The one-electron Schrödinger equation is discussed for a periodic lattice. A variational procedure is applied to a set of trial functions consisting mainly of plane waves of low wave number. Rapid convergence is obtained by use of one or more auxiliary functions whose Fourier coefficients for high wave numbers approximate those of the correct eigenfunctions. The orthogonalized plane wave (OPW) method is a special case of this general method and the equivalence is shown. When applied to lithium the method gives a band structure in substantial agreement with that of cellular methods.

• Received 28 August 1957

DOI:https://doi.org/10.1103/PhysRev.109.30