Thermodynamic properties of ε-Fe with thermal electronic excitation effects on vibrational spectra

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 can contribute 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 on phonon frequencies and the implication for the thermodynamics properties of {\epsilon}-Fe at extreme pressure (P) and temperature (T) conditions. We disregarded phonon-phonon interactions, i.e., anharmonicity and their effect on phonon frequencies. Nevertheless, the current scheme can still be used with temperature-dependent anharmonic frequencies. We conclude that the effect 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 must include thermal excitation effects in a continuum of temperatures. Our results for isentropic state equations show good agreement with data from recent ramp compression experiments up to 1,400 GPa conducted at the National Ignition Facility (NIF).