Toward a quantitative theory of Hofmeister phenomena: From quantum effects to thermodynamics

Fluoride-Ion-Responsive Sol-Gel Transition in an L-Cysteine/AgNO3 System: Self-Assembly Peculiarities and Anticancer Activity

Supramolecular hydrogels based on low-molecular-weight compounds are a unique class of so-called "soft" materials, formed by weak non-covalent interactions between precursors at their millimolar concentrations. Due to the variety of structures that can be formed using different low-molecular-weight gelators, they are widely used in various fields of technology and medicine. In this study, we report for the first time an unusual self-assembly process of mixing a hydrosol obtained from L-cysteine and silver nitrate (cysteine-silver sol-CSS) with sodium halides. Modern instrumental techniques such as viscosimetry, UV spectroscopy, dynamic light scattering, zeta potential measurements, SEM and EDS identified that adding fluoride anions to CSS is able to form stable hydrogels of a thixotropic nature, while Cl-, Br- and I- lead to precipitation. The self-assembly process proceeds using a narrow concentration range of F-. An increase in the fluoride anion content in the system leads to a change in the gel network morphology from elongated structures to spherical ones. This fact is reflected in a decrease in the gel viscosity and a number of gel-sol-gel transition cycles. The mechanism of F-'s interaction with hydrosol includes the condensation of anions on the positive surface of the CSS nanoparticles, their binding via electrostatic forces and the formation of a resulting gel carcass. In vitro analysis showed that the hydrogels suppressed human squamous carcinoma cells at a micromolar sample concentration. The obtained soft gels could have potential applications against cutaneous malignancy and as carriers for fluoride anion and other bioactive substance delivery.

Multiparameter screen optimizes immunoprecipitation

Immunoprecipitation (IP) coupled with mass spectrometry effectively maps protein-protein interactions when genome-wide, affinity-tagged cell collections are used. Such studies have recorded significant portions of the compositions of physiological protein complexes, providing draft 'interactomes'; yet many constituents of protein complexes still remain uncharted. This gap exists partly because high-throughput approaches cannot optimize each IP. A key challenge for IP optimization is stabilizing in vivo interactions during the transfer from cells to test tubes; failure to do so leads to the loss of genuine interactions during the IP and subsequent failure to detect. Our high-content screening method explores the relationship between in vitro chemical conditions and IP outcomes, enabling rapid empirical optimization of conditions for capturing target macromolecular assemblies.

Rhamnolipid Self-Aggregation in Aqueous Media: A Long Journey toward the Definition of Structure–Property Relationships

The need to protect human and environmental health and avoid the widespread use of substances obtained from nonrenewable sources is steering research toward the discovery and development of new molecules characterized by high biocompatibility and biodegradability. Due to their very widespread use, a class of substances for which this need is particularly urgent is that of surfactants. In this respect, an attractive and promising alternative to commonly used synthetic surfactants is represented by so-called biosurfactants, amphiphiles naturally derived from microorganisms. One of the best-known families of biosurfactants is that of rhamnolipids, which are glycolipids with a headgroup formed by one or two rhamnose units. Great scientific and technological effort has been devoted to optimization of their production processes, as well as their physicochemical characterization. However, a conclusive structure–function relationship is far from being defined. In this review, we aim to move a step forward in this direction, by presenting a comprehensive and unified discussion of physicochemical properties of rhamnolipids as a function of solution conditions and rhamnolipid structure. We also discuss still unresolved issues that deserve further investigation in the future, to allow the replacement of conventional surfactants with rhamnolipids.

Carboxylate binding prefers two cations to one

Almost all studies of specific ion binding by carboxylates (-COO^-) have considered only a single cation, but clustering of ions and ligands is a common phenomenon. We apply density functional theory to investigate how variations in the number of acetate ligands in binding to two monovalent cations affects ion binding preferences. We study a series of monovalent (Li⁺, Na⁺, K⁺, Cs⁺) ions relevant to experimental work on many topics, including ion channels, battery storage, water purification and solar cells. We find that the preferred optimal structure has 3 acetates except for Cs⁺, which has 2 acetates. The optimal coordination of the cation by the carboxylate O atoms is 4 for both Na⁺ and K⁺, and 3 for Li⁺ and Cs⁺. There is a 4-fold coordination minimum just a few kcal mol^-1 higher than the optimal 3-fold structure for Li⁺. For two cations, multiple minima occur in the vicinity of the lowest free energy state. We find that, for Li, Na and K, the preferred optimal structure with two cations is favored over a mixture of single cation complexes, providing a basis for understanding ionic cluster formation that is relevant for engineering proteins and other materials for rapid, selective ion transport.

Hydrated Anions: From Clusters to Bulk Solution with Quasi-Chemical Theory

The interactions of hydrated ions with molecular and macromolecular solution and interface partners are strong on a chemical energy scale. Here, we recount the foremost ab initio theory for the evaluation of the hydration free energies of ions, namely, quasi-chemical theory (QCT). We focus on anions, particularly halides but also the hydroxide anion, because they have been outstanding challenges for all theories. For example, this work supports understanding the high selectivity for F^- over Cl^- in fluoride-selective ion channels despite the identical charge and the size similarity of these ions. QCT is built by the identification of inner-shell clusters, separate treatment of those clusters, and then the integration of those results into the broader-scale solution environment. Recent work has focused on a close comparison with mass-spectrometric measurements of ion-hydration equilibria. We delineate how ab initio molecular dynamics (AIMD) calculations on ion-hydration clusters, elementary statistical thermodynamics, and electronic structure calculations on cluster structures sampled from the AIMD calculations obtain just the free energies extracted from the cluster experiments. That theory-experiment comparison has not been attempted before the work discussed here, but the agreement is excellent with moderate computational effort. This agreement reinforces both theory and experiment and provides a numerically accurate inner-shell contribution to QCT. The inner-shell complexes involving heavier halides display strikingly asymmetric hydration clusters. Asymmetric hydration structures can be problematic for the evaluation of the QCT outer-shell contribution with the polarizable continuum model (PCM). Nevertheless, QCT provides a favorable setting for the exploitation of PCM when the inner-shell material shields the ion from the outer solution environment. For the more asymmetrically hydrated, and thus less effectively shielded, heavier halide ions clustered with waters, the PCM is less satisfactory. We therefore investigate an inverse procedure in which the inner-shell structures are sampled from readily available AIMD calculations on the bulk solutions. This inverse procedure is a remarkable improvement; our final results are in close agreement with a standard tabulation of hydration free energies, and the final composite results are independent of the coordination number on the chemical energy scale of relevance, as they should be. Finally, a comparison of anion hydration structure in clusters and bulk solutions from AIMD simulations emphasize some differences: the asymmetries of bulk solution inner-shell structures are moderated compared with clusters but are still present, and inner hydration shells fill to slightly higher average coordination numbers in bulk solution than in clusters.

Understanding specific ion effects and the Hofmeister series

Specific ion effects (SIE), encompassing the Hofmeister Series, have been known for more than 130 years since Hofmeister and Lewith's foundational work. SIEs are ubiquitous and are observed across the medical, biological, chemical and industrial sciences. Nevertheless, no general predictive theory has yet been able to explain ion specificity across these fields; it remains impossible to predict when, how, and to what magnitude, a SIE will be observed. In part, this is due to the complexity of real systems in which ions, counterions, solvents and cosolutes all play varying roles, which give rise to anomalies and reversals in anticipated SIEs. Herein we review the historical explanations for SIE in water and the key ion properties that have been attributed to them. Systems where the Hofmeister series is perturbed or reversed are explored, as is the behaviour of ions at the liquid-vapour interface. We discuss SIEs in mixed electrolytes, nonaqueous solvents, and in highly concentrated electrolyte solutions - exciting frontiers in this field with particular relevance to biological and electrochemical applications. We conclude the perspective by summarising the challenges and opportunities facing this SIE research that highlight potential pathways towards a general predictive theory of SIE.

The electrostatic origins of specific ion effects: quantifying the Hofmeister series for anions

Life as we know it is dependent upon water, or more specifically salty water. Without dissolved ions, the interactions between biological molecules are insufficiently complex to support life. This complexity is intimately tied to the variation in properties induced by the presence of different ions. These specific ion effects, widely known as Hofmeister effects, have been known for more than 100 years. They are ubiquitous throughout the chemical, biological and physical sciences. The origin of these effects and their relative strengths is still hotly debated. Here we reconsider the origins of specific ion effects through the lens of Coulomb interactions and establish a foundation for anion effects in aqueous and non-aqueous environments. We show that, for anions, the Hofmeister series can be explained and quantified by consideration of site-specific electrostatic interactions. This can simply be approximated by the radial charge density of the anion, which we have calculated for commonly reported ions. This broadly quantifies previously unpredictable specific ion effects, including those known to influence solution properties, virus activities and reaction rates. Furthermore, in non-aqueous solvents, the relative magnitude of the anion series is dependent on the Lewis acidity of the solvent, as measured by the Gutmann Acceptor Number. Analogous SIEs for cations bear limited correlation with their radial charge density, highlighting a fundamental asymmetry in the origins of specific ion effects for anions and cations, due to competing non-Coulombic phenomena.

Current Topics in Ionic Liquid Crystals

Ionic liquid crystals (ILCs), that is, ionic liquids exhibiting mesomorphism, liquid crystalline phases, and anisotropic properties, have received intense attention in the past years. Among others, this is due to their special properties arising from the combination of properties stemming from ionic liquids and from liquid crystalline arrangements. Besides interesting fundamental aspects, ILCs have been claimed to have tremendous application potential that again arises from the combination of properties and architectures that are not accessible otherwise, or at least not accessible easily by other strategies. The current review highlights recent developments in ILC research, starting with some key fundamental aspects. Further subjects covered include the synthesis and variations of modern ILCs, including the specific tuning of their mesomorphic behavior. The review concludes with reflections on some applications that may be within reach for ILCs and finally highlights a few key challenges that must be overcome prior and during true commercialization of ILCs.

Condensed Phase Water Molecular Multipole Moments from Deep Neural Network Models Trained on Ab Initio Simulation Data

Ionic solvation phenomena in liquids involve intense interactions in the inner solvation shell. For interactions beyond the first shell, the ion-solvent interaction energies result from the sum of many smaller-magnitude contributions that can still include polarization effects. Deep neural network (DNN) methods have recently found wide application in developing efficient molecular models that maintain near-quantum accuracy. Here we extend the DeePMD-kit code to produce accurate molecular multipole moments in the bulk and near interfaces. The new method is validated by comparing the DNN moments with those generated by ab initio simulations. The moments are used to compute the electrostatic potential at the center of a molecular-sized hydrophobic cavity in water. The results show that the fields produced by the DNN models are in quantitative agreement with the AIMD-derived values. These efficient methods will open the door to more accurate solvation models for large solutes such as proteins.

Free Energies of Hydrated Halide Anions: High Through-Put Computations on Clusters to Treat Rough Energy-Landscapes

With a longer-term goal of addressing the comparative behavior of the aqueous halides F−, Cl−, Br−, and I− on the basis of quasi-chemical theory (QCT), here we study structures and free energies of hydration clusters for those anions. We confirm that energetically optimal (H2O)nX clusters, with X = Cl−, Br−, and I−, exhibit surface hydration structures. Computed free energies, based on optimized surface hydration structures utilizing a harmonic approximation, typically (but not always) disagree with experimental free energies. To remedy the harmonic approximation, we utilize single-point electronic structure calculations on cluster geometries sampled from an AIMD (ab initio molecular dynamics) simulation stream. This rough-landscape procedure is broadly satisfactory and suggests unfavorable ligand crowding as the physical effect addressed. Nevertheless, this procedure can break down when n≳4, with the characteristic discrepancy resulting from a relaxed definition of clustering in the identification of (H2O)nX clusters, including ramified structures natural in physical cluster theories. With ramified structures, the central equation for the present rough-landscape approach can acquire some inconsistency. Extension of these physical cluster theories in the direction of QCT should remedy that issue, and should be the next step in this research direction.

The many-body expansion for aqueous systems revisited: III. Hofmeister ion-water interactions

We report a Many Body Energy (MBE) analysis of aqueous ionic clusters containing anions and cations at the two opposite ends of the Hofmeister series, viz. the kosmotropes Ca²⁺ and SO₄^2- and the chaotropes NH₄⁺ and ClO₄^-, with 9 water molecules to quantify how these ions alter the interaction between the water molecules in their immediate surroundings. We specifically aim at quantifying how various ions (depending on their position in the Hofmeister series) affect the interaction between the surrounding water molecules and probe whether there is a qualitatively different behavior between kosmotropic vs. chaotropic ions. The current results when compared to the ones reported earlier for water clusters [J. P. Heindel and S. S. Xantheas, J. Chem. Theor. Comput., 2020, 16, 6843-6855] as well as for alkali metal and halide ion aqueous clusters of the same size [J. P. Heindel and S. S. Xantheas, J. Chem. Theor. Comput., 2021, 17, 2200-2216], which lie in the middle of the Hofmeister series, offer a complete account of the effect an ion across the Hofmeister series from "kosmotropes" to "chaotropes" has on the interaction between the neighboring water molecules. Through this analysis, noteworthy differences between the MBE of kosmotropes and chaotropes were identified. The MBE of kosmotropes is dominated by ion-water interactions that extend beyond the 4-body term, the rank at which the MBE of pure water converges. The percentage contribution of the 2-B term to the total cluster binding energy is noticeably larger. The disruption of the hydrogen bonded network due to the dominant ion-water interactions results in weak, unfavorable water-water interactions. The MBE for chaotropes, on the other hand, was found to converge more quickly as it more closely resembles that of pure water clusters. Chaotropes exhibit weaker overall binding energies and weaker ion-water interactions in favor of water-water interactions, somewhat recovering the pattern of the 2-4 body terms exemplified by pure water clusters. A remarkable anti-correlation between the 2-B ion-water (I-W) and water-water (W-W) interactions as well as between the 3-B (I-W-W) and (I-W) interactions was found for both kosmotropic and chaotropic ions. This anti-correlation is linear for both monatomic anions and monatomic cations, suggesting the existence of underlying physical mechanisms that were previously unexplored. The consideration of two different structural arrangements (ion inside and outside of a water cluster) suggests that fully solvated (ion inside) chaotropes disrupt the hydrogen bonding network in a similar manner to partially solvated (ion outside) kosmotropes and offers useful insights into the modeling requirements of bulk vs. interfacial ion solvation. It is noteworthy that the 2-B contribution to the total Basis Set Superposition Error (BSSE) correction for both kosmotropic and chaotropic ions follows the universal erf profile vs. intermolecular distance previously reported for pure water, halide ion-water and alkali metal ion-water clusters. When scaled for the corresponding dimer energies and distances, a single profile fits the current results together with all previously reported ones for pure water and halide water clusters. This finding lends further support to schemes for accurately estimating the 2-B BSSE correction in condensed environments.

Weak Anion Binding to Poly(N-isopropylacrylamide) Detected by Electrophoretic NMR

Ion specific effects are ubiquitous in solutions and govern a large number of colloidal phenomena. To date, a substantial and sustained effort has been directed at understanding the underlying molecular interactions. As a new approach, we address this issue by sensitive 1H NMR methods that measure the electrophoretic mobility and the self-diffusion coefficient of poly(N-isopropylacrylamide) (PNIPAM) chains in bulk aqueous solution in the presence of salts with the anion component varied from kosmotropes to chaotropes along the Hofmeister series. The accuracy of the applied electrophoretic NMR experiments is exceptionally high, on the order of 10-10 m2/(V s), corresponding to roughly 10-4 elementary charges per monomer effectively associated with the neutral polymer. We find that chaotropic anions associate to PNIPAM with an apparent Langmuir-type saturation behavior. The polymer chains remain extended upon ion association, and momentum transfer from anion to polymer is only partial which indicates weak attractive short-range forces between anion and polymer and, thereby and in contrast to some other ion-polymer systems, the lack of well-defined binding sites.

Quantum Simulations of Hydrogen Bonding Effects in Glycerol Carbonate Electrolyte Solutions

The need for environmentally friendly nonaqueous solvents in electrochemistry and other fields has motivated recent research into the molecular-level solvation structure, thermodynamics, and dynamics of candidate organic liquids. In this paper, we present the results of quantum density functional theory simulations of glycerol carbonate (GC), a molecule that has been proposed as a solvent for green industrial chemistry, nonaqueous alternatives for biocatalytic reactions, and liquid media in energy storage devices. We investigate the structure and dynamics of both the pure GC liquid and electrolyte solutions containing KF and KCl ion pairs. These simulations reveal the importance of hydrogen bonding that controls the structural and dynamic behavior of the pure liquid and ion association in the electrolyte solutions. The results illustrate the difficulties associated with classical modeling of complex organic solvents. The simulations lead to a better understanding of the underlying mechanisms behind the previously observed peculiar ion-specific behavior in GC electrolyte solutions.

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.

Hofmeister Effect in Self-Organized Chemical Systems

We studied the effect of spectator ions in the prototype of far-from-equilibrium self-organized chemical systems, the Belousov-Zhabotinsky (BZ) reaction. In particular, we investigated the specific ion effect of alkali metal cations, connoted for their kosmotropic and chaotropic properties. By means of combined experimental and numerical approaches, we could show a neat and robust evidence for the Hofmeister effect in this system. Spectator cations induce a marked increment of the induction period that preludes regular oscillations and decrease the oscillation amplitude following the sequence Li⁺ < Na⁺ ≪ K⁺ ∼ Cs⁺. These ions affect the system kinetics by interfering in the interaction between the oxidized form of the catalyst and the organic substrate, responsible for resetting the BZ system to pre-autocatalytic (reduced) conditions. The specific ion effect on these key reactive steps is systematically characterized and correlated with different parameters which describe the interaction of the cations with the solvent.

Specific Ion Effects on the Colloidal Stability of Layered Double Hydroxide Single-layer Nanosheets

The surface charge properties and aggregation behavior of positively charged Mg-Al-NO₃ layered double hydroxide (LDH) single-layer nanosheets dispersed in water were investigated in the presence of K⁺ salts with different mono-, di-, and trivalent anions, using electrophoresis and dynamic light scattering techniques. An increase in the salt concentration can significantly decrease the effective surface charge density (σ_eff) of LDHs, leading to the aggregation of nanosheets. The critical coagulation concentration (CCC) or ionic strength (CCIS) of salts for nanosheets significantly decreases with an increase in the valence of anions. Specific ion effects, with a partially reverse Hofmeister series, are observed. On the basis of the Stern model and the DLVO theory, the relationship of CCC with σ_eff and the ionic valences of salts (z_i) is theoretically analyzed, which can accurately describe the dependence of CCC on the σ_eff and z_i but cannot explain the origin of specific ion effects. To explore the origin of specific ion effects, a correlation between CCIS and the specific adsorption energy (E_sc) of anions within the Stern layer is developed. Especially, an empirical relationship of E_sc with the characteristic physical parameters of anions is proposed. Our model can accurately predict the CCISs of at least monovalent anions and divalent anions (CO₃^2- and SO₄^2-), demonstrating that the specific ion effects observed can be attributed to the differences in ionic size, polarizability, and hydration free energy (or the formation capacity of anion-cation pairs) of different anions. This work not only deepens the understanding of specific ion effects on the colloidal stability but also provides useful information for the potential applications of LDH single-layer nanosheets.

Deep Undercooling of Aqueous Droplets on a Superhydrophobic Surface: The Specific Role of Cation Hydration

An extraordinary prolonged freezing delay was detected for the first time for deeply undercooled sessile droplets of aqueous solutions of alkali metal chlorides deposited onto a superhydrophobic surface. Accounting for the variation in the hydration energy of ions, their distribution in the vicinity of charged interfaces of solution/air and solution/superhydrophobic surface allows qualitative description of the observed ice nucleation kinetics and ionic specificity in freezing phenomena.

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.

An effective partial charge model for bulk and surface properties of cubic ZrO2, Y2O3 and yttrium-stabilised zirconia

In this work a newly parametrised Coulomb plus Buckingham potential formulation for cubic ZrO₂, Y₂O₃ and yttrium-stabilised zirconia (YSZ) is presented. The density and pair distributions obtained for neat ZrO₂ and Y₂O₃ under ambient conditions are in excellent agreement with experimental data, while the vibrational power spectra are highly similar compared to those obtained via ab initio molecular dynamics simulations at the PBEsol level. In addition, it is shown that the use of effective partial charges has several advantages compared to interaction potentials employing the oxidation states in the evaluation of the coulombic interactions: (i) the diffusion coefficient and the associated activation energy of oxygen ions evaluated for YSZn (n = 4 to 12) display the best agreement with experimental data; (ii) no unphysical reorganisation of the interface and the bulk are observed in simulations of the (110) and (111) surfaces of cubic ZrO₂ and Y₂O₃, while due to the strong coulombic contributions in the case of the tested full-charge models a pronounced restructuring of the interface and the bulk is observed in the ZrO₂ case, and (iii) the use of effective partial charges ensures compatibility with existing solvent models and force-fields for the treatment of molecular compounds.

Hofmeister Effects of Monovalent Sodium Salts in the Gelation Kinetics of Gelatin

The gelation kinetics of gelatin depends on the presence of electrolytes, and the influence of cations with variable valency has been recently emphasized. However, acquired knowledge shows that the nature of anions has more influence on various properties of aqueous solutions than the nature of the cations. It is shown herein, using sodium salts of monovalent anions, that the gelation kinetics of gelatin is accelerated by the presence of highly kosmotropic anions like fluoride and strongly slowed, eventually inhibited, by the presence of chaotropic anions like thiocyanate and perchlorate. Overall the parameter characterizing the gelation kinetics, k, is a linear function of the polarizability of the used salt in aqueous solution, which has been quantified independently by refractometry and using the Lorentz-Lorenz formula. It is also found that the same parameter characterizing the gelation kinetics is a linear function of the viscosity B coefficient taken from the literature. The linear correlation coefficients are excellent in the case of halide anions (F^-, Cl^-, Br^-, I^-) but poorer when nonspherical anions like NO₃^-, SCN^-, and ClO₄^- are considered.

Molecular Dynamics Simulations of Ionic Liquids and Electrolytes Using Polarizable Force Fields

Many applications in chemistry, biology, and energy storage/conversion research rely on molecular simulations to provide fundamental insight into structural and transport properties of materials with high ionic concentrations. Whether the system is comprised entirely of ions, like ionic liquids, or is a mixture of a polar solvent with a salt, e.g., liquid electrolytes for battery applications, the presence of ions in these materials results in strong local electric fields polarizing solvent molecules and large ions. To predict properties of such systems from molecular simulations often requires either explicit or mean-field inclusion of the influence of polarization on electrostatic interactions. In this manuscript, we review the pros and cons of different treatments of polarization ranging from the mean-field approaches to the most popular explicit polarization models in molecular dynamics simulations of ionic materials. For each method, we discuss their advantages and disadvantages and emphasize key assumptions as well as their adjustable parameters. Strategies for the development of polarizable models are presented with a specific focus on extracting atomic polarizabilities. Finally, we compare simulations using polarizable and nonpolarizable models for several classes of ionic systems, discussing the underlying physics that each approach includes or ignores, implications for implementation and computational efficiency, and the accuracy of properties predicted by these methods compared to experiments.

Single-Ion Thermodynamics from First Principles: Calculation of the Absolute Hydration Free Energy and Single-Electrode Potential of Aqueous Li+ Using ab Initio Quantum Mechanical/Molecular Mechanical Molecular Dynamics Simulations

A recently proposed thermodynamic integration (TI) approach formulated in the framework of quantum mechanical/molecular mechanical molecular dynamics (QM/MM MD) simulations is applied to study the structure, dynamics, and absolute intrinsic hydration free energy Δ_s G_M⁺,wat^◦ of the Li⁺ ion at a correlated ab initio level of theory. Based on the results, standard values (298.15 K, ideal gas at 1 bar, ideal solute at 1 molal) for the absolute intrinsic hydration free energy [Formula: see text] of the proton, the surface electric potential jump χ_wat^◦ upon entering bulk water, and the absolute single-electrode potential [Formula: see text] of the reference hydrogen electrode are calculated to be -1099.9 ± 4.2 kJ·mol^-1, 0.13 ± 0.08 V, and 4.28 ± 0.04 V, respectively, in excellent agreement with the standard values recommended by Hünenberger and Reif on the basis of an extensive evaluation of the available experimental data (-1100 ± 5 kJ·mol^-1, 0.13 ± 0.10 V, and 4.28 ± 0.13 V). The simulation results for Li⁺ are also compared to those for Na⁺ and K⁺ from a previous study in terms of relative hydration free energies ΔΔ_s G_M⁺,wat^◦ and relative electrode potentials [Formula: see text]. The calculated values are found to agree extremely well with the experimental differences in standard conventional hydration free energies ΔΔ_s G_M⁺,wat^• and redox potentials [Formula: see text]. The level of agreement between simulation and experiment, which is quantitative within error bars, underlines the substantial accuracy improvement achieved by applying a highly demanding QM/MM approach at the resolution-of-identity second-order Møller-Plesset perturbation (RIMP2) level over calculations relying on purely molecular mechanical or density functional theory (DFT) descriptions. A detailed analysis of the structural and dynamical properties of the Li⁺ hydrate indicates that a correct description of the solvation structure and dynamics is achieved as well at this level of theory. Consideration of the QM/MM potential-energy components also shows that the partitioning into QM and MM zones does not induce any significant energetic artifact for the system considered.

Volcano Plots Emerge from a Sea of Nonaqueous Solvents: The Law of Matching Water Affinities Extends to All Solvents

The properties of all electrolyte solutions, whether the solvent is aqueous or nonaqueous, are strongly dependent on the nature of the ions in solution. The consequences of these specific-ion effects are significant and manifest from biochemistry to battery technology. The "law of matching water affinities" (LMWA) has proven to be a powerful concept for understanding and predicting specific-ion effects in a wide range of systems, including the stability of proteins and colloids, solubility, the behavior of lipids, surfactants, and polyelectrolytes, and catalysis in water and ionic liquids. It provides a framework for considering how the ions of an electrolyte interact in manifestations of ion specificity and therefore represents a considerable conceptual advance on the Hofmeister or lyotropic series in understanding specific-ion effects. Underpinning the development of the law of matching water affinities were efforts to interpret the so-called "volcano plots". Volcano plots exhibit a stark inverted "V" shape trend for a range of electrolyte dependent solution properties when plotted against the difference in solvation energies of the ions that constitute the electrolyte. Here we test the hypothesis that volcano plots are also manifest in nonaqueous solvents in order to investigate whether the LMWA can be extended to nonaqueous solvents. First we examine the standard solvation energies of electrolytes in nonaqueous solvents for evidence of volcano trends and then extend this to include the solubility and the activity/osmotic coefficients of electrolytes, in order to explore real electrolyte concentrations. We find that with respect to the solvent volcano trends are universal, which brings into question the role of solvent affinity in the manifestation of specific-ion effects. We also show that the volcano trends are maintained when the ionic radii are used in place of the absolute solvation energies as the abscissa, thus showing that ion sizes, rather than the solvent affinities, fundamentally determine the manifestation of ion specificity. This leads us to propose that specific-ion effects across all solvents including water can be understood by considering the relative sizes of the anion and cation, provided the ions are spherical or tetrahedral. This is an extension of the LMWA to all solvents in which the "water affinity" is replaced with the relative size of the anion and cation.

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.

Quasi-chemical theory of F-(aq): The "no split occupancies rule" revisited

We use ab initio molecular dynamics (AIMD) calculations and quasi-chemical theory (QCT) to study the inner-shell structure of F^-(aq) and to evaluate that single-ion free energy under standard conditions. Following the "no split occupancies" rule, QCT calculations yield a free energy value of -101 kcal/mol under these conditions, in encouraging agreement with tabulated values (-111 kcal/mol). The AIMD calculations served only to guide the definition of an effective inner-shell constraint. QCT naturally includes quantum mechanical effects that can be concerning in more primitive calculations, including electronic polarizability and induction, electron density transfer, electron correlation, molecular/atomic cooperative interactions generally, molecular flexibility, and zero-point motion. No direct assessment of the contribution of dispersion contributions to the internal energies has been attempted here, however. We anticipate that other aqueous halide ions might be treated successfully with QCT, provided that the structure of the underlying statistical mechanical theory is absorbed, i.e., that the "no split occupancies" rule is recognized.

Experimentally quantifying anion polarizability at the air/water interface

The adsorption of large, polarizable anions from aqueous solution on the air/water interface controls important atmospheric chemistry and is thought to resemble anion adsorption at hydrophobic interfaces generally. While the favourability of adsorption of such ions is clear, quantifying adsorption thermodynamics has proven challenging because it requires accurate description of the structure of the anion and its solvation shell at the interface. In principle anion polarizability offers a structural window, but to the best of our knowledge there has so far been no experimental technique that allowed its characterization with interfacial specificity. Here, we meet this challenge using interface-specific vibrational spectroscopy of Cl–O vibrations of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{ClO}}_4^ -$$\end{document}ClO4- anion at the air/water interface and report that the interface breaks the symmetry of the anion, the anisotropy of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{ClO}}_4^ -$$\end{document}ClO4-’s polarizability tensor is more than two times larger than in bulk water and concentration dependent, and concentration-dependent polarizability changes are consistent with correlated changes in surface tension.

Understanding anion-specific interactions with hydrophobic interfaces is challenging due to an absence of local structural probes. Here, the authors experimentally quantify the anisotropy of perchlorate’s polarizability at the air/water interface, a window into anion and solvation shell structure.

Ion-induced alterations of the local hydration environment elucidate Hofmeister effect in a simple classical model of Trp-cage miniprotein

Protein stability is known to be influenced by the presence of Hofmeister active ions in the solution. In addition to direct ion-protein interactions, this influence manifests through the local alterations of the interfacial water structure induced by the anions and cations present in this region. In our earlier works it was pointed out that the effects of Hofmeister active salts on the stability of Trp-cage miniprotein can be modeled qualitatively using non-polarizable force fields. These simulations reproduced the structure-stabilization and structure-destabilization effects of selected kosmotropic and chaotropic salts, respectively. In the present study we use the same model system to elucidate atomic processes behind the chaotropic destabilization and kosmotropic stabilization of the miniprotein. We focus on changes of the local hydration environment of the miniprotein upon addition of NaClO₄ and NaF salts to the solution. The process is separated into two parts. In the first, 'promotion' phase, the protein structure is fixed, and the local hydration properties induced by the simultaneous presence of protein and ions are investigated, with a special focus on the interaction of Hofmeister active anions with the charged and polar sites. In the second, 'rearrangement' phase we follow changes of the hydration of ions and the protein, accompanying the conformational relaxation of the protein. We identify significant factors of an enthalpic and entropic nature behind the ion-induced free energy changes of the protein-water system, and also propose a possible atomic mechanism consistent with the Collins's rule, for the chaotropic destabilization and kosmotropic stabilization of protein conformation.

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.

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

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

Hofmeister Effect on PNIPAM in Bulk and at an Interface: Surface Partitioning of Weakly Hydrated Anions

The effect of sodium fluoride, sodium trichloroacetate, and sodium thiocyanate on the stability and conformation of poly(N-isopropylacrylamide), in bulk solution and at the gold-aqueous interface, is investigated by differential scanning calorimetry, dynamic light scattering, quartz crystal microbalance, and atomic force microscopy. The results indicate a surface partitioning of the weakly hydrated anions, i.e., thiocyanate and trichloroacetate, and the findings are discussed in terms of anion-induced electrostatic stabilization. Although attractive polymer-ion interactions are suggested for thiocyanate and trichloroacetate, a salting-out effect is found for sodium trichloroacetate. This apparent contradiction is explained by a combination of previously suggested mechanisms for the salting-out effect by weakly hydrated anions.

Room-temperature NaI/H2O compression icing: solute–solute interactions

H–O bond energy governs the P_Cx for Na/H₂O liquid–VI–VII phase transition. Solute concentration affects the path of phase transitions differently with the solute type. Solute–solute interaction lessens the P_C2 sensitivity to compression. The P_C1 goes along the liquid–VI boundary till the triple phase joint.