  We demonstrate the accurate calculation of entropies and free energies for a
variety of liquid metals using an extension of the two phase thermodynamic
(2PT) model based on a decomposition of the velocity autocorrelation function
into gas-like (hard sphere) and solid-like (harmonic) subsystems. The hard
sphere model for the gas-like component is shown to give systematically high
entropies for liquid metals as a direct result of the unphysical Lorentzian
high-frequency tail. Using a memory function framework we derive a generally
applicable velocity autocorrelation and frequency spectrum for the diffusive
component which recovers the low frequency (long time) behavior of the hard
sphere model while providing for realistic short time coherence and high
frequency tails to the spectrum. This approach provides a significant increase
in the accuracy of the calculated entropies for liquid metals and is compared
to ambient pressure data for liquid sodium, aluminum, gallium, tin, and iron.
The use of this method for the determination of melt boundaries is demonstrated
with a calculation of the high pressure bcc melt boundary for sodium. With the
significantly improved accuracy available with the memory function treatment
for softer interatomic potentials, the 2PT model for entropy calculations
should find broader application in high energy density science, warm dense
matter, planetary science, geophysics, and material science.
