Scaling of the known exact explicit forms of the non-interacting kinetic-energy density functional

Abstract

It has been previously proven that the Kohn-Sham kinetic energy functional scales homogeneusly under generalized coordinate scaling, in a way that is obeyed by the von Weizäcker functional, but seems to be in contradiction with the scaling of the Thomas-Fermi functional. A very puzzling situation, taking in to account that the von Weizäcker and Thomas-Fermi functionals are exact cases of the Kohn-Sham kinetic energy functional for two electron systems, and the non-interacting electron gas, respectively. The apparent contradiction is resolved in this paper.