Cluster Dynamics-based Parameterization for Sulfuric Acid-Dimethylamine 1 Nucleation: Comparison and Selection through Box-and Three-Dimensional-2 Modeling

ABSTRACT


INTRODUCTION
Atmospheric aerosols have significant impacts on visibility, human health, and global climate (Gordon et al., 2016).New Particle Formation (NPF) is the predominant source of global aerosol population, with nucleation being the key stage of the gas-toparticle transformation (Zhao et al., 2020;Almeida et al., 2013).In polluted regions such as urban China, compelling evidence indicates that sulfuric acid (SA)-driven nucleation enhanced by dimethylamine (DMA) can generate thermodynamically stable SA-DMA clusters and lead to high particle formation rates close to kinetic limit of SA clustering, which is responsible for the observed intensive NPF events (Cai et al., 2021;Yao et al., 2018).Meanwhile, it has been demonstrated that variations in atmospheric conditions, including condensation sinks (CS) arising from background aerosols, along with temperature (T), can exert profound impacts on the cluster dynamics of SA-DMA nucleation by varying the particle formation rates across several orders of magnitude (Cai et al., 2021;Deng et al., 2020).Given that complex interactions exist among various gaseous precursors, molecular clusters, and pre-existing aerosols during nucleation, reasonable representation of the cluster dynamics of SA-DMA nucleation in three-dimensional (3-D) models is important for 3-D NPF modeling and subsequent assessment of its impacts on environment and climate.
Empirical models in form of power law functions have been extensively utilized to examine how particle formation rates respond to precursor concentrations (Semeniuk and Dastoor, 2018).Through parameter fitting, these empirical models can effectively reproduce the particle formation rates observed in both laboratory experiments and field measurements (Kulmala et al., 2006;Riccobono et al., 2014;Semeniuk and Dastoor, 2018).Subsequently, they can be integrated into 3-D models for regional or global NPF simulations.Bergman et al. (2015) and Dunne et al. (2016) have simulated SA-DMA nucleation utilizing global models, which incorporate empirical equations derived from experimental data obtained from CLOUD chamber or flow tube experiments.These parameterization schemes successfully characterize the response of particle formation rates to precursor concentrations, however, they fail to account for dependencies on T and CS due to the ignorance of explicit cluster dynamics.As a result, they are identified to be inadequate for accurately reproducing NPF events in winter Beijing (Li et al., 2023).
We recently developed an analytical equation for SA-DMA nucleation parameterization based on detailed cluster dynamics simulations (abbreviated as Dynamic_Sim) (Li et al., 2023c).To derive an explicit equation, several simplifications have been made in Dynamic_Sim, including 1) only (SA)k(DMA)k (k = 1-4) and (SA)2(DMA)1 clusters are considered; 2) clusters larger than (SA)1(DMA)1 are regarded stable with no evaporation; and 3) (SA)4(DMA)4 cluster is the only terminal cluster in calculating particle formation rates.Subsequent applications in 3-D modeling have demonstrated significantly improved performance of Dynamic_Sim compared to previous data-fitting parameterizations in simulating the particle formation rates, the evolution of particle number size distributions (PNSDs), and NPF events in winter https://doi.org/10.5194/egusphere-2024-642Preprint.Discussion started: 8 April 2024 c Author(s) 2024.CC BY 4.0 License.
Beijing.However, the efficacy of Dynamic_Sim in NPF simulation has yet to be assessed under varying atmospheric conditions, such as the summer season characterized by relatively higher T and lower CS compared to winter.Moreover, the impacts of simplifications made in the derivation of Dynamic_Sim on 3-D NPF simulation under different atmospheric conditions remain unclear.
Atmospheric Cluster Dynamics Code (ACDC) is a flexible box model for simulating cluster dynamics and particle formation rates (Mcgrath et al., 2012).In addition to representing Tand CS-dependencies for particle formation rate as Dynamic_Sim, ACDC considers the source/sink terms of all given molecules/clusters within a nucleation system without simplifications of the clustering processes.By integrating quantum chemical calculations with ACDC, Almeida et al. (2013) discovered that the simulated SA-DMA nucleation provides valuable insights for interpreting the measurements from the CLOUD chamber experiments.Similarly, Lu et al. (2020) demonstrated that ACDC coupled with quantum chemistry calculations can effectively reproduce the particle formation rates observed in urban Shanghai.While ACDC has been extensively utilized in box modeling (Almeida et al., 2013;Lu et al., 2020;Yang et al., 2021), its potential for deriving parameterizations for 3-D models has not been explored in previous studies.Furthermore, ACDC program in modeling the nucleation process is highly reliant on specific thermodynamic data for the molecular clusters of interest, which are primarily obtained through quantum chemical calculations (Elm et al., 2020).The uncertainty surrounding the influence of different quantum chemical calculation approaches adds additional complexity to the application of ACDC-derived parameterization in 3-D NPF modeling.
This study aims to compare different cluster dynamic-based parameterizations for SA-DMA nucleation and identify the robust one applicable for 3-D models.We introduced new parameterizations developed using the ACDC program, incorporating various quantum chemical calculations.Different cluster dynamic-based parameterizations, including ACDC-derived ones as well as Dynamic_Sim, are comprehensively compared and evaluated through a combination of box-model simulations, 3-D modeling, and in-situ observational data.Our findings reveal that by incorporating the latest theoretical understanding and complete representation of cluster dynamics, ACDC-derived parameterization demonstrates reliable performance in 3-D NPF simulation for both winter and summer conditions in Beijing and exhibits potential applicability in diverse atmospheric conditions.The study sheds light on the impacts of employing various simplifications in cluster dynamics and different theoretical approaches in deriving parameterizations on NPF simulation.In addition to contributing to the precise simulation of SA-DMA nucleation and the quantification of its environmental and climatic effects, this study provides valuable references for simulating other nucleation mechanisms in 3-D models.

Configurations of ACDC
Here and DMA molecules in a cluster) are used to build the ACDC-derived parameterizations for SA-DMA nucleation due to their reported much higher stability compared to those containing more DMA molecules than SA molecules (Xie et al., 2017).The conformations and thermodynamics of SA-DMA clusters are taken from our other study (Ning et al., 2024).Briefly, the conformations of selected clusters are taken from the reported global minima from Li et al. (2020), and the key thermodynamic data for ACDC, Gibbs free energy change (ΔG), are recalculated at the DLPNO-CCSD(T)/augcc-pVTZ//ωB97X-D/6-311++G(3df,3pd) level of theory.Based on benchmark studies (Elm et al., 2020), this level of theory provides dependable thermodynamic insights into molecular clusters during nucleation and represents the latest theoretical approach.In addition, the rotational symmetry is consistently considered in quantum calculations following Besel et al. (2020).Following most previous ACDC simulation studies (Xie et al., 2017;Elm et al., 2020;Ning et al., 2020), (SA)4(DMA)3 and (SA)4(DMA)4 clusters are defined as the boundary conditions, i.e. the clusters fluxing out the simulated system and participating in subsequent growth in ACDC simulations, considering their high stability.Since clusters containing SA tetramers are estimated to have an electrical mobility diameter of 1.4 nm (Cai et al., 2023;Jen et al., 2014;Thomas et al., 2016), the formation rates of (SA)4(DMA)3 and (SA)4(DMA)4 clusters are therefore deemed as the particle formation rates at 1.4 nm (J1.4).Size-dependent coagulation sink (CoagS) is counted for each SA-DMA cluster which is consistent with Dynamic_Sim (Li et al., 2023c): where Vi and V1 (m 3 ) represent the volume of cluster i and SA molecule, respectively.The power-law exponent of -1.7 is selected according to typical range in the atmosphere (Lehtinen et al., 2007).In addition, enhancement for collision processes from Van de Waals forces is also considered.We refer to the ACDC-derived parameterization in coupling the DLPNO-CCSD(T)/aug-cc-pVTZ//ωB97X-D/6-311++G(3df,3pd) level of theory and adequate cluster dynamics as ACDC_DB, which is established as the basecase for our discussion of other cluster dynamics-based parameterizations.
In addition to the direct comparison of ACDC_DB to Dynamic_Sim, additional test parameterizations combining ACDC_DB and three simplifications within Dynamic_Sim are established and compared with ACDC_DB to further probe the impacts of these simplifications on NPF simulations.The configurations of all parameterizations are detailed in Table 1.It should be noted that when all simplifications are applied on ACDC_DB, Dynamic_Sim still predicts higher J1.4 compared to ACDC_DB (Figure S1A).This is because the ΔG value of the initial (SA)1(DMA)1 cluster at 298.15 K used in Dynamic_Sim, which is taken from Myllys et al. (Myllys et al., 2019), is slightly lower than that used in ACDC_DB (-13.5 kcal mol -1 for Dynamic_Sim and -12.9 kcal mol -1 for ACDC_DB) (Ning et al., 2024), even though both parameterizations employ the quantum chemical calculation method of DLPNO-CCSD(T).Possible reasons for the discrepancy include the utilization of a https://doi.org/10.5194/egusphere-2024-642Preprint.Discussion started: 8 April 2024 c Author(s) 2024.CC BY 4.0 License.larger basis set (3-zeta 6-311++G(3df,3pd)) and higher convergence criteria (Tight PNO + Tight SCF) in this study compared to that in Myllys et al.. Aligning the ΔG for (SA)1(DMA)1 cluster in Dynamic_Sim with that of ACDC leads to a high consistency in the predicted J1.4 between the two approaches (Figure S1B).The uncertainty of ΔG used in Dynamic_Sim is discussed in our previous study (Li et al., 2023c) and here we mainly focus on the impacts of simplifications in Dynamic_Sim.
While the DLPNO-CCSD(T)/aug-cc-pVTZ//ωB97X-D/6-311++G(3df,3pd) level of theory yields reasonable cluster thermodynamics, quantum chemistry calculations employing the RI-CC2 method predicting lower ΔG for cluster formation (stronger binding between molecules within clusters), has been widely used in conjunction with ACDC to interpret experimental and observed particle formation rates in previous studies (Almeida et al., 2013;Kürten et al., 2018;Ning et al., 2020).The prevalent combination used with the RI-CC2 method is RI-CC2/aug-cc-pV(T+d)Z//M06-2X/6-311++G(3df,3pd) level of theory (Lu et al., 2020;Liu et al., 2021;Ning et al., 2022;Ning and Zhang, 2022;Liu et al., 2019).Based on Elm's work, compared to DLPNO-CCSD(T)/aug-cc-pVTZ//ωB97X-D/6-311++G(3df,3pd), the differences in predicted cluster binding energies primarily stem from discrepancies between DLPNO-CCSD(T) and RI-CC2 in single-point energy calculations, while the ωB97X-D and M06-2X functionals exhibit similar performance (Elm et al., 2013;Elm et al., 2020).Also, in previous studies the RI-CC2 method combined with ACDC was consistently accompanied by application of a sticking factor (SF) of 0.5 in treating collision processes (Almeida et al., 2013;Lu et al., 2020).However, it is noteworthy that, according to Stolzenburg et al.'s work (Stolzenburg et al., 2020), the SF of the neutral SA-DMA cluster system should be unity.Here, we refer to the traditional theoretical approach as employing the RI-CC2/aug-cc-pV(T+d)Z//M06-2X/6-311++G(3df,3pd) level of theory and incorporating the SF of 0.5 in collision processes.An ACDC-derived parameterization coupling the traditional theoretical approach is established to assess the effectiveness of the traditional method in NPF simulation (ACDC_RM_SF0.5).Except for the varied thermodynamic inputs and SF, the remaining configurations of ACDC_RM_SF0.5 are identical to ACDC_DB.Additionally, we establish a test parameterization coupling RI-CC2/aug-cc-pV(T+d)Z//M06-2X/6-311++G(3df,3pd) level of theory with an SF of unity (ACDC_RM) to evaluate the impact solely arising from the quantum chemical calculation method.Note that SF of unity is applied to all parameterizations in this study except for the ACDC_RM_SF0.5.

Incorporating the ACDC-derived Parameterizations into WRF-Chem/R2D-VBS Model
Various parameterizations are subsequently implemented in the Weather Research and Forecasting-Chemistry model (WRF-Chem) integrating an experimentally constrained Radical Two-Dimensional Volatility Basis Set (2D-VBS) (denoted as WRF-Chem/R2D-VBS) (Zhao et al., 2020).Incorporating the box-model ACDC into a 3-D model using the explicit mathematical formula, as Dynamic_Sim, proves to be challenging.Here, we created a four-dimensional look-up table that delineates the  (Yu, 2010).The table is derived based on multiple ACDC runs by varying input variables.The ranges for the input variables correspond to typical conditions of the atmosphere.Except for T, the ranges of variation for all other variables exceed at least one order of magnitude.Therefore, temperature is assumed to follow arithmetic uniform distribution, while the other variables are assumed to follow geometric uniform distribution.Details for the input variables are given in Table S1.In WRF-Chem/R2D-VBS simulations, J1.4 are online calculated by interpolating values from a look-up table based on real-time input parameters.In our previous study, we have developed an emission inventory for China and its surrounding regions (Li et al., 2023c).Here [DMA] is calculated in WRF-Chem/R2D-VBS based on a comprehensive source-sink representation of DMA.More details of including DMA in WRF-Chem/R2D-VBS can be found in our previous study (Li et al., 2023c).In addition, a time-integrated-average [DMA] as well as [SA] of each time step were used to drive SA-DMA nucleation, since SA-DMA nucleation is accompanied with condensation of gaseous SA and DMA on pre-existing aerosols simultaneously in the atmosphere.
Besides SA-DMA nucleation, seven other nucleation mechanisms have already been incorporated in WRF-Chem/R2D-VBS (Zhao et al., 2020), including neutral/ioninduced H2SO4-H2O nucleation, neutral/ion-induced H2SO4-NH3-H2O nucleation, neutral/ion-induced pure organics nucleation, and H2SO4-organics nucleation.The organics involved in nucleation are ultralow-and extremely low-volatility organic compounds (ULVOC and ELVOC) with O:C >0.4.The formation chemistry of ULVOC and ELVOC from monoterpenes, including autoxidation and dimerization, is traced by the R2D-VBS framework (Zhao et al., 2020).Note that the impact of the other seven mechanisms on particle formation rates and particle number concentration is low compared to SA-DMA as revealed by our previous study (Li et al., 2023c).In WRF-Chem/R2D-VBS, the evolution of PNSDs from 1nm to 10 µm is treated by MOSAIC (Model for Simulating Aerosol Interactions and Chemistry) module.The newly formed 1.4 nm particles from SA-DMA nucleation are injected into the smallest size bin (1 -1.5 nm) of the MOSAIC.

Configurations of WRF-Chem/R2D-VBS Model
The WRF-Chem/R2D-VBS model, incorporating various cluster dynamics-based SA-DMA nucleation parameterizations, was employed in a simulation over a domain with a spatial resolution of 27 km.This domain covers eastern Asia, with Beijing situated close to the center of the simulation area.Details of model configurations can be found in our previous study (Li et al., 2023c).Briefly, we use the ABaCAS-EI 2017 and IIASA 2015 emission inventories for mainland China and other areas in the domain, respectively, to represent the anthropogenic emissions (Zheng et al., 2019;Li et al., 2017;Li et al., 2023b); we use Model of Emissions of Gases and Aerosols from Nature (MEGAN) v2.04 to calculate the biogenic emissions (Guenther et al., 2006) The simulation period consists of two parts: the winter period, which spans from January 14 to January 31, 2019, and the summer period, which is from August 18 to August 31, 2019.Previous observational studies have shown that the particle formation rates reach their highest and lowest levels during winter and summer in China, respectively (Deng et al., 2020;Chu et al., 2019).Therefore, periods from these two seasons are selected as representative simulation periods in this study and the specific time periods corresponded to those with relatively complete and continuous PNSDs and J1.4 observations.Since observational data for DMA concentration is only available for the period from January 1, 2019 to January 23, 2019, similar to our other study (Ning et al., 2024), we performed additional simulation for this period to compare observational and simulated DMA concentrations.For each season, all the SA-DMA parameterizations listed in Table 1 were employed for simulation.Among them, ACDC_DB, Dynamic_Sim, and ACDC_RM_SF0.5 serve as three main parameterizations, while ACDC_DB_CE, ACDC_DB_BC, ACDC_DB_CN, and ACDC_RM are set as test cases to investigate the impact of individual simplification or theoretical approach on NPF simulations.In all comparisons, ACDC_DB is set as a reference.

Ambient Measurements
In the 3-D simulations, we utilize measured concentrations of nucleation precursors and PNSDs as a criterion to discuss the model performance with various parameterizations.The duration of the observational data matches that of the simulations mentioned above.Detailed descriptions of the observation site and instruments can be found in our previous research (Deng et al., 2020).Briefly, the observation site is located on the West Campus of the Beijing University of Chemical Technology.CI-TOF-MS (chemical ionization time-of-flight mass spectrometer; Aerodyne Research Inc.) were used to measure the concentrations of SA.Amine concentrations were measured with a modified TOF-MS using H3O + or its clusters as the reagent ions.PNSDs from 1 nm to 10 µm were measured using a PSD (particle size distribution) system and a DEG-SMPS (diethyl glycol scanning mobility particle spectrometer).J1.4 derived from observation is calculated employing an improved aerosol population balance formula (Cai and Jiang, 2017).Figure 1 illustrates the comparison between the reported cluster dynamics-based parameterization with simplifications, Dynamic_Sim, and the base-case parameterization ACDC_DB.The comparison is based on a comprehensive dataset that includes over 40,000 box-model simulations for each parameterization, by varying parameters such as [SA] (1 × 10 5 -1 × 10 8 molec.cm -3 ), [DMA] (5 × 10 6 -1 × 10 8 molec.cm -3 ), CS (5 × 10 -4 -5 × 10 -1 s -1 ), and T (250 -320 K).In most scenarios, J1.4 predicted by ACDC_DB and Dynamic_Sim demonstrates deviations within one order of magnitude, with the majority falling within a factor of 3.However, Dynamic_Sim predicts notably higher J1.4 than ACDC_DB in scenarios where T exceeds ~300 K and CS is below ~3×10 -3 s -1 , characteristic of a clean atmosphere during summer.The discrepancy in these scenarios elevates the overall RDynamic_Sim up to 17.0.Furthermore, no clear correlation is observed between the differences of the two parameterizations and other input parameters such as [DMA] and [SA] (Figure S2).The differences between parameterizations are attributed to the combined effects of the three simplifications and the lower ΔG of (SA)1(DMA)1 cluster in Dynamic_Sim.However, the latter should not be the primary cause for the significant differences of J1.4 prediction under high T and low CS conditions, as it typically results in an overestimation within an order of magnitude (R=3.3)(Figure S1).factor of 3 under conditions where T < ~290 K and CS > ~0.1 s -1 .However, the overestimation of J1.4 prediction by ACDC_DB_CE becomes much greater with increasing T and decreasing CS.The discrepancy between ACDC_DB_CE and ACDC_DB should be primarily attributed to the pivotal role of T in influencing cluster evaporation rates (Ortega et al., 2012;Deng et al., 2020).At low T, the evaporation rates of clusters are low enough to allow efficient nucleation, thus whether setting the concerned SA-DMA clusters to evaporate based on the expected evaporation rates does not lead to a significant impact on J1.4 prediction.However, at high T, the evaporation rates of clusters significantly increase, therefore the simplification in cluster evaporations within ACDC_DB_CE is likely to predict higher J1.4 than those with no simplification.The impact of simplification in cluster evaporations across varying T is also found in a nonbranched SA-DMA nucleation scheme from 280 K to 298 K reported by Li et al. (2023a).Note also that the overestimation of ACDC_DB_CE diminishes as CS increases (Figure 2D), with CS becoming the primary sink in the nucleation system and the impact of cluster evaporations becoming less pronounced.This underscores the connection between the specific deviation arising from simplification in cluster evaporations and the respective contributions of CS and cluster evaporations to the overall sink for clusters in nucleation.In addition, the relative independence of the differences between ACDC_DB_CE and ACDC_DB from variations in precursor concentrations ([SA] and [DMA]) is similar to that between Dynamic_Sim and ACDC_DB (Figure S3).Overall, the scenarios where ACDC_DB_CE predicts higher J1.4 than ACDC_DB only occurs under conditions of both high T and low CS (Figure 2A and Figure 2D).The averaged discrepancy between ACDC_DB_CE and ACDC_DB RACDC_DB_CE is 22.3, closely resembling RDynamic_Sim, indicating that the simplification in cluster evaporations is a major factor contributing to the difference between Dynamic_Sim and ACDC_DB.The underestimations of ACDC_DB_BC and ACDC_DB_CN in J1.4 prediction compared to base-case ACDC_DB are related to the growth pathways of SA-DMA clusters.In the original scheme of ACDC_DB, precursor molecules have the flexibility to pass through any (SA)m(DMA)n clusters (0 < n ≤ m ≤ 3), and terminal 1.4-nm particles are formed when the clusters grow to (SA)4(DMA)4 or (SA)4(DMA)3.As expected, ACDC_DB_BC, which assumes (SA)4(DMA)4 cluster as the only boundary condition with an omission of (SA)4(DMA)3 cluster, predicts lower J1.4 than ACDC_DB.(SA)4(DMA)3 and (SA)4(DMA)4 clusters are primarily formed from (SA)3(DMA)3 cluster by colliding with a SA molecule and a (SA)1(DMA)1 cluster, respectively.As the concentration of (SA)1(DMA)1 cluster is more sensitive to T, we further found that the discrepancy between ACDC_DB_BC and ACDC_DB becomes more pronounced with increasing T (Figure 2B).Furthermore, we found no apparent correlation between the variation of CS and the disparity between ACDC_DB_BC and ACDC_DB (Figure 2E).
In our previous study, we demonstrated improvements in computing CS-dependent J1.4 of SA-DMA nucleation with the Dynamic_Sim compared to the previous powerlaw parameterizations under polluted atmospheric conditions (Li et al., 2023c).Here, we further show that, based on Dynamic_Sim, the new ACDC_DB with complete cluster dynamics can more reasonably simulate J1.4 under previously less studied conditions of high T (> ~300 K) and low CS (< ~3×10 -3 s -1 ), where Dynamic_Sim tends to produce significant overestimation of J1.4.This overestimation is primarily driven by the simplification in cluster evaporations within Dynamic_Sim.Even though a https://doi.org/10.5194/egusphere-2024-642Preprint.Discussion started: 8 April 2024 c Author(s) 2024.CC BY 4.0 License.comparable performance in J1.4 prediction between ACDC_DB and Dynamic_Sim could be achieved under other ambient conditions, cautions should be made that the mutual offsetting effect between overestimation and underestimation resulting from different simplifications in Dynamic_Sim when computing J1.4.

Comparison between ACDC_DB and ACDC_RM_SF0.5
In Figure 3, ACDC_DB is compared with another main ACDC-derived parameterization, ACDC_RM_SF0.5, which uses the RI-CC2/aug-cc-pV(T+d)Z//M06-2X/6-311++G(3df,3pd) level of theory and employs a SF of 0.5 in processing collision.It can be observed that at lower temperatures (~280 K), ACDC_RM_SF0.5 and ACDC_DB exhibit similar performance in predicting J1.4.However, with higher T (accompanied by lower CS with a slight dependency), J1.4 predicted by ACDC_RM_SF0.5 become higher than that predicted by ACDC_DB, reaching even several orders of magnitude at the upper limit of the T range (320 K).Furthermore, we also observed that in scenarios close to the lower limit of the T range (250 K), the J1.4 predicted by ACDC_RM_SF0.5 shift from being higher to lower compared to ACDC_DB.The distinction between ACDC_RM_SF0.5 and ACDC_DB arises from the combined effects of variation in quantum chemical calculation method and the application of the 0.5 SF in collision processing.As depicted in Figure 4, when the SF in ACDC_RM_SF0.5 is set to unity as in ACDC_DB, the resulting ACDC_RM parameterization predicts consistently higher J1.4 than ACDC_DB.This implies that the modified quantum chemical calculation method, which results in lower evaporation rates for clusters within the system compared to ACDC_DB under the same condition, leads to higher J1.4 predictions.The impact from varying quantum chemical calculation method is akin to that from simplification in cluster evaporations discussed earlier.The distinction between ACDC_RM and ACDC_DB_CE lies in the fact that the modified quantum chemical calculation method affects all clusters within the system, whereas https://doi.org/10.5194/egusphere-2024-642Preprint.Discussion started: 8 April 2024 c Author(s) 2024.CC BY 4.0 License. the simplification in cluster evaporations is specific to limited clusters.This contributes to a much higher RACDC_RM (614.5)compared to RACDC_DB_CE (22.3).Despite that, compared to ACDC_DB, the differences for both ACDC_DB_CE, ACDC_RM, as well as ACDC_RM_SF0.5 demonstrate similar sensitivity to T (Figure 3A and Figure 4A) and CS (Figure 3B and Figure 4B) but independence on [SA] (Figure S6A and Figure S7A) and [DMA] (Figure S6B and Figure S7B).Comparing ACDC_RM_SF0.5 and ACDC_RM, it can be inferred that the application of a 0.5 SF in collision processes would result in an underestimation in J1.4 prediction.It can be noted that in most previous studies (Almeida et al., 2013;Kürten et al., 2018;Elm et al., 2020), comparisons of ACDC simulations using the traditional method and measured particle formation rates are conducted at around 280 K.At this temperature, all three main parameterizations of ACDC_RM, ACDC_DB, and Dynamic_Sim tends to yield similar J1.4 predictions and should have consistent applicability in NPF simulation.In summary, based on our base-case parameterization ACDC_DB, the extensive box model simulations above demonstrate the characteristics and applicability conditions of different parameterizations.Specifically, Dynamic_Sim is applicable under most atmospheric conditions with T < ~300 K and CS > ~3.0×10 -3 s -1 , while ACDC_RM_SF0.5 is suitable under conditions with T around 280 K.We further use reported measurements from well-controlled CLOUD chamber experiments to examine the characteristics and applicability of these parameterizations (Xiao et al., 2021).As shown in Figure S8, simulations using three main parameterizations, ACDC_DB, ACDC_RM, and Dynamic_Sim, correspond well to experimental results at low temperature (T = 278 K), proving the applicability of all three parameterizations at this temperature.In the experiments with elevated temperature (T = 293 K), ACDC_DB and Dynamic_Sim continues to exhibit similar performance, with simulated results still corresponding to experimental results.In contrast, ACDC_RM_SF0.between controlled experiments and box-model simulations hence confirms our conclusions above, and provides a solid basis for further discussions on 3-D simulations using these parameterizations with constraint from field observations.

Comparison of Different Parameterizations Based on 3-D Model Simulations
Various cluster dynamics-based parameterizations for SA-DMA nucleation were subsequently integrated into the WRF-Chem/R2D-VBS model.3-D simulations using these parameterizations have been conducted for both wintertime and summertime conditions in Beijing.Given that the concentrations of precursors are crucial input variables for each parameterization, the simulated and observed concentrations of [DMA] and [SA] are compared.Figure S9, Figure S10 and Table S2 illustrates good consistencies in temporal variations and the mean values between simulations and observations in Beijing.This validates the reliability of our representation of sources and sinks for nucleating precursors and serves as a foundation for our discussions on the performances of various parameterizations.In the following sections, we discuss the results of 3-D NPF simulations in Beijing during winter and summer by employing different parameterizations.The evaluation of various parameterizations focuses on their ability to reproduce in situ NPF measurements across different seasons.
The performances of different parameterizations on depicting J1.4 subsequently influences their representations of PNSDs evolution and NPF events, which are shown in Figure 5B.Generally, most parameterizations efficiently reproduce the observed time evolution of PNSDs and captures NPF events, such as those on 01/20, 01/21, 01/30, and 01/31, which are characterized by the burst of aerosol number concentrations in nanometer-sized range.Simulations using ACDC_DB_BC and ACDC_DB_CN result in lower particle concentrations in the low size range (1-10 nm) during the NPF period compared to three main parameterizations and the observations, while simulations with ACDC_RM show higher concentrations, This is consistent with the comparison of J1.4 among different parameterizations and further evident by the comparison of averaged PNSDs in Figure 5C.Notably, when compared to observations, all parameterizations consistently underestimate the averaged PNSDs within the 2-10 nm range but overestimate them in the 10-50 nm range.This discrepancy may stem from simplified https://doi.org/10.5194/egusphere-2024-642Preprint.Discussion started: 8 April 2024 c Author(s) 2024.CC BY 4.0 License.assumptions in particle growth simulation, as discussed in our previous study (Li et al., 2023c).The results show the applicability of all three main parameterizations in NPF modeling during wintertime periods.Importantly, the reliability of the new ACDCderived parameterization based on the latest theoretical approach (ACDC_DB) without simplifications in 3-D NPF simulation, is affirmed.The differences among various parameterizations can be explained by the comprehensive box-model simulations above at corresponding conditions.Compared to ACDC_DB, the J1.4 and PNSDs simulated by other two main parameterizations (Dynamic_Sim and ACDC_RM_SF0.5)agree similarly with observations, but for different reasons.In the case of Dynamic_Sim, the simplification in cluster evaporations has minimal impact on NPF simulation since CS is the dominant sink for clusters under the wintertime conditions (averaged T and CS is 274.7 K and 3.3×10 -2 s -1 , respectively).However, the simplifications in boundary conditions and cluster number lead to the underestimation of the J1.4,consequently https://doi.org/10.5194/egusphere-2024-642Preprint.Discussion started: 8 April 2024 c Author(s) 2024.CC BY 4.0 License.lowering the simulated particle number concentrations in 1-100 nm size range due to the ignorance of clusters contributing to growth.As a result, the agreement of Dynamic_sim to observations should result from a combination of underestimation due to simplifications in boundary conditions and cluster number, along with the compensatory effect of the overestimation caused by lower ΔG for (SA)1(DMA)1 cluster.For another main parameterization ACDC_RM_SF0.5,since the test parameterization ACDC_RM considerably overestimates J1.4 and PNSDs compared to the observations, the general agreement between ACDC_RM_SF0.5 and observations should be attributed to a balance between reduced kinetic limit through the application of SF and the compensatory effect of the overestimation caused by inappropriate representation of cluster thermodynamics.

Summertime Simulations
Figure 6 provides additional insight into the performance of various parameterizations in NPF simulation during summer.It can be noted that there exists a significant difference in particle formation rates between winter and summer in Beijing.As shown in Figure 6 and Figure S11B, ACDC_DB and Dynamic_Sim continues to demonstrate consistent and effective performance in simulating J1.4 (within a factor of 2), PNSDs evolution as well as NPF events.However, distinct differences emerge in the NPF simulation for other parameterizations, including another main parameterization ACDC_RM_SF0.5.Specifically, in contrast to the good performance of ACDC_DB and Dynamic_Sim, ACDC_RM_SF0.5, along with the test case ACDC_RM, exhibits a significant overestimation of J1.4, exceeding the observations by more than 15 times and over two orders of magnitude, respectively.This aligns with their overestimation of NPF occurrences and particle number concentration in the size range of 1-100 nm in comparison to observation, with a more pronounced overestimation for ACDC_RM.Conversely, the test cases of ACDC_DB_BC and ACDC_DB_CN show an underestimation of averaged J1.4 by approximately 4-5 times.They almost fail to depict NPF events, resulting in a significant underestimation of number concentrations in the 1-100 nm size range.Simulations using ACDC_DB_CE notably overestimates J1.4 especially on 08/28 -08/31 (Figure S11B), which results in an overestimation of averaged J1.4 by approximately 4 times compared to the observations.However, apart from a moderate overestimation in the initial particle size, we can observe a closer alignment of particle number concentrations in the 2-100 nm range with observations for ACDC_DB_CE, which should result from a combination of surplus newly formed particles and fast particle growth from inadequate assumptions within the model.Most previous NPF studies combining experiments/observations with simulations are conducted under conditions biased towards winter (~280K) (Almeida et al., 2013;Lu et al., 2020).Under summer conditions with elevated T, there exists a deficiency in parameterization evaluations for simulating NPF.The 3-D simulation results during the summer period provide additional validation for the reliability of ACDC_DB.For ACDC_RM_SF0.5, evidence from both box-model simulations and 3-D simulations suggests that it can accurately reproduce real SA-DMA nucleation at temperatures around 280 K, while it has limitations in higher temperatures.Another main parameterization Dynamic_Sim consistently demonstrates good performance in NPF simulation, akin to its efficacy in winter conditions.With the increased temperature in summer (averaged T is 298.2K), the influence of simplifications in cluster evaporations, cluster number, and boundary conditions becomes more profound, mirroring the trends observed in box-model simulations above.This leads to more significant overestimation for ACDC_DB_CE, and underestimation for ACDC_DB_CN and ACDC_DB_BC compared to the observation as well as the base-case ACDC_DB.Note that CS during the summer period (averaged CS is 2.8×10 -2 s -1 ) decreases compared to https://doi.org/10.5194/egusphere-2024-642Preprint.Discussion started: 8 April 2024 c Author(s) 2024.CC BY 4.0 License.winter but remains significantly higher than typical values in clean regions (~3.0×10 -3 s -1 ) (Dal Maso et al., 2008).According to the limited conditions for Dynamic_Sim described above, although the overestimation of J1.4 prediction resulting from the simplification in cluster evaporations is more pronounced in summer compared to that in winter, impacts from diverse overestimations and underestimations from different simplifications and varied thermodynamics for (SA)1(DMA)1 cluster can still offset each other, thereby allowing Dynamic_Sim to match observations.Based on previous comparisons using box-models, significant differences in J1.4 predictions between Dynamic_Sim and ACDC_DB only exist under conditions of high T > ~300 K and low CS < ~3×10 -3 s -1 , thus similar performance of Dynamic_Sim and ACDC_DB can be expected in the polluted atmosphere (CS > ~1.0×10 -2 s -1 ).In clean atmosphere with high temperature, however, caution is advised when using Dynamic_Sim for 3-D NPF simulations.

CONCLUSIONS
By integrating box modeling, 3-D simulations, also under the constraint from in situ measurements, this study conducts comprehensive comparison of different cluster dynamics-based parameterizations for SA-DMA nucleation.Among them, the ACDCderived parameterization grounded in the latest molecular-level understanding and complete representation of cluster dynamics (ACDC_DB), is identified to effectively model particle formation rates and PNSDs evolution in both winter and summer in Beijing within 3-D simulations.While a previously proposed simplified cluster dynamics-based parameterization (Dynamic_Sim) performs comparably in modeling NPF in Beijing, analysis reveals that their similarity arises from a delicate balance between overestimation and underestimation due to simplifications in cluster dynamics processes and the difference in thermodynamics of initial cluster.Particularly, under specific conditions of high temperature (> ~300 K) and low CS (< ~3×10 -3 s -1 ), Dynamic_Sim tends to make significant overestimation of particle formation rates compared to the reality.Moreover, the study furnishes evidence that integrating ACDCderived parameterizations with the traditional theoretical approach RI-CC2/aug-cc-pV(T+d)Z//M06-2X/6-311++G(3df,3pd) (ACDC_RM_SF0.5)effectively captures particle formation rates and the evolution of PNSDs around 280 K, a temperature range frequently explored in prior experiments and simulations investigating NPF (Kirkby et al., 2011;Almeida et al., 2013;Kirkby et al., 2016;Xie et al., 2017;He et al., 2021;Ma et al., 2019).Therefore, ACDC_RM_SF0.5 exhibits consistent applicability as other two parameterizations at around ~280 K.However, attributed to an inappropriate representation of cluster thermodynamics, ACDC_RM_SF0.5 has limitations in predicting particle formation rates at elevated temperatures.Overall, considering all aspects, we recommend ACDC_DB as a more reliable parameterization for simulating NPF across various atmospheric environments.
In addition to contributing to a more reasonable 3-D modeling of NPF, our research further provides valuable references for the development of parameterizations for other nucleation systems.Firstly, we demonstrate the efficacy of the DLPNO-CCSD(T)/aug-https://doi.org/10.5194/egusphere-2024-642Preprint.Discussion started: 8 April 2024 c Author(s) 2024.CC BY 4.0 License.cc-pVTZ//ωB97X-D/6-311++G(3df,3pd) level of theory in describing the thermodynamic properties of SA-DMA clusters through comprehensive evidence.This approach can thus be referenced when using quantum chemical calculations to obtain thermodynamic data for other nucleation clusters, especially for other alkylamines such as methylamine/trimethylamine-sulfuric acid clusters.It should be also noted, however, that in some qualitative studies, e.g., comparing the enhancing potential or synergistic effects of different precursors in SA-driven nucleation, methods other than DLPNO-CCSD(T)/aug-cc-pVTZ//ωB97X-D/6-311++G(3df,3pd), such as RI-CC2/aug-cc-pV(T+d)Z//M06-2X/6-311++G(3df,3pd), are equally valid (Liu et al., 2019).Secondly, we provide comprehensive modeling evidences that certain simplifications or assumptions in cluster dynamics, such as reducing the number of expected clusters, modifying boundary conditions, and assuming certain clusters to be non-evaporative, can significantly impact the prediction of particle formation rates and hence alter the 3-D NPF simulation under certain conditions.While applying certain simplifications concurrently under specific ambient conditions can offset different influences against each other, leading to a satisfactory model-observation comparison, there is a risk that certain simplifications may drive the model's outcomes away from reality when environmental conditions change.Therefore, caution should be exercised when applying these simplifications in derivation of nucleation parameterizations and subsequent application in 3-D models.Lastly, we note that the development of cluster dynamics-based nucleation parameterizations in the form of explicit mathematical expressions is subject to limitations, especially for systems involving multiple precursor species (Semeniuk and Dastoor, 2018).Given that the original ACDC has been extended to involve more than two precursor species, the ACDC-derived parameterization framework, in the form of a look-up table, is highly meaningful for establishing parameterizations for these multi-component nucleation systems.

Figure 1 .
Figure 1.Comparison of J1.4 predictions between ACDC_DB and Dynamic_Sim correlated with T variation (A) and CS variation (B).Solid dots represent simulated J1.4 values, solid lines indicate a 1:1 line, dotted lines correspond to 1:3 and 3:1 lines, and dashed lines represent 1:10 and 10:1 lines.The impacts of the three simplifications made in Dynamic_Sim are shown in Figure2.Specifically, the simplification in cluster evaporations tends to elevate the predicted J1.4,whereas the simplifications in boundary conditions and cluster number tend to lower them.When applying the simplification in cluster evaporations (clusters larger than (SA)1(DMA)1 are regarded stable with no evaporation) to ACDC_DB, the predicted J1.4 by ACDC_DB_CE only slightly exceed than that of ACDC_DB within a

Figure 2 .
Figure 2. Comparison of J1.4 predictions between ACDC_DB and test cases including

Figure 3 .
Figure 3.Comparison of J1.4 predictions between ACDC_DB and ACDC_RM_SF0.5 correlated with T variation (A) and CS variation (B).Solid dots represent simulated J1.4 values, solid lines indicate a 1:1 line, dotted lines correspond to 1:3 and 3:1 lines, and dashed lines represent 1:10 and 10:1 lines.The distinction between ACDC_RM_SF0.5 and ACDC_DB arises from the combined effects of variation in quantum chemical calculation method and the application of the 0.5 SF in collision processing.As depicted in Figure4, when the SF in ACDC_RM_SF0.5 is set to unity as in ACDC_DB, the resulting ACDC_RM parameterization predicts consistently higher J1.4 than ACDC_DB.This implies that the modified quantum chemical calculation method, which results in lower evaporation rates for clusters within the system compared to ACDC_DB under the same condition, leads to higher J1.4 predictions.The impact from varying quantum chemical calculation method is akin to that from simplification in cluster evaporations discussed earlier.The distinction between ACDC_RM and ACDC_DB_CE lies in the fact that the modified quantum chemical calculation method affects all clusters within the system, whereas

Figure 4 .
Figure 4. Comparison of J1.4 predictions between ACDC_DB and ACDC_RM correlated with T variation (A) and CS variation (B).Solid dots represent simulated J1.4 values, solid lines indicate a 1:1 line, dotted lines correspond to 1:3 and 3:1 lines, and dashed lines represent 1:10 and 10:1 lines.In summary, based on our base-case parameterization ACDC_DB, the extensive box model simulations above demonstrate the characteristics and applicability conditions of different parameterizations.Specifically, Dynamic_Sim is applicable under most atmospheric conditions with T < ~300 K and CS > ~3.0×10 -3 s -1 , while ACDC_RM_SF0.5 is suitable under conditions with T around 280 K.We further use reported measurements from well-controlled CLOUD chamber experiments to examine the characteristics and applicability of these parameterizations(Xiao et al., 2021).As shown in FigureS8, simulations using three main parameterizations, ACDC_DB, ACDC_RM, and Dynamic_Sim, correspond well to experimental results at low temperature (T = 278 K), proving the applicability of all three parameterizations at this temperature.In the experiments with elevated temperature (T = 293 K), ACDC_DB and Dynamic_Sim continues to exhibit similar performance, with simulated results still corresponding to experimental results.In contrast, ACDC_RM_SF0.5only shows a slight T-dependence, which is deviated from the measurements.The comparison Figure 4. Comparison of J1.4 predictions between ACDC_DB and ACDC_RM correlated with T variation (A) and CS variation (B).Solid dots represent simulated J1.4 values, solid lines indicate a 1:1 line, dotted lines correspond to 1:3 and 3:1 lines, and dashed lines represent 1:10 and 10:1 lines.In summary, based on our base-case parameterization ACDC_DB, the extensive box model simulations above demonstrate the characteristics and applicability conditions of different parameterizations.Specifically, Dynamic_Sim is applicable under most atmospheric conditions with T < ~300 K and CS > ~3.0×10 -3 s -1 , while ACDC_RM_SF0.5 is suitable under conditions with T around 280 K.We further use reported measurements from well-controlled CLOUD chamber experiments to examine the characteristics and applicability of these parameterizations(Xiao et al., 2021).As shown in FigureS8, simulations using three main parameterizations, ACDC_DB, ACDC_RM, and Dynamic_Sim, correspond well to experimental results at low temperature (T = 278 K), proving the applicability of all three parameterizations at this temperature.In the experiments with elevated temperature (T = 293 K), ACDC_DB and Dynamic_Sim continues to exhibit similar performance, with simulated results still corresponding to experimental results.In contrast, ACDC_RM_SF0.5only shows a slight T-dependence, which is deviated from the measurements.The comparison

Figure 5 .
Figure 5.Comparison of simulated particle formation rates and particle number size distributions (PNSDs) with observations during January 13, 2019, to January 31, 2019, in Beijing.A represents the averaged particle formation rates during the period, the blue bars and orange bars represent observations and simulations, respectively, while the blue dashed line represents the observed values.Daily maximum values of J1.4 are used following Deng et al. (2020); B for the time series of PNSDs; and C for the averaged PNSDs.The results show the applicability of all three main parameterizations in NPF modeling during wintertime periods.Importantly, the reliability of the new ACDCderived parameterization based on the latest theoretical approach (ACDC_DB) without simplifications in 3-D NPF simulation, is affirmed.The differences among various parameterizations can be explained by the comprehensive box-model simulations above at corresponding conditions.Compared to ACDC_DB, the J1.4 and PNSDs simulated by other two main parameterizations (Dynamic_Sim and ACDC_RM_SF0.5)agree similarly with observations, but for different reasons.In the case of Dynamic_Sim, the simplification in cluster evaporations has minimal impact on NPF simulation since CS is the dominant sink for clusters under the wintertime conditions (averaged T and CS is 274.7 K and 3.3×10 -2 s -1 , respectively).However, the simplifications in boundary conditions and cluster number lead to the underestimation of the J1.4,consequently Figure 6.Comparison of simulated particle formation rates and particle number size distributions (PNSDs) with observations during August 18, 2019, to August 31, 2019, in Beijing.A represents the averaged particle formation rates during the period, the blue bars and orange bars represent observations and simulations, respectively, while the blue dashed line represents the observed values.Daily maximum values of J1.4 are used following Deng et al. (2020); B for the time series of PNSDs; and C for the averaged PNSDs.Most previous NPF studies combining experiments/observations with simulations are conducted under conditions biased towards winter (~280K)(Almeida et al., 2013;Lu et al., 2020).Under summer conditions with elevated T, there exists a deficiency in parameterization evaluations for simulating NPF.The 3-D simulation results during the summer period provide additional validation for the reliability of ACDC_DB.For ACDC_RM_SF0.5, evidence from both box-model simulations and 3-D simulations suggests that it can accurately reproduce real SA-DMA nucleation at temperatures around 280 K, while it has limitations in higher temperatures.Another main parameterization Dynamic_Sim consistently demonstrates good performance in NPF simulation, akin to its efficacy in winter conditions.With the increased temperature in summer (averaged T is 298.2K), the influence of simplifications in cluster evaporations, cluster number, and boundary conditions becomes more profound, mirroring the trends observed in box-model simulations above.This leads to more significant overestimation for ACDC_DB_CE, and underestimation for ACDC_DB_CN and ACDC_DB_BC compared to the observation as well as the base-case ACDC_DB.Note that CS during the summer period (averaged CS is 2.8×10 -2 s -1 ) decreases compared to https://doi.org/10.5194/egusphere-2024-642Preprint.Discussion started: 8 April 2024 c Author(s) 2024.CC BY 4.0 License.