where T s [ρ I ] is the Kohn-Sham kinetic energy of subsystem I, V nuc [ρ tot ] is the electronnuclei attraction energy, J[ρ tot ] is the Coulomb energy, E xc [ρ tot ] is the exchange-correlation (xc) energy, V nn is the nuclear repulsion energy. Finally, the non-additive kinetic energy (NAKE) is given by