# Why kinetic energy in Kohn-Sham equation is the major part of real many-body kinetic energy?

In deriving the Kohn-Sham equation, it is a main step to extract the 'major' part of the true kinetic energy exactly by using the fictitious non-interacting system and calculating its kinetic energy. In the fictitious system the wavefunction is just a single determinant $$\Psi_s$$.

$$T[\rho] = \langle{} \Psi[\rho]| \sum_{i=1}^N -\frac{1}{2}\nabla_i^2|\Psi[\rho]\rangle{}$$

$$T_s[\rho] = \langle{} \Psi_s[\rho]| \sum_{i=1}^N -\frac{1}{2}\nabla_i^2|\Psi_s[\rho]\rangle{}$$

• Why non-interacting kinetic energy is the major part of the true kinetic energy?
• At what level of quantity it is different from the true kinetic energy?

I think the question is slightly equivalent to:

• How different (quantitatively and intuitively) in kinetic energy of an electron state and its Slater approximating state.
• 3 months is long to not get an answer, maybe copy and paste here: materials.stackexchange.com Jul 24 '20 at 2:34