Integral constraint on the density functional for nonadditive kinetic energy in Kohn-Sham theory for subsystems

The exact equation, called the partial “homogeneity” relation, involving the nonadditive kinetic energy functional of the noninteracting electrons is derived within the Kohn–Sham theory for subsystems. It has implications for the functional structure, e.g., predicting its explicit dependence upon the subsystem numbers of electrons. This constraint is not satisfied by the approximate functionals derived from the Thomas–Fermi and Weizsäcker density functionals for the kinetic energy.