Fundamentals

This section elaborates on the known properties of exchange and correlation in DFT. The most important concept is that of the exchange-correlation hole $n_{\hbox {{XC}}}({\bf r},{\bf r'})$, which is a quantum-mechanical zone surrounding every electron in an interacting system that reduces the probability of finding other electrons within the immediate vicinity. This section presents an exact definition of the exchange-correlation energy in DFT, which is given in terms of the hole, and also describes the properties of $n_{\hbox {{XC}}}({\bf r},{\bf r'})$ that are used to construct approximate functionals.