this might be a stupid question but I am really confused at the moment. I'm currently preparing for an exam in computational chemistry. In the lecture I noted always down that the exchange term (Pauli-Principle), which arises as part of the two-electron functions is not determined in Hartree-Fock and added to the cusp-problem, when two electrons come close together. Those two then form the correlation energy, which is determined in post-Hartree-Fock methods.
Then in DFT we have several attempts to solve the exchange part, and I took a note back then, that basically in DFT or in the Kohn-Sham approach, as we do not know the DFT-functional, you create something, that looks like a Fock-operator, with the difference, that it also contains the exchange part.
Now I looked at some tasks and one question was why you do not simply take the HF expression for the exchange part and insert it into the DFT equations. I was a bit shocked what this expression might be and it turns out, when I look into other scripts I cannot find any note that in modern HF the exchange part would be neglected in any way.
So for simple HF (not post-HF) calculations, is the exchange term calculated as well and the only thing you miss would the the correlation?