Jellium

Jellium is the name given to an ** homogeneous electron gas**. The motion of the electrons in the gas is not only affected by the coulomb interaction between them. There is also a purely quantum mechanical process at work. The motion of the electrons is **correlated** by the Pauli Exclusion principle. The electrons with parallel spins, must maintain a certain separation. The anti-parallel spin electrons keep apart to lower their mutual coulomb repulsion. So we can gain energy in two ways. Moving parallel spin electron apart will lower the *exchange energy*, moving anti-parallel spins apart will lower the *correlation energy*.

For the case of a homogeneous electron gas we can work out the average exchange-correlation energy per electron. In fact, values for the exchange-correlation energy for any reasonable electron density can be taken from parameterisations of calculated data.

**back to DFT**

The exchange-correlation effect gives rise to an exchange-correlation hole around each electron in the gas. The hole is just the exclusion radius caused by the Pauli exclusion principle.

The mutual exclusion zone or exchange-correlation hole around an electron in jellium. The radius of the hole corresponds to the exclusion of a single electron thereby giving the hole a single positive charge. The overall charge of the quasiparticle (the electron and its exchange-correlation hole together) is zero. Of course in reality, there is no marked boundary for the exclusion zone as drawn, the boundary is diffuse.

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