Effective Ion-ion Interaction Research Articles

Does an electronic continuum correction improve effective short-range ion-ion interactions in aqueous solution?

Non-polarizable force fields for hydrated ions not always accurately describe short-range ion-ion interactions, frequently leading to artificial ion clustering in bulk aqueous solutions. This can be avoided by adjusting the nonbonded anion-cation or cation-water Lennard-Jones parameters. This approach has been successfully applied to different systems, but the parameterization is demanding owing to the necessity of separate investigations of each ion pair. Alternatively, polarization effects may effectively be accounted for using the electronic continuum correction (ECC) of Leontyev et al. [J. Chem. Phys. 119, 8024 (2003)], which involves scaling the ionic charges with the inverse square-root of the water high-frequency dielectric permittivity. ECC has proven to perform well for monovalent salts as well as for divalent salts in water. Its performance, however, for multivalent salts with higher valency remains unexplored. The present work illustrates the applicability of the ECC model to trivalent K3PO4 and divalent K2HPO4 in water. We demonstrate that the ECC models, without additional tuning of force field parameters, provide an accurate description of water-mediated interactions between salt ions. This results in predictions of the osmotic coefficients of aqueous K3PO4 and K2HPO4 solutions in good agreement with experimental data. Analysis of ion pairing thermodynamics in terms of contact ion pair (CIP), solvent-separated ion pair, and double solvent-separated ion pair contributions shows that potassium-phosphate CIP formation is stronger with trivalent than with divalent phosphate ions.

Interatomic repulsion softness directly controls the fragility of supercooled metallic melts

We present an analytic scheme to connect the fragility and viscoelasticity of metallic glasses to the effective ion-ion interaction in the metal. This is achieved by an approximation of the short-range repulsive part of the interaction, combined with nonaffine lattice dynamics to obtain analytical expressions for the shear modulus, viscosity, and fragility in terms of the ion-ion interaction. By fitting the theoretical model to experimental data, we are able to link the steepness of the interionic repulsion to the Thomas-Fermi screened Coulomb repulsion and to the Born-Mayer valence electron overlap repulsion for various alloys. The result is a simple closed-form expression for the fragility of the supercooled liquid metal in terms of few crucial atomic-scale interaction and anharmonicity parameters. In particular, a linear relationship is found between the fragility and the energy scales of both the screened Coulomb and the electron overlap repulsions. This relationship opens up opportunities to fabricate alloys with tailored thermoelasticity and fragility by rationally tuning the chemical composition of the alloy according to general principles. The analysis presented here brings a new way of looking at the link between the outer shell electronic structure of metals and metalloids and the viscoelasticity and fragility thereof.

Equation of state of metallic helium

The effective ion-ion interaction, free energy, pressure, and electric resistance of metallic liquid helium have been calculated in wide density and temperature ranges using perturbation theory in the electron-ion interaction potential. In the case of conduction electrons, the exchange interaction has been taken into account in the random-phase approximation and correlations have been taken into account in the local-field approximation. The solid-sphere model has been used for the nuclear subsystem. The diameter of these spheres is the only parameter of this theory. The diameter and density of the system at which the transition of helium from the singly ionized to doubly ionized state occurs have been estimated by analyzing the pair effective interaction between helium atoms. The case of doubly ionized helium atoms has been considered. Terms up to the third order of perturbation theory have been taken into account in the numerical calculations. The contribution of the third-order term is significant in all cases. The electric resistance and its temperature dependence for metallic helium are characteristic of simple divalent metals in the liquid state. The thermodynamic parameters—temperature and pressure densities-are within the ranges characteristic of the central regions of giant planets. This makes it possible to assume the existence of helium in the metallic state within the solar system.

Structural properties of warm dense matter

We investigate the structure in warm dense matter by ab initio simulations and classical fluid equations. This comparison yields valuable information on the system properties such as effective ion-ion interactions and charge states. Extensions to systems with multiple ion species are discussed and the limits of reduced descriptions are demonstrated. The structural information is then used to predict the signal strength in x-ray scattering experiments which, in turn, can be used as diagnostics for warm dense fluids. Here, we need to consider the inelastic feature due to the dynamic response of free electrons as well as the elastic (Rayleigh) peak related to the static ion structure. In a last example, we apply ab initio simulations to calculate the ionic structure in highly excited graphite close to melting.

Two-center potential correlations and its use to determine effective ion-ion interactions and dielectric permittivities in dipolar solvents

General expressions for two-center electrostatic potential correlations and its use to determine (i) the effective interaction between simple ions in a dipolar solvent and (ii) the dielectric permittivity of the solvent are proposed. Such two-center potential correlations were determined from Monte Carlo simulations of spherically confined dipolar particles embedded in a dielectric medium described by using an image charge approximation. The deduced dielectric permittivities increased with increasing dipolar moment, and at large dipole moments the effective interaction displayed an attractive first minimum.

Ion-specific thermodynamics of multicomponent electrolytes: A hybrid HNC/MD approach

Using effective infinite dilution ion-ion interaction potentials derived from explicit-water molecular dynamics (MD) computer simulations in the hypernetted-chain (HNC) integral equation theory we calculate the liquid structure and thermodynamic properties, namely, the activity and osmotic coefficients of various multicomponent aqueous electrolyte mixtures. The electrolyte structure expressed by the ion-ion radial distribution functions is for most ions in excellent agreement with MD and implicit solvent Monte Carlo (MC) simulation results. Calculated thermodynamic properties are also represented consistently among these three methods. Our versatile HNC/MD hybrid method allows for a quick prediction of the thermodynamics of multicomponent electrolyte solutions for a wide range of concentrations and an efficient assessment of the validity of the employed MD force-fields with possible implications in the development of thermodynamically consistent parameter sets.

Potential of Mean Force Calculations of Ion Permeation in Gramicidin A Channel

The potential of mean force (PMF) for K+ ion permeation through the gramicidin A (gA) channel were calculated from the molecular dynamics (MD) simulations with four different force fields (FF): CHARMM27, CHARMM27 with dihedral-based correction map (CHARMM27+CMAP), CHARMM27 with a improved FF parameters for tryptophan indole ring (CHARMM27+Trp), and CHARMM27 with the CMAP and the improved FF parameters for Trp (CHARMM27+CMAP+Trp). When comparing the PMFs obtained with these four different FF, we find that both CHARMM27 and CHARMM27+Trp predict free energy profiles that are in semi-quantitative agreement with measurements of the conductance and dissociation constant. The combination CHARMM27+Trp gives the best agreement. However, the CHARMM27+CMAP yields a larger barrier in the PMF and CHARMM27+CMAP+Trp generates a deeper binding potential well. These calculations illustrate the sensitivity of the PMF controlling ion permeation to subtle changes in the FF. We also compute a 2-ion PMF for a doubly occupied gA channel. The effect of the number of water molecules in the channel on the effective ion-ion interactions is also studied. Elucidating the properties of the doubly occupied channel is important because experiments are often carried out at fairly high concentration where double ion occupancy is predominant.

Formation and interaction of hydrated alkali metal ions at the graphite-water interface

Ion hydration at a solid surface ubiquitously exists in nature and plays important roles in many natural processes and technological applications. Aiming at obtaining a microscopic insight into the formation of such systems and interactions therein, we have investigated the hydration of alkali metal ions at a prototype surface-graphite (0001), using first-principles molecular dynamics simulations. At low water coverage, the alkali metal ions form two-dimensional hydration shells accommodating at most four (Li, Na) and three (K, Rb, Cs) waters in the first shell. These two-dimensional shells generally evolve into three-dimensional structures at higher water coverage, due to the competition between hydration and ion-surface interactions. Exceptionally K was found to reside at the graphite-water interface for water coverages up to bulk water limit, where it forms an "umbrellalike" surface hydration shell with an average water-ion-surface angle of 115 degrees . Interactions between the hydrated K and Na ions at the interface have also been studied. Water molecules seem to mediate an effective ion-ion interaction, which favors the aggregation of Na ions but prevents nucleation of K. These results agree with experimental observations in electron energy loss spectroscopy, desorption spectroscopy, and work function measurement. In addition, the sensitive dependence of charge transfer on dynamical structure evolution during the hydration process, implies the necessity to describe surface ion hydration from electronic structure calculations.

Osmotic coefficients of atomistic NaCl (aq) force fields

Solvated ions are becoming increasingly important for (bio)molecular simulations. But there are not much suitable data to validate the intermediate-range solution structure that ion-water force fields produce. We compare six selected combinations of four biomolecular Na-Cl force fields and four popular water models by means of effective ion-ion potentials. First we derive an effective potential at high dilution from simulations of two ions in explicit water. At higher ionic concentration multibody effects will become important. We propose to capture those by employing a concentration dependent dielectric permittivity. With the so obtained effective potentials we then perform implicit solvent simulations. We demonstrate that our effective potentials accurately reproduce ion-ion coordination numbers and the local structure. They allow us furthermore to calculate osmotic coefficients that can be directly compared with experimental data. We show that the osmotic coefficient is a sensitive and accurate measure for the effective ion-ion interactions and the intermediate-range structure of the solution. It is therefore a suitable and useful quantity for validating and parametrizing atomistic ion-water force fields.

Internal energy of high-density hydrogen: Analytic approximations compared with path integral Monte Carlo calculations

The internal energy of high-density hydrogen plasmas in the temperature range T=10000–50000 K is calculated by two different analytic approximation schemes—the method of an effective ion-ion interaction potential and the Pade approach within the chemical picture—and are compared with direct path integral Monte Carlo results. A reasonable agreement between the results obtained from the three independent calculations is found and the reasons for still existing differences are investigated. Interesting high-density phenomena such as the onset of ion crystallization are discussed.

Strain field due to transition metal impurities in Ni and Pd

The strain field due to body centered substitutional transition metal impurities in Ni and Pd metals are investigated. The calculations are carried out in the discrete lattice model of the metal using Kanzaki lattice static method. The effective ion-ion interaction potential due to Wills and Harrison is used to evaluate dynamical matrix and the impurity-induced forces. The results for atomic displacements due to 3d, 4d and 5d impurities (Fe, Co, Cu, Nb, Mo, Pd, Pt and Au) in Ni and (Fe, Co, Cu, Ni, Nb, Mo, Pt and Au) impurities in Pd are given up to 25 NN’s of impurity and these are compared with the available experimental data. The maximum displacements of 4.6% and 3.8% of 1NN distance are found for NiNb and PdNb alloys respectively, while the minimum displacements of 0.63% and 0.23% of 1NN distance are found for NiFe and PdFe alloys respectively. Except for Cu, the atomic displacements are found to be proportional to the core radii and d state radius. The relaxation energies for 3d impurities are found less than those for 4d and 5d impurities in Ni and Pd metals. Therefore, 3d impurities may easily be solvable in these metals.

On the Influence of Dielectric Saturation and Medium Granularity on Ion−Ion Interaction and Reorganization Energies Associated with Electron-Transfer Processes in Condensed Matter

The influence of dielectric saturation effects and the granularity of a medium on the effective ion-ion interaction and the reorganization energy for electron-transfer processes have been studied using a medium built from dipoles and polarizabilities that are placed on a lattice. It was found that these effects lead to an increased repulsion between equally charged ions and an increased attraction between oppositely charged ions at short distances. It was also found that the estimate of the outer-sphere reorganization energy contribution to the activation energy for electron-transfer processes, made by Marcus and Hush, is at least a factor of 2 too large for small ions with large charges.

Strain field due to point defects in Ni dilute alloys

We report the results for strain field due to substitutional transition metal impurities in Ni. The Kanzaki lattice static method has been used to calculate the strain field, the effective ion-ion interaction potential due to Wills and Harrison is used to calculate dynamical matrix with first nearest neighbour and the impurity-induced force with second nearest neighbour. The results for 3d, 4d and 5d impurities (Fe, Co, Cu, Nb, Mo, Pd, Pt and Au) are compared with the experimental data, which are found in agreement.

Influence of the Screening Function on Theoretical Calculations of the Structure Factor of Liquid Aluminum

The structure factor S(k) of liquid aluminum is calculated using the Metropolis Monte Carlo method. The effective two-body ion-ion interaction used in the calculations are the Shaw optimized model and the local approximation suggested by Harrison calculated using two screening function in each case, the screening function of Vashishta and Singwi and that of Utsumi and Ichimaru. The calculated structure factors from each case are compared with experiment.

Pressure-Variation of Structure Factor of Liquid Rb

We have calculated the atomic and the electronic structures of compressed liquid rubidium under high pressures up to 6 GPa on the basis of the quantal hypernetted chain equations in combination with the Rosenfeld bridge functional. The calculated structure factors are in reasonable agreement with the experimental results by Tsuji et al. under these high pressures using synchrotron radiation. All structure factors calculated for this pressure-variation coincide almost into a single curve if wavenumbers are scaled in units of the Wigner-Seitz radius; the compression in liquid rubidium is uniform with increasing pressures. The effective ion-ion interactions remains almost unchanged under this pressure-variation. Results of calculation on liquid lithium confirm that effective ion-ion potentials for alkali metals have the specific feature of scaling property in common. Furthermore, it is shown that the uniform compression of liquid Rb can be explained simply by the effective ion-ion interaction based on the Aschcroft pseudopotenital at the room pressure with use of the scaling property.

Structure factor and electronic structure of compressed liquid rubidium

We have applied the quantal hypernetted-chain equations in combination with the Rosenfeld bridge functional to calculate the atomic and the electronic structure of compressed liquid rubidium under high pressure (0.2, 2.5, 3.9, and 6.1 GPa); the calculated structure factors are in reasonable agreement with experimental results measured by Tsuji et al. along the melting curve as a whole. It is found that the effective ion-ion interaction is practically unchanged with respect to the potential at room pressure under these high pressures. All structure factors calculated for this pressure-variation coincide almost into a single curve if wave numbers are scaled in units of the Wigner-Seitz radius $a$ although no corresponding scaling feature is observed in the effective ion-ion interaction. This scaling property of the structure factors signifies that the compression in liquid rubidium is uniform with increasing pressure; in absolute $Q$ values this means that the first peak position ${(Q}_{1})$ of the structure factor increases proportionally to ${V}^{\ensuremath{-}1/3}$ ($V$ being the specific volume per ion), as was experimentally observed by Tsuji et al. Obviously, this scaling property comes from a specific feature characteristic for effective ion-ion potentials of alkali liquids. We have examined and confirmed this feature for the case of a liquid-lithium potential: starting from the liquid-lithium potential at room pressure we can easily find two sets of densities and temperatures for which the structure factors become practically identical, when scaling $Q$ in units of $a.$

Equation of state and structure factor of mercury

A quantum statistical approach is utilized to give a unified treatment of the metal-non-metal and liquid-vapour transition in expanded mercury. An equation of state is proposed with respect to thermodynamic stability. The resulting coexistence curve and the location of the critical point are in good agreement with experimental data. The static structure factor is calculated along the coexistence line within the MHNC approximation. The limiting cases of the metallic liquid and the insulating vapour are treated by an effective ion-ion interaction potential derived within the nearly free electron model and a Lennard-Jones potential, respectively. The resulting structure factors are compared with experiments.

First-principles molecular dynamics of liquid alkali metals based on the quantal hypernetted chain theory.

A first-principles molecular dynamics (MD) scheme is presented on the basis of the density-functional (DF) theory with use of the the quantal hypernetted chain (QHNC) approximation. The DF theory brings about exact expressions for the ion-electron and ion-ion radial distribution functions (RDF) of an electron-ion mixture as a model of a simple liquid metal. These exact expressions prove that an ion-electron mixture can be treated as a one-component liquid interacting only via a pairwise interaction in the evaluation of the ion-ion RDF, and provide a set of integral equations: one is an exact integral equation for the ion-ion RDF and another for an effective ion-ion interaction, which depends on the ion configuration specified by the ion-ion RDF. Hence, after some approximations are introduced, the MD simulation can be performed to get the ion-ion RDF using the ion-ion interaction determined so as to be consistent to the ion-ion RDF: the MD simulation and the procedure to determine the effective interaction from the QHNC equation are performed iteratively. This MD simulation coupled with the QHNC equation (QHNC-MD method) for the effective interaction provides a first-principles calculation of structures of simple liquid metal: the ion-ion and electron-ion RDF's, the charge distributions of an ion and a pseudoatom, the effective ion-ion interaction and the ion-ion bridge function are evaluated in a self-consistent manner from the atomic number as the only input. We have applied this QHNC-MD method to Li, Na, K, Rb, and Cs near the melting temperature using up to 16 000 particles for the MD simulation. It is found that the convergence of the effective ion-ion interaction is fast enough for practical application to alkali metals; two MD runs are enough for convergence within accuracy of 3 to 4 digits, if the initial effective potential is properly set up. The structure factors, thus obtained, show excellent agreement with the experimental data observed by x-ray and/or neutron scattering. \textcopyright{} 1996 The American Physical Society.

Polarization interaction in relation to structure of liquid metals

Following a short review of progress in understanding structure and forces in simple liquid metals such as Na and K, and in particular the role of the conduction electrons in mediating long-range oscillatory effective ion-ion interactions, attention is focused on polarization interactions. In such bulk liquid metals, oscillatory pair potentials o(R) of the long-range asymptotic form cos(2k F R)/R 3, where k F is the Fermi wavenumber, are shown to be corrected at large R by a polarization term falling off as R -4. The modifications brought about when the polarization interaction takes place in a heterogeneous environment such as that in a metal surface liquid or solid are discussed. The oscillatory interaction for a pair of ions parallel to such a planar metal surface is already known to be of shorter range than in bulk liquid metals, namely, cos (2k F R)/R 5. It is demonstrated here that for this same parallel configuration the polarization is also of short range, falling off as R -8. The case of arbitrar...

Ionic and electronic structures of liquid aluminium from the quantal hypernetted-chain equations combined with the molecular dynamics method

Liquid aluminium is a simple metal which can be modelled as an electron-ion mixture with pairwise interparticle interactions. On the basis of the density functional theory, the quantal hypernetted-chain (QHNC) formulation for the electron-ion mixture provides exact expressions for the electron-ion and ion-ion radial distribution functions (RDF), and shows that this electron-ion mixture can be treated as a quasi-one-component liquid interacting only through a pairwise interaction without many-body forces. Using the approximation that the exchange-correlation effect of the conduction electrons in the mixture is represented by the local-field correction (LFC) of the jellium model, the QHNC formulation offers a procedure for performing a first-principles molecular dynamics (MD) simulation where the effective ion-ion interaction is determined self-consistently with its liquid structure. Using the Geldart-Vosko (GV) LPC the structure factor of liquid aluminium near its melting point is calculated by this procedure (QHNC-MD) and is in fairly good agreement with experiment, in conjunction with the bridge function and the direct correlation function. The calculated ion-ion RDF exhibits a significant dependence on which kind of LFC is adopted in the QHNC-MD method in contrast with what is found in the case of liquid alkali metals where the LFC of the GV type and of the local-density-approximation type yield almost the same structure factors. The effective ion-ion potential from the QHNC-MD method with the GV LFC becomes a deep negative well where the potential of Dagens, Geldart and Taylor has a positive minimum. The electron-ion RDF is obtained in a consistent way with the density profile rho (r) of a neutral pseudoatom. The Ashcroft model potential with core radius rc=1.12aB produces an electron density distribution rho (r) and ion-ion RDF almost identical with the QHNC-MD results.