The Thomas-Fermi method, developed by Thomas and Fermi, is one of the oldest methods for finding the solution of the many-electron problem . In this method, the electron density ρ(r) is considered as a central variable rather than wavefunction. Thus, the total energy of the system, composed of three terms as given below, can be defined as a functional 𝐸 𝑇𝐹 [𝜌(𝑟)].