No abstract

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.

A method is presented for efficiently computing the Fourier transform of a function, such as (charge density)'13, known numerically at a number of points in the unit cell of a crystal. The method utilizes an implicit interpolant which would be maximally smooth, consistent with the data. However, the interpolant is not computed, but the Fourier coefficients are obtained directly. Specialization of the formulas to a uniform grid is made and results in an enormous saving of computation.