Free energy aqueous clusters

M. D. Tissandier, K.A. Cowen, W.Y. Feng, E. Gundlach, M. H. Cohen,A. D. Earhart, J. V Coe, T. R. Tuttle Jr. The Proton s Absolute Aqueous Enthalpy and Gibbs Free Energy of Solvation from Cluster-Ion Solvation Data. J. Phys. Chem. A 1998, 102, 7787-7794. 

C. P. Kelly, C. J. Cramer and D. G. Truhlar, SM6 A density functional theory continuum solvation model for calculating aqueous solvation free energies of neutrals, ions, and solute-water clusters, J. Chem. Theory Comput., 1 (2005) 1133-1152. 

Our calculations have shown that the global anharmonicities in the Helmholtz free energies for both pure water clusters [4] and aqueous ionic clusters [6,8,71] fundamental to nucleation are essential to include in the prediction of accurate equilibrium constants and free energies. For example, the size-dependent anharmonic chemical potentials of water clusters are wildly different from the RRHOA results underscoring the importance of configurations far removed from min-... 

Through this approximation they were able to arrive at an absolute value for the free energy of solvation of the proton by analysing a large number of experimental results. Subsequently, they could determine the free energy of solvation for any other ion, without or with a cluster of water molecules. Some representative results are listed in Table 16, where it is seen that the aqueous solvation energy for clustered ions show a clear convergence trend when the number of water molecules in the cluster exceeds 2. Ultimately, the authors also compared calculated values with experimental values and found that the calculated values in most cases were within 3-5 kcal/mol of the experimental values. 

Table 16 Selected absolute aqueous solvation free energies (in kcal/mol) for M and M ions clustered by n water molecules. All results are from ref 55... 

To supplement their previous publication, Kelly, Cramer, and Truhlar also conducted an extensive study surrounding the absolute aqueous solvation free energies of ions and ion-water clusters containing a single water molecule. They reported the following mean unsigned errors using values from their recent [12] and previous publication [25]. 

Kelly, C.P., Cramer, C.J., Truhlar, D.G. Aqueous solvation free energies of ions and ion-water clusters based on an accurate value for the absolute aqueous solvation free energy of the proton. J. Phys. Chem. B 2006,110(32), 16066-81. 

One of our important contributions in the field of aqueous clusters has been to provide quantitative estimates of the effects of anharmonicity on zero point vibrational energies (ZPVE) and thermodynamic energies at finite temperatures [41]. For the water dimer, MP2/[13s8p4d2f/8s4p2d] calculations yielded values of enthalpy (AH = —3.19kcal/ mol), free energy (AG = 3.39 kcal/mol), and entropy (AS = —17.7 cal/moI/K) at 373 K, which are well within the experimental bounds (A//=—3.59 0.5 kcal/mol. 

Kelly, Cramer, and Truhlar used the cluster-continuum model in their study of aqueous acid dissociation constants [39]. They compared the correlation between experimental pK values and the calculated acid dissociation Gibbs free energies of anions with and without an additional explicit water molecule using SM6. Note that because ol the relation between pK and AG q as shown in equation 2.1, a plot of pK, versus AG should yield a slope of 1/2.303RT. or 1/RTlnaO). 

Mean Unsigned Errors in Absolute Aqueous Solvation Gibbs Free Energies of Ions and Ion-Water Clusters, with a Single Water Molecule, for Various Continuum Solvent Models... 

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