Testing the kinetic energy functional : Kinetic energy density as a density functional

A new method for defining an energy density for the noninteracting kinetic energy of density functional theory is given. The resulting energy density is a density functional determined completely by the kinetic energy functional itself. Although this method is not constructive, it allows for a direct comparison between exact and approximate functionals pointwise in space. For simple systems, the new energy density is calculated exactly, and compared with traditional choices, on both formal and physical grounds. Finally, the energy densities of both the gradient expansion and the von Weizsäcker approximation are calculated, and compared with the exact quantity. The errors in the von Weizsäcker approximation are identified. © 2003 American Institute of Physics. @DOI: 10.1063/1.1565316#