The role of solvation in proton transfer reactions: implications for predicting salt/co-crystal formation using the ΔpKa rule

Abstract

The ΔpK_a rule is commonly applied by chemists and crystal engineers as a guideline for the rational design of molecular salts and co-crystals. For multi-component crystals containing acid and base constituents, empirical evidence has shown that ΔpK_a > 4 almost always leads to salts, ΔpK_a < −1 almost always leads to co-crystals and ΔpK_a between −1 and 4 can be either. This paper reviews the theoretical background of the ΔpK_a rule and highlights the crucial role of solvation in determining the outcome of the potential proton transfer from acid to base. New data on the frequency of the occurrence of co-crystals and salts in multi-component crystal structures containing acid and base constituents show that the relationship between ΔpK_a and the frequency of salt/co-crystal formation is influenced by the composition of the crystal. For unsolvated co-crystals/salts, containing only the principal acid and base components, the point of 50% probability for salt/co-crystal formation occurs at ΔpK_a ≈ 1.4, while for hydrates of co-crystals and salts, this point is shifted to ΔpK_a ≈ −0.5. For acid–base crystals with the possibility for two proton transfers, the overall frequency of occurrence of any salt (monovalent or divalent) versus a co-crystal is comparable to that of the whole data set, but the point of 50% probability for observing a monovalent salt vs. a divalent salt lies at ΔpK_a,II ≈ −4.5. Hence, where two proton transfers are possible, the balance is between co-crystals and divalent salts, with monovalent salts being far less common. Finally, the overall role played by the “crystal” solvation is illustrated by the fact that acid–base complexes in the intermediate region of ΔpK_a tip towards salt formation if ancillary hydrogen bonds can exist. Thus, the solvation strength of the lattice plays a key role in the stabilisation of the ions.