Probing the Free Energy of Small Water Clusters: Revisiting Classical Nucleation Theory

Abstract

By addressing the defects in classical nucleation theory (CNT), we develop an approach for extracting the free energy of small water clusters from nucleation rate experiments without any assumptions about the form of the cluster free energy. For temperatures higher than ∼250 K, the extracted free energies from experimental data points indicate that their ratio to the free energies predicted by CNT exhibits nonmonotonic behavior as the cluster size changes. We show that this ratio increases from almost zero for monomers and passes through (at least) one maximum before approaching one for large clusters. For temperatures lower than ∼250 K, the behavior of the ratio between extracted energies and CNT’s prediction changes; it increases with cluster size, but it remains below one for almost all of the experimental data points. We also applied a state-of-the-art quantum mechanics model to calculate free energies of water clusters (2–14 molecules); the results support the observed change in behavior based on temperature, albeit for temperatures above and below ∼298 K. We compared two different model chemistries, DLPNO-CCSD(T)/CBS//ωB97xD/6-31++G** and G3, against each other and the experimental value for formation of the water dimer.

The driving effects of common atmospheric molecules for formation of prenucleation clusters: the case of sulfuric acid, formic acid, nitric acid, ammonia, and dimethyl amine

“…3,4 The precise way that gaseous vapor comes together to form prenucleation complexes, which eventually build to aerosols, and thus form CCN, is a very active area of research. 3,5–74 Much of this activity is driven by the uncertainty in how much aerosols and clouds will impact global warming. 75,76 While it is thought that in general more aerosols will lead to a cooling effect, the uncertainty in our knowledge exceeds the actual size of the predicted cooling.…”

Quantum chemical modeling of organic enhanced atmospheric nucleation: A critical review

“…Scaling and the quasiharmonic approach costs nothing in terms of computing time and we recommend their use. There is a broad range of computational evidence that reveals that while scaling is helpful, its impact is less than might be expected because we are commonly concerned with computing changes in the Gibbs free energies, ∆ G Ꝋ , and scaled versus unscaled ∆ G Ꝋ values tend to be within 1 kcal/mol for clusters up to five molecules 82–85,92,136,140,141,144–152 . While scaling systematically reduces the DLPNO‐CCSD(T)/CBS ∆ G Ꝋ values relative to the unscaled RRHO approach for hydration of glycine by fractions of a kcal/mol, the quasi‐harmonic approach increases the ∆ G Ꝋ values by several kcal/mol for a glycine hydrated with three or four waters 84 …”

The driving effects of common atmospheric molecules for formation of clusters: the case of sulfuric acid, formic acid, hydrochloric acid, ammonia, and dimethylamine

“…5,6 Many studies have demonstrated the driving effect of sulfuric acid (SA) in forming prenucleation clusters, especially in the presence of other atmospheric acids and bases. 7–74 Hydrochloric acid (HCl), on the other hand, has not been as well studied for its potential role in the formation of pre-nucleation clusters. 75 It is estimated that 85% of the HCl in the atmosphere is produced from acid displacement of sea salt aerosols.…”