Grand canonical Monte Carlo simulation of liquid argon

Abstract

A grand canonical Monte Carlo procedure with fixed values of the chemical potential μ, volume V, and temperature T, is described which is suitable to simulate simple fluids with only a minor increase in computer time in comparison with canonical (N,V,T) simulations and considerably faster than (N,p,T) ones. The method is rapidly convergent for rather dense systems with a reduced density of about ρσ3=0.88. The rapid convergence is attained by decreasing the vain attempts in the regime when new particles are added. The chance to find a place for an additional particle is increased by locating the cavities suitable to house a particle with the aid of the Dirichlet–Voronoi polyhedra. As an example, liquid argon is simulated with Lennard-Jones potentials at T=86.3 K and μ=−73.4 J/mol. The simulated density has been found to be 1.468 g/cm3 which is to be compared with the experimental value of 1.425 g/cm3. The same density was obtained by starting the procedure with both 216 and 250 particles in the simulation box of length 2.1895 nm. The pair correlation function is also in very good agreement with both earlier (N,V,T) simulations and diffraction experiments. The configurations obtained are analyzed by the second- and third-order invariants of the even-l spherical harmonics as order parameters characterizing the nearest neighbors of argon atoms. These results as well as some other statistics on the geometry of the coordination sphere indicate that the prevailing cluster geometry in liquid argon is a distorted hexagonal close packed arrangement which is nevertheless distinguishable from face centered cubic or icosahedral clusters distorted to the same degree or more. The surroundings of vacancies, however, are completely random with no characteristic symmetry properties.