A hybrid approach using a combination of explicit solvent molecules and the isodensity polarizable continuum model (IPCM) method is proposed for the calculation of the solvation thermodynamic properties of ions. This model, denominated cluster-continuum, has been applied to the calculation of the solvation free energy of 14 univalent ions, mainly organic species, and compared with the results obtained with the IPCM, polarizable continuum solvation model (PCM), and SM5.42R continuum methods. The average error in our calculated solvation free energies with respect to experimental data is 8.7 kcal mol -1 . However, the great merit of our model resides in the homogeneous treatment for different ions, resulting in a standard deviation of only 2.9 kcal mol -1 for the average error. Our results suggest that the cluster-continuum model must be superior to the IPCM, PCM, and SM5.42R methods for studying chemical reactions in the liquid phase, because these continuum methods present a standard deviation of ∼8 kcal mol -1 for the average error for the species studied in this work. The model can also be used to calculate the solvation entropy of ions. Predicted solvation entropies for five ionic species are in good agreement with available experimental data.

The pK a's of 17 species from −10 to 50 were calculated using the ab initio MP2/6-311+G(2df,2p) level of theory and inclusion of solvent effects by the cluster−continuum model, a hybrid approach that combines gas-phase clustering by explicit solvent molecules and solvation of the cluster by the dielectric continuum. In addition, the pure continuum methods SM5.42R and PCM were also used for comparison purposes. Species such as alcohols, carboxylic acids, phenol, acetaldehyde and its hydrate, thiols, hydrochloric acid, amines, and ethane were included. Our results show that the cluster−continuum model yields much better agreement with experiment than do the above-mentioned pure continuum methods, with a rms error of 2.2 pK a units as opposed to 7 pK a units for the SM5.42R and PCM methods. The good performance of the cluster−continuum model can be attributed to the introduction of strong and specific solute−solvent interactions with the molecules in the first solvation shell of ions. This feature decreases the dielectric continuum contribution to the difference in the solvation free energy between ions, making the method less susceptible to error because of the continuum contribution to solvation. Because the method is not based on extensive parametrizations and it is shown to fare well for several functional groups, the present results suggest that this method could be used as a general approach for predicting reliable pK a values.

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The pK a values of over 41 organic acids in dimethyl sulfoxide (DMSO) solution were calculated using ab initio electronic structure methods at MP2 and MP4 levels of electron correlation and including basis set of 6-31+G(d) and 6-311+G(2df,2p) quality. The solvation was included through the polarizable continuum model (PCM), using the recent parametrization of Pliego and Riveros. The root-mean-square (RMS) error over this set of molecules having different functional groups is only 2.2 units. A linear fit on this data set decreases this error by only 0.2 units, indicating that this empirical correction is not necessary. The major error in the calculated pK a value was −5.3 units for the CH3SO3H solute. Halogenated carboxylic acids have also presented a high deviation (∼4 units). An explanation for these high deviations is the possibility of strong hydrogen-bond formation involving the neutral acid molecule and DMSO. The pK a values were also calculated using a combination of theoretical solvation data with experimental gas-phase data. In this case, the RMS error increased to 2.3 units for a set of 36 acids. Our results show that the performance of the PCM model with a fixed atomic radius in DMSO solution is very superior to its performance in aqueous solution, which is a behavior that can be attributed to the presence of strong and specific solute−solvent interactions of ionic solutes with water molecules. In addition, no extensive parametrization of the PCM model is needed to describe the solvation of anions in DMSO solution.

Hybrid discrete‐continuum approaches for solvation have been widely applied for diverse problems in chemistry suck as pKa calculation in aqueous and nonaqueous solvents, activation free energy barriers for ionic processes in solution, and surface reactions. A special version of this approach, the cluster‐continuum quasichemical model, has also been used for establishing a single‐ion solvation free energy scale in different solvents compatible with the tetraphenylarsonium tetraphenylborate assumption. The use of discrete‐continuum solvation methods can lead to meaningful improvement with respect to pure continuum solvation models for modeling diverse chemical process in solution. In the case of pKa calculations, there are cases where the root mean squared error is as large as 7 pKa units with pure continuum solvation model and becomes around 1 pKa unit with the hybrid approach. For complex reactions in solution, errors as large as 10 kcal/mol for activation free energies with the pure continuum approach can be substantially reduced with the inclusion of explicit solvent molecules. A discussion of the theory of hybrid discrete‐continuum methods is also presented and further development is expected in the coming years. This article is categorized under: Structure and Mechanism > Reaction Mechanisms and Catalysis Software > Quantum Chemistry Molecular and Statistical Mechanics > Free Energy Methods

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