An explicit expression for the static structure factor for a multi-Yukawa fluid: the one-component case

By using the mean spherical approximation, we obtain an analytical expression for the static structure factor (SSF) for a monodisperse system of particles interacting through a potential given by a hard-sphere contribution and M Yukawa terms. This expression depends on scaling matrix Γ, which is determined by solving a set of nonlinear equations. Our theoretical results show that using three Yukawa terms in the closure relation greatly improves the accuracy when compared with hypernetted-chain closure and Monte Carlo simulation data, which display a secondary low-k peak in the SSF, due to the formation of an intermediate range order structure governed by a short-range attraction and a long-range repulsion. We discuss the appearance of such a peak in terms of the microstructure order given by the radial distribution function. Following the original proposal made by Waisman (Mol Phys. 1973; 25:45–48), we give an explicit expression that improves the structural properties of a hard-sphere system.     

A generalized any-particle propagator theory: Calculations of nucleon's binding energies

Generalized one-particle propagator calculations were performed for fermions in atoms: neutrons, protons, and electrons. For this purpose, multicomponent Hartree-Fock equations were implemented using Gaussian basis sets where, for nucleons, we consider a non-Coulombic interaction, through a two-term Yukawa scalar potential and the interaction between electrons and the electrons with positive charge (protons) through a Coulombic potential. The strategy for evaluating the required interaction integrals follows Obara-Saika and Head-Gordon recurrence relations combined with the generalized Boys function suggested by Ten-no. Calculations on the isotopes ²H, ³H, ³He, ⁴He, ⁶Li, ⁶Be, ⁷Li, and ⁸Be were realized to test the accuracy of Koopmans' approximation and a second-order generalized one-particle propagator. Yukawa potentials were parametrized to reproduce nuclear properties as kinetic energies and radial distributions of density. These potentials produced the reference nuclear Hartree-Fock calculations on which fully ab initio propagator calculations were performed for these non-Coulombic potentials. This allowed us to explore the electronic structure of isotopes in an extended nucleus context.     

Thermodynamic and structural properties of repulsive hard-core Yukawa fluid: integral equation theory, perturbation theory and Monte Carlo simulations

The thermodynamic and structural properties of purely repulsive hard-core Yukawa particles in the fluid state are determined through Monte Carlo simulation and modeled using perturbation theory and integral equation theory in the mean spherical approximation (MSA). Systems of particles with Yukawa screening lengths of 1.8, 3.0, and 5.0 are examined with results compared to variations of MSA and perturbation theory. Thermodynamic properties were predicted well by both theories in the fluid region up to the fluid-solid phase boundary. Further, we found that a simplified exponential version of the MSA is the most accurate at predicting radial distribution function at contact. Radial distribution function of repulsive hard-core Yukawa particles are also reported. The results show that methods based on MSA and perturbation theory that are typically applied to the attractive hard-core Yukawa potential can also be extended to the purely repulsive hard-core Yukawa potential.     

Critical parameters and spherical confinement of H atom in screened Coulomb potential

Critical parameters in three screened potentials, namely, Hulthén, Yukawa, and exponential cosine screened Coulomb potential are reported. Accurate estimates of these parameters are given for each of these potentials, for all states having . Comparison with literature results is made, wherever possible. Present values compare excellently with reference values; for higher n, ?, our results are slightly better. Some of these are presented for first time. Further, we investigate the spherical confinement of H atom embedded in a dense plasma modeled by an exponential cosine screened potential. Accurate energies along with their variation with respect to box size and screening parameter are calculated and compared with reference results in literature. Sample dipole polarizabilities are also provided in this case. The generalized pseudospectral method is used for accurate determination of eigenvalues and eigenfunctions for all calculations. © 2016 Wiley Periodicals, Inc.     

Convergent perturbation studies in screened coulomb potential systems: analytic evaluations up to third order for the Yukawa case

This is the first of a series of papers on the perturbative treatment of screened coulomb potential systems in quantum mechanics. Its content is mainly devoted to the evaluation of first four terms in a convergent energy expansion of Yukawa potential. For this purpose, a weighted eigenvalue problem of Laplacian accompanied by spherical symmetry is employed to find the inverse of the Schrödinger operator for unperturbed case (which is assumed to be the Hamiltonian of Hydrogen-like systems). Some very encouraging numerical results are also given for illustrative purposes.     

Convergent perturbation studies in screened coulomb potential systems: a high precision numerical algorithm via Laguerre basis set

In this work, a high precision algorithm is developed to determine the discrete spectrum of screened coulomb potential systems. The algorithm is mainly based upon the use of the perturbation of a hydrogen-like operator by a bounded operator. The Laguerre basis set expansion is employed in the procedure to obtain the operator inversion. Although a functional analytic analysis of errors and proof of convergence theorem are still lacking, it appears, numerically, that the method rapidly converges for bounded screened coulomb potential. Extremely accurate numerical results for the bound-state energies, in the case of Yukawa potential, are presented for illustrative purposes.     

硬核Yukawa流体中胶体粒子间的耗尽势

基于Roth、Evans和Dietrich有关耗尽势的密度泛函理论研究了硬核Yukawa(HCY)流体中胶体粒子间的耗尽势.在极稀溶液条件下,通过计算两个胶体粒子在不同条件下的耗尽势,分析了HCY流体的相关因素对耗尽势的影响.结果表明,胶体粒子与溶剂分子的尺寸比率、HCY流体分子间的相互作用、HCY流体分子的体相密度以及胶体粒子与流体分子之间的相互作用等因素均可对胶体粒子间耗尽势产生显著影响.研究结果可为实验上调控胶体粒子间的相互作用提供可能的线索.     

Phase diagram of a binary symmetric hard-core Yukawa mixture

We assess the accuracy of the self-consistent Ornstein-Zernike approximation for a binary symmetric hard-core Yukawa mixture by comparison with Monte Carlo simulations of the phase diagrams obtained for different choices of the ratio alpha of the unlike-to-like interactions. In particular, from the results obtained at alpha=0.75 we find evidence for a critical endpoint in contrast to recent studies based on integral equation and hierarchical reference theories. The variation of the phase diagrams with range of the Yukawa potential is investigated.     

One-range addition theorems for combined Coulomb and Yukawa like central and noncentral interaction potentials and their derivatives

In this work we present the combined one-range addition theorems for arbitrary Coulomb and Yukawa like central and noncentral interaction potentials and their first and second derivatives occurring in the Hartree–Fock–Roothaan approximation and explicitly correlated methods, and also in the study of electric field and its gradient induced by electrons at the nuclei of a molecule. The relationships obtained for addition theorems are valid for the arbitrary parameters of potentials. PACS: 21.60.-n, 21.60.Gx AMS Subject classification: 81-V55, 81V45     

A new method to determine electrostatic potential around a macromolecule in solution from molecular wave functions

The three-dimensional reference interaction site model integral equation theory (3D-RISM) combined with the ab initio molecular orbital method (3D-RISM-SCF) is applied to a solvated macromolecular system. The solvation structure around a solute molecule is obtained from the 3D-RISM integral equation under the electrostatic potential of the solute molecule, calculated by the ab initio molecular orbital theory. The electrostatic potential should be calculated on each grid point in the three-dimensional real space. Therefore, the calculation of the electrostatic potential is the most time consuming part in this method. In this article, we propose a new procedure to save the computational cost for calculating the electrostatic potential and the solvated fock matrix. The strategy of this procedure is to evaluate the electrostatic potential and the solvated fock matrix in different ways, depending on the distance between solute and solvent. Inside the repulsive cores of solute atoms, it is possible to avoid the calculation of electrostatic potential and solvated Fock matrix by assuming the potential to be infinity. In the region sufficiently far from solute, they are evaluated classically by putting the effective point charge on each atom. In the intermediate region, the electrostatic potential is evaluated directly by integrating the molecular orbitals of the solute molecule. The electronic structure and the energy gradient of Methionine-Enkephalin and solvation structure are estimated by using this procedure in aqueous solution, and are compared with the results from other procedures. The results are compared also with those from the continuum model.     

Transport Properties of Simple Fluids from the Soft‐Core Double Yukawa Potential

The present work is concerned with checking a new and simple pair potential function (soft‐core double Yukawa potential) for noble gases by calculation of the transport properties. The viscosity, thermal conductivity and self diffusion coefficient in dilute gas limit in the temperature range of 298‐1400 K are calculated and agreement with the measurements is, in general, within the experimental error. A comparison of the calculated and experimental values of the viscosity, thermal conductivity and the diffusion coefficients yields an average absolute deviation of 0.5%, 1.5% and 1.2%, respectively. Also, the calculated transport properties from this potential have been compared with those calculations via the accurate experimental potential and also the corresponding state.     

Melting line of charged colloids from primitive model simulations

We develop an efficient simulation method to study suspensions of charged spherical colloids using the primitive model. In this model, the colloids and the co- and counterions are represented by charged hard spheres, whereas the solvent is treated as a dielectric continuum. In order to speed up the simulations, we restrict the positions of the particles to a cubic lattice, which allows precalculation of the Coulombic interactions at the beginning of the simulation. Moreover, we use multiparticle cluster moves that make the Monte Carlo sampling more efficient. The simulations are performed in the semigrand canonical ensemble, where the chemical potential of the salt is fixed. Employing our method, we study a system consisting of colloids carrying a charge of 80 elementary charges and monovalent co- and counterions. At the colloid densities of our interest, we show that lattice effects are negligible for sufficiently fine lattices. We determine the fluid-solid melting line in a packing fraction eta-inverse screening length kappa plane and compare it with the melting line of charged colloids predicted by the Yukawa potential of the Derjaguin-Landau-Verwey-Overbeek theory. We find qualitative agreement with the Yukawa results, and we do not find any effects of many-body interactions. We discuss the difficulties involved in the mapping between the primitive model and the Yukawa model at high colloid packing fractions (eta>0.2).     

Use of the Yukawa fluid as the reference system in perturbation theory

The Weeks-Chandler-Anderson (WCA) perturbation theory is studied utilising recent results for the Yukawa model fluid. Replacing the attractive tail of the Lennard-Jones potential with a Yukawa tail, where the Yukawa parameters are chosen using a least squares fit, it is shown that accurates field dstribution functions can be generated via the EXP approximation of the WCA optimized cluster theory. The comparative case and accuracy with which the correlation functions for the Yukawa fluid can be compared render this a very useful method for studying the equilibrium properties of simple liquids.     

Effective multipoles and Yukawa electrostatics in dressed molecule theory

In this paper we derive the multipolar expansion of the screened Coulomb potential in electrolyte solutions with molecular solvent. The solute and solvent molecules can have arbitrary sizes, shapes, and internal charge distributions. We use the exact statistical mechanical definition of renormalized charge distributions coming from "dressed molecule theory" to determine the effective multipoles of a molecule immersed in an electrolyte. The effects of many-body correlations are fully included in our formally exact theory. We restrict ourselves to sufficiently dilute solutions so the screened Coulomb potential decays for large distances like a Yukawa function, exp(-kappa r)/r, where r is the distance and 1/kappa is the decay length (it is normally different from the Debye length). The resulting "Yukawa electrostatics" differ in many respects from ordinary, unscreened electrostatics. The "Yukawa charge" of a molecule (the lowest order moment in the multipolar expansion) is in general not equal to its Coulombic charge and it is not the integral of the renormalized charge distribution of the molecule. Moreover, as shown in this paper, the multipolar expansion of the Yukawa potential does not correspond, contrary to the case of the Coulomb potential, to its asymptotic expansion for large r. As a consequence, the charge term in the multipolar expansion is not the leading term in the asymptotic expansion. Instead, for large r values, multipoles of all orders contribute to the leading asymptotic term. Thus, the electrostatic potential from, for example, an electroneutral solvent molecule in an electrolyte solution has generally the same range as that from an ion. The proper asymptotic expansion for electrostatic interactions in electrolytes is derived. It is briefly shown how the multipole expansion formalism can also be applied in the Poisson-Boltzmann approximation for primitive model electrolytes.     

用重整化群理论研究胶体模型体系的相行为

用yukawa势能函数表达胶体颗粒之间的吸引作用。用Duh-Mier-Y-Teran状态方 程表达液相Helmholtz自由能。用一阶微扰理论、固体硬球径向分布函数解析式和 改进的胞腔模型建立固相状态方程，结合建立的状态方程和重整化群理论。研究了 胶体模型体系的液-液相平衡和液-固相平衡。研究表明，颗粒之间色散作用量程参 数的变化对胶休到本世纪末茶杯 系的相行为有特殊需要影响。所得结果与分子模 拟数据吻合良好。     

Fundamental aspects of electrostatic interactions and charge renormalization in electrolyte systems

The consistent inclusion of ion-ion correlations and molecular solvent effects in electrolyte theory can be expressed in a physical formalism, where the particles acquire a renormalized charge density and where they interact electrostatically via a generalized screened Coulomb potential. The latter usually decays for large distances r like a Yukawa function exp(-κr)/r, where 1/κ is the decay length (normally different from the Debye length), but, for smaller r, the screened Coulomb potential is a more complicated function. The resulting electrostatic theory, “Yukawa electrostatics”, differs in many important aspects from ordinary (unscreened) Coulomb electrostatics. In the present paper, we give illustrations and explanations of some important differences between Coulomb and Yukawa electrostatics. The effective “Yukawa charge” of a particle differs from the ordinary Coulombic charge. Furthermore, contributions from multipoles of all orders contribute, in general, to the leading asymptotic term in the potential for large r, which decays like exp(-κr)/r. Thus, the electrostatic potential from, for example, an electroneutral molecule with an internal charge distribution has generally the same range as the potential from an ion. Some implications of these facts are pointed out. The presentation is based on exact statistical mechanical analysis where all particles are treated on the same fundamental level, but the main focus lies on physical consequences and interpretations of the theory. The text was submitted by the author in English.     

Interfacial and coexistence properties of soft spheres with a short-range attractive Yukawa fluid: molecular dynamics simulations

Molecular dynamics simulations have been carried out to obtain the interfacial and coexistence properties of soft-sphere attractive Yukawa (SAY) fluids with short attraction range, κ = 10, 9, 8, 7, 6, and 5. All our simulation results are new. These data are also compared with the recently reported results in the literature of hard-core attractive Yukawa (HAY) fluids. We show that the interfacial and coexistence properties of both potentials are different. For the surveyed systems, here we show that all coexistence curves collapse into a master curve when we rescale with their respective critical points and the surface tension curves form a single master curve when we plot γ* vs. T/T(c).     

Application of the optimized Baxter model to the hard-core attractive Yukawa system

We perform Monte Carlo simulations on the hard-core attractive Yukawa system to test the optimized Baxter model that was introduced by Prinsen and Odijk [J. Chem. Phys. 121, 6525 (2004)] to study a fluid phase of spherical particles interacting through a short-range pair potential. We compare the chemical potentials and pressures from the simulations with analytical predictions from the optimized Baxter model. We show that the model is accurate to within 10% over a range of volume fractions from 0.1 to 0.4, interaction strengths up to three times the thermal energy, and interaction ranges from 6% to 20% of the particle diameter, and performs even better in most cases. We furthermore establish the consistency of the model by showing that the thermodynamic properties of the Yukawa fluid computed via simulations may be understood on the basis of one similarity variable, the stickiness parameter defined within the optimized Baxter model. Finally, we show that the optimized Baxter model works significantly better than an often used, naive method determining the stickiness parameter by equating the respective second virial coefficients based on the attractive Yukawa and Baxter potentials.     

Steric interactions between physically adsorbed polymer-coated colloidal particles: soft or hard?

The steric interaction potential between colloidal particles imparted by adsorbed polymer layers is directly related to their structure. Due to the complexity of these interfacial structures, the steric potential may behave differently at different interparticle separations. In this study, we proposed a combined model of the equivalent hard-sphere model (EHS) and the Hayter-Penfold/Yukawa model (HPY) to describe the steric potential due to adsorbed homopolymers on colloidal particles. The EHS potential describes the dense train/small-loop region and the HPY potential the more diffuse tail/long-loop region. The steric potential was extracted from the structure factors measured by small-angle neutron scattering (SANS). It was found that this combined model gave better agreement with experimental data than either of its component models alone. This study also shows that the adsorbed polymer layer in a good solvent partially collapses when the layers approach one another, which is also supported by an NMR solvent relaxation study.     

Density functional theory for Yukawa fluids

We develop an approximate field theory for particles interacting with a generalized Yukawa potential. This theory improves and extends a previous splitting field theory, originally developed for counterions around a fixed charge distribution. The resulting theory bridges between the second virial approximation, which is accurate at low particle densities, and the mean-field approximation, accurate at high densities. We apply this theory to charged, screened ions in bulk solution, modeled to interact with a Yukawa potential; the theory is able to accurately reproduce the thermodynamic properties of the system over a broad range of conditions. The theory is also applied to "dressed counterions," interacting with a screened electrostatic potential, contained between charged plates. It is found to work well from the weak coupling to the strong coupling limits. The theory is able to reproduce the counterion profiles and force curves for closed and open systems obtained from Monte Carlo simulations.