Finite-temperature Thomas–Fermi–Dirac-Weizsäcker model in the warm dense matter regime

Abstract

The Thomas–Fermi–Dirac-Weizsäcker model for finite temperature is presented. Starting with the free energy density, consistent expressions for the Helmholtz free energy, total energy, pressure and virial theorem are derived. The exchange and correlation terms are cast in a form that is suitable for derivation of their contributions to energy and pressure. The Euler–Lagrange equation is written in Schrödinger-like form and solved in spherical symmetry in a Wigner–Seitz cell. The challenges associated with its numerical solution are discussed and a viable approach to obtain a non-negative solution is proposed. The model is benchmarked for two materials, Al and Cu, by comparing the pressure at solid density in the temperature range , as well as the cold pressure curves.