Kohn-Sham Energy Functional and Equations

A key to the application of DFT in handling the interacting electron gas was given by Kohn and Sham [51] who used the variational principle implied by the minimal properties of the energy functional to derive effective singleparticle Schrodinger equations. The functional F[ ] can be split into four parts  

Thus the interacting multi-electron system can be simulated by the noninteracting electrons under the influence of the effective potential l eff(r)- Kohn and Sham [51] took advantage of the fact that the case of non-interacting electrons allows an exact computation of the particle density and kinetic energy as 

Writing the Euler-Lagrange equations in terms of the single-particle wave functions (tpi) the variation principle finally leads to the effective singleelectron equation, well-known as the Kohn-Sham (KS) equation  

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