Variational Modified Hypernetted Chain Research Articles

Simulations and integral-equationtheories for dipolar density interacting disks.

Integral equationtheories (IETs) based on the Ornstein-Zernike (OZ) relation can be used as an analytical tool to predict structural and thermodynamic properties and phase behavior of fluids with low numerical cost. However, there are no studies of the IETs for the dipolar density interaction potential in two-dimensional systems, a relevant interdomain interaction in lipid monolayers with phase coexistence. This repulsive interaction arises due to the excess dipole density of the domains, which are aligned perpendicular to the interface. This work studies the performance of three closures of the OZ equationfor this novel system: Rogers-Young (RY), modified hypernetted chain (MHNC), and variational modified hypernetted chain (VMHNC). For the last two closures the bridge function of a reference system is required, with the hard disk being the most convenient reference system. Given that in two dimensions there is no analytical expressions for the hard disk correlation functions, two different approximations are proposed: one based on the Percus-Yevick (PY) approximation, and the other based on an extension of the hard spheres Verlet-Weis-Henderson-Grundke (LB) parametrization. The accuracy of the five approaches is evaluated by comparison of the pair correlation function and the structure factor with Monte Carlo simulation data. The results show that RY closure is satisfactory only for low-structured regimes. MHNC and VMHNC closures perform globally well, and there are no significant differences between them. However, the reference system in some cases affects their performance; when the pair correlation function serves as the measure, the LB-based closures quantitatively outperform the PY ones. From the point of view of its applicability, LB-based closures do not have a solution for all studied interaction strength parameters, and, in general, PY-based closures are numerically preferable.

A comparative study on surface tension, diffusion coefficient and shear viscosity coefficient of liquid transition metals

Surface tensions of liquid transition metals of the 3d, 4d and 5d series have been calculated using modified Mayer’s formula involving hard sphere (HS) interaction of liquids derived from first and second order approximations of Percus–Yevick (PY) solutions of isothermal compressibility. Effective HS diameter and packing fraction are key ingredients of this study. To determine them, we have used effective pair potential derived from both Bretonnet–Silbert (BS) pseudopotential model and many body potential obtained from embedded atom method (EAM) in conjunction with variational modified hypernetted chain (VMHNC) integral equation theory of liquid structure. Calculated values of surface tension are used to evaluate transport coefficients such as diffusion and shear viscosity coefficients. Comparing with experimental and simulated data, calculated results suggest that expression derived from second order approximation of PY solution with the combination of EAM potential and VMHNC theory works better than any other combinations for the concerned systems.

Calculation of diffusion coefficient of liquid less simple metals

Diffusion coefficient of liquid less simple metals has been studied using linear trajectory (LT) and small-step (SS) diffusion theories of liquid metals with Carnahan–Stirling (CS) approximation. Friction coefficients, the key ingredients of this study, are calculated using effective pair potentials, v(r), and static structure factors, S(q). For v(r), Brettonet–Silbert pseudopotential model has been chosen whereas for S(q), both variational modified hypernetted chain (VMHNC) integral equation and linearized Weeks–Chandler–Andersen (LWCA) perturbation theory have been employed. Calculated friction coefficients are found comparable to the available simulated data. Inclusion of CS approximation increases the value of friction coefficient obtained from hard part which dominates over rest of the coefficients. Applied LWCA theory provides slightly larger values of diffusion coefficients than those obtained from VMHNC. Comparing with literature values, calculated results suggest that the combination of LWCA theory along with LT and SS theories with CS approximation is excellent for calculation of diffusion coefficient.

Effects of interionic pair interactions on atomic transport properties of liquid Al

The effects of parameters used for tuning the interionic pair interaction of the Ashcroft’s pseudopotential model on the temperature-dependent atomic transport properties of liquid Al have been studied employing the Universal Scaling Laws (USLs) and Hard Sphere (HS) theories of liquid metals. Temperature-dependent effective HS diameter and excess entropy are the key ingredients of the applied theories. We have calculated them by using Ashcroft’s empty core (EMC) pseudopotential and the variational modified hypernetted chain (VMHNC) integral equation theory of liquid. Obtained results clearly suggest that the core radius in the interaction plays a major role in determining atomic transport properties of liquid Al for both USLs and HS theory. It is also observed that USLs are more sensitive than HS theories in response to variation of core radius.

Validity of the Stokes−Einstein relation in liquid 3d transition metals for a wide range of temperatures

The validity of Stokes−Einstein (SE) relations obtained from both slip and stick boundary conditions has been investigated for an extending temperature range approximately 250 K from the melting points of liquid Fe, Co and Ni using Dzugutov scaling scheme for transport coefficients. The basic ingredients of Dzugutov scaling scheme are the temperature dependent effective hard-sphere (HS) diameter, σ(T), and the excess entropy, Sex(T). Sex is calculated considering both two (S2) and many body approximations (ST) of liquid atoms. For both ingredients, we have applied variational modified hypernetted chain (VMHNC) integral equation theory in conjunction with both Brettonet−Silbert (BS) pseudopotential and many body potential obtained from embedded atom method (EAM). Calculated transport coefficients using the combination of EAM and ST are in better agreement with available literature values than any other applied combinations. We observe that SE relation holds for the studied representative systems when the combination of EAM potential and ST has been considered.

Surface entropy of liquid transition and noble metals

Abstract Surface entropy of liquid transition and noble metals has been investigated using an expression obtained from the hard-sphere (HS) theory of liquid. The expression is developed from the Mayer's extended surface tension formula [Journal of Non-Crystalline Solids 380 (2013) 42–47]. For interionic interaction in metals, Brettonet–Silbert (BS) pseudopotentials and embedded atom method (EAM) potentials have been used. The liquid structure is described by the variational modified hypernetted chain (VMHNC) theory. The essential ingredient of the expression is the temperature dependent effective HS diameter (or packing fraction), which is calculated from the aforementioned potentials together with the VMHNC theory. The obtained results for the surface entropy using the effective HS diameter are found to be good in agreement with the available experimental as well as other theoretical values.

Surface tension of liquid transition and noble metals

We have studied the surface tension of all liquid transition and noble metals using extended Mayer's empirical formula. For interionic interaction in metals, Bretonnet and Silbert (BS) pseudopotentials and the embedded atom method (EAM) potentials are chosen. Self-consistent variational modified hypernetted chain (VMHNC) integral equation theory is used to describe liquid state. The premier ingredients of the extended Mayer's formula are the effective hard sphere (HS) diameter and packing fraction. We calculated HS diameter using both BS and EAM potentials in conjunction with the VMHNC theory. We have found that the surface tension obtained using EAM potentials are in very good agreement with the available experimental data.

Calculation of surface entropy of liquid transition and noble metals

The surface entropies of liquid transition and noble metals Fe, Co, Ni, Cu, and Ag have been investigated. Surface entropy expression involving hard–sphere (HS) interaction in closed form is used. Since the HS diameter depends on metallic properties and temperature, the temperature dependent effective HS diameter is determined from a well-known perturbation theory, linearized Weeks–Chandler–Andersen (LWCA) and integral equation theory, variational modified hypernetted chain (VMHNC). Theoretical calculations are compared with the available experimental data, and found good agreement for some concerned systems.

Electronic Transport Properties of Liquid Less-Simple Metals

Electronic transport properties, namely the electrical resistivity and the thermoelectric power, of liquid less-simple metals, Zn, Cd, Hg, In, Tl, Sn, Pb, Sb, and Bi, are calculated using Ziman's theory. The effective electron–ion and ion–ion interactions are described by the Bretonnet-Silbert model. The static structure factors are evaluated by the self-consistent Variational Modified Hypernetted Chain (VMHNC) integral equation of liquids. The results for the electrical resistivity are fairly good when compared with experimental data, but the agreement improves significantly when the blurring of the Fermi surface due to the finite electron mean free path is accounted for. The values of the thermoelectric power, for most systems, have the same sign and order of magnitude as the experimental ones. The results for the thermopower also show that the contribution of the energy dependent term of the electron–ion potential is significant for the concerned systems.

Transferable Pair Potentials for Liquid Iron, Cobalt and Nickel

Effective inter-ionic pair potentials for liquid iron, cobalt and nickel are derived from second order pseudopotential perturbation theory with the transferable electron-ion potential of Fiolhais and co-workers which was originally developed for the solid state. The liquid structure is obtained by the thermodynamically self consistent liquid state theory, the variational modified hypernetted chain (VMHNC) approximation. It has been found that the calculated structural properties at the investigated thermodynamic states just above the melting point agree well with experiment. In this work we have determined the parameters of liquids Fe, Co and Ni for the universal choice of the evanescent core pseudopotentials of Fiolhais'. We have shown that this pseudopotential is transferable to the liquid state if used this parameterisation.

Structural, Thermodynamic and Transport Troperties of Liquid Noble and Transition Metals

We have investigated a number of structural, thermodynamic and atomic transport properties of various liquid noble and transition metals. The underlying theory combines a simple form of the N-body potential and the thermodynamically self-consistent variational modified hypernetted chain (VMHNC) theory of liquid. The static structure factors calculated by using the VMHNC resemble, as expected, the hard sphere (HS) values. Consequently the HS model is used to calculate thermodynamic properties, viz. the specific heat, entropy, isothermal compressibility and the shear viscosity of liquid Ni, Cu, Ag, and Au. The results are in reasonable accord with the experimental values.

Investigations of the Static and Dynamic Properties of Liquid Less Simple Metals

Static structure factors, S(q), thermodynamic properties and shear viscosities for liquid Zn, Cd, Hg. In. Tl, Sn, Pb, Sb, and Bi are investigated systematically. A model pseudotential which combines the sp- and d-band contributions is employed to derive interionic interactions. The liquid state is described by using the thermodynamically self-consistent variational modified hypernetted chain (VMHNC) integral equation theory, and also by using the linearised version of the Weeks-Chandler-Andersen (LWCA) thermodynamic perturbation theory of liquids. Results of calculations for all of the above properties are found to be in good agreement with available experimental data. The calculated results also reveal qualitatively that there is a relationship between the rate of change of viscosity with temperature and the depth of the potential well concerned.

Liquid state structure of some noble and transition metals

The static structure factors, S( q), for a number of liquid noble and transition metals are calculated. The underlying theory combines together a simple form of the N-body potential and the thermodynamically self-consistent variational modified hypernetted chain (VMHNC) theory of liquid. The static structure factors calculated by using the VMHNC resemble the hard sphere (HS) and these are consistent with experiments.

Calculations of g(r) for Liquid Cu and Ni Using Many-Body

The pair distribution function, g(r), for Ni and Cu at various temperatures above melting are investigated by using the Finnis-Sinclair (FS) many-body potentials and the thermodynamically self-consistent Variational Modified Hypernetted Chain (VMHNC) theory. The overall agreement with experiment is reasonably good. The calculations indicate that the many-body interactions, precisely taken care of by the FS potentials, are important for the study of g(r) for the liquid transition and noble metals. The results also permit us to examine the applicability of the temperature independent approximation of the FS potentials.

Static dielectric function of liquid lithium

The static dielectric function, ɛ(q, 0), of liquid lithium was calculated at four different temperatures, treating the liquid metal as a binary mixture of conduction electrons and ions. For the ions, a potential of interaction derived from the neutral pseudo atom (NPA) method and the variational modified hypernetted chain (VMHNC) theory of liquids were used. For the electrons, the response function which includes exchange and correlations obtained from the local field factor derived from the local density approximation (LDA) was used, in order to be consistent with the NPA method. the results show that, at the temperatures for which the calculations were carried out, the behaviour of ɛ(q) is dominated by the ionic contributions.

Structure and thermodynamic properties of liquid transition metals: An embedded-atom-method approach.

We have obtained the volume term and effective pair potentials for liquid transition metals using the embedded-atom method (EAM). The EAM embedding functions are fitted to bulk solid-state properties: the experimental Voigt average bulk and shear moduli and sublimation energies. The same fitting procedure is used for all the transition metals. This potential is used in conjunction with the variational modified hypernetted chain (VMHNC) theory of liquids to compute the static structure factors, Helmholtz free energies, internal energies, and entropies of the 3d, 4d, and 5d liquid transition metals. There is overall good qualitative agreement with experiment. The computed thermodynamic properties exhibit trends in accordance with experiment. They also exhibit the correct behavior as a function of temperature. But the calculations also reveal shortcomings in the interatomic potential. \textcopyright{} 1996 The American Physical Society.

A theoretical study of the static structure and thermodynamics of liquid lithium

The authors have studied the static structure and some thermodynamic properties of liquid lithium by using the variational modified hypernetted chain (VMHNC) approximation as the liquid state theory and several effective interatomic pair potentials, derived from different pseudopotentials already proposed in the literature. They also propose a new interatomic pair potential derived from the neutral pseudoatom method (NPA).

Liquid structure of titanium and vanadium; VMHNC calculations

The first successful calculations for the liquid structure S(q) of the early 3d transition metals are presented; they use effective pair interionic potentials and an integral equation theory of liquids. The effective pair potentials are obtained from a local form that assumes the superposition of the nearly free electron band, described by the empty-core model, and the d-band contribution, which is calculated by using an inverse scattering approach. The liquid state theory used in the calculations is the variational modified hypernetted chain (VMHNC) approximation. The agreement between the calculated S(q) and the available X-ray diffraction data for vanadium is reasonably good, but for titanium is only fair.

The pair distribution functions of the liquid alkali metals: Comparison between the VMHNC theory and molecular dynamics simulations

We discuss the application of a recently proposed thermodynamically self-consistent integral equation, the variational modified hypernetted chain (VMHNC) approximation, to the study of the structural properties of liquid metals. We show a comparison between the structure of the liquid alkali metals, as obtained within the VMHNC, and molecular dynamics simulations carried out using the same potentials and parametrization. The results show that the VMHNC is an accurate approximation for the study of the structure of liquid metals.

Comments on the variational modified-hypernetted-chain theory for simple fluids

The variational modified-hypernetted-chain (VMHNC) theory, based on the approximation of universality of the bridge functions, is reformulated. The new formulation includes recent calculations by Lado and by Lado, Foiles, and Ashcroft, as two stages in a systematic approach which is analyzed. A variational iterative procedure for solving the exact (diagrammatic) equations for the fluid structure which is formally identical to the VMHNC is described, featuring the theory of simple classical fluids as a one-iteration theory. An accurate method for calculating the pair structure for a given potential and for inverting structure factor data in order to obtain the potentialand the thermodynamic functions, follows from our analysis.