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I do not understand how the DFT, LDA approximation gives energy that can have some exchange part and some correlation part. My understanding is as follows:
Exchange energy is defined as the difference in Hartree and HF energy. Correlation energy is defined as difference between HF and exact energy. If the energy predicted by DFT using LDA approximation lies between HF and exact energy, the energy term has entire exchange energy and some correlation energy. And if the approximation gives an energy between Hartree and HF energy, the energy term has some exchange energy and no correlation energy. How can the energy term have some correlation energy without having the entire exchange energy?Immagine you want to make a fruit juice of mixed orange and lemon. You can start by adding water (exchange term) and then orange/lemon sugary flavor (correlation term). That would be hartree-fock
Or you can start by adding lemon, that would be a DFT approximation that contains both water and flavor without being the exact solution
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