Virial coefficients and equation of state of the penetrable sphere model†
We study the penetrable sphere (alias square mound) model in the fluid phase by means of the virial expansion, molecular dynamics simulations, and Ornstein–Zernike integral equation. The virial coefficients up to B8 are expressed as polynomials in the Boltzmann factor with the coefficients calculated by a Monte Carlo integration. New data for pressure and internal energy are obtained by molecular dynamics simulations with attention paid to finite-size errors and properties of the Andersen thermostat. The data and virial coefficients are correlated by a formula for the Helmholtz free energy. We also propose a new closure for the Ornstein–Zernike equation and test several other closures.