The influence of water interfacial potentials on ion hydration in bulk water and near interfaces

Variation of Surface Propensity of Halides with Droplet Size and Temperature: The Planar Interface Limit

The radial number density profiles of halide and alkali ions in aqueous clusters with equimolar radius ≲1.4 nm, which correspond to ≲255 H2O molecules, have been extensively studied by computations. However, the surface abundance of Cl-, Br-, and I- relative to the bulk interior in these smaller clusters may not be representative of the larger systems. Indeed, here we show that the larger the cluster is, the lower the relative surface abundance of chaotropic halides is. In droplets with an equimolar radius of ≈2.45 nm, which corresponds to ≈2000 H2O molecules, the polarizable halides show a clear number density maximum in the droplet's bulk-like interior. A similar pattern is observed in simulations of the aqueous planar interface with halide salts at room temperature. At elevated temperature the surface propensity of Cl- decreases gradually, while that of I- is partially preserved. The change in the chaotropic halide location at higher temperatures than the room temperature may considerably affect photochemical reactivity in atmospheric aerosols, vapor-liquid nucleation and growth mechanisms, and salt crystallization via solvent evaporation. We argue that the commonly used approach of nullifying parameters in a force field in order to find the factors that determine the ion location does not provide transferable insight into other force fields.

Ion-Size Dependent Adsorption Crossover on the Surface of a Water Droplet

The adsorption of ionic and neutral spherical solutes on the surface of a liquid water droplet are investigated using molecular dynamics simulations and theoretical analyses. The results reveal a crossover in the sign of the adsorption free energy as a function of ion size, with ions larger than iodide predicted to be increasingly surface active. Adsorption free energies are decomposed into competing energetic and entropic contributions arising from direct solute-water interaction energy and its fluctuations. The entropically driven surface activity of large ions is predicted to increase with ion size, while small ions are typically driven away from the interface by a more delicate balance of energetic and entropic contributions, with a nonmonotonic ion size dependence linked to the ion's hydration-shell structure and stability. The physical interpretation of the results is illuminated by comparisons with dielectric linear response and cavity formation predictions and implications to interfacial acidity and enhanced chemical reactivity are discussed.

Local Molecular Field Theory for Coulomb Interactions in Aqueous Solutions

Coulomb interactions play a crucial role in a wide array of processes in aqueous solutions but present conceptual and computational challenges to both theory and simulations. We review recent developments in an approach addressing these challenges─local molecular field (LMF) theory. LMF theory exploits an exact and physically suggestive separation of intermolecular Coulomb interactions into strong short-range and uniformly slowly varying long-range components. This allows us to accurately determine the averaged effects of the long-range components on the short-range structure using effective single particle fields and analytical corrections, greatly reducing the need for complex lattice summation techniques used in most standard approaches. The simplest use of these ideas in aqueous solutions leads to the short solvent (SS) model, where both solvent-solvent and solute-solvent Coulomb interactions have only short-range components. Here we use the SS model to give a simple description of pairing of nucleobases and biologically relevant ions in water.

Electrokinetic, electrochemical, and electrostatic surface potentials of the pristine water liquid-vapor interface

Although conceptually simple, the air-water interface displays rich behavior and is subject to intense experimental and theoretical investigations. Different definitions of the electrostatic surface potential as well as different calculation methods, each relevant for distinct experimental scenarios, lead to widely varying potential magnitudes and sometimes even different signs. Based on quantum-chemical density-functional-theory molecular dynamics (DFT-MD) simulations, different surface potentials are evaluated and compared to force-field (FF) MD simulations. As well explained in the literature, the laterally averaged electrostatic surface potential, accessible to electron holography, is dominated by the trace of the water molecular quadrupole moment, and using DFT-MD amounts to +4.35 V inside the water phase, very different from results obtained with FF water models which yield negative values of the order of -0.4 to -0.6 V. Thus, when predicting potentials within water molecules, as relevant for photoelectron spectroscopy and non-linear interface-specific spectroscopy, DFT simulations should be used. The electrochemical surface potential, relevant for ion transfer reactions and ion surface adsorption, is much smaller, less than 200 mV in magnitude, and depends specifically on the ion radius. Charge transfer between interfacial water molecules leads to a sizable surface potential as well. However, when probing electrokinetics by explicitly applying a lateral electric field in DFT-MD simulations, the electrokinetic ζ-potential turns out to be negligible, in agreement with predictions using continuous hydrodynamic models. Thus, interfacial polarization charges from intermolecular charge transfer do not lead to significant electrokinetic mobility at the pristine vapor-liquid water interface, even assuming these transfer charges are mobile in an external electric field.

Impacts of targeting different hydration free energy references on the development of ion potentials

Hydration free energy (HFE) as the most important solvation parameter is often targeted in ion model development, even though the reported values differ by dozens of kcal mol^-1 mainly due to the experimentally undetermined HFE of the proton ΔG°(H⁺). The choice of ΔG°(H⁺) obviously affects the hydration of single ions and the relative HFE between the ions with different (magnitude or sign) charges, and the impacts of targeted HFEs on the ion solvation and ion-ion interactions are largely unrevealed. Here we designed point charge models of K⁺, Mg²⁺, Al³⁺, and Cl^- ions targeting a variety of HFE references and then investigated the HFE influences on the simulations of dilute and concentrated ion solutions and of the salt ion pairs in gas, liquid, and solid phases. Targeting one more property of ion-water oxygen distances (IOD) leaves the ion-water binding distance invariant, while the binding strength increases with the decreasing (more negative) HFE of ions as a result of a decrease in ΔG°(H⁺) for the cation and an increase in ΔG°(H⁺) for the anion. The increase in ΔG°(H⁺) leads to strengthened cation-anion interactions and thus to close ion-ion contacts, low osmotic pressures, and small activity derivatives in concentrated ion solutions as well as too stable ion pairs of the salts in different phases. The ion diffusivity and water exchange rates around the ions are simply not HFE dependent but rather more complex. Targeting both the aqueous IOD and salt crystal properties of KCl was also attempted and the comparison between different models indicates the complexity and challenge in obtaining a balanced performance between different phases using classical force fields. Our results also support that a real ΔG°(H⁺) value of -259.8 kcal mol^-1 recommended by Hünenberger and Reif guides ion models to reproduce ion-water and ion-ion interactions reasonably at relatively low salt concentrations. Simulations of a metalloprotein show that a relatively more positive ΔG°(H⁺) for Mg²⁺ model is better for a reasonable description of the metal binding network.

Ionic mobility driven by correlated van der Waals and electrostatic forces

Classical theories of dielectric friction make two critical assumptions: (i) friction due to van der Waals (vdW) forces is described by hydrodynamic drag and is independent of the ionic charge and (ii) vdW and electrostatic forces are statistically independent. Both assumptions turn out to be incorrect when tested against simulations of anions and cations with varying charge magnitude dissolved in water. Both the vdW and electrostatic components of the force variance scale linearly with the ionic charge squared. The two components are strongly anticorrelated producing simple relations for the total force variance in terms of self-variances. The inverse diffusion constant scales linearly with the charge squared. Solvation asymmetry between cations and anions extends to linear transport coefficients.

Magnesium Force Fields for OPC Water with Accurate Solvation, Ion-Binding, and Water-Exchange Properties: Successful Transfer from SPC/E

Magnesium plays a vital role in a large variety of biological processes. To model such processes by molecular dynamics simulations, researchers rely on accurate force field parameters for Mg2+ and water. OPC is one of the most promising water models yielding an improved description of biomolecules in water. The aim of this work is to provide force field parameters for Mg2+ that lead to accurate simulation results in combination with OPC water. Using twelve different Mg2+ parameter sets, that were previously optimized with different water models, we systematically assess the transferability to OPC based on a large variety of experimental properties. The results show that the Mg2+ parameters for SPC/E are transferable to OPC and closely reproduce the experimental solvation free energy, radius of the first hydration shell, coordination number, activity derivative, and binding affinity toward the phosphate oxygens on RNA. Two optimal parameter sets are presented: MicroMg yields water exchange in OPC on the microsecond timescale in agreement with experiments. NanoMg yields accelerated exchange on the nanosecond timescale and facilitates the direct observation of ion binding events for enhanced sampling purposes.

Optimized Magnesium Force Field Parameters for Biomolecular Simulations with Accurate Solvation, Ion-Binding, and Water-Exchange Properties in SPC/E, TIP3P-fb, TIP4P/2005, TIP4P-Ew, and TIP4P-D

Magnesium is essential in many vital processes. To correctly describe Mg2+ in physiological processes by molecular dynamics simulations, accurate force fields are fundamental. Despite the importance, force fields based on the commonly used 12-6 Lennard-Jones potential showed significant shortcomings. Recently progress was made by an optimization procedure that implicitly accounts for polarizability. The resulting microMg and nanoMg force fields (J. Chem. Theory Comput. 2021, 17, 2530-2540) accurately reproduce a broad range of experimental solution properties and the binding affinity to nucleic acids in TIP3P water. Since countless simulation studies rely on available water models and ion force fields, we here extend the optimization and provide Mg2+ parameters in combination with the SPC/E, TIP3P-fb, TIP4P/2005, TIP4P-Ew, and TIP4P-D water models. For each water model, the Mg2+ force fields reproduce the solvation free energy, the distance to oxygens in the first hydration shell, the hydration number, the activity coefficient derivative in MgCl2 solutions, and the binding affinity and distance to the phosphate oxygens on nucleic acids. We present two parameter sets: MicroMg yields water exchange on the microsecond time scale and matches the experimental exchange rate. Depending on the water model, nanoMg yields accelerated water exchange in the range of 106 to 108 exchanges per second. The nanoMg parameters can be used to enhance the sampling of binding events, to obtain converged distributions of Mg2+, or to predict ion binding sites in biomolecular simulations. The parameter files are freely available at https://github.com/bio-phys/optimizedMgFFs.

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.

Low Density Interior in Supercooled Aqueous Nanodroplets Expels Ions to the Subsurface

The interaction between water and ions within droplets plays a key role in the chemical reactivity of atmospheric and man-made aerosols. Here we report direct computational evidence that in supercooled aqueous nanodroplets a lower density core of tetrahedrally coordinated water expels the cosmotropic ions to the denser and more disordered subsurface. In contrast, at room temperature, depending on the nature of the ion, the radial distribution in the droplet core is nearly uniform or elevated toward the center. We analyze the spatial distribution of a single ion in terms of a reference electrostatic model. The energy of the system in the analytical model is expressed as the sum of the electrostatic and surface energy of a deformable droplet. The model predicts that the ion is subject to a harmonic potential centered at the droplet's center of mass. We name this effect "electrostatic confinement". The model's predictions are consistent with the simulation findings for a single ion at room temperature but not at supercooling. We anticipate this study to be the starting point for investigating the structure of supercooled (electro)sprayed droplets that are used to preserve the conformations of macromolecules originating from the bulk solution.

Insight into the Ionizing Surface Potential Method and Aqueous Sodium Halide Surfaces

Complementing the microscopic picture of the surface structure of electrolyte solutions set out by previous theoretical and experimental studies, the ionizing surface potential technique offers a unique approach to quantifying the impact of aqueous inorganic ions upon the interfacial electric field of the air-aqueous interface. In this Feature Article, we review the vulnerability of theoretical and empirically derived χ_water values as a normative reference for aqueous ion surface potentials. Instead, we recognize and evaluate aqueous ion surface potentials relative to well-known ionic surfactants cetyltrimethylammonium bromide (CTAB) and sodium dodecyl sulfate (SDS). Additionally, we also explore factors that impact the magnitude of the measured surface potentials using the ionizing method, particularly in the type of reference electrode and ionizing gas environment. With potential measurements of sodium halide solutions, we show that iodide has a dominant effect on the air-aqueous electric field. Compared to chloride and bromide, iodide is directly observed with a net negatively charged surface electric field at all salt concentrations measured (0.2 to 3.0 mol/kg water). Also, above the 2 M region, bromide is observed with a net negatively charged surface. Although several scenarios contribute to this effect, it is most likely due to the surface enrichment of bromide and iodide. While the results of this study are pertinent to determining the specific interfacial reactivity of aqueous halides, these anions seldom transpire as single-halide systems in the natural environment. Therefore, we also provide an outlook on future research concerning surface potential methods and more complex aqueous electrolyte systems.

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.

Uncovering Differences in Hydration Free Energies and Structures for Model Compound Mimics of Charged Side Chains of Amino Acids

Free energies of hydration are of fundamental interest for modeling and understanding conformational and phase equilibria of macromolecular solutes in aqueous phases. Of particular relevance to systems such as intrinsically disordered proteins are the free energies of hydration and hydration structures of model compounds that mimic charged side chains of Arg, Lys, Asp, and Glu. Here, we deploy a Thermodynamic Cycle-based Proton Dissociation (TCPD) approach in conjunction with data from direct measurements to obtain estimates for the free energies of hydration for model compounds that mimic the side chains of Arg+, Lys+, Asp-, and Glu-. Irrespective of the choice made for the hydration free energy of the proton, the TCPD approach reveals clear trends regarding the free energies of hydration for Arg+, Lys+, Asp-, and Glu-. These trends include asymmetries between the hydration free energies of acidic (Asp- and Glu-) and basic (Arg+ and Lys+) residues. Further, the TCPD analysis, which relies on a combination of experimental data, shows that the free energy of hydration of Arg+ is less favorable than that of Lys+. We sought a physical explanation for the TCPD-derived trends in free energies of hydration. To this end, we performed temperature-dependent calculations of free energies of hydration and analyzed hydration structures from simulations that use the polarizable Atomic Multipole Optimized Energetics for Biomolecular Applications (AMOEBA) force field and water model. At 298 K, the AMOEBA model generates estimates of free energies of hydration that are consistent with TCPD values with a free energy of hydration for the proton of ca. -259 kcal/mol. Analysis of temperature-dependent simulations leads to a structural explanation for the observed differences in free energies of hydration of ionizable residues and reveals that the heat capacity of hydration is positive for Arg+ and Lys+ and negative for Asp- and Glu-.

Absolute ion hydration free energy scale and the surface potential of water via quantum simulation

With a goal of determining an absolute free energy scale for ion hydration, quasi-chemical theory and ab initio quantum mechanical simulations are employed to obtain an accurate value for the bulk hydration free energy of the Na⁺ ion. The free energy is partitioned into three parts: 1) the inner-shell or chemical contribution that includes direct interactions of the ion with nearby waters, 2) the packing free energy that is the work to produce a cavity of size λ in water, and 3) the long-range contribution that involves all interactions outside the inner shell. The interfacial potential contribution to the free energy resides in the long-range term. By averaging cation and anion data for that contribution, cumulant terms of all odd orders in the electrostatic potential are removed. The computed total is then the bulk hydration free energy. Comparison with the experimentally derived real hydration free energy produces an effective surface potential of water in the range -0.4 to -0.5 V. The result is consistent with a variety of experiments concerning acid-base chemistry, ion distributions near hydrophobic interfaces, and electric fields near the surface of water droplets.

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.

Molecular reactions at aqueous interfaces

This Review aims to critically analyse the emerging field of chemical reactivity at aqueous interfaces. The subject has evolved rapidly since the discovery of the so-called 'on-water catalysis', alluding to the dramatic acceleration of reactions at the surface of water or at its interface with hydrophobic media. We review critical experimental studies in the fields of atmospheric and synthetic organic chemistry, as well as related research exploring the origins of life, to showcase the importance of this phenomenon. The physico-chemical aspects of these processes, such as the structure, dynamics and thermodynamics of adsorption and solvation processes at aqueous interfaces, are also discussed. We also present the basic theories intended to explain interface catalysis, followed by the results of advanced ab initio molecular-dynamics simulations. Although some topics addressed here have already been the focus of previous reviews, we aim at highlighting their interconnection across diverse disciplines, providing a common perspective that would help us to identify the most fundamental issues still incompletely understood in this fast-moving field.

Prediction of Solvation Free Energies of Ionic Solutes in Neutral Solvents

The prediction of solvation free energies is essential for a variety of applications. Solvation free energies of neutral systems can be predicted quite accurately. The accuracy of predictions for solvation free energies of ionic solutes dissolved in neutral solvents, however, has been reported to be worse by at least 1 order of magnitude. In this study, the performance of three approaches for solvation free energy prediction of several hundred ions dissolved in neutral solvents is evaluated. The applied methods are COSMO-RS, cluster continuum model (CCM) together with COSMO-RS, and COSMO-RS-ES. It is emphasized that the reference data for model evaluation are subject to large uncertainties stemming from the impossibility to measure the so-called elusive absolute free energies of solvation of a single ion. Consequently, such uncertainty must be considered during the evaluation of prediction methods. Therefore, a straightforward approach to account for the underlying uncertainty is applied here. Hereby, it is revealed that the true performance of the method is better than what is often reported. The average absolute deviation (AAD) of COSMO-RS is calculated to be 2.3 kcal mol^-1, while applying the CCM and COSMO-RS-ES each results in AADs of 2.0 kcal mol^-1. This accuracy allows for qualitative assessment of solvation free energy-dependent quantities, such as reaction rate constants.

First-principles modeling of chemistry in mixed solvents: Where to go from here?

Mixed solvents (i.e., binary or higher order mixtures of ionic or nonionic liquids) play crucial roles in chemical syntheses, separations, and electrochemical devices because they can be tuned for specific reactions and applications. Apart from fully explicit solvation treatments that can be difficult to parameterize or computationally expensive, there is currently no well-established first-principles regimen for reliably modeling atomic-scale chemistry in mixed solvent environments. We offer our perspective on how this process could be achieved in the near future as mixed solvent systems become more explored using theoretical and computational chemistry. We first outline what makes mixed solvent systems far more complex compared to single-component solvents. An overview of current and promising techniques for modeling mixed solvent environments is provided. We focus on so-called hybrid solvation treatments such as the conductor-like screening model for real solvents and the reference interaction site model, which are far less computationally demanding than explicit simulations. We also propose that cluster-continuum approaches rooted in physically rigorous quasi-chemical theory provide a robust, yet practical, route for studying chemical processes in mixed solvents.

Hydration Mimicry by Membrane Ion Channels

Ions transiting biomembranes might pass readily from water through ion-specific membrane proteins if these protein channels provide environments similar to the aqueous solution hydration environment. Indeed, bulk aqueous solution is an important reference condition for the ion permeation process. Assessment of this hydration mimicry concept depends on understanding the hydration structure and free energies of metal ions in water in order to provide a comparison for the membrane channel environment. To refine these considerations, we review local hydration structures of ions in bulk water and the molecular quasi-chemical theory that provides hydration free energies. In doing so, we note some current views of ion binding to membrane channels and suggest new physical chemical calculations and experiments that might further clarify the hydration mimicry concept.

Electromechanics of the liquid water vapour interface

Two collective properties distinguishing the thin liquid water vapour interface from the bulk liquid are the anisotropy of the pressure tensor giving rise to surface tension and the orientational alignment of the molecules leading to a finite dipolar surface potential. Both properties can be regarded as capillary phenomena and are likely to be coupled. We have investigated this coupling by determining the response of the tangential component of the surface tension to the application of an electric field normal to the surface using finite field molecular dynamics simulations. We find an upside down parabola with a maximum shifted away from zero field. Comparing the molecular dynamics results to a phenomenological electromechanical model we relate the zero field derivative of the tangential part of the surface tension to the electrostatic potential generated by the spontaneous interface polarization. When interpreted with this model our simulations also indicate that Kelvin forces due to electric field gradients at a polarized interface play an important role in the effective dielectric response.

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.

Machine Learning-Guided Approach for Studying Solvation Environments

Molecular-level understanding and characterization of solvation environments are often needed across chemistry, biology, and engineering. Toward practical modeling of local solvation effects of any solute in any solvent, we report a static and all-quantum mechanics-based cluster-continuum approach for calculating single-ion solvation free energies. This approach uses a global optimization procedure to identify low-energy molecular clusters with different numbers of explicit solvent molecules and then employs the smooth overlap for atomic positions learning kernel to quantify the similarity between different low-energy solute environments. From these data, we use sketch maps, a nonlinear dimensionality reduction algorithm, to obtain a two-dimensional visual representation of the similarity between solute environments in differently sized microsolvated clusters. After testing this approach on different ions having charges 2+, 1+, 1-, and 2-, we find that the solvation environment around each ion can be seen to usually become more similar in hand with its calculated single-ion solvation free energy. Without needing either dynamics simulations or an a priori knowledge of local solvation structure of the ions, this approach can be used to calculate solvation free energies within 5% of experimental measurements for most cases, and it should be transferable for the study of other systems where dynamics simulations are not easily carried out.

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.

Aqueous Nanoclusters Govern Ion Partitioning in Dense Polymer Membranes

The uptake and sorption of charged molecules by responsive polymer membranes and hydrogels in aqueous solutions is of key importance for the development of soft functional materials. Here, we investigate the partitioning of simple monatomic (Na⁺, K⁺, Cs⁺, Cl^-, I^-) and one molecular ion (4-nitrophenolate; NP^-) within a dense, electroneutral poly(N-isopropylacrylamide) membrane using explicit-water molecular dynamics simulations. Inside the predominantly hydrophobic environment, water distributes in a network of polydisperse water nanoclusters. The average cluster size determines the mean electrostatic self-energy of the simple ions, which preferably reside deeply inside them; we therefore find substantially larger partition ratios K ≃10^-1 than expected from a simple Born picture using a uniform dielectric constant. Despite their irregular shapes, we observe that the water clusters possess a universal negative electrostatic potential with respect to their surroundings, as is known for aqueous liquid-vapor interfaces. This potential, which we find concealed in cases of symmetric monatomic salts, can dramatically impact the transfer free energies of larger charged molecules because of their weak hydration and increased affinity to interfaces. Consequently, and in stark contrast to the simple ions, the molecular ion NP^- can have a partition ratio much larger than unity, K ≃10-30 (depending on the cation type) or even 10³ in excess of monovalent salt, which explains recent observations of enhanced reaction kinetics of NP^- reduction catalyzed within dense polymer networks. These results also suggest that ionizing a molecule can even enhance the partitioning in a collapsed, rather hydrophobic gel, which strongly challenges the traditional simplistic reasoning.

Screening of Coulomb interactions in liquid dielectrics

The interaction of charges in dielectric materials is screened by the dielectric constant of the bulk dielectric. In dielectric theories, screening is assigned to surface charges appearing from preferential orientations of dipoles along the local field in the interface. For liquid dielectrics, such interfacial orientations are affected by the interfacial structure characterized by a separate interfacial dipolar susceptibility. We argue that dielectric properties of polar liquids should be characterized by two distinct susceptibilities responsible for local response (solvation) and long-range response (dielectric screening). A microscopic model for dipolar screening in polar liquids is developed here. It shows that the standard bulk dielectric constant is responsible for screening at large distances. The potential of mean force between ions in polar liquids becomes oscillatory at short distances. Oscillations arise from the coupling of collective longitudinal excitations (dipolarons) of the polar liquid with its interfacial density profile. Interfacial electrostatics demonstrates a crossover beyond the solute radius of  ∼1 nm from the scaling laws roughly consistent with continuum expectations for small solutes to new scaling trends characterizing the much softer nano-scale solute-solvent interface. This crossover also marks the transition to a continuum-type electrostatic screening between ions, when short-distance oscillation of the potential of mean force become strongly damped. Screening oscillations are enhanced for more structured interfaces.

Quasi-Chemical Theory with Cluster Sampling from Ab Initio Molecular Dynamics: Fluoride (F-) Anion Hydration

Accurate predictions of the hydration free energy for anions typically has been more challenging than that for cations. Hydrogen bond donation to the anion in hydrated clusters such as F(H₂O) _n ^- can lead to delicate structures. Consequently, the energy landscape contains many local minima, even for small clusters, and these minima present a challenge for computational optimization. Utilization of cluster experimental results for the free energies of gas-phase clusters shows that even though anharmonic effects are interesting they need not be of troublesome magnitudes for careful applications of quasi-chemical theory to ion hydration. Energy-optimized cluster structures for anions can leave the central ion highly exposed, and application of implicit solvation models to these structures can incur more serious errors than those for metal cations. Utilizing cluster structures sampled from ab initio molecular dynamics simulations substantially fixes those issues.

Probing the Ion-Specific Effects at the Water/Air Interface and Water-Mediated Ion Pairing in Sodium Halide Solution with Ab Initio Molecular Dynamics

The ion-specific effects at the water/air interface represent a fundamentally essential topic of research, and high-level ab initio simulations are still demanding to reveal the microscopic picture of the interactions between ions and water at the solvation interface. In this work, we present a fragment-based ab initio molecular dynamics (AIMD) simulation of sodium halide solution droplet (in a neutral mixture of Na⁺, F^-, Cl^-, and Br^- ions) at the MP2/aug-cc-pVDZ level. We show that the studied halide ions exhibit surface preference in the order (F^- < Cl^- < Br^-) which is in accordance with the experimental observation. The resulting potential of mean force (PMF) for Br^- produces a distinct minimum at the water/air interface, while the minimum of the PMF for F^- appears in the bulk region. The ion-pairing interactions between halide anions and Na⁺ cations are characterized, and it reveals that the specific solvent-separated ion pairs (SIPs) are more preferred than the direct contact ion pairs (CIPs). The transition between different types of SIPs is observed. Other structural and dynamical properties of ions and ion-hydration shells are investigated. These results provide broader and new physical insights for understanding the ion-specific behavior in interfacial solvation at the atomistic level.

Understanding the scale of the single ion free energy: A critical test of the tetra-phenyl arsonium and tetra-phenyl borate assumption

The tetra-phenyl arsonium and tetra-phenyl borate (TATB) assumption is a commonly used extra-thermodynamic assumption that allows single ion free energies to be split into cationic and anionic contributions. The assumption is that the values for the TATB salt can be divided equally. This is justified by arguing that these large hydrophobic ions will cause a symmetric response in water. Experimental and classical simulation work has raised potential flaws with this assumption, indicating that hydrogen bonding with the phenyl ring may favor the solvation of the TB^- anion. Here, we perform ab initio molecular dynamics simulations of these ions in bulk water demonstrating that there are significant structural differences. We quantify our findings by reproducing the experimentally observed vibrational shift for the TB^- anion and confirm that this is associated with hydrogen bonding with the phenyl rings. Finally, we demonstrate that this results in a substantial energetic preference of the water to solvate the anion. Our results suggest that the validity of the TATB assumption, which is still widely used today, should be reconsidered experimentally in order to properly reference single ion solvation free energy, enthalpy, and entropy.

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

The interactions between metal ions and proteins are ubiquitous in biology. The selective binding of metal ions has a variety of regulatory functions. Therefore, there is a need to understand the mechanism of protein-ion binding. The interactions involving metal ions are complicated in nature, where short-range charge-penetration, charge transfer, polarization, and many-body effects all contribute significantly, and a quantitative description of all these interactions is lacking. In addition, it is unclear how well current polarizable force fields can capture these energy terms and whether these polarization models are good enough to describe the many-body effects. In this work, two energy decomposition methods, absolutely localized molecular orbitals and symmetry-adapted perturbation theory, were utilized to study the interactions between Mg²⁺/Ca²⁺ and model compounds for amino acids. Comparison of individual interaction components revealed that while there are significant charge-penetration and charge-transfer effects in Ca complexes, these effects can be captured by the van der Waals (vdW) term in the AMOEBA force field. The electrostatic interaction in Mg complexes is well described by AMOEBA since the charge penetration is small, but the distance-dependent polarization energy is problematic. Many-body effects were shown to be important for protein-ion binding. In the absence of many-body effects, highly charged binding pockets will be over-stabilized, and the pockets will always favor Mg and thus lose selectivity. Therefore, many-body effects must be incorporated in the force field in order to predict the structure and energetics of metalloproteins. Also, the many-body effects of charge transfer in Ca complexes were found to be non-negligible. The absorption of charge-transfer energy into the additive vdW term was a main source of error for the AMOEBA many-body interaction energies.

Alchemical free energy calculations and umbrella sampling with local molecular field theory

Understanding the thermodynamic driving forces underlying any chemical process requires a description of the underlying free energy surface. However, computation of free energies is difficult, often requiring advanced sampling techniques. Moreover, these computations can be further complicated by the evaluation of any long-ranged interactions in the system of interest, such as Coulomb interactions in charged and polar media. Local molecular field theory is a promising approach to avoid many of the conceptual and computational difficulties associated with long-ranged interactions. We present frameworks for performing alchemical free energy calculations and non-Boltzmann sampling with local molecular field theory. We demonstrate that local molecular field theory can be used to perform these free energy calculations with accuracy comparable to traditional methodologies while eliminating the need for explicit treatment of long-ranged interactions in simulations.

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.

Mechanism of ion adsorption to aqueous interfaces: Graphene/water vs. air/water

The adsorption of ions to aqueous interfaces is a phenomenon that profoundly influences vital processes in many areas of science, including biology, atmospheric chemistry, electrical energy storage, and water process engineering. Although classical electrostatics theory predicts that ions are repelled from water/hydrophobe (e.g., air/water) interfaces, both computer simulations and experiments have shown that chaotropic ions actually exhibit enhanced concentrations at the air/water interface. Although mechanistic pictures have been developed to explain this counterintuitive observation, their general applicability, particularly in the presence of material substrates, remains unclear. Here we investigate ion adsorption to the model interface formed by water and graphene. Deep UV second harmonic generation measurements of the SCN^- ion, a prototypical chaotrope, determined a free energy of adsorption within error of that for air/water. Unlike for the air/water interface, wherein repartitioning of the solvent energy drives ion adsorption, our computer simulations reveal that direct ion/graphene interactions dominate the favorable enthalpy change. Moreover, the graphene sheets dampen capillary waves such that rotational anisotropy of the solute, if present, is the dominant entropy contribution, in contrast to the air/water interface.