Atom-in-jellium calculations of equations of state for warm dense matter

Recent path-integral Monte Carlo and quantum molecular dynamics simulations have shown that average-atom models can predict thermodynamic states in warm dense matter to within a few percent. Atom-in-jellium models have typically been used to predict the electron-thermal behavior only, although they can calculate the Einstein frequency of ion oscillations and hence to predict the entire equation of state (EOS). We have extended this approach to calculate the mean displacement of an ion over a wide range of compression and temperature. Expressed as a fraction of the Wigner-Seitz radius, the displacement is a measure of the asymptotic freedom of the ion at high temperature, and thus of the change in heat capacity from 6 to 3 modes per atom. A functional form for free energy was proposed with a single free parameter representing the effective number of potential modes to be saturated, and investigated using molecular dynamics simulations. The ion-thermal contribution was thus estimatedwithout requiring a large number of molecular dynamics simulations.