Predicting aqueous solubilities from aqueous free energies of solvation and experimental or calculated vapor pressures of pure substances

In this work, we explore the possibility of making predictions of solubilities from free-energy calculations by utilizing the relationship between solubility, free energy of solvation, and solute vapor pressure. Because this relationship is only strictly valid when all activity and fugacity coefficients are unity, it is not clear when it will hold and when it will break down for a given solute–solvent system. So we have tested the validity of this relationship using a variety of liquid solutes and solid solutes in liquid water solvent. In particular, we used a test set of 75 liquid solutes and 15 solid solutes composed of H, C, N, O, F, and Cl. First we compared aqueous free energies of solvation calculated from experimental solute vapor pressures and aqueous solubilities to experimental aqueous free energies of solvation for the 90 solutes in the test set and obtained a mean-unsigned error (MUE) of 0.26 kcal/mol. Second, we compared aqueous solubilities calculated from experimental solute vapor pressures and aqueous free energies of solvation to experimental aqueous solubilities for the 90 solutes in the test set and obtained a mean-unsigned error of the logarithm (MUEL) of the aqueous solubility of 0.20. These results indicate that the relation has useful accuracy. Using this relationship, we have also investigated the utility of three continuum solvation models, in particular Solvation Model 5.42R implemented at the Hartree–Fock, Becke-3–Lee–Yang–Parr, and Austin Model 1 levels (SM5.42R/HF, SM5.42R/B3LYP, and SM5.42R/AM1, respectively) to predict aqueous solubilities of liquid solutes and solid solutes in water solvent. The SM5.42R solvation model can predict the aqueous free energy of solvation and, given several solvent descriptors, it can also predict the free energy of self-solvation (which can be converted to a solute vapor pressure). We compared aqueous solubilities calculated from experimental solute vapor pressures and SM5.42R aqueous free energies of solvation to experimental aqueous solubilities for the 90 solutes in the test set and obtained an MUEL of the aqueous solubility of 0.40 for SM5.42R/HF, 0.35 for SM5.42R/B3LYP, and 0.43 for SM5.42R/AM1. We also compared aqueous solubilities calculated from SM5.42R aqueous free energies of solvation and SM5.42R vapor pressures to experimental aqueous solubilities for all 75 liquid solutes and the 7 solid solutes for which vapor pressures can be predicted by the SM5.42R solvation model; these computations yielded an MUEL of the solubility of 0.39 for SM5.42R/HF, 0.37 for SM5.42R/B3LYP, and 0.36 for SM5.42R/AM1.