  The thermodynamic properties of hcp-iron ({\epsilon}-Fe) are essential for
investigating planetary cores' internal structure and dynamic properties.
Despite their importance to planetary sciences, experimental investigations of
{\epsilon}-Fe at relevant conditions are still challenging. Therefore, ab
initio calculations are crucial to elucidating the thermodynamic properties of
this system. Here we use a free energy calculation scheme based on the phonon
gas model compatible with temperature-dependent phonon frequencies. We
investigate the effects of electronic thermal excitations, which introduces a
temperature dependence on phonon frequencies, and the implication for the
thermodynamic properties of {\epsilon}-Fe at extreme pressure (P) and
temperature (T) conditions. We disregard phonon-phonon interactions, i.e.,
anharmonicity and their effect on phonon frequencies. Nevertheless, the current
scheme is also applicable to T-dependent anharmonic frequencies. We conclude
that the impact of thermal electronic excitations on vibrational properties is
not significant up to ~ 4,000 K at 200 GPa but should not be ignored at higher
temperatures or pressures. However, the static free energy, Fst, must always
include the effect of thermal excitation fully in a continuum of Ts. Our
results for isentropic equations of state show good agreement with data from
recent ramp compression experiments up to 1,400 GPa conducted at the National
Ignition Facility (NIF).
