Conditions on the Kohn–Sham kinetic energy and associated density

Effective, explicitly density‐dependent (i.e., orbital‐free) approximations to the Kohn–Sham kinetic energy functional Ts remain elusive. In the course of developing such functionals in collaboration with Frank Harris, various issues have arisen that have gone unaddressed. We consider four of them here: positivity of the KS kinetic energy density, supposed requirements on its functional dependence, the use of cutoffs to insure positivity, and the role of the Coulomb virial theorem in the asymptotic analysis of Ts.