[morten925]

In Kohn-Sham DFT, the expression for the energy is:

E_DFT=T_s[ρ]+E_ne[ρ] + J[ρ]+E_xc[ρ], now, I am looking in the book of Frank Jensen (2007): Introduction to computational chemistry, and he says that by equating this energy to the exact energy, E_xc[ρ] is:
E_xc[ρ] = (T[ρ]-T_s[ρ])+(E_ee[ρ]-J[ρ])

But I am not sure how he has defined the exact energy, I hope it is simply E_exact[ρ]= T[ρ]+E_ne[ρ] + E_ee[ρ], does anyone here have an idea?

[Irlanur]

The point here is that you don't know the exact energy. You don't know the exact electron-electron interaction energy and you don't know the exact kinetic energy. That's why the "Exchange correlation functional" not only contains correcting terms for the electron correlation, but also correcting terms for the kinetic energy.

[morten925]

Thanks