Fermi hole independent electron approximation

This work W,ie(r) is path-independent for the symmetrical density systems noted previously since the V x = 0 for these cases. It is important to note, however, that the corresponding Fermi-Coulomb hole charge distribution Pxc(r r ) which gives rise to the field need not possess the same symmetry for arbitrary electron position. For example, in either closed shell atoms or open-shell atoms in the central-field approximation for which the density is spherically symmetric, the Fermi-Coulomb hole is not, the only exception being when the electron is at the nucleus. 

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