Hole pseudo-spin

The pseudopotential/pseudo-orbital pair are linked and what is achieved by the formulation of the valence orbital problem is a replacement of the effect of the Pauli principle. The Pauli principle causes electrons (of like spin) to avoid each other independently of their mutual repulsion it generates the so-call Fermi hole around a particular electron. Now as the valence electron penetrates the core space it must have a distribution which reflects this Fermi hole it must avoid the phantom core electrons or they must avoid it. So the pseudopotential/pseudo-orbital pair must reflect this fact and this is why they are linked. If we choose to make the pseudo-orbital smooth then the local form of the pseudopotential becomes oscillatory and vice versa, so that the imposition of pseudo-orbital smoothness may have some ramifications for the choice of a model potential to simulate the effect of the pseudopotential. 

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