Interpolation Scheme for Energy Bands in Solids

Abstract

The orthogonalized plane wave method is formulated as an interpolation scheme for use in conjunction with calculations made at symmetry points in the Brillouin zone. The Fourier coefficients of the crystal potential and the matrix components of the Hamiltonian between core functions are treated as parameters to be fitted to other calculations made at symmetry points by such methods as the cellular, orthogonalized plane wave, and augmented plane wave. The interpolation scheme then provides a method for making calculations at a general point in the Brillouin zone. The scheme is most useful for the case of valence and excited states where the wave function on one center overlaps many of its neighbors.