Response in the local, non-negative kinetic energy density of a perturbed free electron gas: potential functionals and density functionals

We discuss two sets of response functionals for estimating the local, non-negative kinetic energy density of initially free electrons that are perturbed by a static external potential. We begin with first- and second-order functionals of the perturbing potential, which are directly analogous to known response functionals for the electron density and the integrated kinetic energy. We provide reciprocal-space formulations of these functionals that complement previously known real-space expressions. We then present alternate first- and second-order response functionals that operate on the induced electron density and do not depend explicitly on the applied potential. The structure of these latter functionals will help guide the design of the more sophisticated kinetic energy functionals that enable orbital-free density functional theory simulations of materials. We examine the performance of the response functionals, in density-functional form, when applied to electron densities generated from local pseudopotential calculations for Li, Al, and Si solids.