Role of Local Response in Ion Solvation: Born Theory and Beyond

A Gaussian field approach to the solvation of spherical ions in electrolyte solutions

In this work, the electrostatic response of an electrolyte solution to a spherical ion is studied with a Gaussian field theory. In order to capture the ionic correlation effect in concentrated solutions, the bulk dielectric response function is described by a two-Yukawa response function. The modified response function of the solution is solved analytically in the spherical geometry, from which the induced charge density and the electrostatic energy are also derived analytically. Comparisons with results for small ions in electrolyte solutions from the hyper-netted chain theory demonstrate the validity of the Gaussian field theory.

Quantifying the Molecular Polarization Response of Liquid Water Interfaces at Heterogeneously Charged Surfaces

The hydration shells of proteins mediate interactions, such as small molecule binding, that are vital to their biological function or in some cases their dysfunction. However, even when the structure of a protein is known, the properties of its hydration environment cannot be easily predicted due to the complex interplay between protein surface heterogeneity and the collective structure of water's hydrogen bonding network. This manuscript presents a theoretical study of the influence of surface charge heterogeneity on the polarization response of the liquid water interface. We focus our attention on classical point charge models of water, where the polarization response is limited to molecular reorientation. We introduce a new computational method for analyzing simulation data that is capable of quantifying water's collective polarization response and determining the effective surface charge distribution of hydrated surfaces over atomistic length scales. To illustrate the utility of this method, we present the results of molecular dynamics simulations of liquid water in contact with a heterogeneous model surface and the CheY protein.

Renormalized site density functional theory for models of ion hydration

The development of accurate statistical mechanics models of molecular liquid systems is a problem of great practical and fundamental importance. Site-density functional theory (SDFT) is one of the promising directions in this area, but its success hinges upon the ability to efficiently reconcile the co-existence of two distinct intra- and inter-molecular interaction regimes in a molecular liquid. The renormalized formulation of SDFT (RSDFT), which we have recently developed, resolves this problem by introducing an additional potential field variable that decouples two interaction scales and maps the molecular liquid problem onto the effective simple liquid mixture. This work provides a critical assessment of RSDFT for the hydrated ion system-a problem that historically has always been one of the most difficult cases for SDFT applications. Using a two-site model of water, we perform a comprehensive analysis of hydrated alkali metal and halogen ions, including both structural and free energy based characteristics. The results indicate that RSDFT provides a significant improvement over conventional three-dimensional reference interaction site model implementations and may prove useful in coarse grained simulations based on two-site solvent models.

Quadrupole-mediated dielectric response and the charge-asymmetric solvation of ions in water

Treating water as a linearly responding dielectric continuum on molecular length scales allows very simple estimates of the solvation structure and thermodynamics for charged and polar solutes. While this approach can successfully account for basic length and energy scales of ion solvation, computer simulations indicate not only its quantitative inaccuracies but also its inability to capture some basic and important aspects of microscopic polarization response. Here, we consider one such shortcoming, a failure to distinguish the solvation thermodynamics of cations from that of otherwise-identical anions, and we pursue a simple, physically inspired modification of the dielectric continuum model to address it. The adaptation is motivated by analyzing the orientational response of an isolated water molecule whose dipole is rigidly constrained. Its free energy suggests a Hamiltonian for dipole fluctuations that accounts implicitly for the influence of higher-order multipole moments while respecting constraints of molecular geometry. We propose a field theory with the suggested form, whose nonlinear response breaks the charge symmetry of ion solvation. An approximate variational solution of this theory, with a single adjustable parameter, yields solvation free energies that agree closely with simulation results over a considerable range of solute size and charge.

Assessing long-range contributions to the charge asymmetry of ion adsorption at the air-water interface

Anions generally associate more favorably with the air–water interface than cations. In addition to solute size and polarizability, the intrinsic structure of the unperturbed interface has been discussed as an important contributor to this bias. Here we assess quantitatively the role that intrinsic charge asymmetry of water's surface plays in ion adsorption, using computer simulations to compare model solutes of various size and charge. In doing so, we also evaluate the degree to which linear response theory for solvent polarization is a reasonable approach for comparing the thermodynamics of bulk and interfacial ion solvation. Consistent with previous works on bulk ion solvation, we find that the average electrostatic potential at the center of a neutral, sub-nanometer solute at the air–water interface depends sensitively on its radius, and that this potential changes quite nonlinearly as the solute's charge is introduced. The nonlinear response closely resembles that of the bulk. As a result, the net nonlinearity of ion adsorption is weaker than in bulk, but still substantial, comparable to the apparent magnitude of macroscopically nonlocal contributions from the undisturbed interface. For the simple-point-charge model of water we study, these results argue distinctly against rationalizing ion adsorption in terms of surface potentials inherent to molecular structure of the liquid's boundary.

Cations and anions have different affinities for the air-water interface. The intrinsic orientation of surface molecules suggests such an asymmetry, but the bias is dominated by solvent response that is spatially local and significantly nonlinear.

Dielectric response with short-ranged electrostatics

The dielectric nature of polar liquids underpins much of their ability to act as useful solvents, but its description is complicated by the long-ranged nature of dipolar interactions. This is particularly pronounced under the periodic boundary conditions commonly used in molecular simulations. In this article, the dielectric properties of a water model whose intermolecular electrostatic interactions are entirely short-ranged are investigated. This is done within the framework of local molecular-field theory (LMFT), which provides a well-controlled mean-field treatment of long-ranged electrostatics. This short-ranged model gives a remarkably good performance on a number of counts, and its apparent shortcomings are readily accounted for. These results not only lend support to LMFT as an approach for understanding solvation behavior, but also are relevant to those developing interaction potentials based on local descriptions of liquid structure.

The Born model can accurately describe electrostatic ion solvation

The solvation free energies of ions in water are consistent with the Born linear response model if the centre on which the ion–water repulsion force acts is moved from the oxygen atom towards the hydrogens.

Quantifying the hydration structure of sodium and potassium ions: taking additional steps on Jacob's Ladder

The ability to reproduce the experimental structure of water around the sodium and potassium ions is a key test of the quality of interaction potentials due to the central importance of these ions in a wide range of important phenomena.

Electrostatic solvation and mobility in uniform and non-uniform electric fields: From simple ions to proteins

A number of observations related to interfacial electrostatics of polar liquids question the traditional assumption of dielectric theories that bulk dielectric properties can be continuously extended to the dividing surface separating the solute from the solvent. The deficiency of this approximation can be remedied by introducing local interface susceptibilities and the interface dielectric constant. Asymmetries of ionic hydration thermodynamics and of the mobility between cations and anions can be related to different propensities of the water molecules to orient their dipole toward and outward from solutes of opposite charges. This electrostatic asymmetry is reflected in different interface dielectric constants for cations and anions. The interface of water with neutral solutes is spontaneously polarized due to preferential water orientations in the interface. This phenomenon is responsible for a nonzero cavity potential directly related to a nonzero surface charge. This connection predicts that particles allowing a nonzero cavity potential must show mobility in an external electric field even if the net charge of the particle is zero. The theory predicts that a positive cavity potential and a positive surface charge translate to an effectively negative solute charge reported by mobility measurements. Passing of the cavity potential through a minimum found in simulations might be the origin of the maximum of mobility vs the ionic size observed experimentally. Finally, mobility of proteins in the field gradient (dielectrophoresis) is many orders of magnitude greater than predicted by the traditionally used Clausius-Mossotti equation. Two reasons contribute to this disagreement: (i) a failure of Maxwell's electrostatics to describe the cavity-field susceptibility and (ii) the neglect of the protein permanent dipole by the Clausius-Mossotti equation. An analytical relation between the dielectrophoretic susceptibility and dielectric spectroscopy of solutions provides direct access to this parameter, confirming the failure of the Clausius-Mossotti equation in application to protein dielectrophresis.

Interfacial Adsorption of Neutral and Ionic Solutes in a Water Droplet

Direct (solute-water) and indirect (water-water) contributions to adsorption at an air-water interface are identified using the Widom potential distribution theorem and quantified using molecular dynamics simulations of a liquid water droplet containing either neopentane or iodide-like solutes with charges of 0 or ±1. The results are used to quantitatively compare direct and indirect energetic and entropic contributions to adsorption, as well as to critically test surface capillary wave, linear response (LR), and mean field (MF) predictions. The negative signs of the total adsorption energies and entropies of both the anionic and cationic solutes are found to result from indirect adsorption induced changes in water-water interactions, rather than from surface capillary wave perturbations, which are found to be asymmetric with respect to solute charge. The LR and MF approximations both accurately describe the adsorption of neutral (hydrophobic) solutes, while for ionic solutes the MF approximation is entirely inappropriate and LR predictions are qualitatively (but not quantitatively) accurate.

Real single ion solvation free energies with quantum mechanical simulation

Single ion solvation free energies are one of the most important properties of electrolyte solutions and yet there is ongoing debate about what these values are. Only the values for neutral ion pairs are known. Here, we use DFT interaction potentials with molecular dynamics simulation (DFT-MD) combined with a modified version of the quasi-chemical theory (QCT) to calculate these energies for the lithium and fluoride ions. A method to correct for the error in the DFT functional is developed and very good agreement with the experimental value for the lithium fluoride pair is obtained. Moreover, this method partitions the energies into physically intuitive terms such as surface potential, cavity and charging energies which are amenable to descriptions with reduced models. Our research suggests that lithium's solvation free energy is dominated by the free energetics of a charged hard sphere, whereas fluoride exhibits significant quantum mechanical behavior that cannot be simply described with a reduced model.