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The new interpolation procedure of Shankland is applied to interpolation problems found in a periodic lattice. Two problems, the method of averaging the valence electron density over the Brillouin zone and the method of interpolating energy bands throughout the Brillouin zone from values at symmetry points, are discussed in detail. To illustrate the advantages of this procedure, examples are taken from self-consistent cubic ZnS and ZnSe orthogonalized-plane-wave calculations.

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