Table 1. 72 Distinct Values for the Proton Free Energy of Hydration Collated from the Literaturea.
| ΔμhH+ (kcal/mol) | reference | methods |
|---|---|---|
| –247.00 | Lamoureux et al.25 | Molecular dynamics simulations with a polarizable forcefield based on the Drude model |
| –251.43 | Schmid et al.26 | Hydration entropy is obtained based on the thermodynamics of the dissociation of water. Hydration enthalpy is obtained based on the relation between hydration entropy and hydration enthalpy proposed by Krestov.27 |
| –252.39, −253.08, −253.18, −253.27, −253.30, −253.49, −253.54, −253.66, −254.90, −255.23 | Marković et al.28 | Quantum mechanical (QM) calculations with the solvation model based on density (SMD) |
| –258.26 | Grossfield et al.11 and this work | The intrinsic free energy of hydration was estimated by Grossfield et al., using the known free energy difference between K+ and H+ and AMOEBA derived intrinsic free energies of hydration for K+. The value reported by Grossfield et al., was −252.5 kcal/mol for the intrinsic free energy of hydration. Beck has estimated the Galvani potential for the AMOEBA water model to be −0.25 V, which corresponds to a correction of −5.76 kcal/mol, leading to the final estimate of −258.26 kcal/mol for the corrected free energy of hydration of the proton for the AMOEBA model. |
| –254.60 | Asthagiri et al.29 | Quasi-chemical theory |
| –253.40 | Latimer et al.30 | The Born equation with additional assumptions is used to calculate the free energy of cations and ions. |
| –253.40 | Carvalho and Pliego31 | Cluster continuum quasi-chemical theory |
| –254.28 | Marcus32 | A correction term for the compression of the space available to the ion on its transfer from its gaseous to its aqueous standard states is made to the value −252.39 kcal/mol (−1056 kJ/mol) |
| –256.93 | Duignan et al.33 | Estimates are made using the established difference in the free energy of hydration between Li+ and H+. The free energy of hydration of Li+ is calculated using DFT interaction potentials with molecular dynamics simulations (DFT-MD) combined with a modified version of the quasi-chemical theory. |
| –259.50 | Pearson(13) | Based on the absolute potential of hydrogen electrode |
| –260.28 | Vlcek et al.34 | A correction for the surface potential is made to the value from cluster pair approximation. |
| –260.50 | Friedman and Krishnan(35) | Parsing of data using a reference salt tetraphenyl arsonium tetraphenyl borate (TATB) method |
| –260.76 | Fawcett(36) | Fit to data from measurements of the ionic work function |
| –258.80 | Yu et al.37 | Simulations based on a forcefield that uses the Drude model for atomic polarizabilities |
| –262.40 | Zhan and Dixon38 | QM calculations for the ion–water cluster and a self-consistent reaction field model for the interaction between the cluster and solvent |
| –262.38, −261.86 | Hofer and Hünenberger39 | QM/MM simulations and thermodynamic integration |
| –261.73, −262.23, −262.27, −262.67, | Tawa et al.40 | QM calculations for the ion–water cluster and a self-consistent reaction field model for the interaction between the cluster and solvent |
| –261.86, −262.38, −262.89 | Prasetyo et al.41 | QM/MM simulations and thermodynamics integration |
| –262.91 | Reif and Hünenberger42 | Inferred from hydration structures obtained using classical molecular dynamics simulations |
| –263.79 | Tuttle et al.43 | Cluster pair approximation method |
| –263.98 | Tissandier et al.18 | Cluster pair approximation method |
| –264.20 | Pollard and Beck44 | Quasi-chemical theory analysis of cluster pair approximation |
| –256.75, −254.26, −259.75, −262.46, −254.75, −261.50, −252.05, −268.35, −265.22, −265.15, −267.54, −267.30, −266.67, −265.17, −266.04, −265.43, −265.46 | Matsui et al.45 | Based on the relationship between pKa value, free energy of solvation of the neutral and charged versions of small molecules and free energy of solvation of proton. Experimental pKa values are used. Free energy of solvation of the neutral and charged versions of small molecules are calculated from QM with continuum solvent model. |
| –266.10, −268.40, −266.60, −265.10, −267.80, −265.80, −264.40, −271.30, −267.70, −263.70, −269.30, −266.80, −266.10, −268.00 | Kelly et al.46 | Cluster pair approximation method |
| –266.40 | Rossini and Knapp47 | Uses quantum chemical density functional theory calculations of proton affinity in the gas phase and use of the Poisson equation to compute solvation contributions. |
| –252.50, −266.70 | Bryantsev et al.48 | Cluster Continuum Model |
| –267.88 | Ishikawa and Nakai49 | Cluster Continuum Model |
a
Rows that are bold-faced are estimates from an analysis of experimental data without the use of any simulations. This is noteworthy because the mean value of −260.89 is closest to estimates derived from parsing of experimental data, sans any calculations.