Abstract: Objective　The impact of atmospheric particulate matter is profound, they affect human health, visibility, and climate. Understanding how particles form and grow in the air is a critical endeavor for developing strategies to mitigate their overall impact. New particle formation (NPF) is the first step in the complex process leading to the formation of cloud condensation nuclei, which primarily consists of two processes: critical nucleus formation and subsequent growth. Therefore, studying the formation process of critical nuclei is particularly crucial for understanding the source mechanisms of atmospheric aerosols. Although NPF has received extensive attention and been studied for a long time, the formation mechanisms of critical nuclei at the molecular level and the species involved in nucleation have not yet been fully understood. As important nucleation precursors, methylglyceric acid (MGA), methanesulfonic acid (MSA), and water possess excellent nucleation conditions, further theoretical and experimental studies are needed to elucidate their nucleation potential and underlying mechanisms. Methods　This study used theoretical computational methods to investigate the effect of H2O addition on the stability of (MGA)(MSA) dimer clusters, the possible mechanisms of ternary nucleation involving MGA-MSA-H2O, and the influence of the atmosphere. The initial structures of (MGA)(MSA)(H2O)n (n = 0–4) clusters were obtained by combining the Basin- Hopping (BH) algorithm with the semi-empirical PM7 method in MOPAC2016. For each cluster, 400 structures were sampled via random molecular displacement within the cluster, and the isomers were ranked based on their relative energies. Then 30 initial lowest-energy structures were selected for optimization at the M06-2X/6-31++G(d,p) level, and the isomers with energy differences within 25 kcal/mol were further optimized at the M06-2X/6-311++G(3df,3pd) theoretical level to determine the final geometric structures. This stepwise optimization approach required significantly less computational time than direct optimization at the M06-2X/6-311++G(3df, 3pd) level. In addition, frequency calculations were performed to ensure that the structure does not contain imaginary frequencies. The convergence criteria used for optimization were the default settings in the Gauss 09 software package. Single-point energy calculations were performed using Molpro 2010.1 at the DF-MP2-F12/VDZ-F12 theoretical level. Zero-point correction energies and other thermodynamic parameters were evaluated by combining thermodynamic corrections calculated at the M06-2X/6-311++G(3df, 3pd) level with single-point energies calculated at the DF-MP2-F12 level. Results and Discussion　The results show that the formation of (MGA) (MSA) (H2O)n (n = 0 – 4) clusters can all occur spontaneously. The addition of H2O promotes the acid dissociation of MSA, which makes the clusters more stable. In addition, H2O is more preferably added to the reaction in the form of (H2O)n clusters. The (MGA)(MSA)(H2O)n (n = 0–4) clusters exist in various forms of isomers, and the proportion of each isomer varies with temperature but the most stable structure is dominated. The cluster formation rate of the MGA-MSA-H2O system is sufficiently high to make an effective contribution to NPF in the atmosphere. The cluster formation rate increases significantly with increase of relative humidity. At a certain relative humidity, the cluster formation rate shows a trend of first increasing and then decreasing with decreasing temperature. Conclusions　In summary, this study provides a detailed account of the ternary nucleation mechanism involving MGA, MSA, and H2O, and demonstrates that the MGA-MSA-H2O system can form stable clusters efficiently under atmospheric conditions, and its cluster formation rate is significantly affected by relative humidity and temperature, making it an effective contributor to atmospheric NPF. This work provides a starting point for research on atmospheric nucleation involving MGA, MSA, and H2O.

Key words: atmospheric aerosols, clusters, new particle formation, density functional theory