Thermodynamic benchmarking of hydrated atmospheric clusters in early particle formation

To improve computational modeling of hydrated atmospheric molecular clusters, we systematically evaluated quantum-chemical methods for predicting accurate structural and energetic properties of clusters containing a variety of atmospherically relevant acids and bases, with up to five water molecules. We find that the commonly applied ω B97X-D/6-31++G(d,p) method with DLPNO NormalPNO –CCSD(T 0 )/aug-cc-pVTZ electronic energy correction is suitable for hydrated clusters. Composite density functional methods such as B97-3c, r 2 SCAN-3c, and ω B97X-3c are effective for pre-screening or modeling large clusters, while the local natural orbital approach LNO–CCSD(T)/aug ′ -cc-pVTZ is well suited for accurate refinement due to its low memory requirements, high accuracy, and favorable computational scaling. Nevertheless, the ω B97X-3c method has a reasonable accuracy even without the electronic energy correction. We also assessed thermochemical corrections beyond the conventional harmonic oscillator approximation applied only to the lowest free-energy structure. For the limiting cases of no corrections and the ideal maximum corrections, we calculated hydration distributions and particle formation rates, with a specific emphasis on sulfuric acid–ammonia (SA–AM), sulfuric acid–dimethylamine (SA–DMA), and methanesulfonic acid–methylamine (MSA–MA) clusters. Hydration of small clusters is generally limited, with only selected SA- and MSA-containing clusters showing substantial hydration. Due to the high water concentration in the atmosphere, hydration equilibrates quickly, increasing the number of accessible states and thus stabilizing clusters. However, its effect on cluster formation and new particle formation is highly system-dependent. MSA–MA particle formation rates are more sensitive to hydration than those of SA–AM or SA–DMA, though the enhancement remains modest. Despite being more hydrated than SA–DMA clusters, MSA–MA clusters form new particles at relatively low rates, comparable to SA–AM. Under typical atmospheric conditions, SA–DMA is expected to dominate new particle formation, even at high humidity.