Kinetic-energy systems, density scaling, and homogeneity relations in density-functional theory

We examine the behavior of the Kohn-Sham kinetic energy Tₛ[ρ] and the interacting kinetic energy T[ρ] under homogeneous density scaling, ρ(r)→ζρ(r). Using convexity arguments, we derive simple inequalities and scaling constraints for the kinetic energy. We also demonstrate that a recently derived homogeneity relation for the kinetic energy [S. B. Liu and R. G. Parr, Chem. Phys. Lett. 278, 341 (1997)] does not hold in real systems, due to nonsmoothness of the kinetic-energy functional. We carry out a numerical study of the density scaling of Tₛ[ρ] using ab initio densities, and find it exhibits an effective homogeneity close to 5/3. We also explore alternative reference systems for the kinetic energy which have fewer particles than the true N-particle interacting system. However, we conclude that the Kohn-Sham reference system is the only viable choice for accurate calculation, as it contains the necessary physics.