The law of matching water affinities (LMWA) is explored in classical molecular dynamics simulations of several alkali halide ion pairs, spanning the size range from small kosmotropes to large chaotropes. The ion–ion potentials of mean force (PMFs) are computed using three methods: the local molecular field theory (LMFT), the weighted histogram analysis method (WHAM), and integration of the average force. All three methods produce the same total PMF for a given ion pair. In addition, LMFT-based partitioning into van der Waals and local and far-field electrostatic free energies and assessment of the enthalpic, entropic, and ion–water components yield insights into the origins of the observed free energy profiles in water. The results highlight the importance of local electrostatic interactions in determining the shape of the PMFs, while longer-ranged interactions enhance the overall ion–ion attraction, as expected in a dielectric continuum model. The association equilibrium constants are estimated from the smooth WHAM curves and compared to available experimental conductance data. By examining the variations in the average hydration numbers of ions with ion–ion distance, a correlation of the water structure in the hydration shells with the free energy features is found.

•Specific ion effects (SIE) are ubiquitous in physics, chemistry, and biology.•Progress has been made, but a quantitative theory of SIE is lacking.•Results are discussed related to developing a single-ion free energy scale.•Progress on studies of local structure and other thermodynamic quantities is presented.•New methods and results for partitioning free energies and studying ion–ion interactions are discussed.Several recent developments have enhanced our understanding of specific ion hydration. These advances have included the Law of Matching Water Affinities and the realization that many-body dispersion forces and polarization can play important roles in ion specificity. Efforts have been made to partition the relevant ion free energies into their physically contributing parts in order to gain further insights into the driving forces. Yet a quantitative theory of ion specificity that links the necessary molecular-level treatment of the inner hydration shell with the many-body response of Lifshitz theory at longer range is still lacking. This review summarizes some steps toward quantitative models of specific ion hydration and discusses a possible path looking forward.

Ethylene carbonate (EC) and propylene carbonate (PC) are organic solvents used extensively in energy storage applications such as lithium-ion batteries and supercapacitors. Using statistical mechanical theory and computer simulations, this paper compares and contrasts the thermodynamics of ion solvation in EC and PC with the behavior observed in water. The EC and PC solvents are modeled with the AMBER (GAFF) force field. Ion–solvent interactions are treated with two point-charge models: one using an existing Lennard-Jones ion parameter set optimized for solvation in water, and the other based on high-level quantum calculations on ion–solvent dimers and fitting to a Buckingham-type potential form. The second model produces a coordination number for the Li+ ion in closer agreement with experiment. Neither model yields consistently accurate solvation thermodynamic quantities (free energies, enthalpies, and entropies), however. The simulations and thermodynamic analysis illustrate key physical aspects of the solvation; the studies also point to necessary modifications of these simple models. In particular, the calculations show that polarization and associated dispersion forces are important and that well-optimized polarizable or quantum models are likely required to accurately reproduce condensed-phase properties of ions in these technologically important solvents.

The chloride channel/transporter family of proteins facilitates anion transport across biological membranes. There is extensive physiological and bioinformatic evidence that the channels and transporters are closely related. Each monomer of a homodimeric CLC transport protein contains a narrow selectivity filter. Investigating the ion binding properties inside the filter is crucial for understanding key mechanistic states during ion transit. Here computer simulations are used to explore the free energies of Cl– ions in the binding sites of the wild-type CLC-ec1 transporter and its mutant E148A. Specifically, a local molecular field theory approach for free energy calculations is exploited to compute the absolute free energies in water and in the protein binding sites. The calculations indicate a close synergy between anion binding and protonation of the external glutamate gate. Electrostatic differences between the bacterial CLC-ec1 and eukaryotic CmCLC transporters revealed by these and other simulations help to rationalize the observed differing structures in the pore region. In addition, quantum chemical calculations on the F–, Cl–, and Br– ions in the central binding site are used to examine ion selectivity. The calculations show a significant extent of charge transfer from the ion to the nearby residues. The computed free energies, in conjunction with experimental measurements, place constraints on proposed mechanisms for the transport cycle.

The surface potential at the water liquid–vapor interface is discussed in relation to experimental determinations of bulk absolute ion hydration free energies. It is shown that, rather than the surface potential itself, the net electrostatic potential at the center of an uncharged solute can aid both in relating differences between tabulations of hydration free energies and in explaining differing classical and quantum surface potential estimates. Quantum mechanical results for the net potential are consistent with conclusions from previous classical simulations, suggesting a contribution from the net potential that can influence ion density profiles for single ions in water droplets.Graphical abstractFigure optionsDownload full-size imageDownload high-quality image (37 K)Download as PowerPoint slideHighlights► Surface potentials. ► Ion hydration free energies. ► Driving forces. ► Water interfaces. ► Specific ion effects.

The gramicidin dipeptide is a small, cation-selective ion channel. Recent experiments have indicated that gramicidin can conduct ions at elevated temperatures. Since gramicidin is an efficient proton conductor, it is possible that this channel may have applications in fuel cell technology. In this study, we examine the temperature dependence of gramicidin A channel transport and structure with molecular dynamics simulations. In particular, the potentials of mean force (PMFs) for potassium ion motion through the channel are computed at five temperatures in the range 300–360 K. The channel displays a decrease in the free energy barrier height as the temperature increases. In addition, the enthalpic and entropic components of the free energy are computed, indicating a substantial enthalpy–entropy compensation and a positive entropy change when the ion enters the channel. The positive entropy change results from a reduction in fluctuations of ion interaction energies in the pore relative to those in the bulk solvent. The overall dimeric channel structure is maintained at 360 K for time scales up to 100 ns. In addition, higher temperatures affect the distributions of hydrogen bonds at the dimer interface, conformations of the N-terminal domain that may block the pore, channel bending angles, and distances between dimers. These findings may be related to the gating of the channel, although no complete dimer dissociation events were observed in the simulations.

Monovalent ion hydration entropies are analyzed via energetic partitioning of the potential distribution theorem free energy. Extensive molecular dynamics simulations and free energy calculations are performed over a range of temperatures to determine the electrostatic and van der Waals components of the entropy. The far-field electrostatic contribution is negative and small in magnitude, and it does not vary significantly as a function of ion size, consistent with dielectric models. The local electrostatic contribution, however, varies widely as a function of ion size; the sign yields a direct indication of the kosmotropic (strongly hydrated) or chaotropic (weakly hydrated) nature of the ion hydration. The results provide a thermodynamic signature for specific ion effects in hydration and are consistent with experiments that suggest minimal perturbations of water structure outside the first hydration shell. The hydration entropies are also examined in relation to the corresponding entropies for the isoelectronic rare gas pairs; an inverse correlation is observed, as expected from thermodynamic hydration data.

We present molecular dynamics simulations of interfaces relevant to the selective chemical extraction of uranyl ions from aqueous solution. These molecular-level simulations model ion transfer in the PUREX process and in synthetic, selective membranes. We first present simulations of water/oil interfaces modified by incorporation of tributyl phosphate (TBP) into the oil phase (hexane). A range of concentrations is examined, from a single TBP molecule to values close to those utilized in the PUREX process. The TBP molecules exhibit strong interfacial activity, and the interface broadens relative to the water/oil case with increasing TBP concentrations. Additional structural features, including radial distribution functions and orientational distributions, are examined to elucidate the molecular ordering at the interface; the interface structure changes substantially with increasing TBP concentration. Finally, free-energy profiles are computed for (1) a single TBP molecule and a single uranyl nitrate complex [UO2(NO3)2] across the water/oil interface and (2) a UO2(NO3)2·TBP2 complex across both water/oil and water/(oil+TBP) interfaces. The UO2(NO3)2 complex is strongly repelled from the water/oil interface, while the UO2(NO3)2·TBP2 complex exhibits interfacial activity that decreases with increasing TBP concentration. The UO2(NO3)2·TBP2 complex displays a net free-energy driving force for partitioning into the oil phase that increases with increasing TBP concentration.