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

We examine the behavior of the Kohn-Sham kinetic energy Tₒ and the interacting kinetic energy T under homogeneous density scaling, (r) (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 Tₒ 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.