Tunable non-interacting free-energy functionals: development and applications to low-density aluminum

We introduce the concept of tunable orbital-free non-interacting free-energy density functionals and present a generalized gradient approximation (GGA) with a subset of parameters defined from constraints and a few free parameters. Those free parameters are tuned to reproduce reference Kohn-Sham (KS) static-lattice pressures for Al at T=8 kK for bulk densities between 0.6 and 2 g/cm$^3$. The tuned functional then is used in OF molecular dynamics (MD) simulations [1] for Al with densities between 0.1 and 2 g/cm$^3$ and T between 6 and 50 kK to calculate the equation of state and generate configurations for electrical conductivity calculations [2]. The tunable functional produces accurate results. Computationally it is very effective especially at elevated temperature. Kohn-Shiam calculations for such low densities are affordable only up to T=10 kK, while other OF approximations, including two-point functionals, fail badly in that regime. 1. V.V. Karasiev, T. Sjostrom, and S.B. Trickey, Comput. Phys. Commun. 185, 3240 (2014). 2. V.V. Karasiev, L. Calder{\'i}n, and S.B. Trickey, Phys. Rev. E 93, 063207 (2016).