What is the difference between these four approaches?
My current understanding is that Hartree-Fock uses only 1 slater-determine (accounting for antisymmetry) but neglects correlation between electrons. HF orbitals are primarily determined self-consistently.
DFT is the idea that there is a functional (presently unknown) that maps energy in terms of density. Hohenberg and Kohn found a proof that it exists but did not actually find it.
$E[p] = T[p] + E(EE)[P] + E(EN)[P]$
I am rather confused about where kohn-sham theory fits into all of this. Is it's entire purpose simply to define kinetic energy? How does it do this?