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[StijnVanVooren]

I would say because quantum mech introduces the Pauli exclusion principle. The Hartree state, although describing a state of independant particles, lacks anti-symmetry, which is required if the state is to be fermionic (which it should be) in our case. Then on the other hand the slater determinant is anti-symmetric, while maximizing the independancy of each particle.

In this sense in quantum the correlation energy is analogue to the correlation energy in classical physics, but staying in bounds of all possible states. By this i mean that indeed it is the energy difference between the exact solution and the independant solution, while still being physical (obeying Pauli exclusion principle).

Then the exchange energy account for the energy difference between a true independant solution compared to one which is maximally independant while obeying Pauli’s exclusion principle.

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