Virial coefficients, equation of state, and solid-fluid coexistence for the soft sphere model

Virial coefficients up to B₈ are calculated for the soft-sphere model, φ = ε(σ/r)ⁿ with exponents n = 12, 9 and 6. It is demonstrated that for n = 12, the virial series truncated at B₈ describes well the equation of state (EOS) of the fluid phase up to the freezing density, while for n = 9 and 6 the series departs from the correct behaviour for densities of 75% and 18% of the freezing density, respectively. For these cases Padé approximants provide a much improved description of the equation of state at high density. The EOS for these different exponent-n values are further improved by a one-parameter fit of each to corresponding simulation data, using a form consistent with the known virial coefficients. Fluid-solid coexistence properties are evaluated and the results are in reasonably good agreement with the more-recent literature values.