An Improved Cluster Pair Correlation Method for Obtaining the Absolute Proton Hydration Energy and Enthalpy Evaluated with an Expanded Data Set

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An improved cluster pair correlation method that is based on the method originally introduced by Tuttle et al. ( Tuttle et al. J. Phys. Chem. A 2002 , 106 , 925 - 932 ) was developed and evaluated using a significantly larger data set than used previously. With this larger data set, values for the absolute proton hydration free energy of -259.3 and -265.0 kcal/mol were obtained using the original and improved method, respectively. The former value is ∼4.5 kcal/mol less negative than previously reported values obtained with the same method but with smaller data sets. The dependence of this value on data set size indicates that the uncertainty in the original method may be greater than previously realized. The improved method has the advantages of higher precision, and the effects of cluster size on the proton hydration free energy and enthalpy values can be more readily evaluated. Data for ions with extreme pK(a)s, many of which were included in previous estimates of the proton hydration free energy, were found to be unreliable and were eliminated from the extended data set. There is only a subtle effect of cluster size on the Gibbs free energy values, and within the limits of the approximation inherent in the cluster pair correlation method, the "best" value for the standard absolute proton hydration free energy obtained with this new method and larger data set is -263.4 kcal/mol (average for clusters with 4-6 water molecules). The absolute proton hydration enthalpy values decrease from -273.1 to -275.3 kcal/mol with increasing cluster size (one to six water molecules, respectively). This trend, along with an anomalously high value for the absolute proton hydration entropy, indicates that the enthalpy obtained with this method may not have converged for these relatively small clusters.