Ion-ion Radial Distribution Functions Research Articles

THERMODYNAMIC PROPERTIES OF DENSE HYDROGEN PLASMAS WITH PARTIALLY DEGENERATE SEMICLASSICAL IONS

In this article, we investigated the thermodynamic properties of a one-component dense non-ideal hydrogen plasma with semiclassical non-ideal ions against the background of degenerate quantum electrons. The effective potential of the ion-ion interaction that takes into account the quantum mechanical effects of diffraction was used as a model for the interaction. Ion-ion radial distribution functions were calculated based on the solution of the Ornstein-Zernike integral equation in the hypernetted-chain (HNC) approximation. In the calculations, the effective interaction potential was used as a micropotential since only the screening due to the uniform background (i.e., electrons) was taken into account, but not the screening due to the interaction between the ions themselves. In addition, the effective potential takes into account only the quantum effect of ion diffraction. Thermodynamic properties, such as the correlation energy and the non-ideal component of the equation of state, were calculated based on the obtained radial distribution functions and the interparticle interaction potential. Thermodynamic properties were presented as a percentage between the results based on the effective potential and the Yukawa potential depending on the density and coupling parameter values. The difference between the results is greater in denser plasma and at higher values of the coupling parameters.

A Neutron Diffraction and Molecular Dynamics Investigation of Acetate-Based Ionic Liquids as Solvents for Glucose

The liquid state structure of the ionic liquid, 1-ethyl-3-methylimidazolium acetate, and the solute/solvent structure of glucose dissolved in the ionic liquid at a 1:6 molar ratio have been investigated at 323 K by molecular dynamics simulations and neutron diffraction experiments using H/D isotopically substituted materials. Interactions between hydrogen-bond donating cation sites and polar, directional hydrogen-bond accepting acetate anions are examined. Ion-ion radial distribution functions for the neat ionic liquid, calculated from both MD and derived from the empirical potential structure refinement model to the experimental data, show the alternating shell-structure of anions around the cation, as anticipated. Spatial probability distributions reveal the main anion-to-cation features as in-plane interactions of anions with imidazolium ring hydrogens and cation-cation planar stacking. Interestingly, the presence of the polarised hydrogen-bond acceptor anion leads to increased anion-anion tail-tail structuring within each anion shell, indicating the onset of hydrophobic regions within the anion regions of the liquid.

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.

Shear viscosity of molten alkali halides from equilibrium and nonequilibrium molecular-dynamics simulations

The shear viscosity of molten NaCl and KCl was calculated through equilibrium (EMD) and nonequilibrium molecular-dynamics (NEMD) simulations in the canonical (N,V,T) ensemble. Two rigid-ion potentials were investigated, namely, the Born-Mayer-Huggins-Tosi-Fumi potential and the Michielsen-Woerlee-Graaf-Ketelaar potential with the parameters proposed by Ladd. The NEMD simulations were performed using the SLLOD equations of motion [D. J. Evans and G. P. Morriss, Phys. Rev. A 30, 1528 (1984)] with a Gaussian isokinetic thermostat and the results are compared with those obtained from Green-Kubo EMD (N,V,T) simulations and experimental shear viscosity data. The NEMD zero strain rate shear viscosity, eta(0), was obtained by fitting a simplified Carreau-type equation and by application of mode-coupling theory, i.e., a eta-gamma(1/2) linear relationship. The values obtained from the first method are found to be significantly lower than those predicted by the second. The agreement between the EMD and NEMD results with experimental data is satisfactory for the two potentials investigated. The ion-ion radial distribution functions obtained with the two rigid-ion potentials for both molten salts are discussed in terms of the differences between the two models.

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.

Microscopic structure of liquid dimethyl sulphoxide and its electrolyte solutions: molecular dynamics simulations

Molecular dynamics (MD) simulations of pure dimethyl sulphoxide (DMSO) and solutions of Na+, Ca2+, Cl−, NaCl and CaCl2 in DMSO have been performed at 298.15 K and 398.15 K in NVT ensembles by using a four-interaction-site model of DMSO and reaction field method for Coulombic interactions. The structure of solvent, ion-solvation shells and ion-pairs have been analysed by employing a concept of coordination centres and characteristic vectors of the solvent molecule. Results are given for atom-atom (corresponding to DMSO), ion-atom and ion-ion radial distribution functions (RDFs), orientation of the DMSO molecules and their geometrical arrangements in the first solvation shells of the ions (Na+, Ca2+, Cl−). A preferential formation of cyclic dimers with antiparallel alignment between dipole moments of nearest-neighbour molecules in the pure solvent is found. Geometrical models of the first coordination shells of the ions in ‘infinitely dilute solutions’ are proposed. Ion-ion RDFs in NaCl-DMSO and CaCl2-DMSO solutions reveal the presence of both solvent separated (SSIP) and contact (CIP) ion pairs. The structures of the solvation shells of such ion pairs are also discussed.

Detailed microscopic study of 1 M aqueous NaCl solution by computer simulations

Abstract Structural and dynamics properties of aqueous NaCl 1M solution were studied from molecular dynamics simulation data obtained with 2117 rigid water molecules, 40 Na + and 40 Cl − at 293K. The stability of the local structures formed by ion pairs was determined first by their life times: 0.13, 0.14 and 0.27 ps for, respectively, negatively charged, neutral and positively charged ion pairs. The non-neutral pairs are stabilized by, at least, one counterion. The nature of the peaks and bumps of the ion-ion radial distribution functions can be recovered from structural analysis so that it is possible to conclude that large ionic clusters stabilized by hydration molecules can be formed in electrolyte solutions. Self-diffusion coefficient analyses reinforced the clusters' formation.

Osmotic and activity coefficients from effective potentials for hydrated ions

Based on a method we previously suggested [Phys. Rev. E 52, 3730 (1995)], effective interaction potentials between ${\mathrm{Na}}^{+}$ and ${\mathrm{Cl}}^{\mathrm{\ensuremath{-}}}$ ions have been derived from interionic radial distribution functions (RDF) in molecular dynamics (MD) simulations of aqueous NaCl solution. The effective interaction potentials between the hydrated ions, which reproduce the original ion-ion RDF curves, can be used further to construct a corresponding ionic solution in a much larger scale and to calculate any properties dependent on the structure of the electrolyte solution. In a subsequent Monte Carlo (MC) simulation, using the effective potentials, the osmotic and activity coefficients are calculated for the ions. Calculation of these properties directly from atomic MD or MC simulations is beyond the capacity of the present computers due to the very large number of molecules required in the simulations to obtain reliable results. A very good agreement with the experimental results is obtained. Effects of three-body interactions and concentration dependencies of the effective potentials are discussed.

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.

Calculation of effective interaction potentials from radial distribution functions: A reverse Monte Carlo approach.

An approach is presented to solve the reverse problem of statistical mechanics: reconstruction of interaction potentials from radial distribution functions. The method consists of the iterative adjustment of the interaction potential to known radial distribution functions using a Monte Carlo simulation technique and statistical-mechanics relations to connect deviations of canonical averages with Hamiltonian parameters. The method is applied to calculate the effective interaction potentials between the ions in aqueous NaCl solutions at two different concentrations. The reference ion-ion radial distribution functions, calculated in separate molecular dynamics simulations with water molecules, are reproduced in Monte Carlo simulations, using the effective interaction potentials for the hydrated ions. Application of the present method should provide an effective and economical way to simulate equilibrium properties for very large molecular systems (e.g., polyelectrolytes) in the presence of hydrated ions, as well as to offer an approach to reduce a complexity in studies of various associated and aggregated systems in solution.

A simple test for evaluating the truncation effects in simulations of systems involving charged groups

We report the results from a molecular dynamics (MD) simulation on a 1.0 M aqueous NaCl solution using the classical SPC water model and a treatment of long-range electrostatic forces involving a 9–16 Å twin-range cut-off. This study was undertaken to explore the importance of truncation effects in simulations involving charged species which employ cut-offs at longer range than typically used in MD. Artefacts were discerned in the ion-ion radial distribution functions at ≈ 16 Å, indicating that increasing the length scale of the truncation scheme does not necessarily lead to reliable trajectories. Our results indicate that ‘charge group-charge group’ radial distribution functions are a sensitive test for the detection of artefacts due to truncation and it is suggested that they should be used as a routine screening device in the analysis of MD systems involving charged groups.

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.

Ion-ion and electron-ion correlations in liquid metallic sodium calculated from the nucleus-electron model

On the basis of the density-functional theory with the use of the hypernetted-chain approximation, a set of integral equations for the ion-ion and electron-ion radial distribution functions (RDFs) have been derived for a liquid metal as a nucleus-electron mixture; its liquid and electronic structures can be determined from the atomic number ZA. This formulation is applied to liquid metallic sodium at temperature 100 degrees C; these integral equations are solved in a self-consistent manner to obtain the ion-ion and electron-ion RDFS, the electron-density distribution of a pseudoatom rho (r), and the effective interatomic potential veff(r) at the same time. The ion-ion structure factor of Na at 100 degrees C, thus calculated, shows an excellent agreement with the experiment as well as the ion-on RDF; the effective interatomic potential veff(r) giving this ion-on RDF indicates a quite similar behaviour to that extracted from the measured structure factor by Reatto et al. (1986), especially near the repulsive-core region. However, the electron-ion RDF and the pseudoatom-electron density rho (r), obtained recently from the difference between structure factors from X-ray and neutron experiments, show large deviations from the calculated ones; this means that to extract these quantities the experiment should be performed in a more precise manner. For comparison, an effective interatomic potential is constructed by the use of the Ashcroft pseudopotential with a core radius 0.905 AA, which yields almost the same electron-ion RDF and the same screening charge rho (r) except near the core region in addition to the ion-ion RDF as obtained by the full self-consistent method; the Ashcroft pseudopotential is shown to be appropriate in treating liquid Na in contrast with liquid Li, where it is totally invalid.