Definitions of correlation

[Maxim Vermorgen]

Using the same definition of correlation in classical and quantum system, namely the energy difference between the independent particle solution and the exact solution, is not sufficient to describe correlation in quantum systems. In quantum systems, we have to specify this definition because there are two different ways to define such an independent particle solution: the Hartree solution is an independent particle solution in which the many-body wave function is written as a product and the Hartree-Fock solution is an independent particle solution in which the many-body wave function is written as a Slater-determinant. The Hartree-Fock solution lies closer to the exact solution. Therefore, to define correlation in quantum systems, we say this is the energy difference between the HF-solution and the exact solution, while we call the energy difference between the HF- and Hartree-solution the exchange energy.

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