Heine-Animalu pseudopotential

In Fig. 4 we have plotted the BHS pseudopotential for Na, Mg, Al and Si as a function of distance for the angular momenta 1 = 0,1, 2, as compared to the Heine-Animalu pseudopotential, for which the pseudopotential is a (1-dependent) constant inside the core region. 

The tiny constant curves give the corresponding Heine-Animalu pseudopotentials. 

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... 

These Heine-Animalu pseudopotentials are also model potentials, in the sense that some parameters are fitted, but they are fitted to atomic properties. For applications in solids, this is a fundamental difference with the fitting procedures of model potentials with parameters to be determined from properties of the solid, since they still allow a first principle study of the typical solid state effects one wants to describe. 

As discussed in the chapter on the pseudopotential concept, an extension of the Heine-Animalu pseudopotentials was provided by Bachelet, Hamann and Schliiter, who calculated norm-conserving ionic pseudopotentials from atomic calculations for all the elements, including relativistic effects, and fitted their results with a relatively small set of analytic functions, the parameters of which were tabulated. The resulting matrix elements - - ... 

The phonon calculation from the pseudopotential perturbation theory, with the Heine-Animalu and the BHS pseudopotential, raises the question whether the perturbation approach is sufficiently adequate. 

A plot of the form factor for the empty-core pseudopotential, from Eq. (16-7), for aluminum. For comparison, the points give the model potential (Animalu and Heine, 1965). The choice of i is such that the two curves cross the axis at the same point. 

The occurrence of a fairly well-defined molecular group TI2 Te or of the ionic assembly Tf, Tf, Te" cannot be approached in terms of perturbation theory because it involves the formation of bound states. Stem (1966) and others have shown how these can arise if the atomic potentials of the two species are very different. A rough measure of the differences in potentials can be obtained from published tables of electronegativities or stability ratios (Sanderson (I960)), or the well depths which characterise the Heine-Abarenkov-Animalu model potential (see, for instance, Animalu and Heine (1965)). The connection between pseudopotentials and electronegativity implied by this remark has recently been justified by Heine and Weaire (1970). 

Fig. 10. A typical pseudopotential (for Sn), as calculated by Heine and Animalu/" shown together with points which have been fitted in semiempirical studies of (O) (semiconducting) gray and ( ) (metallic) white...

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