Generalized-gradient-approximation noninteracting free-energy functionals for orbital-free density functional calculations

We develop a framework for orbital-free generalized gradient approximations (GGAs) for the noninteracting free energy density and its components (kinetic energy, entropy) based upon analysis of the corresponding gradient expansion. From that we obtain a new finite-temperature GGA (ftGGA) pair. We discuss implementation of the finite-temperature Thomas-Fermi, second-order gradient expansion, and our new ftGGA free energy functionals in an orbital-free density functional theory (OF-DFT) code, including the construction and validation of required local pseudopotentials. Then we compare results of self-consistent OF-DFT calculations on hydrogen using those noninteracting free energy functionals (in combination with the zero-temperature local density approximation (LDA) for exchange-correlation) with results from conventional finite-temperature Kohn-Sham calculations and the same LDA. As an aid to implementation, we provide analytical expressions for the temperature-dependent scaling factors involved.