Constraint-based analysis of a physics-guided kinetic energy density expansion

An approach guided by physical consistency in determining the general forms of D-dimensional kinetic energy density functionals (KEDF) has been demonstrated previously, producing an expansion which contains the majority of the known one-point KEDF forms. It has also been shown that any noninteracting KEDF must necessarily have a homogeneity degree of 2 in coordinate scaling, and that the ratio of the collective KED to electron density must approach the ionization energy as (Formula presented.). This article demonstrates that the scaling condition is already satisfied in the general expansion despite not being conceived with the scaling as a constraint, and that the second condition places a restriction on the expansion terms of the KED. The discussion is extended as well for some known KEDs for comparison.