Towards accurate orbital-free simulations: a generalized gradient approximation for the non-interacting free energy density functional

For orbital-free {\it ab initio} molecular dynamics, especially on systems in extreme thermodynamic conditions, we provide the first pseudo-potential-adapted generalized gradient approximation (GGA) functional for the non-interacting free energy. This is achieved by systematic finite-temperature extension of our recent LKT ground state non-interacting kinetic energy GGA functional (Phys. Rev. B \textbf{98}, 041111(R) (2018)). We test the performance of the new functional first via static lattice calculations on crystalline aluminum and silicon. Then we compare deuterium equation of state results against both path-integral Monte Carlo and conventional (orbital-dependent) Kohn-Sham results. The new functional, denoted LKTF, outperforms the previous best semi-local free energy functional, VT84F (Phys.\ Rev.\ B \textbf{88}, 161108(R) (2013)), and provides modestly faster simulations. We also discuss subtleties of identification of kinetic and entropic contributions to non-interacting free-energy functionals obtained by extension from ground state orbital-free kinetic energy functionals.