E.R. Smith

Simulation of electrostatic systems in periodic boundary conditions. III: Further theory and applications

This paper makes some developments and clarifications of the theory for the application of periodic boundary conditions to the numerical simulation of the statistical mechanics of a cubic sample of dipolar particles. The reaction-field effect is treated rigorously. The anisotropies inherent in the periodic boundary condition Hamiltonian are allowed for in the derivation of a new fluctuation formula. A perturbation theory to account for anisotropic long-ranged terms is described, giving two di-electric constant estimates from one simulation. These new results are illustrated with Monte Carlo simulations of the Stockmayer system at reduced density 0.8, reduced square dipole moment 2.0 and scaled temperature 1.35, giving a dielectric constant estimate of 25 ± 2 from all the data, and showing that the perturbation theories are very accurate. It appears possible to claim that periodic boundary conditions should be used with infinite external dielectric constant in almost all circumstances, because they then give a chain of configurations that provide comparatively very stable estimates of dielectric constant.

Liquid—gas transition for hard spheres with attractive Yukawa tail interactions

Abstract We describe the liquid-gas transition in the hard sphere system with Yukawa tail interactions in the mean spherical approximation. The dependence of critical temperature and density on the range of the interaction is shown and the spinodal curve for a short-ranged potential and a long—ranged potential is presented. The compressibility, energy and virial pressures are presented for a long-ranged potential. Liquid phase pressures are calculated by integrating round the coexistence region, rather than through it.

The solution of the RISM equation for diatomic symmetric molecules

The RISM equation for diatomic symmetric molecules is solved using a Weiner-Hopf factorization technique. This procedure introduces a function Q(r) which is related to both the site-site total correlation function h(r) and the site-site direct correlation function c(r). Determining Q(r) effectively solves the RISM equation. We show that Q(r) can be written as an infinite sum, for r greater than the hard sphere diameter R, and using this form, solve for Q(r) when 0 < r < R. To generate a solution, this infinite series must be truncated. A method to determine the coefficients in the truncated series is outlined.

Molecular dynamics studies of dielectric behaviour and orientational correlations of liquid ethylene oxide (oxirane)

We report molecular dynamics simulations of 64 model ethylene oxide (oxirane) molecules at a mass density of 0·9 g cm-3 and a temperature in the vicinity of 260 K. We obtained a dielectric constant of 12·6 ± 0·05 which compares well with the experimental value of 13·9 at 272·15 K.

Simulation of two dimensional systems with two dimensional electrostatics

Some of the problems associated with Monte Carlo and molecular dynamics simulations of three dimensional ionic and dipolar systems are discussed, with emphasis on the use of periodic boundary conditions (PBC). It is shown that analogous problems may arise in two dimensional systems provided that the interactions are two dimensional electrostatic interactions, that is, interactions derived from the two dimensional Laplace equation. The PBC hamiltonian is evaluated by considering the appropriate two dimensional lattice sums, and a computable form for the effective pair interactions in PBC developed. The idea of an external dielectric constant is introduced and its effects included in the PBC hamiltonian. Formulae for evaluating the dielectric constant from a simulation with any external dielectric constant are given. Perturbation formulae showing the effects on the structure and mean square dipole moment of a dipolar system which are caused by a change in external dielectric constant are derived. A formula ...

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

Abstract 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.

Perturbation theory for the dielectric constant

The structure and dielectric properties of the hard sphere dipolar fluid, calculated using both perturbation theory and computer simulation, are reported. Both methods predict a short ranged h Δ(r), a much lower dielectric constant than previously obtained, and non-zero higher spherical harmonic coefficients of the angular correlation function.

Mean spherical approximation for simple hard sphere fluids

A method of solution of the mean spherical approximation (MSA) is given for systems of hard spheres whose interaction potential is of the form outside the hard core. The method thus allows solution of the MSA for a wide range of potentials. Details are given for the cases and +φ2 exp (−μ2 r). The method is also used to study the MSA for systems in which the interparticle potential is of the form The difficulties of an exact solution for such systems are pointed out and an approximate method of solution developed. The limit μ →0 is considered. Details are given for the case

Electrostatic potential at an ionic crystal surface. Energy expressions for simulation of polar surfaces

A geometry for simulation of polar surfaces of ionic crystals is described. The simulation cells form a two-dimensional periodic array with one side bounded by the polar surface of a large piece of rigid ionic crystal. To simulate a polar surface in this way, the surface must carry excess charge to ensure that the cells are a model of the surface of a piece of crystal in bulk thermodynamic equilibrium. The electrostatic energy of the simulation cells is presented as a sum of convergent two dimensional lattice sums. The cancellation of divergences implicit in this energy because of the excess charge distributions is described in detail.

Electrostatic potential at a plane surface of a point ionic crystal

The electrostatic potential near a plane surface slab shaped piece of simple cubic structured point ionic crystal is calculated as a lattice sum which is absolutely convergent. The resulting potential can be shape dependent, the shape dependent terms depending on the unit cell dipole and quadrupole moments. The representation developed shows how the potential changes from its bulk values inside the crystal to zero outside the crystal.