Core shifts and pseudo-potential trajectories

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Abstract
A pseudo-potential description is used as the basis for a close comparison of the experimentally determined band structures and the various existing ‘first principles’ band calculations for Al and the group IV elements. Our analysis shows that, in the case of Al, differences between various calculations are attributable to a ‘core shift’. The latter can be represented by a single parameter in a pseudo-potential scheme and the best calculations of this shift from ‘first principles’ are in error by about 0.3 Ry. For Si and Ge, it seems that very few first principles band calculations are internally consistent. This may also emphasize the importance of the pseudo-potential scheme in approaching the band structure problem for open (covalently bonded) crystal structures. For these structures also the ‘core shift’ concept proves an aid to understanding not only differences between various calculations for the same element but also chemical shifts in structure, e.g. from Si to Ge to grey Sn.