Finite size effects for liquids in cyclic boundary conditions

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Abstract
The effect of a system size on thermodynamic properties is studied for a model Lennard-Jones liquid in cyclic (simple cubic periodic) boundary conditions. The HNC and PY integral equations are solved numerically and compared with molecular dynamics simulation data at two state points (reduced temperature and density T = 1·2, ρ = 0·8 and T = 0·81, ρ = 0·8645, respectively). The convergence of internal energy and virial pressure to the infinite system values observed in the pseudo-experimental data is semi-quantitatively predicted by both HNC and PY equations for the first state point and HNC for the second point. The PY integral equation (solved by the direct iteration method) diverges for dense periodic liquid. This may be interpreted to mean the liquid structure described by the usual isotropic PY equation is unstable with respect to anisotropic perturbations.