Stanislav Labík

A rapidly convergent method of solving the OZ equation

A new method is proposed for solving numerically the Ornstein-Zernike equation for systems with a spherically symmetrical pair-potential. The method is based on expansion of the function Γ(r)=r[h(r) - c(r)] in suitable basis functions and on a combination of Newton-Raphson and direct iterations. Tests on the PY and HNC approximations for hard spheres and Lennard-Jones fluid have shown that the proposed method is three to nine times as rapid as the related and so far the most efficient method of Gillan. Other advantages besides the speed are low sensitivity to the choice of initial estimate and a relatively simple computational scheme.

The bridge function for hard spheres

The paper presents an empirical formula for expressing the bridge function (the sum of elementary graphs) in terms of the interparticle separation and the density. The formulae is fully consistent with the best computer-simulation thermodynamic and structural data for hard spheres in the fluid region. It can serve as both a direct and convenient testing ground for the integral-equation theories of hard spheres and an input to the reference-hypernetted chain approximation for simple fluids.

Accurate equation of state of the hard sphere fluid in stable and metastable regions

New accurate data on the compressibility factor of the hard sphere fluid are obtained by highly optimized molecular dynamics calculations in the range of reduced densities 0.20–1.03. The relative inaccuracy at the 95% confidence level is better than 0.00004 for all densities but the last deeply metastable point. This accuracy requires careful examination of finite size effects and other possible sources of errors and applying corrections. The data are fitted to a power series in y/(1 − y), where y is the packing fraction; the coefficients are determined so that virial coefficients B2 to B6 are reproduced. To do this, values of B5 and B6 are accurately recalculated. Virial coefficients up to B11 are then estimated from the equation of state.

Bridge function for hard spheres in high density and overlap regions

The reliability of a recently proposed parameterization of the bridge function for hard spheres (1987, Molec. Phys., 60, 663) has been tested for densities near the phase transition. We carried out simulations of the radial distribution function at reduced densities of 0·925 and 0·94. The radial distribution function calculated from the parameterized bridge function by means of the Ornstein-Zernike equation is in perfect agreement with the simulated values. A parameterization of the bridge function for separations below contact has been proposed.

The bridge function of hard spheres by direct inversion of computer simulation data

The bridge function of the hard sphere fluid has been calculated from our new highly accurate Monte Carlo and molecular dynamics simulation data on the radial distribution function using the (inverted) Ornstein-Zernike equation. Both the systematic errors (finite size, grid size, tail) and statistical errors are analysed in detail and ways to suppress them are proposed. Uncertainties in the resulting values of B(r) are about 0.001. In contrast with many previous findings the bridge function is both positive and negative.

Monte Carlo simulation of the background correlation function of non-spherical hard body fluids

A new Monte Carlo technique for the calculation of the function y = g exp (βu) is proposed for hard body systems. The method is especially suitable at low and moderate densities and separations below the contact. The y-function was calculated for hard spheres and hard diatomics. For hard spheres surprisingly small deviations from Grundke-Henderson formula were found. For the diatomics at Ls = 0·6 radial slices at four special orientations were determined. The applicability of the proposed method and of the umbrella sampling technique due to Patey and Torrie are compared.

Fluid of general hard triatomic molecules

The fluid of symmetric non-linear molecules with the valency angle θ = 105° and σB/σA = 0·6 has been studied at several densities by means of the Monte Carlo simulation method. The site-site correlation functions, G αβ, generalized harmonic coefficients Γ100 αβ, and the equation of state have been computed and compared with currently available theoretical results.

An accurate integral equation for molecular fluids.: I. Hard homonuclear diatomics

Percus-Yevick (PY), hypernetted chain (HNC) and modified Verlet (VM) integral equation theories are used to study the structure and thermodynamic properties of hard prolate ellipsoids of revolution in the isotropic fluid region. Results for the spherical harmonic coefficients of the pair distribution function and for the compressibility factors are compared with new Monte Carlo results reported in this work for length-to-breadth ratios a/b = 2, 3, and 5. For a/b = 2 and 3, the VM harmonic coefficients are in good agreement with the simulation results and are better than those of PY and HNC theories. For a/b = 5, HNC theory gives numerically precise harmonic coefficients, the VM results being only slightly inferior, a behaviour consistent with that found previously for very long spherocylinders. VM theory gives equation of state results in excellent agreement with the simulation data at all values of a/b and densities, whereas the PY and HNC results are generally poor. The thermodynamic consistency of each...

Correlation functions of hard body fluids from thermodynamic properties of their mixtures

An exact relation between the structural properties of a fluid and the thermodynamic properties of an infinitely dilute mixture is derived. A recurrence formula for the virial coefficients of the infinitely dilute mixtures is proposed and used to calculate the background correlation function of the hard sphere and dumbbell fluids. The results are superior to those obtained by other methods currently available.

Integral equation study of additive two-component mixtures of hard spheres

The Ornstein-Zernike equation for additive hard sphere mixtures is solved numerically by using the Martynov-Sarkisov (MS) closure and a recent modification of the Verlet (MV) closure. A comparison of the predictions for the equation of state and, to a lesser extent, the contact values of the radial distribution function, shows both theories to give similar, reasonably accurate, results in most situations. However, an examination of the pair cavity functions for zero separation shows the two closures to give quite different results, and the MV closure results are believed to be better. More attention should be given to the cavity function at zero separation. In addition, the MV closure satisfies known asymptotic relations for a small concentration of exceedingly large spheres, whereas the MS and Percus-Yevick closures do not satisfy these relations.