Local behavior of the first-order gradient correction to the Thomas-Fermi kinetic energy functional

The first-order gradient correction to the Thomas-Fermi functional proposed by Haq et al. [Chem. Phys. Lett. 111, 79 (1984)] has been tested by evaluating both the total kinetic energy and the local kinetic energy density. For the kinetic energy density, we have evaluated its deviation from the exact orbital-based result through a quality factor that reflects the quality of the functionals in a better way than their relative errors. The study is performed on two different systems: Light atoms (up to Z=18) and a noninteracting model of fermions confined in a Coulombic-type potential, a system that provides useful insights about the performance of the functionals when the ground state is degenerate. It is found that this approximation gives very low relative errors and a better local behavior than any other kinetic energy density functional.