Accuracy pseudopotential fitting

The accuracy of the pseudopotential fit procedure also plays an important role, like the number of reference states used [26,126]. 

Accurate energy bands obtained from first principles by computer calculation are available for most covalent solids. A display of the bands obtained by the Empirical Pseudopotential Method for Si, Ge, and Sn and for the compounds of groups 3-5 and 2-6 that are isoclec-tronic with Ge and Sn shows the principal trends with mctallicity and polarity. The interpretation of trends is refined and extended on the basis of the LCAO fitting of the bands, which provides bands of almost equal accuracy in the form of analytic formulae. This fitting is the basis of the parameters of the Solid State Table, and a plot of the values provides the test of the d dependence of interatomic matrix elements. 

It is necessary to determine the volume dependence of each of the terms in Eq. (3.29). This can be done with quite high accuracy for most of the terms. The exception is the term Aq. If the volume is an important variable, the usual pseudopotential approach must be modified (Ashcroft and Langreth, 1967 Hasegawa and Young, 1981) to obtain Aq. Up to now, unfortunately, this has been done only by simply adopting empirical expressions with parameters fitted to the data at specific reference points. 

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