Interionic Potentials Of Mean Force Research Articles

Ionic screening in bulk and under confinement.

Recent experiments have shown that the repulsive force between atomically flat, like-charged surfaces confining room-temperature ionic liquids or concentrated electrolytes exhibits an anomalously large decay length. In our previous publication [J. Zeman, S. Kondrat, and C. Holm, Chem. Commun. 56, 15635 (2020)], we showed by means of extremely large-scale molecular dynamics simulations that this so-called underscreening effect might not be a feature of bulk electrolytes. Herein, we corroborate these findings by providing additional results with more detailed analyses and expand our investigations to ionic liquids under confinement. Unlike in bulk systems, where screening lengths are computed from the decay of interionic potentials of mean force, we extract such data in confined systems from cumulative charge distributions. At high concentrations, our simulations show increasing screening lengths with increasing electrolyte concentration, consistent with classical liquid state theories. However, our analyses demonstrate that-also for confined systems-there is no anomalously large screening length. As expected, the screening lengths determined for ionic liquids under confinement are in good quantitative agreement with the screening lengths of the same ionic systems in bulk. In addition, we show that some theoretical models used in the literature to relate the measured screening lengths to other observables are inapplicable to highly concentrated electrolytes.

Understanding ion–ion interactions in bulk and aqueous interfaces using molecular simulations

In addition to its scientific significance, the distribution of ions in the bulk and at aqueous interfaces is also very important for practical reasons. Providing a quantitative description of the ionic distribution, and describing interactions between ions in different environments, remains a challenge, and is the subject of current debate. In this study, we found that interionic potentials of mean force (PMFs) and interfacial properties are very sensitive to the ion-ion interaction potential models. Our study predicted a Sr(2+)--CI- PMF with no contact ion-pair state and a shallow solvent-separated ion-pair state. In addition, we were able to quantitatively capture the experimental X-ray reflectivity results of the aqueous salt interface of the Sr(2+)--Cl- ion-pair, and provided a detailed physical description of the interfacial structure for this system. We also predicted the Xray reflectivity results for SrBr2 and SrI2 systems.

Note: Interionic potentials of mean force for Ca2+-Cl− in polarizable water

We describe our molecular dynamics simulation studies of the inter-ionic potentials of mean force (PMF) for the Ca2+-Cl− ion pair in water. Ion-water and ion-ion polarizable potential models were constructed to reproduce experimental ion-hydration enthalpies as well as the electronic-structure calculations of the minimum energy for the Ca2+-Cl− interactions. Our study predicted a PMF with no contact ion pair state and a shallow solvent-separated ion-pair state. In addition, our computed radial distribution function, gCa-Cl, for a 1-M CaCl2 electrolyte solution indicated that there is no contact ion pair but, instead, showed a maximum near 5 Å. This observation is consistent with our PMF calculation. These new results are discussed and compared to the recent classical and ab initio PMF calculations on the same system reported by Timko et al. [J. Chem. Phys. 134, 204510 (2011)]10.1063/1.3595261.

Removing systematic errors in interionic potentials of mean force computed in molecular simulations using reaction-field-based electrostatics.

The performance of reaction-field methods to treat electrostatic interactions is tested in simulations of ions solvated in water. The potential of mean force between sodium chloride pair of ions and between side chains of lysine and aspartate are computed using umbrella sampling and molecular dynamics simulations. It is found that in comparison with lattice sum calculations, the charge-group-based approaches to reaction-field treatments produce a large error in the association energy of the ions that exhibits strong systematic dependence on the size of the simulation box. The atom-based implementation of the reaction field is seen to (i) improve the overall quality of the potential of mean force and (ii) remove the dependence on the size of the simulation box. It is suggested that the atom-based truncation be used in reaction-field simulations of mixed media.

Water mediated attraction between repulsive ions: A cluster-based simulation approach

Could two like ions be attractive to each other in the presence of water? To address this question and to further interrogate the intriguing solvent effects at a molecular level on multiply charged species, a "bottom-up" simulation approach was formulated, from which the inter-ionic potential of mean force and other properties were monitored closely with the gradual addition of the water molecules. This approach was first tested on a commonly studied ion pair (namely, Na+ and Cl-), where excellent agreement with the published bulk-phase data was found. Further application of this approach to the like-ion pair indicated that an attractive interaction between two anions or two cations can be induced by the addition of an appropriate number of water molecules. This result corroborates a recent experimental report of an intriguing folding of a dianionic polymer into a more compact structure with the addition of water molecules in gas phase as well as previous theoretical findings of possible attraction between like-ion pairs in bulk aqueous phases.

The solvation of ions in acetonitrile and acetone: A molecular Ornstein–Zernike study

The solvation of alkali and halide ions in acetonitrile and acetone has been investigated via the molecular Ornstein–Zernike theory using the hypernetted chain approximation. Theoretical Gibbs solvation energies and solvation numbers are compared with experiments and numerical simulations. The calculated single-ion solvation energies are used to check the hypotheses serving to split-up the measured solvation energies of salts into their single-ion components. The solvation structure around the ions is discussed in detail and shown to be strongly influenced by the solvent–solvent spatial correlations. The calculated interionic potentials of mean force are presented and used to compute ion-ion association constants which are compared with experiment. The influence of the Lennard-Jones parameters of the ions upon the calculated properties is emphasized.

Comment on ‘‘Mean force potential for the calcium–chloride ion pair in water’’ [J. Chem. Phys. 99, 4229 (1993)

The interionic potential of mean force (pmf) for the Ca++–Cl− ion pair in water is computed using the molecular dynamics computer simulation technique. The calculated pmf indicates a stable contact pair (CIP) and a solvent-separated pair (SSIP) centered at 2.9 and 5.0 Å with a 2.8 kcal/mol barrier to dissociation. The SSIP well is about 2.0 kcal/mol deeper than the CIP suggesting that water molecules in the first hydration shell are strongly coordinated to the Ca++ ion. Our results do not agree with the pmf reported recently by Guardia, Robinson, Padro [J. Chem. Phys. 99, 4229 (1993)]. Possible reasons for the discrepancy are discussed.

Interionic potentials of mean force for SrCl 2 in polarizable water : A computer simulation study

Potentials of mean force (PMFs) and solvation properties of SrCl 2 in polarizable water have been studied using molecular dynamics simulations. The PMF between isolated Sr 2+ and Cl − ions involves a stable contact ion-pair state with a binding free energy of −1.8 kcal mol and a dissociation barrier of 3.5 kcal/mol. A solvent-separated state is observed to have comparable free energy and a minimal barrier for dissociation to free ions. The PMF between a second Cl − ion and the Sr 2+⋯Cl − contact ion pair has also been calculated. The Cl −⋯Sr 2+⋯Cl − complex is nonlinear and involves a bridging water molecule strongly hydrogen-bound to both chlorine ions.

Iso‐energy cutoff for the calculation of interionic potential of mean force in water

AbstractAn iso‐energy cutoff scheme is introduced for the calculation of the potential of mean force between two ions in water. The cutoff criterion is based on the optimal interaction of the water dipole with the ion pair, for which analytical expressions are derived. Formulas are also derived to characterize the solvent reorganization contribution to the potential of mean force. Treatment of the contributions from waters outside the cutoff is also discussed. © 1994 John Wiley & Sons, Inc.

Monte Carlo simulations on the like-charged guanidinium-guanidinium ion pair in water

Monte Carlo simulations using the statistical perturbation theory were carried out for the guanidinium-guanidinium ion pair in water at 25 o C and 1 atm using the isothermal-isobaric (NPT) ensemble to obtain interionic potentials of mean force and to evaluate «effective» interactions in water at short distances. The system is found to be attractive with a deep and large minimum at a C...C distance of approximately 3.30 A. Our results address fundamental questions about interionic interactions in recognition processes involving like-charged binding sites. Contrary to the simple electrostatic picture, they may attract locally due to related induced solvent effects

Alkali halides in water: Ion–solvent correlations and ion–ion potentials of mean force at infinite dilution

Using the specialization of the extended RISM equation to infinitely dilute systems, we have calculated correlation functions and interionic potentials of mean force for a set of models corresponding to the first few alkali halides in water. From the results obtained at infinite dilution we calculate the lowest order corrections to the solution properties of the ions. Higher concentrations are explored by using the interionic potentials of mean force at infinite dilution as effective solvent mediated pair potentials. Our results indicate that certain thermodynamic properties, such as the mean activity coefficients and osmotic pressures, are quite sensitive to the details of both the theory and the potential models.

The interionic potential of mean force in a molecular polar solvent from an extended RISM equation

The generalization of a recently proposed extension of the RISM integral equation to infinitely dilute isolated ions and ion pairs in polar, interaction site model, molecular solvents is outlined. An essential element of the development is the explicit separation of the contributions which yield a continuum dielectric solvent model from the remainder. Thus, it is only for this correction that one relies on the integral equation. Application is made to a system consisting of a diatomic polar solvent and atomic ions of varied charge and radius. The results of these calculations show that the present approach produces sensible qualitative features of ionic solvation including an appropriately varying degree of solvent orientational saturation with ionic charge and radius. Correspondingly, the calculated interionic potentials of mean force reproduce the same basic features manifest in already available studies of dipolar hard sphere solvents, including the positions of oscillatory features in the structure and the relatively short spatial range of the corrections to the continuum dielectric theory. A quantitative evaluation of the accuracy of the present predictions is not possible with presently available data.

Electrolyte theory - improvements since Debye and Hueckel

First we recall that there is not yet an adequate theory for water (or for other ionizing solvents); hence any theory must start with assumptions concerning the interionic potentials of mean force in the solvent. From that point, however, we now have an exact theory which can be applied numerically to obtain as accurately as desired the interionic radial distribution functions and thermodynamic properties. There is no longer any need to speculate about the net inaccuracies in the Debye--Hueckel theory, or extensions thereof, or of other approximate theories. These questions can be answered by comparison with calculations based on exact theories. The original Debye--Hueckel (D--H) expression which contained no contribution from the direct effects of short-range forces is seriously inadequate outside of the range of the limiting law. But the D--H calculation of interionic distribution functions is found to be surprisingly accurate in either the exponential or three-term expansion form (at least for the model for aqueous l--l electrolytes with ionic diameters near 4 A). The three-term expansion form of these distributions can be used in the ''pressure'' equation to yield a simple but relatively accurate expression for the osmotic coefficient up to about 1 M for this model. Itmore » is now feasible also to investigate more realistic interionic potentials. This should be very valuable in the future, although the requirement of fitting osmotic and activity coefficient data is not likely to yield a unique determination of the short-range potential. The recent theory suggested important improvements in the form of semiempirical equations. Reasonably simple equations are now available which fit within experimental accuracy a wide variety of data on pure and mixed electrolytes. Also, since the more important parameters are determined from the single solutes, the equations allow prediction of the properties of mixtures.« less

A Monte Carlo method for obtaining the interionic potential of mean force in ionic solution

A Monte Carlo method for obtaining the solvent-averaged interionic potential of mean force is described. The potential of mean force is obtained for two charged hard spheres immersed in a dipolar hard sphere solvent. The ions and solvent particles have the same hard sphere diameters and the ions bear single charges of opposite sign. The solvent particles are characterized by a reduced dipole moment μ*=1.0 which corresponds to a dielectric constant ε?7.8. The Monte Carlo result is compared with the ’’primitive model’’ and other approximations which have been suggested for the potential of mean force. These approximations are all found to be inadequate for small ionic separations. Some implications with respect to ’’ion pairing’’ are mentioned.