The framework of COSMOtherm calculations treats electrolytes (i.e., solvent and one salt) as ternary solutions (solvent, cation, anion). This affects the mole fractions (input) and activity coefficients (output) of the program. All mole fractions presented with the results were converted to the laboratory-binary framework (solvent, salt) for easier comparison with experiments.

The highest level of theory parameterization in COSMOtherm (BP_TZVPD_FINE_21, abbreviated FINE, using BP/TZVPD//BP/TZVP level cosmo files) works poorly with the strong charges of small ions, such as atomic ions and strong small semi-spherical ions (such as SO42-, NH4+) . The use of an electrolyte parameterization (BP_TZVP_ELYTE_21; abbreviated ELYTE; using BP/TZVP level cosmo files) is recommended for up to 6 mol kg-1 solutions, corresponding to around 0.1 mole fraction of salt in water . However, the use of ELYTE is not recommended for large ions . Based on these recommendations, the use of ELYTE should be limited to systems for which it was developed unless the calculated values can be corroborated by experiments.

The different COSMOtherm parameterizations are compared in Sect. S1 of the Supplement. Overall, the experimental water activities agree equally well with both ELYTE and FINE parameterizations with the exception of ammonium sulfate, with which FINE significantly overestimates the experiments (see Figs. S2–S4). For some cations (e.g., ARG), ELYTE results are highly inconsistent with the results of FINE and the BP_TZVP_21 parameterization (abbreviated TZVP), which for most salts give fairly similar estimates. Additionally, the current electrolyte parameterization is only available for the lower level of theory BP/TZVP cosmo files and not for the higher level of theory BP/TZVPD cosmo files, corresponding to the FINE parameterization. In case there are systematic errors within the different parameterizations or levels of theory, the comparison of the different salts is more reliable when the same parameterization is used in all calculations. The FINE parameterization is therefore used for all of the studied salts, with the exception of ammonium sulfate, which is calculated using the ELYTE parameterization.

Using the selected parameterizations, COSMOtherm agrees with the experimental water activities of aminium sulfate, bisulfate, and nitrate solutions (xsalt<0.2) within factors of 1.39, 1.18, and 1.23, respectively. Similar uncertainties can be expected for other aminium salts. Additionally, as can be seen from Figs. S2–S4, the disagreement between calculations and experiments increases with the increasing salt mole fraction in the solution.

The input files for COSMOtherm calculations (cosmo-files) were obtained through a series of density functional theory calculations with increasing levels of theory. The process has been discussed in more detail in a previous publication . In short, all conformers were found using the systematic conformer search algorithm in the Spartan20 program . The geometries of all conformers were optimized, and duplicate conformers were removed using the BIOVIA COSMOconf program , which uses the Turbomole program for the quantum chemistry calculations. The final cosmo-files were computed at the BP/def2-TZVPD-FINE//BP/def-TZVP level of theory (BP/def-TZVP for ELYTE and TZVP calculations).

Many of the studied cations have multiple conformers. At most the 10 lowest chemical potential conformers were selected as input for the COSMOtherm calculations. However, only conformers with chemical potentials within 2 kcal mol-1 of the lowest chemical potential were used in order to avoid including conformers with low COSMO energies but high chemical potentials . More specifically, COSMOtherm gives high weights to conformers containing intramolecular H bonds because intramolecular H bonds are favored in the COSMO energies . There is an excellent correlation between chemical potentials in water and in electrolyte solutions (see Fig. S7). This indicates that conformer distributions are similar in pure water and electrolytes. The conformer sets for electrolyte calculations can therefore be selected using the chemical potentials of the ions in water.

Water activities were calculated in solutions ranging from pure water to 0.2 mole fraction of salt. It should be noted that the water solubility of some salts at 298.15 K may be below 0.2 mole fraction. However, all salt was assumed to be dissolved in the solvent water as ions. Additionally, all cations in the calculations are singly charged for simpler comparison, even if some contain multiple amine groups. Figure  shows COSMOtherm-derived water activities in selected salt solutions at 298.15 K. The values are given in Tables S1–S16 in the Supplement and in Fig. S8. Unfortunately, determining reliable error estimates of water activities in these salts is not possible due to the lack of experimental data for similar salts. However, the errors are likely to be systematic for similar compounds, such as aminium ions. The order of the cations may therefore be more reliable than the order of the anions.

Figure  shows that both the anion and cation affect the water activity of the solutions. Assuming that the ions investigated here follow the Hofmeister series, the order of cations should be similar regardless of counter ion. Based on COSMOtherm estimates, the order of the cations is fairly similar in sulfate (Fig. d), iodate and methylsulfonate (Fig. f) salts. Similarly, bisulfate and nitrate (Fig. e) salts have a similar order for the cations. This indicates that the effect of the cation on water uptake also partially depends on the anion. Additionally, the order of the studied anions is not the same for all of the cations.

Some patterns can be seen between the different functional groups of the cations. For example, water uptake is enhanced in the following order: tertiary amine > secondary amine > primary amine (Fig. a). This order follows the hygroscopicity of aminium sulfate salts and is the same as found for water uptake of aminium methylsulfonate salts (TMA > DMA > MMA). Additionally, two amine groups in the cation lead to lower water activity than one amine group, even though only one of the amine groups is protonated. This is seen in the comparison between TMA and TMEDA, as well as MMA and EDA (Fig. a).

Carboxylic acid groups have inconsistent effects on water activity. Amino acids have lower water activities than MMA in some salts (bisulfate, nitrate; Fig. f) and higher in others (sulfate; Fig. d, iodate, methylsulfonate; Fig. e). Additionally, there is no clear trend between the studied amino acids with one (ALA, GLY, SER) or two (GLU, ASP) acid groups. On the other hand, water activity is lower in all five ARG (one carboxylic acid group) salts than in the corresponding AGM (no carboxylic acid group) salts (Fig. d–f).

In sulfate solutions, the water activities have the largest dependence on the cation compared to the other studied anions. Additionally, GLY and ASP sulfates are predicted to inhibit water uptake at low salt concentrations (water activity coefficients above one, see Tables S12 and S14). It should be noted that the ionic strength of the sulfate solutions is 3 times the ionic strength of the other studied solutions with the same salt mole fraction.

In their experiments, observed similar osmotic coefficients of aqueous AM, MMA, DMA, TMA, and DEA bisulfate solutions, indicating similar water activities independent of the cation. Similarly, the COSMOtherm-derived water activities in the bisulfate solutions are similar (within a factor of 1.1 in xsalt=0.1 solutions) for all studied cations. Due to uncertainties in the calculated values, it is possible that there are no real differences between the water activities of the different aminium bisulfate solutions. Conversely, MMA, DMA, TMA, and DEA sulfate solutions had lower experimental water activities than the corresponding bisulfate solutions, while water activities in AM bisulfate solutions were similar to those in AM sulfate solutions . A similar trend is seen in the COSMOtherm-derived water activities.

studied the effect of water on the growth of acid–guanidine clusters in the gas phase computationally. At the molecular level, water was seen to enhance particle formation at 298 K in systems containing nitric acid and methylsulfonic acid at relatively low acid concentrations. No significant effect was seen in sulfuric acid systems. The same order in these three acids is seen in COSMOtherm bulk-phase calculations. Nitrate enhances water uptake to the aqueous phase more than the other two anions, methylsulfonate enhances water uptake slightly less than nitrate, and the bisulfate has the weakest enhancing effect. However, COSMOtherm predicts the lowest water activity in solutions containing sulfate ions, indicating the strongest water uptake. However, since the concentration of guanidine was lower than the sulfuric acid concentration in the simulations of , the sulfuric acid is expected to form bisulfate ions and not sulfate ions. If the correlation between COSMOtherm-estimated water activities and the enhancement on cluster formation at high RH holds for other acid–base pairs, the relative effect of RH on particle formation could be estimated using the computationally simple water activity calculations instead of the more time-consuming molecular cluster calculations.

Higher equilibrium water content in aerosol particles indicates a higher hygroscopic growth factor. Because the salts have different molar masses, mass fraction water content provides a more direct comparison for the hygroscopic growth factors of the salts. Table  shows the mass fraction water content of each of the studied salts at 70 % RH as an example. Comparing the anions, the highest water content is found in either the sulfate or the nitrate salt for all studied cations. For most of the studied cations (all except TMEDA), the lowest water content in terms of mass fraction is in the iodate salt. COSMOtherm predicted water mass fractions at 70 % RH vary between 0.19 (ASP-IO3) and 0.64 (TMA2-SO4) for the studied salts.

Next, an organic compound was added to the aqueous salt solutions to investigate the effect of the salts on water activity in the presence of an organic component. An isoprene-derived epoxydiol (trans-β-IEPOX; C5H10O3) was selected as the organic compound because of its high estimated gas-phase production rate in the atmosphere (100 Tg C per year; ). Additionally, COSMOtherm predicts miscibility between water and IEPOX and only slight deviation from ideality in all mixing ratios . This is important, as limited solubility between water and the chosen organic would lead to strong deviation from ideality for water by the organic. In such cases, liquid–liquid phase separation should be taken into account in the activity coefficient calculations.

A hydrophobic water-insoluble organic matter (WIOM; CC(=O)C1OC2OC(OC2(C)O1)C1=CC(C)=CC(C)=C1) proposed by has often been used as a proxy in COSMO-RS calculations of atmospheric aerosol properties . COSMOtherm-predicted solubility of water in WIOM is low (0.07 mole fraction; ), indicating that relatively high RH is needed to increase the water content in pure WIOM particles. For example, at equilibrium in 70 % and 90 % RH, the predicted water mole fraction in WIOM is only 0.047 and 0.065, respectively. Adding a salt to the mixture increases equilibrium water content compared to pure WIOM. However, high mole fractions of salt lead to the salting out of WIOM from the aqueous salt solution.

When the salt–WIOM–water mixtures phase separate into an aqueous phase and a organic-rich phase, the aqueous phase will contain mostly water and salt, while the organic-rich phase is almost pure WIOM. The COSMOtherm-derived solubility of WIOM in water at 298.15 K is very low, only 2.5×10-5 mole fraction. The solubility of WIOM further decreases with the addition of salt (salting out of WIOM). The predicted water activity in the aqueous phase is very close to that of the binary salt–water mixtures (see Fig. S13). The effect of very hydrophobic organics on water activity of salts is therefore expected to be negligible, as water activity in both phases at equilibrium is equal according to the LLE condition of Eq. (3).