Dispersion self-free energies and interaction free energies of finite-sized ions in salt solutions

The role for many-body dipolar (dispersion) potentials in ion-solvent and ion-solvent-interface interactions is explored. Such many-body potentials, accessible in principle from measured dielectric data, are necessary in accounting for Hofmeister specific ion effects. Dispersion self-energy is the quantum electrodynamic analogue of the Born electrostatic self-energy of an ion. We here describe calculations of dispersion self-free energies of four different anions (OH-, Cl-, Br-, and I-) that take finite ion size into account. Three different examples of self-free energy calculations are presented. These are the self-free energy of transfer of an ion to bulk solution, which influences solubility; the dispersion potential acting between one ion and an air-water interface (important for surface tension calculations); and the dispersion potential acting between two ions (relevant to activity coefficient calculations). To illustrate the importance of dispersion self-free energies, we compare the Born and dispersion contributions to the free energy of ion transfer from water to air (oil). We have also calculated the change in interfacial tension with added salt for air (oil)-water interfaces. A new model is used that includes dispersion potentials acting on the ions near the interface, image potentials, and ions of finite size that are allowed to spill over the solution-air interface. It is shown that interfacial free energies require a knowledge of solvent profiles at the interface.     

Ion specific surface forces between membrane surfaces

Entities such as ion distributions and forces between lipid membranes depend on effects due to the intervening salt solution that have not been recognized previously. These specific ion or Hofmeister effects influence membrane fusion. A typical illustrative example is this: measurements of forces between double-chained cationic bilayers adsorbed onto molecularly smooth mica surfaces across different 0.6-2 mM salt solutions have revealed a large degree of ion specificity [Pashley et al. J. Phys. Chem. 1986, 90, 1637]. This has been interpreted in terms of very specific anion "binding" to the adsorbed bilayers, as it would too for micelles and other self-assembled systems. However, we show here that inclusion of nonelectrostatic (NES) or ionic dispersion potentials acting between ions and the two surfaces explains such "ion binding". The observed Hofmeister sequence for the calculated pressure without any direct ion binding is given correctly. This demonstrates the importance of a source of ion specificity that has been ignored. It is due to ionic physisorption caused by attractive NES ionic dispersion potentials. There appear to be some far reaching consequences for interpretations of membrane intermolecular interactions in salt solutions.     

Effects of ion solvation on phase equilibrium and interfacial tension of liquid mixtures

We study the bulk thermodynamics and interfacial properties of electrolyte solution mixtures by accounting for electrostatic interaction, ion solvation, and inhomogeneity in the dielectric medium in the mean-field framework. Difference in the solvation energy between the cations and anions is shown to give rise to local charge separation near the interface, and a finite Galvani potential between two coexisting solutions. The ion solvation affects the phase equilibrium of the solvent mixture, depending on the dielectric constants of the solvents, reflecting the competition between the solvation energy and translation entropy of the ions. Miscibility is decreased if both solvents have low dielectric constants and is enhanced if both solvents have high dielectric constant. At the mean-field level, the ion distribution near the interface is determined by two competing effects: accumulation in the electrostatic double layer and depletion in a diffuse interface. The interfacial tension shows a nonmonotonic dependence on the salt concentration: it increases linearly with the salt concentration at higher concentrations and decreases approximately as the square root of the salt concentration for dilute solutions, reaching a minimum near 1 mM. We also find that, for a fixed cation type, the interfacial tension decreases as the size of anion increases. These results offer qualitative explanations within one unified framework for the long-known concentration and ion size effects on the interfacial tension of electrolyte solutions.     

Hofmeister effects: interplay of hydration, nonelectrostatic potentials, and ion size

The classical Derjaguin-Landau-Verwey-Overbeek (DLVO) theory of colloids, and corresponding theories of electrolytes, are unable to explain ion specific forces between colloidal particles quantitatively. The same is true generally, for surfactant aggregates, lipids, proteins, for zeta and membrane potentials and in adsorption phenomena. Even with fitting parameters the theory is not predictive. The classical theories of interactions begin with continuum solvent electrostatic (double layer) forces. Extensions to include surface hydration are taken care of with concepts like inner and outer Helmholtz planes, and "dressed" ion sizes. The opposing quantum mechanical attractive forces (variously termed van der Waals, Hamaker, Lifshitz, dispersion, nonelectrostatic forces) are treated separately from electrostatic forces. The ansatz that separates electrostatic and quantum forces can be shown to be thermodynamically inconsistent. Hofmeister or specific ion effects usually show up above ≈10(-2) molar salt. Parameters to accommodate these in terms of hydration and ion size had to be invoked, specific to each case. Ionic dispersion forces, between ions and solvent, for ion-ion and ion-surface interactions are not explicit in classical theories that use "effective" potentials. It can be shown that the missing ionic quantum fluctuation forces have a large role to play in specific ion effects, and in hydration. In a consistent predictive theory they have to be included at the same level as the nonlinear electrostatic forces that form the skeletal framework of standard theory. This poses a challenge. The challenges go further than academic theory and have implications for the interpretation and meaning of concepts like pH, buffers and membrane potentials, and for their experimental interpretation. In this article we overview recent quantitative developments in our evolving understanding of the theoretical origins of specific ion, or Hofmeister effects. These are demonstrated through an analysis that incorporates nonelectrostatic ion-surface and ion-ion dispersion interactions. This is based on ab initio ionic polarisabilities, and finite ion sizes quantified through recent ab initio work. We underline the central role of ionic polarisabilities and of ion size in the nonelectrostatic interactions that involve ions, solvent molecules and interfaces. Examples of mechanisms through which they operate are discussed in detail. An ab initio hydration model that accounts for polarisabilities of the tightly held hydration shell of "cosmotropic" ions is introduced. It is shown how Hofmeister effects depend on an interplay between specific surface chemistry, surface charge density, pH, buffer, and counterion with polarisabilities and ion size. We also discuss how the most recent theories on surface hydration combined with hydrated nonelectrostatic potentials may predict experimental zeta potentials and hydration forces.     

A size-modified poisson–boltzmann ion channel model in a solvent of multiple ionic species: Application to voltage-dependent anion channel

We present a new size-modified Poisson–Boltzmann ion channel (SMPBIC) model and use it to calculate the electrostatic potential, ionic concentrations, and electrostatic solvation free energy for a voltage-dependent anion channel (VDAC) on a biological membrane in a solution mixture of multiple ionic species. In particular, the new SMPBIC model adopts a membrane surface charge density and a natural Neumann boundary condition to reflect the charge effect of the membrane on the electrostatics of VDAC. To avoid the singularity difficulties caused by the atomic charges of VDAC, the new SMPBIC model is split into three submodels such that the solution of one of the submodels is obtained analytically and contains all the singularity points of the SMPBIC model. The other two submodels are then solved numerically much more efficiently than the original SMPBIC model. As an application of this SMPBIC submodel partitioning scheme, we derive a new formula for computing the electrostatic solvation free energy. Numerical results for a human VDAC isoform 1 (hVDAC1) in three different salt solutions, each with up to five different ionic species, confirm the significant effects of membrane surface charges on both the electrostatics and ionic concentrations. The results also show that the new SMPBIC model can describe well the anion selectivity property of hVDAC1, and that the new electrostatic solvation free energy formula can significantly improve the accuracy of the currently used formula. © 2019 Wiley Periodicals, Inc.     

Single-ion solvation free energies and the normal hydrogen electrode potential in methanol, acetonitrile, and dimethyl sulfoxide

The division of thermodynamic solvation free energies of electrolytes into contributions from individual ionic constituents is conventionally accomplished by using the single-ion solvation free energy of one reference ion, conventionally the proton, to set the single-ion scales. Thus, the determination of the free energy of solvation of the proton in various solvents is a fundamental issue of central importance in solution chemistry. In the present article, relative solvation free energies of ions and ion-solvent clusters in methanol, acetonitrile, and dimethyl sulfoxide (DMSO) have been determined using a combination of experimental and theoretical gas-phase free energies of formation, solution-phase reduction potentials and acid dissociation constants, and gas-phase clustering free energies. Applying the cluster pair approximation to differences between these relative solvation free energies leads to values of -263.5, -260.2, and -273.3 kcal/mol for the absolute solvation free energy of the proton in methanol, acetonitrile, and DMSO, respectively. The final absolute proton solvation free energies are used to assign absolute values for the normal hydrogen electrode potential and the solvation free energies of other single ions in the solvents mentioned above.     

How ions affect the structure of water

We model ion solvation in water. We use the MB model of water, a simple two-dimensional statistical mechanical model in which waters are represented as Lennard-Jones disks having Gaussian hydrogen-bonding arms. We introduce a charge dipole into MB waters. We perform (NPT) Monte Carlo simulations to explore how water molecules are organized around ions and around nonpolar solutes in salt solutions. The model gives good qualitative agreement with experiments, including Jones-Dole viscosity B coefficients, Samoilov and Hirata ion hydration activation energies, ion solvation thermodynamics, and Setschenow coefficients for Hofmeister series ions, which describe the salt concentration dependence of the solubilities of hydrophobic solutes. The two main ideas captured here are (1) that charge densities govern the interactions of ions with water, and (2) that a balance of forces determines water structure: electrostatics (water's dipole interacting with ions) and hydrogen bonding (water interacting with neighboring waters). Small ions (kosmotropes) have high charge densities so they cause strong electrostatic ordering of nearby waters, breaking hydrogen bonds. In contrast, large ions (chaotropes) have low charge densities, and surrounding water molecules are largely hydrogen bonded.     

Quantum chemical model of solvation for calculation of electrode potentials of redox processes involving ferrocene,cobaltocene, and their ions

Quantum chemical calculations of solvation energy for ferrocene and cobaltocene molecules and their ionic forms in water, acetonitrile, methanol, and acetone are performed in terms of the B3LYP density functional method by taking into account solvation effects and using the polarized continuum model (PCM). Standard electrode potentials of the corresponding redox pairs, the effect of solvent on them, and the overall energy of the transfer of cobaltocene cation and anion between two solvents are calculated. The calculation results well agree with the available experimental data. The present study provides sufficiently reliable grounds for the application of an ion—metallocene molecule redox pair as a pilot system for the comparison of electrode potentials and solvation energies in different solvents.     

Why pH titration in protein solutions follows a Hofmeister series

Measurements of pH in single-phase cytochrome c suspensions are reported. The pH, as determined by a glass electrode, has a fixed value. With the addition of salt, the supposedly fixed pH changes strongly. The pH depends on salt type and concentration and follows a Hofmeister series. A theoretical interpretation is given that provides insights into such Hofmeister effects. These occur generally in protein solutions. While classical electrostatic models provide partial understanding of such trends in protein solutions, they fail to explain the observed ion specificity. Such models neglect electrodynamic fluctuation (dispersion) forces acting between ions and proteins. We use a Poisson-Boltzmann cell model that takes these ionic dispersion potentials between ions and proteins into account. The observed ion specificity can then be accounted for. Proteins act as buffers that display similar salt-dependent pH trends not previously explained.     

The interaction between colloids in polar mixtures above Tc

We calculate the interaction potential between two charged colloids immersed in an aqueous mixture containing salt near or above the critical temperature. We find an attractive interaction far from the coexistence curve due to the combination of preferential solvent adsorption at the colloids' surface and preferential ion solvation. We show that the ion-specific interaction strongly depends on the amount of salt added as well as on the mixture composition. The calculations are in good agreement with recent experiments. For a highly antagonistic salt of hydrophilic anions and hydrophobic cations, a repulsive interaction at an intermediate inter-colloid distance is predicted even though both the electrostatic and adsorption forces alone are attractive.     

Effect of cation size and charge on the interaction between silica surfaces in 1:1, 2:1, and 3:1 aqueous electrolytes

Application of two complementary AFM measurements, force vs separation and adhesion force, reveals the combined effects of cation size and charge (valency) on the interaction between silica surfaces in three 1:1, three 2:1, and three 3:1 metal chloride aqueous solutions of different concentrations. The interaction between the silica surfaces in 1:1 and 2:1 salt solutions is fully accounted for by ion-independent van der Waals (vdW) attraction and electric double-layer repulsion modified by cation specific adsorption to the silica surfaces. The deduced ranking of mono- and divalent cation adsorption capacity (adsorbability) to silica, Mg(2+) < Ca(2+) < Na(+) < Sr(2+) < K(+) < Cs(+), follows cation bare size as well as cation solvation energy but does not correlate with hydrated ionic radius or with volume or surface ionic charge density. In the presence of 3:1 salts, the coarse phenomenology of the force between the silica surfaces as a function of salt concentration resembles that in 1:1 and 2:1 electrolytes. Nevertheless, two fundamental differences should be noticed. First, the attraction between the silica surfaces is too large to be attributed solely to vdW force, hence implying an additional attraction mechanism or gross modification of the conventional vdW attraction. Second, neutralization of the silica surfaces occurs at trivalent cation concentrations that are 3 orders of magnitude smaller than those characterizing surface neutralization by mono- and divalent cations. Consequently, when trivalent cations are added to our cation adsorbability series the correlation with bare ion size breaks down abruptly. The strong adsorbability of trivalent cations to silica contrasts straightforward expectations based on ranking of the cationic solvation energies, thus suggesting a different adsorption mechanism which is inoperative or weak for mono- and divalent cations.     

Free energy of solvation of simple ions: molecular-dynamics study of solvation of Cl- and Na+ in the ice/water interface

Molecular-dynamics simulations of Cl(-) and Na(+) ions are performed to calculate ionic solvation free energies in both bulk simple point-charge/extended water and ice 1 h at several different temperatures, and at the basal ice 1 h/water interface. For the interface we calculate the free energy of "transfer" of the ions across the ice/water interface. For the ions in bulk water in the NPT ensemble at 298 K and 1 atm, results are found to be in good agreement with experiments, and with other simulation results. Simulations performed in the NVT ensemble are shown to give equivalent solvation free energies, and this ensemble is used for the interfacial simulations. Solvation free energies of Cl(-) and Na(+) ions in ice at 150 K are found to be approximately 30 and approximately 20 kcal mol(-1), respectively, less favorable than for water at room temperature. Near the melting point of the model the solvation of the ions in water is the same (within statistical error) as that measured at room temperature, and in the ice is equivalent and approximately 10 kcal mol(-1) less favorable than the liquid. The free energy of transfer for each ion across ice/water interface is calculated and is in good agreement with the bulk observations for the Cl(-) ion. However, for the model of Na(+) the long-range electrostatic contribution to the free energy was more negative in the ice than the liquid, in contrast with the results observed in the bulk calculations.     

The Hofmeister series effect in adsorption of cationic surfactants--theoretical description and experimental results

Interfacial properties of cationic surfactants show strong dependence on the type of surfactant counterion or on the type of anion of a salt added to the surfactant solution. In the paper, the models of ionic surfactant adsorption that can take into account ionic specific effects are reviewed. Model of ionic surfactant adsorption based on the assumption that the surfactant ions and counterions undergo nonequivalent adsorption within the Stern layer was selected to describe experimental surface tension isotherms of aqueous solutions of a number of cationic surfactants. The experimental isotherms for: n-alkyl trimethylammonium cationic surfactants, namely: C(16)TABr (CTABr or CTAB), C(16)TACl, C(16)TAHSO(4), C(10)TABr and C(12)TABr as well as decyl- and dodecylpyridinium salts with and without various electrolyte anions as Cl(-), Br(-), F(-), I(-), NO(3)(-), ClO(4)(-) and CH(3)COO(-) were described in terms of the model and a good agreement between the theory and experiment was obtained for a wide range of surfactants and added electrolyte concentrations. A very pronounced Hofmeister effect in dependence of surface tension of cationic surfactants on the type of anion was found. Analysing this dependence in terms of the proposed model of ionic surfactant adsorption, strong correlation between "anion surface activity" (the model parameter accounting for ion penetration into the Stern layer), and the ion polarizability was obtained. That suggests that the mechanism related to the dispersive interaction of polarized ion with electric field at interface is responsible for Hofmeister series effects in surface activity of cationic surfactants. The same mechanism was proposed recently to explain the dependence of surface tension increase with electrolyte concentration on anion and cation type.     

Microsolvation of the sodium and iodide ions and their ion pair in acetonitrile clusters: a theoretical study

The structural and thermodynamic properties of Na+(CH3CN)n, I-(CH3CN)n, and NaI(CH3CN)n clusters have been investigated by means of room-temperature Monte Carlo simulations with model potentials developed to reproduce the properties of small clusters predicted by quantum chemistry. Ions are found to adopt an interior solvation shell structure, with a first solvation shell containing approximately 6 and approximately 8 acetonitrile molecules for large Na+(CH3CN)n and I-(CH3CN)n clusters, respectively. Structural features of Na+(CH3CN)n are found to be similar to those of Na+(H2O)n clusters, but those of I-(CH3CN)n contrast with those of I-(H2O)n, for which "surface" solvation structures were observed. The potential of mean force calculations demonstrates that the NaI ion pair is thermodynamically stable with respect to ground-state ionic dissociation in acetonitrile clusters. The properties of NaI(CH3CN)n clusters exhibit some similarities with NaI(H2O)n clusters, with the existence of contact ion pair and solvent-separated ion pair structures, but, in contrast to water clusters, both types of ion pairs adopt a well-defined interior ionic solvation shell structure in acetonitrile clusters. Whereas contact ion pair species are thermodynamically favored in small clusters, solvent-separated ion pairs tend to become thermodynamically more stable above a cluster size of approximately 26. Hence, ground-state charge separation appears to occur at larger cluster sizes for acetonitrile clusters than for water clusters. We propose that the lack of a large Na+(CH3CN)n product signal in NaI(CH3CN)n multiphoton ionization experiments could arise from extensive stabilization of the ground ionic state by the solvent and possible inhibition of the photoexcitation mechanism, which may be less pronounced for NaI(H2O)n clusters because of surface solvation structures. Alternatively, increased solvent evaporation resulting from larger excess energies upon photoexcitation or major solvent reorganization on the ionized state could account for the observed solvent-selectivity in NaI cluster multiphoton ionization.     

The Calculation of Interfacial Tension and Electrostatic Free Energy of Spherical Ionic Micelles with High Surface Potentials

Based on extended Langmuir's method on the dressed micelles, approximate expressions for the calculation of interfacial tension and electrostatic free energy of spherical ionic micelles with high surface potentials have been presented. These expressions are derived from nonlinear Poisson‐Boltzmann equation. The present formulae for the calculation of interfacial tension and electrostatic free energy of spherical ionic micelles are in quite good agreement with Hayter's results.     

Toward robust computational electrochemical predicting the environmental fate of organic pollutants

A number of density functionals was utilized for the calculation of electron attachment free energy for nitrocompounds, quinones and azacyclic compounds. Different solvation models have been tested on the calculation of difference in free energies of solvation of oxidized and reduced forms of nitrocompounds in aqueous solution, quinones in acetonitrile, and azacyclic compounds in dimethylformamide. Gas‐phase free energies evaluated at the mPWB1K/tzvp level and solvation energies obtained using SMD model to compute solvation energies of neutral oxidized forms and PCM(Pauling) to compute solvation energies of anion‐radical reduced forms provide reasonable accuracy of the prediction of electron attachment free energy, difference in free solvation energies of oxidized and reduced forms, and as consequence yield reduction potentials in good agreement with experimental data (mean absolute deviation is 0.15 V). It was also found that SMD/M05‐2X/tzvp method provides reduction potentials with deviation of 0.12 V from the experimental values but in cases of nitrocompounds and quinones this accuracy is achieved due to the cancelation of errors. To predict reduction ability of naturally occurred iron containing species with respect to organic pollutants we exploited experimental data within the framework of Pourbaix (E_h ? pH) diagrams. We conclude that surface‐bound Fe(II) as well as certain forms of aqueous Fe(II)_aq are capable of reducing a variety of nitroaromatic compounds, quinones and novel high energy materials under basic conditions (pH > 8). At the same time, zero‐valent iron is expected to be active under neutral and acidic conditions. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

New approach to free energy of solvation applying continuum models to molecular dynamics simulation

A new approach to the calculation of the free energy of solvation from trajectories obtained by molecular dynamics simulation is presented. The free energy of solvation is computed as the sum of three contributions originated at the cavitation of the solute by the solvent, the solute-solvent nonpolar (repulsion and dispersion) interactions, and the electrostatic solvation of the solute. The electrostatic term is calculated based on ideas developed for the broadly used continuum models, the cavitational contribution from the excluded volume by the Claverie-Pierotti model, and the Van der Waals term directly from the molecular dynamics simulation. The proposed model is tested for diluted aqueous solutions of simple molecules containing a variety of chemically important functions: methanol, methylamine, water, methanethiol, and dichloromethane. These solutions were treated by molecular dynamics simulations using SPC/E water and the OPLS force field for the organic molecules. Obtained free energies of solvation are in very good agreement with experimental data.     

Anisotropic inertial term of the solvation energy in binary solutions

An expression based on the Fröhlich theorem is given for the anisotropic inertial solvation potential of solutions. The principle of the additivity of the anisotropic inertial solvation potentials of solution components is put forward and substantiated. A model thermodynamic function of the anisotropic inertial solvation potential of a binary solution is suggested. The effect of formation of 1:1 complexes and bimolecular associates on the anisotropic inertial solvation potential of a binary solution is analyzed. The composition dependences of the anisotropic inertial solvation potentials of binary solutions of nitrobenzene, acetonitrile, nitromethane, and tetrachloromethane in associated and nonassociated polar and nonpolar solvents and in water are determined. The dependences obtained are compared to the corresponding model functions. Changes in the contribution of specific intermolecular interactions to the anisotropic inertial term of the Helmholtz energy of solvation of binary solutions are revealed by this method. Previously unknown anisotropic inertial solvation potentials are obtained for associated and polar nonassociated liquids in relation to their content in hexane. Conclusions on the magnitude and character of changes in the microstructure of solutions are made. The transformation of the anisotropic inertial to isotropic noninertial term of the Helmholtz energy of solvation is noted by the example of a solution with the ethanol volume fraction in hexane of 0.13.     

The oxidation of tyrosine and tryptophan studied by a molecular dynamics normal hydrogen electrode

The thermochemical constants for the oxidation of tyrosine and tryptophan through proton coupled electron transfer in aqueous solution have been computed applying a recently developed density functional theory (DFT) based molecular dynamics method for reversible elimination of protons and electrons. This method enables us to estimate the solvation free energy of a proton (H(+)) in a periodic model system from the free energy for the deprotonation of an aqueous hydronium ion (H(3)O(+)). Using the computed solvation free energy of H(+) as reference, the deprotonation and oxidation free energies of an aqueous species can be converted to pK(a) and normal hydrogen electrode (NHE) potentials. This conversion requires certain thermochemical corrections which were first presented in a similar study of the oxidation of hydrobenzoquinone [J. Cheng, M. Sulpizi, and M. Sprik, J. Chem. Phys. 131, 154504 (2009)]. Taking a different view of the thermodynamic status of the hydronium ion, these thermochemical corrections are revised in the present work. The key difference with the previous scheme is that the hydronium is now treated as an intermediate in the transfer of the proton from solution to the gas-phase. The accuracy of the method is assessed by a detailed comparison of the computed pK(a), NHE potentials and dehydrogenation free energies to experiment. As a further application of the technique, we have analyzed the role of the solvent in the oxidation of tyrosine by the tryptophan radical. The free energy change computed for this hydrogen atom transfer reaction is very similar to the gas-phase value, in agreement with experiment. The molecular dynamics results however, show that the minimal solvent effect on the reaction free energy is accompanied by a significant reorganization of the solvent.