Approximate electron kinetic-energy functionals

We believe that a useful kinetic-energy functional should not only incorporate known limiting forms but also have accurate functional derivatives, so that it can be used for obtaining the correct ground-state density via variational calculations. Furthermore, an accurate functional for the kinetic energy should be obtained by fitting to smooth pseudoelectron systems rather than to all-electron calculations as is often done. In this paper, by working on simple model atoms and group-IV pseudoatoms, we demonstrate that an accurate kinetic-energy functional with a correct functional derivative, and meeting most limiting forms, cannot be obtained from a simple expression containing only the density and its gradient. At least the Laplacian of the density should also be included in a useful generalized gradient approximation to the kinetic-energy functional.