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The first order gradient correction to the Thomas-Fermi functional, proposedby Haq, Chattaraj and Deb (Chem. Phys. Lett. vol. 81, 8031, 1984) has beenstudied by evaluating both the total kinetic energy and the local kineticenergy density. For testing the kinetic energy density we evaluate itsdeviation from an exact result through a quality factor, a parameter thatreflects the quality of the functionals in a better way than their relativeerrors. The study is performed on two different systems: light atoms (up toZ=18) and a noninteracting model of fermions confined in a Coulombic-typepotential. It is found than this approximation gives very low relative errorsand a better local behavior than any of the usual generalized gradientapproximation semilocal kinetic density functionals.

Local Behavior of the First-Order Gradient Correction to the Thomas-Fermi Kinetic Energy Functional