Austin-Heine-Sham pseudopotential

Austin-Heine-Sham pseudopotential Indeed, any pseudopotential of the form ... 

An alternative development in the theory rather concentrated on the Austin-Heine-Sham type of pseudopotential, to construct a model pseudopotential, which is rather flat, but which gives the same electron scattering as the true potential . This model potential has been parametrized, and tables of the parameters have been published for many elements of the... 

Of course, this relation follows quite naturally from the general pseudopotential, given explicitly in Elq. (3.7). But the general proof for model potentials of the Austin-Heine-Sham type, is less trivial. (Note that this relation implies that in a local approximation to the pseudopotential, one should neglect the orthogonalisation hole together with the non-locality). 

It should be emphasized that this replacement of the band energy by its first order expansion, breaks the exactness of the formulation from the original pseudopotential, and the arbitrariness in the pseudo wave function no longer exists. The pseudopotential is now of the Austin-Heine-Sham type (see Eq. 3.12), still giving the exact valence energies, but the pseudo wave function is now unique. 

As mentioned at the end of the previous section, the factors containing the energy can be replaced by an arbitrary expression of the Austin-Heine-Sham type. This fact can be further exploited, as is e.g. done in the Heine-Animalu pseudopotential, based on the Heine-Abarenkov derivation (see Ref. 26-27 of the previous chapter). Heine and Animalu determined the ionic contribution to the pseudopotential by imposing that it correctly describes the electron scattering from the atom. This potential is parametrized as... 

The second term on the right hand side of Equation 6 is small and can be neglected. This form of the pseudopotential can be derived from the general expression obtained by Austin, Heine, and Sham (3) ... 

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