The Kohn-Sham equation (given in Equation ) is exact and has not used any approximation for the solution of the many-body Schrödinger equation. With the mapping of the fully interacting system to the auxiliary non-interacting system, we can find the same ground-state density. Since Kohn-Sham kinetic energy is not a true kinetic energy, therefore, we have to define the exchange-correlation energy (E XC [ρ(𝐫)]) implicitly as given below;