reason for difference

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An extra step is required for the quantum systems (Slater Determinant in order to satisfy the asymmetry property), where products of the independent particle solutions are summed. Two components of the total energy difference(one from the “product to Slater” step, and another from the “Slater to exact” step) are, therefore, present, which are the exchange and the correlation, respectively.

Whereas in classical systems, there is only one component- correlation i.e. the difference between the total energy and the sum of the independent particle solutions.

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