In the present work, we compare the thermal contribution of electrons to thermodynamic functions of metals in different models at high densities and electron temperatures. One of the theoretical approaches, the full-potential linear-muffin-tin-orbital method, treats all electrons in the framework of density functional theory (DFT). The other approach, VASP, uses projector-augmented-wave pseudopotentials for the core electrons and considers the valent electrons also in the context of DFT. We analyze the limitations of the pseudopotential approach and compare the DFT results with a finite-temperature Thomas-Fermi model and two semiempirical equations of state.

We propose a method of calculation of thermodynamic functions in the Thomas–Fermi model at finite temperature θ. Expressions for first and second derivatives of the free energy are analytically obtained in the framework of the model. A special treatment of thermodynamic functions at low temperatures is provided by asymptotic series expansion at θ → 0. A special algorithm is used to ensure required accuracy for all values in a wide range of volumes and temperatures. We compare the results of our computations with ideal Boltzmann and Fermi gas models.