizuki et al., 2017). Considering atmospheric SO3 field measurements (Yao et al., 2020), its concentration is considered in the range of 104–106 molec. cm-3. Based on the above equations, the estimated concentration of the reaction product, GAS, is about 2.14×102–5.24×106 molec. cm-3, and the GASA is about 2.30×10-7–5.62×10-3 molec. cm-3. Thus, a range of concentrations for the GAS, from 102 to 106 molec. cm-3, is selected for the discussion in this work (Fig. 3, Table S1 and Fig. S9 in the Supplement).

The ACDC simulations form a dynamical model where the time development of molecular cluster concentrations is solved by integrating numerically the birth–death equations using the MATLAB-R2019b program (McGrath et al., 2012; Olenius et al., 2013; Ortega et al., 2012; Shampine and Reichelt, 1997). In the current research, the ACDC was employed to investigate the formation pathways and formation rates of the clusters. The birth–death equations can be written as 1dcidt=12∑j<iβj,(i-j)cjc(i-j)+∑jγ(i+j)→ici+j-∑jβi,jcicj-12∑j<iγi→jci+Qi-Si, where i and j are the clusters given in the system, ci and cj are the concentrations of clusters i and j, βi,j is the collision coefficient between clusters i and j, and γ(i+j)→i is the evaporation coefficient of cluster (i+j) evaporating into clusters i and j. Qi is the possible additional sources of cluster i, and Si is the sink term for taking into account external losses of cluster i. The collision coefficient β is calculated using the kinetic gas theory as Eq. (2) (taking βi,j as an example): 2βij=(34π)1/6(6kbTmi+6kbTmj)1/2(Vi1/3+Vj1/3)2, where kb is the Boltzmann constant; T is the temperature; mi and mj are the masses of i and j, respectively; and Vi and Vj are their respective volumes. The evaporation coefficient γ(i+j)→i is calculated using the Gibbs free energies of the formation of the clusters 3γ(i+j)→i=βijciecjeci+je=βijcrefexp⁡ΔGi+j-ΔGi-ΔGjkbT, where cie is the equilibrium concentration of cluster i, ΔGi is the Gibbs free energy of the formation of cluster i, and cref is the monomer concentration at the reference vapor corresponding to the pressure of 1 atm at which the Gibbs free energies were determined.

Here, the ACDC simulation system is regarded as a “3×3” box containing the (GA)x(SA)y(DMA)z, (GAS)x(SA)y(DMA)z and (GASA)x(SA)y(DMA)z (where the total number of x and y is from 0 to 3 and z from 0 to 3) clusters. Among these clusters, only the clusters including an equal number of z and x+y or the clusters with smaller numbers of z and x+y were considered, as only these clusters have the potential to further grow into larger sizes (Li et al., 2018; Olenius et al., 2013).

A detailed description of the boundary clusters that are allowed to leave the simulation and contribute to NPF is presented in the Supplement. In the current study, [GA] ranged from 107 to 1010 molec. cm-3, and the corresponding [GAS] was 103–106 molec. cm-3 (Miyazaki et al., 2014; Mochizuki et al., 2017, 2019; Stieger et al.,  2021). A constant coagulation sink of 2.6×10-3 s-1 was applied to account for scavenging by larger particles. The simulations were mainly run at 278 K, with additional runs at 258 and 298 K to investigate the influence of temperature. These conditions correspond to a typical sink value and temperature in the boreal forest environment (Olenius et al., 2013; Dal Maso et al., 2008).

The potential energy surfaces (PESs) of the reaction between GA and SO3, along with the optimized structures of the pre-reaction complexes (R), transition states (TSs) and products (P), are presented in Fig. 1. Since GA contains both the -OH and -COOH functional groups, two reaction pathways for GA and SO3 are considered in this study: (1) the esterification reaction between the hydroxyl group of GA and SO3 [(GA + SO3)-OH] and (2) the cycloaddition reaction between the carboxyl group of GA and SO3 [(GA + SO3)-COOH]. In the presumed reaction pathway (1) (without a catalyst), the hydroxyl oxygen atom of GA could react with the sulfur atom of SO3 to form sulfate GAS (Fig. 1a), followed by simultaneous proton transfer from GA to SO3. However, the Gibbs free energy barrier is 23.08 kcal mol-1, which shows that a direct reaction between the hydroxyl group and SO3 is a thermodynamically unfavorable pathway for the formation of GAS. The high-energy barrier of the (GA + SO3)-OH reaction partly ascribes to the ring tension a rather closed four-membered ring transition state structure. Differently, the Gibbs free energy barrier of the (GA + SO3)-COOH reaction path without a catalyst is significantly lower, only 3 kcal mol-1 (Fig. 1b).

With a high abundance (∼ 1017 cm-3) being detected in the troposphere (Huang et al., 2015), H2O has been reported as effectively acting as a catalyst in chemical reactions (Liu et al., 2019). Herein, we investigated the catalytic effect of H2O on the reaction of GA and SO3. As can be seen in Fig. 1a, the free energy barrier of the (GA + SO3)-OH reaction catalyzed by H2O is 3.41 kcal mol-1, which is substantially lower than that for the direct reaction without a catalyst. The free energy barrier for the H2O-catalyzed (GA + SO3)-COOH reaction is 0.92 kcal mol-1. These results indicate that both reaction pathways for GA + SO3 are favorable with the catalysis of H2O to generate GAS and GASA, respectively. Therefore, as the relative humidity (RH) increases, it should be conducive to the formation of GAS and GASA. The abundances of hydrated GA clusters GA–n(H2O) (n= 0–3) were also calculated at different RHs (Fig. S3 and Table S3). The relative equilibrium abundance of GA hydrates is less than 7 % at RH = 90 % and 298 K. Since the hydration of GA is weak, the effect of the hydrated GA clusters on the formation of GAS and GASA is not considered further. SA can also act as both an acceptor and a donor of hydrogen, thereby promoting various proton transfer reactions to facilitate the formation of GAS and GASA with a low barrier (Yao et al., 2018; Liu et al., 2017; Tan et al., 2018). As shown in Fig. 1a (black line), the energy barrier of the GA + SO3 reaction in the presence of the catalyst SA sharply decreases with the value of 2.83 kcal mol-1 for the formation of GAS and with that of 1.13 kcal mol-1 for the formation of GASA (black line in Fig. 1b). As the geometry structures of the transition states (TS1 to TS6) shown in Fig. 1, the participation of the catalysts could efficiently decrease the ring tension of the transition state geometry by increasing the ring size, followed by the reduction in the related energy barrier.

Hence, the catalysts H2O or SA could make the GA + SO3 reaction barrier-less and readily occur in the atmosphere. Indeed, many SO3-involved gas-phase reactions can be effectively catalyzed by H2O or SA (Li et al., 2018; Liu et al., 2019). Note that previous computational studies have proved that organic acids can act as catalysts for the reaction of SO3 and H2O to form sulfuric acid (Hazra and Sinha, 2011). Although we pay more attention to the catalytic effect of H2O on the reaction of α-hydroxy acid with SO3 in this study, the possible pathway of GA catalyzing the SO3+ H2O → SA reaction should not be ignored. Its PES (black line) is considered and compared with H2O catalytic reaction paths (see the details in Fig. S1 and the related discussions in the Supplement). It is worth noting that the product GAS generated from GA and SO3, with a more negative Gibbs free energy of formation (-12.75 kcal mol-1), is more stable than the product GASA (-1.42 kcal mol-1) as displayed in Fig. 1. This may suggest a possible formation pathway for the gas-phase GAS observed in the atmosphere. To the best of our knowledge, the gas-phase GAS has been detected for the first time in the Finnish boreal forest (Ehn et al., 2010). Le Breton et al. (2018) identified and measured 17 sulfur-containing organics (including organosulfates, and GAS is one of them) at a regional site 40 km northwest of Beijing. They successfully identified a persistent gas-phase presence of organosulfates in the ambient air. The mean contribution from gas-phase sulfur-containing organics to the total was found up to be 11.6 % and ∼ 23 ng m-3. Ye et al. (2021) also detected the ion C2H3SO6- with a diurnal peak in the afternoon in both the gas phase and the particle phase, whose ion was attributed to GAS, in Guangzhou in southern China during the fall of 2018. Unfortunately, atmospheric field observation data on gas-phase organosulfates and organic sulfuric anhydrides are still relatively scarce. In order to explore their impacts on the atmospheric NPF, we calculated the atmospheric concentrations of the GAS and GASA based on the thermodynamic equilibrium of the chemical reactions. The estimated concentration of GAS is in the range of 103–105 molec. cm-3, and that of GASA is ∼ 10-6–10-4 molec. cm-3 (see the details in Table S1 and the first part of the Supplement).

In order to evaluate the enhancing potential of GA and its different reaction products GAS and GASA in the typical SA–DMA-driven NPF process, we analyzed the global minima of the GA–SA–DMA, GAS–SA–DMA and GASA–SA–DMA clusters. The identified lowest free energy structures of the (GA)x(SA)y(DMA)z, (GAS)x(SA)y(DMA)z and (GASA)x(SA)y(DMA)z (0≤z≤x+y≤3) clusters are depicted in Figs. S4, S5 and S6, respectively. In general, both intermolecular hydrogen bond and ion electrostatic interactions formed by proton transfer reactions are found to play a key role in stabilizing these clusters. Hydrogen bond interactions are observed in all the clusters. The -OH/-COOH group in GA/GAS/GASA participates in at least one hydrogen bond formation and acts as a donor or acceptor of hydrogen. The proton transfer reactions that generally occurred in the acid–base clusters are found in most of the DMA-containing heteromolecular clusters but are not observed in the acidic homomolecular (GA)x, (GAS)x and (GASA)x (x= 1–3) clusters and the GA–SA, GAS–SA and GASA–SA clusters, in which only hydrogen bond interactions are found. Interestingly, there is no proton transfer in the (GA)1(DMA)1, (GAS)1(DMA)1 and (GASA)1(DMA)1 clusters. However, when another extra molecule is added to these three clusters, not only is the hydrogen bond interaction enhanced, but the proton is also transfer-promoted. This is because the trimer or large clusters are sufficient for converting a hydrogen-bonded system to an ion electrostatic interaction system, a consequence of proton transfer reaction.

The formation Gibbs free energies ΔG and evaporation rate values of the GA–SA–DMA, GAS–SA–DMA and GASA–SA–DMA clusters are obtained along with the acquisition of global minimum structures. More details about the ΔG and evaporation rates are shown in Tables S4–S6 and Fig. S7. Previous studies have verified that DMA is one of the strongest compounds for stabilizing SA clusters (Yao et al., 2018; Almeida et al., 2013; Jen et al., 2014). Since the (SA)3(DMA)3 cluster is the most stable cluster of the SA–DMA system, its ΔG and evaporation rate were taken as a reference value for comparison. In Fig. 2, the formation free energies ΔG (orange histograms) and evaporation rates ∑γ (black points) at 278 K of the (SA)3(DMA)3 cluster are presented along with the (GA)x(SA)y(DMA)3, (GAS)x(SA)y(DMA)3 and (GASA)x(SA)y(DMA)3 (x= 0–3, x+y= 3) clusters as a comparison. The ΔG of the (GA)1-3(SA)0-2(DMA)3 clusters are in all cases much more positive than that of the (SA)3(DMA)3 cluster, within a difference in the range of 18.49–58.74 kcal mol-1. For the (GAS)1-3(SA)0-2(DMA)3 clusters, their ΔG is close to that of the (SA)3(DMA)3 cluster, which is slightly negative, and the difference is in the range of 3.61–9.69 kcal mol-1. Notably, the ΔG of the (GASA)1-3(SA)0-2(DMA)3 clusters becomes more negative than that of the (SA)3(DMA)3 cluster. Their value discrepancies are -4.13, -4.63 and -11.83 kcal mol-1, respectively, with the number of the GASA increasing from 1 to 3. The above results indicate that the various organic compounds generated via the chemical reaction, such as GA and its products GAS and GASA, can apparently lead to different formation Gibbs free energies of clusters with the same scale when participating in the nucleation of the SA–DMA system due to their unequal intermolecular hydrogen bond and ion electrostatic interaction capacities with acidic and basic molecules, respectively.

The comparison of the evaporation rates of these clusters is more interesting. For the (Org)x(SA)y(DMA)3 (Org = GA, GAS and GASA; x= 1–3, x+y= 3) clusters, the evaporation rate of (Org)x(SA)y(DMA)3 does not simply change with the increasing number of organic molecules. The evaporation rate of (Org)2(SA)(DMA)3 (Org = GA, GAS and GASA) is largest. The evaporation rates of the (GAS)1(SA)2(DMA)3, (GAS)3(DMA)3, (GASA)1(SA)2(DMA)3 and (GASA)3(DMA)3 clusters vary from 10-13 to 10-4 s-1, which are smaller than that of the (SA)3(DMA)3 cluster, implying that the substitutions of one or three SAs by the GAS and GASA molecules are beneficial for stabilizing clusters. However, the evaporation rates of the GA–SA–DMA clusters are found to be largest when comparing them with that of the corresponding GAS–SA–DMA, GASA–SA–DMA and (SA)3(DMA)3 clusters displayed in Fig. 2. Actually, the evaporation rates of all the GA–SA–DMA clusters we calculated are larger than 101 s-1 (Fig. S7), indicating the instability of the participation of GA in the SA–DMA cluster system. The more negative ΔG and smaller evaporation rates of the GAS/GASA–SA–DMA clusters suggest that they are thermodynamically more favorable than the GA–SA–DMA system in the cluster formation process, resulting from the greater binding ability between the GAS–GASA and SA–DMA systems than that between the GA and SA–DMA systems. Hence, we can draw an initial conclusion that the GAS or GASA produced from a GA + SO3 reaction may efficiently stabilize the SA–DMA system, in contrast to GA itself.

The corresponding formation rates of the clusters in the GA–SA–DMA, GAS–SA–DMA and GASA–SA–DMA systems were further investigated and compared to achieve a deeper understanding of the influence of GA/GAS/GASA on the SA–DMA-based system using ACDC simulations. Figure 3 presents the comparison of the cluster formation rate as a function of the concentration of GA (1.1×107–2.7×109 molec. cm-3), GAS (2.1×103–5.2×105 molec. cm-3) and GASA (2.3×10-6–5.6×10-4 molec. cm-3) for the Org-SA–DMA systems at 278 and 258 K, under the condition of [SA] = 105 molec. cm-3. The concentration of DMA is selected to be 108 molec. cm-3, according to the typical concentrations observed in the gas phase in high mountains (F. Liu et al., 2018; Matsumoto et al., 2023). To compare the enhancing potential of GAS and GA on the SA–DMA-based NPF, Fig. 3a presents the cluster formation rates as a function of [GAS] and [GA] at 278 K. The cluster formation rate of the GAS–SA–DMA system markedly increases with the increasing concentration of [GAS] compared to that of the GA–SA–DMA system, especially in the case of [GAS] >3×104 molec. cm-3. As the concentration of GAS increased from 2.1×103 to 5.2×105 molec. cm-3, the cluster formation rate of the GAS–SA–DMA system yields a 10-fold increase (Fig. 3a), whereas the cluster formation rate of the GA–SA–DMA system basically remains unchanged (from ∼ 3.48×10-3 to ∼ 3.52×10-3 cm-3 s-1, as displayed more clearly in Fig. 3b) with the increase in the corresponding concentration of GA. Although the concentration of GAS is typically 4 orders of magnitude lower than that of GA, it has a significantly higher enhancing potential than GA in the SA–DMA-based nucleation system. The cluster formation rate as a function of [GASA] for the GASA–SA–DMA system is also compared with that of [GA] for the GA–SA–DMA system at 278 K in Fig. 3b. The growing trend of the cluster formation rate for the GASA–SA–DMA system is even smaller than that for the GA–SA–DMA system. Combined with the cluster thermodynamic results discussed in the previous section, we can conclude that such different trends should be responsible for the combined impact of the cluster ΔG, cluster evaporation rate and organic species concentration of these systems, respectively. The most rapid increasing trend of the cluster formation rate of the GAS–SA–DMA system is a consequence of the favorable ΔG and low evaporation rates of the (GAS)x(SA)y(DMA)z clusters and the non-low-equilibrium concentration of GAS. The unfavorable ΔG and large evaporation rates of the (GA)x(SA)y(DMA)z clusters make the GA–SA–DMA system kinetically unfavorable, even with a high GA concentration. For the trend of the GASA–SA–DMA system, the extremely low-equilibrium concentration of GASA makes its cluster formation rate hard to promote, even with the thermodynamically favorable conditions for the (GASA)x(SA)y(DMA)z cluster formation. [SO3] = 104 and 106 molec. cm-3 are also considered and compared with the results shown in Fig. 3a (as displayed in Fig. S9). In the case of [SO3] = 104 molec. cm-3, it is worth noting that the cluster formation rate of the GAS–SA–DMA system slightly increases with the increasing [GAS] compared to that of the GA–SA–DMA system with a corresponding [GA], where JGAS-SA-DMA reaches twice the value of JGA-SA-DMA. For [SO3] = 106 molec. cm-3, the trend of this difference becomes relatively obvious, and JGAS-SA-DMA grows up to 2 orders of magnitude higher than JGA-SA-DMA.

The effects of temperature and SA concentration on the cluster formation rates of these systems were also explored. As the temperature decreases to 258 K (Fig. 3c and d), the cluster formation rates of all the considered systems increase by about 2 to 3 orders of magnitude compared to that of 278 K. This behavior mainly results from the clusters becoming thermodynamically favorable at relatively low temperatures, making the clusters more stabilized. The simulated cluster formation rates J (cm-3 s-1) of these systems under different [SA] (104, 106 and 107 molec. cm-3) at 278 K are presented in Fig. S8. Their increasing trends of cluster formation rates as a function of organic species concentration are consistent with those obtained above at [SA] = 105 molec. cm-3. The cluster formation rates of these systems also become large with an [SA] increase. For example, the highest cluster formation rate of the GAS–SA–DMA system is ∼ 4×10-2 cm-3 s-1 within the considered GAS concentration at 278 K when [SA] = 105 molec. cm-3 (Fig. 3a), while this value could be up to 2.1×103 cm-3 s-1 when [SA] increases to 107 molec. cm-3 (Fig. S8). These results suggest that the particle formation rate of the GAS-involved SA–DMA system tends to become even larger under low-temperature and high-sulfuric-acid-concentration conditions.

To further evaluate the enhancement potential of GAS on the SA–DMA-driven NPF, JGAS-SA-DMA and JSA-DMA are compared by defining a ratio rGAS, which stands for the ratio of the cluster formation rate with GAS to that without GAS: 4rGAS=J(GAS=x,SA=y,DMA=z)J(SA=y,DMA=z), where [GAS], [SA] and [DMA] represent monomer concentrations of GAS, SA and DMA, respectively. rGAS was calculated under the conditions of [GAS] = 103 to ∼ 105 molec. cm-3, [SA] = 104–107 molec. cm-3 and [DMA] = 108 molec. cm-3, which are the typical observed values in the atmosphere (Li et al., 2018; Riipinen et al., 2007; Kürten et al., 2014; Ge et al., 2011).

Figure 4 shows the enhancement strength rGAS, which presents a dependence on [GAS] and [SA]. The rGAS increases with the increase in [GAS] and can reach as high as ∼  800 at 278 K with [GAS] ​​​​​​​≃ 105 molec. cm-3 and [SA] ≃ 104 molec. cm-3, suggesting that the GAS can substantially enhance the formation rates of the SA–DMA-driven NPF, especially under relevant low [SA] atmospheric conditions. For instance, low concentrations of SA ∼ 104 molec. cm-3 together with relatively high NPF rates (5–9 cm-3 s-1) were observed at Hyytiälä in Finland and Hohenpeissenberg in Germany (Mikkonen et al., 2011; Birmili et al., 2003; Dal Maso et al., 2007). Since relatively high concentrations of hydroxy acids (259 ng m-3) were also observed in the same period in nearby regions (Stieger et al., 2021), the new particles may be mainly formed through the ternary GAS–SA–DMA pathway rather than the SA–DMA pathway in these scenarios. With the [SA] increase, the rGAS becomes smaller as shown in Fig. 4. This is likely due to the abundance advantage of SA compared to GAS in the concentration range we considered. When their concentrations are equal, GAS exhibits a certain enhancement effect. For example, rGAS still can reach ∼ 3 with the condition of [GAS] = [SA] = 105 molec. cm-3, which indicates that the nucleation capability between GAS and DMA is not inferior to that of SA and DMA when the concentration of GAS and SA is at the same level. Previous studies have shown that the concentrations of organic precursors are usually several orders of magnitude higher than that of SA, when the enhancement strength r is slightly larger than 1 (Li et al., 2017; J. R. Liu et al., 2021; H. Zhang et al., 2018). For example, the enhancement effect of lactic acid (LA) on the SA–DMA-driven NPF at 260 K is approximately equal to 1 under the condition of [LA] = 1010 and [SA] = 105 molec. cm-3 (Li et al., 2017). Overall, this suggests that GAS has a non-negligible enhancement effect on the formation rate of the SA–DMA binary nucleation system in view of its binding property and the estimated equilibrium concentration in the atmosphere.

A series of kinetic simulations were further carried out by ACDC under different temperatures and [DMA] so as to achieve a deeper understanding of the enhancing potential of GAS. The influence of the varying temperature (258, 278 and 298 K) and [DMA] (107, 108 and 109 molec. cm-3) on the cluster formation rates is shown in Fig. 5. As shown in Fig. 5a, the increasing trends of JGAS-SA-DMA are similar at different temperatures, but JGAS-SA-DMA markedly increases and reaches 10-4 to 5 cm-3 s-1 as the temperature changes from 298 to 258 K. The relatively low temperature can promote the cluster formation rate, probably due to its effect on the decrease in evaporation rates for the related clusters, because the low temperature inhibits the endothermic thermodynamic process of cluster evaporation to some extent. The JGAS-SA-DMA also tends to increase by 3 orders of magnitude with increasing [DMA] from 107 to 109 molec. cm-3 (Fig. 5b). This is possibly due to the fact that hydrogen bonding interaction increases between acidic molecules (GAS and SA) and the increased base molecules (DMA), which further results in the phenomenon of formation rate increase. These results demonstrate that the produced GAS from the chemical reaction of SO3 with GA can speed up the SA–DMA nucleation even more dramatically under high [DMA] and at low temperature. This suggests that the enhancing potential of organosulfates in the SA–DMA-driven NPF deserves more attention in highly amine-polluted regions, especially with lower temperature, such as high mountains and cold polar areas.

Figure 6 presents the main growth pathways of the GAS–SA–DMA-based clusters at different [GAS] (104–106 molec. cm-3) with an [SA] of 105  molec. cm-3 and a [DMA] of 108 molec. cm-3 at 278 K, traced employing ACDC. When [GAS] is 104 or 105 molec. cm-3 (Fig. 6a, b), the nucleation involves two primary pathways: (1) the pure SA–DMA nucleation pathway and (2) the GAS–SA–DMA nucleation pathway. In both pathways, the formation of the (SA)1⋅ (DMA)1 cluster is the first step from monomers of SA and DMA. The pure SA–DMA cluster (black arrows) grows by the stepwise addition of either SA or DMA; i.e., each addition of an SA molecule is followed by one additional DMA molecule. In the case of the GAS–SA–DMA nucleation pathway (green arrows), the initially formed GAS-involved cluster is (GAS)1⋅ (SA)1⋅ (DMA)1, generated from GAS collision with the pre-existing (SA)1⋅ (DMA)1 cluster. Then the (GAS)1⋅ (SA)1⋅ (DMA)1 cluster grows via a base-stabilization mechanism, which is similar to the pure SA–DMA nucleation pathway. The ternary cluster growth path follows the sequence (GAS)1⋅ (SA)1⋅ (DMA)1 → (GAS)1⋅ (SA)1⋅ (DMA)2 → (GAS)1⋅ (SA)2⋅ (DMA)2 → (GAS)1⋅ (SA)2⋅ (DMA)3 → flux-out. With the increase in [GAS] to 106 molec. cm-3 (Fig. 6c), another alternative GAS-involved pathway appears. Of particular note, the third growth pathway forms from the (GAS)1⋅ (SA)1⋅ (DMA)2 cluster. Thereafter, the cluster growth proceeds by adding one GAS monomer to the (GAS)1⋅ (SA)1⋅ (DMA)2 cluster, leading to the formation of the (GAS)2⋅ (SA)1⋅ (DMA)2 cluster. Then, the (GAS)2⋅ (DMA)2 clusters flux out after the subsequent evaporation of the SA molecule. In this case, the contribution of GAS to the main cluster growth pathway increases from 3 % (Fig. 6a) to 78 % (73 % + 5 %) (Fig. 6c), with [GAS] increasing from 104 to 106 molec. cm-3. The GAS molecules do participate in the growth of clusters and further flux-out instead of evaporating from the existing clusters. Interestingly, in a previous study on methyl hydrogen sulfate (MHS) (Li et al., 2018; Liu et al., 2019), which is mainly produced from atmospheric chemical reactions, the reported cluster pathway of the MHS–SA–DMA system is very similar to that of the GAS–SA–DMA system we observed. Therefore, the cluster growth pathway of the GAS–SA–DMA system may represent a common feature for the mechanism of organosulfates participating in the SA–DMA-driven NPF.

The main growth pathways of the GA–SA–DMA system were also investigated and compared with that of the GAS–SA–DMA system (Fig. S10). By contrast, GA is not substantially conducive to the SA–DMA-based cluster growth, and the path only involves pure SA–DMA clusters at [GA] = 109 molec. cm-3 (Fig. S10b). Till [GA] increases to 1010 molec. cm-3 (Fig. S10c), and GA can indirectly participate in the cluster growth, acting as a “mediate bridge” and finally evaporating. This is consistent with the probed mediate bridge mechanism of the GA–SA–NH3 system (Zhang et al., 2017). The GA molecule in the GA–SA–DMA system initially participates in the cluster growth and then evaporates from the newly formed clusters, mainly on account of the high evaporation rates of GA-containing clusters, which range from 20 to 106 s-1 for the (GA)1(SA)2(DMA)3, (GA)2(SA)1(DMA)3 and (GA)3(DMA)3 clusters. The growth pathways of the GAS–SA–DMA and GA–SA–DMA systems are obviously different. It can be concluded that GAS is an important “participator” rather than GA just as a mediate bridge when participating in the SA–DMA nucleation. This difference could mainly result from the higher stability of the (GAS)1(SA)2(DMA)3 and (GAS)3(DMA)3 clusters compared to those of the (GA)1(SA)2(DMA)3, (GA)2(SA)1(DMA)3 and (GA)3(DMA)3 clusters with high evaporation rates (in all cases larger than 101 s-1) at the studied precursor concentrations (Figs. 2 and S7 and Table S6), with the GA-involved clusters evaporating into smaller clusters.

The cluster growth pathways of the GAS–SA–DMA system at different temperatures (258, 278 and 298 K) were also compared (Fig. S11). The proportion of the GAS-involved path increases with the decreasing temperature. At 258 K, the (SA)2(DMA)2 cluster can directly form the (GAS)1(SA)2(DMA)2 cluster through the addition of one GAS molecule. In that case, SA–DMA-based clusters can even assist the growth of clusters containing GAS from the 2:2 size, contributing to another growth pathway to form large GAS-involved clusters. The founded alternative pathway emerges from the SA–DMA-based cluster to form (GAS)1⋅ (SA)2⋅ (DMA)2, leading to the proportion of a GAS-involved path increase of up to 53 %. This phenomenon may be because low temperature could efficiently promote the thermodynamical stabilization of ternary clusters. Such a positive correlation of cluster stability with low temperature has also been suggested as a common feature in studies of other ternary systems containing acidic compounds, e.g., MSA, MSIA or NA (L. Liu et al., 2021b; Ning and Zhang, 2022; Ning et al., 2020).

Intense NPF events as well as emission of a suite of various nucleation precursors have been observed at the summit of Mt. Tai in China in recent years (Mochizuki et al., 2017; Lv et al., 2018). The gaseous concentration of GA reaches 343 ng m-3 during more field-burning-influenced periods at Mt. Tai (Mochizuki et al., 2017). The formation rates of 3 nm particles lie in the range of 0.82–25.04 cm-3 s-1 (Lv et al., 2018). The condensation sink (CS) (with an average of 1.4×10-2 s-1) and air temperature were found to be lower, whereas the concentration of SO2 was higher on NPF days than that on non-NPF days. A strong correlation existed between the continental air mass passing through the polluted regions and NPF, which was partly because of the higher SO2 concentration, indicating that SA was an important precursor on Mt. Tai. However, the pure SA–base nucleation could not fully explain the observed cluster formation rates (Jobs) attributed to the deficiency of the SA concentration. Given the fact that GA has only a slight influence on the nucleation and growth processes of atmospheric clusters, the reaction between GA and SO3 may provide a secondary source of the potential precursor since high concentrations of sulfur oxides were detected. Interestingly, in this work, its product, GAS, was identified as having the ability to stabilize SA–DMA-based clusters and being able to speed up SA–DMA nucleation obviously. Hence, coupled with the published observational evidence at Mt. Tai in China (Mochizuki et al., 2017; Lv et al., 2018) and our aforementioned theoretical analysis, it can be supposed that these NPF events involve GAS.

In Fig. 7, we plotted the cluster formation rates for the pathways SA–DMA, GA–SA–DMA and GAS–SA–DMA, individually. Note that the calculated cluster formation rates via ACDC simulation in this work have a cluster size of about ∼ 1.3 nm. The observed cluster formation rates (J3) at Mt. Tai were measured at 3 nm. According to the revised Kerminen–Kulmala equation (Anttila et al., 2010; Lehtinen et al., 2007), the cluster formation rate is J3≈ 0.5 J1.3 (see the details in the Supplement). Hence, the J3nm-(SA-DMA), J3nm-(GA-SA-DMA) and J3nm-(GAS-SA-DMA) presented in Fig. 7 are calculated from 0.5 times their associated cluster formation rates (JSA-DMA, JGA-SA-DMA and JGAS-SA-DMA, respectively) obtained via the ACDC simulations. Here we can see that the needed concentration of SA for the binary SA–DMA (dotted lines) is clearly higher than those for the ternary GA–SA–DMA (dashed lines) and GAS–SA–DMA (solid lines) systems under the condition of the same formation rates. The needed [SA] for the GAS–SA–DMA system is obviously lower than that for GA–SA–DMA and markedly reduces with a [GAS] increase. In contrast, although [GA] is higher than [GAS] in Fig. 7, the variation of the needed [SA] for the GA–SA–DMA system is minor with the increase in [GA]. These results imply that the influence of GAS on the SA–DMA system is stronger than that of GA, and the ternary GAS–SA–DMA mechanism provides a new pathway for the NPF events with the condition of relatively low [SA] observed at Mt. Tai. The shaded area shown in Fig. 7 represents the globally observed [GA] as well as the corresponding [GAS]. The [SA] at Mt. Tai on 30 September 2014 is observed at 1.09×106 molec. cm-3 (the top red line pointing from an inverted triangle to the left arrow). If the new particles at Mt. Tai on 30 September 2014 are presumed to be produced from the pure SA–DMA system with the typical [DMA] of 108 molec. cm-3, the concentration of SA around ∼ 1.35×106 molec. cm-3 is needed (the black dotted line), which is a bit higher than the observed [SA]. To reach the observed J30September (7.94 cm-3 s-1), the required [GAS] relevant to the observed [SA] on 30 September 2014 is ∼ 4.70×105 molec. cm-3 in the shaded area as shown in Fig. 7. This indicates that the ternary GAS–SA–DMA nucleation mechanism corresponds well to the observed records of the [SA] and NPF events. As for the GA–SA–DMA pathway, the required [GA] and [SA] are presented by black and red dashed lines. It is very clear that the GA–SA–DMA ternary system is not sufficient enough to unravel the observed NPF at Mt. Tai, for which the [GA] corresponding to the observed [SA] is beyond the boundary of the shaded area. In another example, if the new particles on 6 October 2014 are assumed to be generated from the pure SA–DMA system, the required [SA] is estimated to be ∼ 9.01×105 molec. cm-3 (the red dotted line), which is also too high for the observed [SA] (5.3×105 molec. cm-3, the bottom red line pointing from the inverted triangle to the left arrow). Although GAS can speed up the SA–DMA-driven NPF (the red line), to reach the observed J6October (2.54 cm-3 s-1), a fairly high concentration of GAS is required, which is outside the shaded area. This suggests that there may be other potential enhanced mechanisms for atmospheric new particle formation, which require more in-depth studies. These results and analyses suggest that the GAS–SA–DMA nucleation mechanism can explain the field observation of the atmospheric SA-involved particles at Mt. Tai, while the binary SA–DMA nucleation is incompatible with the observed new particle formation rates. Therefore, it can be concluded that the GAS produced from the chemical reaction of GA and SO3 could play an important role in speeding up the SA–DMA-driven NPF events at Mt. Tai. In the light of the deficiency of field observations of GAS in the gas phase, further detection of GAS is still needed.