Modeling the Binding Free Energy of Large Atmospheric Sulfuric Acid–Ammonia Clusters

Abstract

Sulfuric acid and ammonia are believed to account for a large fraction of new-particle formation in the atmosphere. However, it remains unclear how small clusters grow to larger sizes, eventually ending up as stable aerosol particles. Here we present the largest sulfuric acid–ammonia clusters studied to date using quantum chemical methods by calculating the binding free energies of (SA) n (A) n clusters, with n up to 20. Based on benchmark calculations, we apply the B97-3c//GFN1-xTB level of theory to calculate the cluster structures and thermochemical parameters. We find that the cluster structures drastically evolve at larger sizes. We identify that an ammonium ion is fully coordinated in the core of the cluster at n = 7, and at n = 13 we see the emergence of the first fully coordinated bisulfate ion. We identify multiple ammonium and bisulfate ions that are embedded in the core of the cluster structure at n = 19. The binding free energy per acid–base pair levels out around n = 8–10, indicating that at a certain point the thermochemistry of the clusters converges toward a constant value.

Toward Modeling the Growth of Large Atmospheric Sulfuric Acid–Ammonia Clusters

“…We note that the binding free energy value is half of the value previously reported in the study by Engsvang and Elm because we report the binding energy per monomer, while the previously reported value is the binding energy per acid–base dimer.…”

“…The change in the trend is believed to be due to changes in the coordination environment inside the cluster, which was also noted in our previous study. 23 At small cluster sizes up to (SA) 6 (AM) 6 all of the molecules are exposed to the exterior, which was also observed by DePalma et al 49 For clusters larger than this we start to observe coordination of molecules in the interior. This same tendency toward coordination of the acid by ammonium was also observed for larger nitric acid− ammonia clusters by Ling et al 50 For the smaller clusters, this is observed to be ammonium which is marked for the (SA) 8 (AM) 8 cluster in Figure 1, but as the cluster grows it instead becomes favorable to coordinate one or more bisulfate ions, which has been marked for the (SA) 13 (AM) 13 cluster in Figure 1.…”

“…Extension of the Data Set. We followed the general workflow and level of theory of our previous study 23 for the newly generated clusters. For each cluster, we generate an initial ensemble of starting structures using ABCluster 24,25 with the CHARMM 26 force field in order to probe the configurational space.…”

“…38 The m = [6−20] structures and energies were taken from our previous study. 23 The binding free energy of the (SA) m (AM) n clusters is defined as…”

“…The calculated binding free energies, at the PW91/6-31++G­(d,p) level of theory, were found to decrease almost linearly with cluster size. In our previous study, we expanded upon this work by calculating SA–AM clusters up to the size of (SA) 20 (AM) 20 , where the sampling was carried out using ABCluster. , For the (SA) n (AM) n clusters, with n = 6–8, it was found that our sampling method resulted in cluster structures lower in free energy than the ones found by DePalma et al when we reoptimized our cluster structures at the PW91/6-31++G­(d,p) level of theory. Due to the massive size of the clusters ( n up to 20), the level of theory for calculating the cluster structure and binding energies had to be lowered.…”