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This need arises because an ‘independent particle wave function’ is not an unambiguous thing: the total wavefunction could be a simple product of the individual wave functions, or could be a Slater determinant. This complication does not arise is classical physics but is very important in quantum mechanics because the Slater determinant is consistent with the antisymmetry requirement and therefore accounts for an energy difference due to the quantum mechanical exchange effect. Therefore, in DFT, the correlation energy is the difference between this latter type of wavefunction using a Slater determinant and the exact solution.
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