**Fermi hole, Fermi correlation** The Hartree-Fock wavefunction ensures that the space coordinates of two electrons of the same spin cannot coincide. This is referred to as Fermi correlation. Even when the electrons are in the vincinity of eachother this effect will be noticable. Around each electron there will be a hole in which there is relatively less electron with equal spin: the Fermi hole. The "exchange forces" that play a role are relatively localised. Fermi correlation is accounted for by using the antisymmetriser. It is accounted for in HF. It is independent of Coulomb interactions. Fermi correlation = exchange.

In Atkins, Molecular Quantum Mechanics this is explained with the example of the excited state of He: 1s

^{1}2s

^{1}. The wavefunction for this state can be written as a(1)b(2) or a(2)b(1). When no interaction exists between the electrons the energy is Ea+Eb. When interaction is allowed then the energy is E=Ea+Eb+JąK and the corresponding wavefunctions are: a(1)b(2)ąa(2)b(1). When the probablilities are plotted for the minus combination it shows that it becomes zero when r1=r2.

See Atkins, MQM 4th ed, p223

That electrons cannot coincide for their Coulomb repulsion is called the Coulomb hole.

__See also:__ Coulomb hole, Coulomb correlation

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