Free-Energy Calculations of Ionic Hydration Consistent with the Experimental Hydration Free Energy of the Proton

Abstract

Computational free-energy correction strategies and the choice of experimental proton hydration free energy, ΔG(H), are analyzed to investigate the apparent controversy in experimental thermodynamics of ionic hydration. Without corrections, the hydration free-energy (ΔG) calculations match experiments with ΔG(H) = -1064 kJ/mol as reference. Using the Galvani surface potential the resulting (real) ΔG are consistent with ΔG(H) = -1098 kJ/mol. When applying, in an ad hoc manner, the discrete solvent correction, ΔG matching the "consensus" ΔG(H) of -1112 kJ/mol are obtained. This analysis rationalizes reports on ΔG calculations for ions using different experimental references. For neutral amino acid side chains ΔG are independent of the water model, whereas there are large differences in ΔG due to the water model for charged species, suggesting that long-range ordering of water around ions yields an important contribution to the ΔG. These differences are reduced significantly when applying consistent corrections, but to obtain the most accurate results it is recommended to use the water model belonging to the force field.

Study of interactions between metal ions and protein model compounds by energy decomposition analyses and the AMOEBA force field

“…For acetate, the AMOEBA result coincides with the upper bound of experimental values. Considering the large discrepancies between experimental solvation free energies of acetate and the uncertainties of each value (∼2 kcal/mol), 69,84 We note that the surface potential of the AMOEBA water model is smaller in magnitude than the values of other water models around 0.5 V. 67,85 Quantum mechanical calculations also suggest that the AMOEBA geometry has a smaller surface potential than the geometries obtained from fixed charge models. 86 The AMOEBA solvation free energy results that include this surface potential contribution are tabulated and compared with experimental references with ∆G * solv H + = −265.9 kcal/mol and −262.2 kcal/mol in Table S2 of the supplementary material.…”

“…A summary of approaches used to derive ∆G o solv H + can be found in the work of Grossfield et al 66 There are large discrepancies between the reported values of ∆G o solv H + , and most of them fall within two categories that differ by ∼8-15 kcal/mol. [67][68][69] This difference has been attributed to the water surface potential. 68 For example, the extrathermodynamic assumptions of Schmid et al 64 and Marcus 70 do not include the surface potential, while the cluster-pair approximation of Tissandier et al 71 does.…”

“…No corrections for the finite size effects were applied since they are very small for a system containing 500 or more water molecules. 69,72,73 The calculated results do not include the surface potential, so they can be directly compared to the experimental solvation free energies using the reference proton solvation free energy of Schmid et al This scheme for comparing computed and experimental ionic solvation free energies has been adopted by several studies, 68,72,73 and it is considered to be one of the most reliable ways. 72 The surface potential of the AMOEBA water model was also computed in order to derive the "real" solvation free energies.…”

Phase-Transferable Force Field for Alkali Halides

“…A database of quantum-chemical properties that lies at the foundation of the force field has recently been published 51,52 based on quantum chemistry calculations reported previously 53 and distributed charge parameters for general organic compounds have been derived. 54 Other input to the force field development is an extensive set of benchmarks of classical force fields used in simulations of liquids and model systems [55][56][57][58][59][60][61][62][63][64] which can be found at the http://virtualchemistry.org repository. 65 We strive for a phase transferable force field (g, l, s) such as demonstrated for example by Jordan et al for molecular nitrogen 66 or NaCl.…”

Molecular dynamics simulations of Y(iii) coordination and hydration properties

“…In this paper, in the pure YCl 3 aqueous solution in simulation a, the number of water molecules in the rst shell of H 2 O to Y(III) is 3.0, when the g(r) was integrated to the second RDF peak valley, and the short-range H 2 O molecule number is 9.1, but we consider that only 3.0 H 2 O molecules in the rst shell coordinate with Y(III), and the H 2 O molecules in the second shell are considered to be under the action of electrostatic attraction. With increasing CO 3 2À concentration in the YCl 3 -Na 2 CO 3 solution system, eqn (2) is integrated to the second peak valley of the Y(III) short-range order, 37,38 that is, in the short-range order, the total H 2 O molecular number decreases from 9.1 to 7.0 while the coordination number of H 2 O for Y(III) decreases from 3.0 to 2.2 within r < 2.6Å. Interestingly, research results reported by Migliorati et al 39 shows, analysis of the simulation results has shown that both Lennard-Jones and Buckingham potentials are able to properly describe the radial distribution of water molecules around the Ln 3+ ions, the smooth decrease of the hydration number along the lanthanoid series.…”