Some consequences of scaling in density-functional theory and the virial as a density functional

Consequences of uniform coordinate scaling of the independent particle kinetic energy functional T_s[n] of density functional theory are investigated. A scaling relation for the functional derivative of T_s[n] is obtained which leads to a scaling relation for the Kohn-Sham potential, while the scaling of the Kohn-Sham equations also provides information on the scaling of the eigenvalues. An expression is deduced for the virial in terms of the ground-state density and the corresponding Kohn-Sham potential. It is shown that the virial is the kinetic energy functional for a two-electron systems while for N-electron systems the external potential as a functional of the density preclude us from having an explicit form for the noninteracting kinetic energy functional. An approximated kinetic energy functional for N-electron systems, based on the virial, is presented and some numerical results discussed.