Effective Ion-ion Potential Research Articles

Dynamic Ion Structure Factor of Warm Dense Matter

The dynamics of the ion structure in warm dense matter is determined by molecular dynamics simulations using an effective ion-ion potential. This potential is obtained from abinitio simulations and has a strong short-range repulsion added to a screened Coulomb potential. Models based on static or dynamic local field corrections are found to be insufficient to describe the data. An extended Mermin approach, a hydrodynamic model, and the method of moments with local constraints are capable of reproducing the numerical results but have rather limited predictive powers as they all need some numerical data as input. The method of moments is found to be the most promising.

Primitive models of ions in solution from molecular descriptions: A perturbation approach

The development of simple, primitive model descriptions for electrolyte solutions is usually carried out by fitting the system parameters to reproduce some experimental data. We propose an alternative method, that allows one to derive implicit solvent models of electrolyte solutions from all-atom descriptions. We obtain analytic expressions for the thermodynamic and structural properties of the ions, which are in good agreement with the underlying explicit solvent representation, provided that ion association is taken into account. Effective ion-ion potentials are derived from molecular dynamics simulations and are used within a first-order perturbation theory to derive the best possible description in terms of charged hard-spheres. We show that our model provides a valid description for a series of 1-1 electrolytes.

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.

Solvent-averaged potentials for alkali-, earth alkali-, and alkylammonium halide aqueous solutions

We derive effective, solvent-free ion-ion potentials for alkali-, earth alkali-, and alkylammonium halide aqueous solutions. The implicit solvent potentials are parametrized to reproduce experimental osmotic coefficients. The modeling approach minimizes the amount of input required from atomistic (force field) models, which usually predict large variations in the effective ion-ion potentials at short distances. For the smaller ion species, the reported potentials are composed of a Coulomb and a Weeks-Chandler-Andersen term. For larger ions, we find that an additional, attractive potential is required at the contact minimum, which is related to solvent degrees of freedom that are usually not accounted for in standard electrostatics models. The reported potentials provide a simple and accurate force field for use in molecular dynamics and Monte Carlo simulations of (poly-)electrolyte systems.

Effective Interaction Potentials for Alkali and Alkaline Earth Metal Ions in SPC/E Water and Polarization Model of Hydrated Ions

In the first paper (J. Phys. Chem. B, 2006, 110, 10878), effective ion-ion potentials in SPC/E water were obtained for Me-Me, Me-Cl-, and Cl(-)-Cl- pairs, where Me is Li+, Na+, K+, Mg2+, Ca2+, Sr2+, and Ba2+ cations. In this second part of the study of effective interionic potentials, ion-ion distribution functions obtained from implicit-water Monte Carlo simulations of electrolyte solution with these potentials have been explored. This analysis verifies the range of applicability of the primitive model of electrolyte. It is shown that this approximation can be applied to monovalent electrolyte solutions in a wide range of concentrations, whereas the nature of ion-ion interactions is notably different for 2:1 electrolytes. An improved model of ions is discussed. The model includes approximations of the ion hydration shell polarization and specific short-range ion-ion interaction. It allows approximation of the potential of mean force acting on ions in strong electric fields of highly charged macromolecules and bilayers.

Effective Interaction Potentials for Alkali and Alkaline Earth Metal Ions in SPC/E Water and Prediction of Mean Ion Activity Coefficients

The potential of mean force (PMF) acting between two simple ions surrounded by SPC/E water have been determined by molecular dynamics (MD) simulations using a spherical cavity approach. Such effective ion-ion potentials were obtained for Me-Me, Me-Cl-, and Cl(-)-Cl- pairs, where Me is a Li+, Na+, K+, Mg2+, Ca2+, Sr2+, and Ba2+ cation. The ionic sizes estimated from the effective potentials are not pairwise additive, a feature in the frequently used primitive model for electrolytes. The effective potentials were used in Monte Carlo (MC) simulations with implicit water to calculate mean ion activity coefficients of LiCl, NaCl, KCl, MgCl2, CaCl2, SrCl2, and BaCl2. Predicted activities were compared with experimental ones in the electrolyte concentration range 0.1-1 M. A qualitative agreement for LiCl and a satisfactory agreement for NaCl were found, whereas the predictions for KCl by two K+ models were less coherent. In the case of alkaline earth metal ions, all experimental activities were successfully reproduced at c = 0.1 M. However, at higher concentrations, similar deviations occurred for all divalent cations, suggesting that the dependence of the permittivity on the salt concentration and the polarization deficiency arising from the ordering of water molecules in the ion hydration shells are important in such systems.

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.

Modeling Multibody Effects in Ionic Solutions with a Concentration Dependent Dielectric Permittivity

We report a new strategy to parametrize effective ion-ion potentials for implicit solvent simulations of charged systems. The effective potential includes a pair term and a Coulomb term that by means of a concentration dependent dielectric permittivity takes into account multibody effects. We demonstrate that this approach allows us to accurately reproduce the solution osmotic properties and the ion coordination up to concentrations of 2.8 M aqueous NaCl.

Vibrational dynamics of liquid gallium at 320 and970K

The microscopic ion dynamics of liquid gallium was investigated at $320\phantom{\rule{0.3em}{0ex}}\mathrm{K}$---that is, just above the melting point---and $970\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ by inelastic neutron scattering experiments and molecular dynamics simulations. The high quality of the experimental data allowed the observation of density fluctuation modes extending up to $1.0\phantom{\rule{0.3em}{0ex}}{\mathrm{\AA{}}}^{\ensuremath{-}1}$ and existing at both temperatures. At melting, an acousticlike mode propagating with a velocity definitely exceeding the sound velocity was observed, in agreement with the results of a recent inelastic x-ray scattering experiment. The mode velocity and damping were found to be almost temperature independent. The experimental response function was compared with the results of a molecular dynamics simulation, based on a simple model for the effective ion-ion potential which, however, did not contain any temperature-dependent parameter. The result worth noting is that, despite the simple potential, the simulation was capable to reproduce all the observed features of the measured dynamicstructure factor quantitatively and at both the temperatures.

An Accurate and Efficient Empirical Approach for Calculating the Dielectric Self-Energy and Ion−Ion Pair Potential in Continuum Models of Biological Ion Channels

This paper presents empirical formulas for calculating the dielectric self-energy and ion-ion pair interactions in cylindrical ion channels. The proposed approach can be extended to more complex channel structures, for example, (i) a "straight" channel with variable radius and (ii) a "curved" channel with constant radius. For calibration purposes, we compare results obtained based on the approximate effective potentials developed herein to exact electrostatic calculations obtained via the algorithm of Graf et al.: the agreement is satisfactory. A dynamic lattice Monte Carlo (DLMC) technique is used to further assess the accuracy and efficiency of the proposed empirical potentials. The concentration profiles and current-voltage curves produced with our simple empirical energy formulas are in excellent agreement with numerical results obtained using the algorithm of Graf et al., which calculates all relevant electrostatic forces exactly. The use of effective ion-ion potentials greatly reduces the computer memory required to perform DLMC ion permeation simulations in dielectrically inhomogeneous environments, thus enabling treatment of larger systems than can be handled by numerically exact techniques.

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.

Evaluation of effective ion-ion potentials in aqueous electrolytes.

We present high-accuracy simulation data for ion-ion radial distribution functions in NaCl aqueous electrolyte. From the data we evaluate ion-ion effective potentials via inverse Monte Carlo simulation procedure. Alternatively, we first evaluate effective direct correlation functions and then obtain effective potentials using the hypernetted-chain (HNC) approximation. Both methods are in excellent agreement, indicating that HNC approximation performs well with effective ion-ion potentials in aqueous solutions.

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.

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 $a.$

Density-functional theory of pair correlations in metallic hydrogen

The pair correlations in the metallic phase of hydrogen are reconsidered on the basis of a simple density-functional formulation of the free energy of the ion-electron plasma, which includes a square-gradient correction to the Thomas-Fermi kinetic energy of the degenerate electrons. A robust prescription is given for the prefactor of the square-gradient correction. The functional leads to a hypernetted-chain--like closure for the ion-ion and ion-electron correlation functions, which is solved iteratively, in conjunction with the coupled Ornstein-Zernike equations relating the matrices of pair and direct correlation functions. The resulting structure agrees well with available ab initio simulation data based on the Kohn-Sham functional. A density- and temperature-dependent effective ion-ion pair potential is obtained by formally reducing the initial two-component system to a one-component fluid of pseudoatoms. The results show strong deviations of the present nonlinear theory from the standard linear screening approach for ${r}_{s}>1$ (where ${r}_{s}$ is the usual inverse density parameter equal to the ratio of the electron sphere radius over the Bohr radius). The long-wavelength ion density fluctuations are strongly enhanced as the density drops, and at the lowest density ${(r}_{s}=1.5)$ the ion-ion pair structure and effective potential exhibit an unusual behavior, at the lower temperature explored in this paper $(T=3\ifmmode\times\else\texttimes\fi{}{10}^{3}\mathrm{K}),$ which may be interpreted as a precursor to an incipient plasma-insulator transition. Thermodynamic properties are estimated from the pair structure. The influence of nonlinear electron polarization on the equation of state is found to be surprisingly small, but the isothermal compressibility increases sharply at the lowest density.

Evaluation of thermodynamic functions of elemental crystals and liquids

Techniques are summarized for evaluating thermodynamic functions for pure elements in crystal and liquid phases. An accurate evaluation of the ion-motional free energy is given by quasiharmonic lattice dynamics at quantum temperatures, and computer simulations (e.g., molecular dynamics) at classical temperatures for both crystal and liquid. The computer simulations require knowledge of the effective ion-ion potentials, and since these are not generally available, two approximations for proceeding without them are discussed. First, neglecting anharmonicity in crystals leaves only the quasiharmonic ion-motional free energy, depending almost entirely on the characteristic temperature {theta}{sub 0}, which is the logarithmic moment of the quasiharmonic phonon frequencies. Second, identifying in the constant-density entropy of melting a universal disordering contribution {Delta}{approx_equal}0.80Nk provides approximate evaluation of the thermodynamic properties of liquids at melt. The errors of these approximations are assessed. {copyright} {ital 1997} {ital The American Physical Society}

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.

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.