Coulomb interactions in a computer simulation of a system periodic in two directions

The integral representation of the gamma function and the Poisson summation formula are used to calculate the interaction energy of charged particles in a 3-dimensional system periodic in two directions. A parallelogram shape simulation box is considered. Calculations are carried out for interactions described by any inverse power, and analytical continuation of the energy function leads to the final expression for the Coulomb interaction energy. Summation over the simulation box replica along one or the other side of the box base is replaced by summation in reciprocal space. Therefore there are two equivalent formulas for the potential energy that offer the possibility of avoiding slowly convergent series. The energy expressions are identical to those obtained from the Lekner method. The special case is considered where the functions defining the energy are infinite, i.e. when two charges lie on a line parallel to the simulation box side that was chosen to convert real space summation into reciprocal space.     

A behavior model of a magnetorheological fluid in direct shear mode

A model that considers the mutual interaction between particles and the external field in a magnetorheological (MR) fluid is proposed. The model predicts the magnetization, interaction energy density, and shear stress against an imposed strain along the planar direction under a uniform magnetic field. Using the Lekner summation method, slowly convergent magnetization functions are transformed into rapidly convergent ones. By applying the proposed model to an application suitable for commercial clutches and dampers working in direct shear mode, it is revealed that the mean magnetization vector and the associated functional quantities of the MR fluid behave harmonically with respect to the imposed shear strain.     

Lekner summations and Ewald summations for quasi-two-dimensional systems

The purpose of this work is to carry out a comparison between the Ewald quasi-2D and Lekner summation methods. These methods were derived to treat the long-range electrostatic interactions in systems periodic in two directions, but bound in the third. The comparison is performed by Monte Carlo simulations on a very simple system, a bilayer of point ions; samplings of the phase space, average energies and structure functions are compared. When correctly implemented, the Lekner summation method is found to be in close agreement with the Ewald quasi-2D method; otherwise, a very complicated bias may plague computations.     

Yukawa potentials in systems with partial periodic boundary conditions. II. Lekner sums for quasi-two-dimensional systems

Yukawa potentials may be long-ranged when the Debye screening length is large. In computer simulations, such long-ranged potentials have to be taken into account with convenient algorithms to avoid systematic bias in the sampling of the phase space. Recently, we provided Ewald sums for quasi-two-dimensional systems with Yukawa interaction potentials [J. Chem. Phys. 126, 056101 (2007); Molec. Phys. paper I of this series]. Sometimes, Lekner sums are used as an alternative to Ewald sums for Coulomb systems. In the present work, we derive the Lekner sums for quasi-two-dimensional systems with Yukawa interaction potentials and we give numerical tests for practical implementations. The main result of this paper is to emphasize that Lekner sums cannot be considered as an alternative to Ewald sums for Yukawa potentials. As a conclusion to this work: Lekner sums should not be used for quasi-two-dimensional systems with Yukawa interaction potentials.     

Behavioral model for magnetorheological fluid under a magnetic field using Lekner summation method

Magnetorheological (MR) fluid is used for various applications due to its controllable viscosity. To predict the behavior of MR fluid under certain three-dimensional (3D) magnetic and shear strain fields, it is essential to model the fluid in an appropriate manner. The behavioral models used in the previous research, however, have serious limitations because most of them oversimplify the inter-particle interactions and employ assumptions valid only under specific geometric configurations and field conditions. In this study, a new model that can predict the behavior of MR fluid under arbitrary 3D magnetic and shear strain fields is proposed. The present work considers an MR fluid configured as a 3D infinite lattice structure. Using the proposed model, the shear stress components themselves, not the dipolar interaction energy, are calculated directly to avoid the mathematical singularity otherwise encountered. The resulting stress functions of the proposed model are transformed into rapidly convergent functions using the Lekner summation method. Finally, the characteristics of the stiffened MR fluid under a magnetic field are investigated using the transformed functions. Numerical computations on the original and transformed functions are performed and compared under selected conditions to ensure the validity and prove the high convergence efficiency of the proposed model.     

On the force of electrostatic interaction between two conducting spheres

A compact solution is obtained to the problem on the force of interaction between two conducting spheres with preset charges on their surfaces in zero external field. The derivation is based on exact solution of the problem of the potential distribution in the bispherical coordinate system. The expression for the force was derived by differentiating the potential energy of interaction between the spheres with respect to the distance between their centers. It is shown using numerical calculations that with decreasing distance between the spheres, the ratio of their charges for which the forces of interaction between the charges are zero tends to the ratio of the charges of contacting spheres. It follows hence that for any ratio of charges of the same polarity, which differs from the ratio of charges of the contacting spheres, there always exists a small distance between the spheres, at which they attract each other.     

Lekner summation of dipolar interaction in quasi-two-dimensional simulations

The Lekner method for calculation of electrostatic interactions in periodically replicated simulation cells is extended to quasi-two-dimensional systems of particles with dipolar interactions. The electric field, potential energy, forces and torques are expressed through rapidly converging series of modified Bessel functions. The method contains no arbitrary parameters, and has no limitations on the simulation box width.     

Interaction of two macroparticles in a nonequilibrium plasma

The interaction of two macroparticles in a nonequilibrium plasma at elevated pressures has been investigated. An asymptotic theory of screening, which leads to a two-exponential dependence of the macroparticle potential on distance with different screening constants, is used to determine the electrostatic energy of the system of charges associated with the two macroparticles. The dependence of the electrostatic energy on interparticle distance has been found to have a minimum, as in an equilibrium plasma. The interaction force between the macroparticles has been determined; it turned out to be asymmetric—for different charges, the forces acting on the first and second macroparticles are not equal. This is the result of an asymmetric charge separation near macroparticles with differing charges and indicates that the interaction force in a nonequilibrium plasma is nonpotential. The forces are equal for identical macroparticles or in an equilibrium plasma and the potential energy of the interaction between the macroparticles has been determined for these cases. Attraction between likely charged particles with different (in magnitude) charges has been found to be possible when they come very close together. Relations to determine the modified coupling parameter for an interaction potential that consists of two exponential terms with different screening constants have been derived.     

Molecular dynamics simulations of liquid water using various long-range electrostatics techniques

Water is one of the most extensively studied molecules, owing to its crucial role in biological processes. The water molecule is both highly polar and highly polarizable. Properties of water computed from molecular simulations are therefore critically dependent on both the intermolecular potential and the method for computing long-range electrostatic corrections. In this paper, the effects of the potential and the long-range electrostatic corrections are quantified for liquid water from 260 to 400?K. Simulations were carried out for a system of 256 molecules in the NVT ensemble. Thermodynamic, structural, dynamical, hydrogen bonding and dielectric properties have been computed for the flexible SPC and rigid SPC, SPC/E, TIP4P, TIP4P-Ew and TIP4P-FQ potentials, using the Lekner, Ewald and reaction field techniques to handle long-range electrostatics. The Lekner method gave the best overall agreement with experimental data, while the reaction field approach produced poorer results. Some measurable differences were found between the Lekner and Ewald techniques. For dielectric properties, the performance of the TIP4P-FQ model was superior relative to other potentials. For 256 molecules, the computational speeds of the Ewald and reaction field methods were found to be 2.5 to 3 times and 3.5 to 5 times faster than the Lekner technique, respectively.     

Electron correlations in crystals and molecules

An expression for the Green’s function of a disordered crystal is obtained with allowance for the electron-electron interaction. The electron states of the system are described in the framework of a multiband tight-binding model. The possibility of using the proposed approach for describing the energy spectrum of molecules is demonstrated in the limit of an infinitely large primitive cell of the crystal. The energy spectrum and effective charges of atoms of a tricyanobutadienecarbazole molecule are calculated.     

Calculation of the surface tension and the surface energy of Lennard–Jones fluids from the radial distribution function in the interface zone

A detailed study is presented of the calculation of the surface tension and the surface energy of Lennard–Jones fluids from the radial distribution function and the density profile. To do so, a modification is made to Lekner and Henderson's statistical mechanics approach by introducing two simple analytical expressions for the radial distribution function of the interface zone. In these expressions the radial distribution functions of the liquid and vapour phases are weighted via step or exponential variations. The well- known exponential model for the density profile in the interface zone is considered. Finally, results are compared with values from experiment, from computer simulation and from relevant theoretical developments. It is shown that the use of the proposed radial distribution function in the interface zone represents a significant improvement in applying Lekner and Henderson's approach.     

On generalization of the hard-sphere model for the structure factor

Another closed form expression for the static structure factor of dense fluids, in the generalized Ashcroft Lekner hard sphere model, is presented. It incorporates the correct hard sphere equation of state given by Carnahan and Starling. This model has, as usual, one independent parameter which can be adjusted by a fit to the experimental data at one point.     

Delocalization effects and charge reorganizations induced by repulsive interactions in strongly disordered chains

We study the delocalization effect of a short-range repulsive interaction on the ground state of a finite density of spinless fermions in strongly disordered one dimensional lattices. The density matrix renormalization group method is used to explore the charge density and the sensitivity of the ground state energy with respect to the boundary condition (the persistent current) for a wide range of parameters (carrier density, interaction and disorder). Analytical approaches are developed and allow to understand some mechanisms and limiting conditions. For weak interaction strength, one has a Fermi glass of Anderson localized states, while in the opposite limit of strong interaction, one has a correlated array of charges (Mott insulator). In the two cases, the system is strongly insulating and the ground state energy is essentially invariant under a twist of the boundary conditions. Reducing the interaction strength from large to intermediate values, the quantum melting of the solid array gives rise to a more homogeneous distribution of charges, and the ground state energy changes when the boundary conditions are twisted. In individual chains, this melting occurs by abrupt steps located at sample-dependent values of the interaction where an (avoided) level crossing between the ground state and the first excitation can be observed. Important charge reorganizations take place at the avoided crossings and the persistent currents are strongly enhanced around the corresponding interaction value. These large delocalization effects become smeared and reduced after ensemble averaging. They mainly characterize half filling and strong disorder, but they persist away of this optimal condition. Received 5 July 2000 and Received in final form 8 November 2000     

线电荷串产生的史密斯-帕塞尔辐射

采用积分方法分析了线电荷串,沿周期性理想金属光栅表面平行移动时产生的史密斯帕塞尔辐射。分别对短周期光栅、低能量线电荷串与长周期光栅、高能量线电荷串的辐射情况进行了数值计算。相对单个线电荷而言,N个线电荷与反射光栅作用产生的辐射场密度,在频率是线电荷串调制频率的整数倍处出现最大,辐射谱宽变窄;随电荷能量增高,辐射能量向高频方向移动,并具有强烈的定向性;可以通过调节线电荷调制频率等参量实现辐射电磁波频率锁定。研究结果表明,对高能量与低能量的电荷参量,适当选择光栅尺寸与线电荷串间隔周期,都可使辐射波工作于太赫兹波段。     

Arrays of Charged (±2π)-Twist Disclinations in Ferroelectric Liquid Crystals

The notion of an electrostatic charge of (±2)-twist disclinations is used to approximate the evaluation of the electrostatic interaction energy among disclinations forming arrays in finite samples of ferroelectric chiral smectic C liquid crystals. Screening effects of free charges in a material surrounding the disclination are taken into account by introducing a phenomenological depolarisation factor.The electrostatic interaction energy is important in chiral smectic C materials with high values of the spontaneous polarisation when screening effects of free charges are small. Then the electrostatic interaction leads to elimination of disclinations from the sample. When there is a high concentration of free charges in the sample (smaller value of depolarisation factor), the electrostatic interaction energy is of the order of the elastic interaction energy of disclinations what influences the equilibrium of disclination arrays in the sample. Two disclination configurations are considered. In the Brunet-Williams configuration the disclinations of opposite topological charge have also the opposite electrostatic charge so their attraction is augmented. This attraction can be balanced by the helical structure in the central part of the sample when the sample thickness is rather high.On the contrary, in the Glogarová-Pavel configuration the disclinations of opposite topological charge have the electrostatic charge of the same sign. The equilibrium in this configuration is either a balance of elastic attraction and electrostatic repulsion if elastic and Coulomb forces are of the same order or it is governed by the value of the anchoring energy when electrostatic interaction prevails over the elastic one.     

Energy Mechanism of Charges Analyzed in Real Current Environment

We analyze in this work the energy transfer process of accelerated charges, the mass fluctuations accompanying this process, and their inertial properties. Based on a previous work, we use here the dipole antenna, which is a very convenient framework for such analysis, for analyzing those characteristics. We show that the radiation process can be viewed by two energy transfer processes: one from the energy source to the charges and the second from the charges into the surrounding space. Those processes, not being in phase, result in mass fluctuations. The same principle is true during absorption. We show that in a transient period between absorption and radiation the dipole antenna gains mass according to the amount of absorbed energy and loses this mass as radiated energy. We rigorously prove that the gain of mass, resulting from electrical interaction has inertial properties in the sense of Newton's third low. We arrive to this result by modeling the reacting spacetime region by an electric dipole.     

Study on the electronic structure of Al12N12 and Al12P12 fullerene-like nano-clusters upon adsorption of CH3F and CH3Cl

ABSTRACT

We study the interaction of two mono-halomethanes (CH₃F and CH₃Cl) on Al₁₂N₁₂ and Al₁₂P₁₂ fullerene-like nano-clusters based on density functional theory (DFT). We search on fully optimised adsorbed systems by theoretical investigation considering binding energies, total density of states, natural bond orbital (NBO) charges, and molecular electrostatic potential. We found that the direction of electron transfer is from halomethane to nano-cluster for all systems, indicating p-type semiconductor property of the mentioned nano-clusters. The interaction energy of halomethanes on nano-clusters is evaluated with dispersion corrected (wB97XD) and non-corrected (B3LYP) methods in order to estimate the dispersion effects. The binding energies are found in order of Al₁₂N₁₂–CH₃F > Al₁₂N₁₂–CH₃Cl > Al₁₂P₁₂–CH₃F > Al₁₂P₁₂–CH₃Cl with the values of ?102.7, ?83.7, ?64.2, and ?48.9 kJ mol^?1 based on wB97XD, respectively. We found significant changes in the location of HOMO as well as LUMO of nano-clusters upon adsorption of the above-mentioned molecules. As a result, we suggest the suitability of Al₁₂N₁₂ nano-cluster as a strong adsorbent for practical applications.     

I: METHODOLOGY

Since standard molecular simulations use different energy expressions for charge and gradient calculations, there are severe problems such as incompleteness in the optimization and simulation of the system with electrostatic (ES) interaction. Here, a new concept is proposed to solve this problem. The consistent charge equilibration (CQEq) equation has been derived which uses the same energy expression for both charge and gradient calculations. The ES energy is given by the atomic partial charge shielded with a nuclear charge described by a normalized S type Slater function located at each atomic site. The partial charge is determined by the variational principal for the ES energy with a constraint that the total sum of the partial charges is constant. Also the first derivative has been determined for the ES energy to the internal coordinates from the same ES energy expression. Although the CQEq is a little heavier than the original QEq for the charge calculation, the CQEq completely satisfies the variational principle for the ES energy of a set of partial charge, and satisfies the consistency requirement in the optimization of the system with ES interaction. A new code has been created and applied to test cases.     

Electric field gradients in simple tetragonal lattice at interstitial site

Electric field gradient (efg) is calculated at the centre of the cell in the simple tetragonal crystal. The method uses Euler-Maclaurin summation formula and makes the planewise summation in the direct crystal space without any special regrouping of charges in point charge model. The results are in fair agreement with previous results of de Wette on the same system using Fourier transform to reciprocal space.