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

Abstract

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.