Kinetic energy density of nearly free electrons. II. Response functionals of the electron density

We present electron-density-based response functionals yielding the non-negative kinetic energy density (KED) of nearly free electron systems. In a previous paper, for a canonical free-electron system perturbed by an external potential, we derived the first- and second-order corrections to the KED as functionals of the potential, providing the response functions in reciprocal space. Here, we formulate the KED response in terms of the electron density by converting the potential-based functionals into density functionals. We also determine the related response of the Pauli KED, which is the KED in excess of the von Weizs\"acker KED. We anticipate that the structure of these density functionals will help guide the design of the more sophisticated kinetic energy functionals required for orbital-free density functional theory simulations. We conclude by examining the performance of the first- and second-order density functionals for the KED when applied to electron densities generated from local pseudopotential calculations for Li, Al, and Si crystals.