By switching over to the Kohn-Sham scheme, we have effectively changed our problem from a system of many interacting particles with 3N coordinates in an external potential to a system of non-interacting particles in an effective potential with only 3 coordinates. The contribution of the unknown energy in the total energy of the non-interaction electron system is reduced as much as possible by Kohn and Sham with the implementation of the concept of exchange-correlation energy . The treatment of the exchange-correlation term is discussed below.