  Atom-in-jellium calculations of the Einstein frequency were used 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 quadratic
degrees of freedom per atom. A functional form for free energy was proposed
based on the Maxwell-Boltzmann distribution as a correction to the Debye free
energy, with a single free parameter representing the effective density of
potential modes to be saturated. This parameter was investigated using
molecular dynamics simulations, and found to be ~0.2 per atom. In this way, the
ion-thermal contribution can be calculated for a wide-range equation of state
(EOS) without requiring a large number of molecular dynamics simulations.
Example calculations were performed for carbon, including the sensitivity of
key EOS loci to ionic freedom.
