Exchange and correlation
I. THE ELECTRON GAS
We have defined the exchange and correlation energy before as the difference between the exact total energy of a system and the classical Hartree energy. Except in very simple cases it is impossible to treat exchange and correlation exactly and an approximation is in order. The quality of a DFT calculation is determined by how close the approximate exchange and correlation comes to the exact value. In this section, we shall get a glimpse of the -by now- huge literature on different methods of dealing with exchange and correlation in atomistic systems. Before going into exchange and correlation in real systems, it’s important to understand the behavior of a much simpler system, the interacting electron gas not only because it is the system that can be dealt with analytically the most easily but also due to the fact that approximations to exchange and correlation are built upon this simple system. Let us first start with the noninteracting electron gas in order to to familiarize ourselves with concepts and establish some terminology.
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