Optimal basis sets for detailed Brillouin-zone integrations

A method is given to obtain optimal basis sets for certain electronic-structure calculations, starting with solutions of Schr\"odinger's equation at a few crystal momenta and finding periodic functions that best span the periodic parts of such wave functions at all momenta. This is done within a pseudopotential, plane-wave framework. The derived basis sets should be most helpful for modeling quantities such as optical properties of materials: they have enabled the author to solve Schr\"odinger's equation at thousands of crystal momenta from 4 to 3500 times faster than did a basis set of plane waves. However, one still obtains reasonable wave functions expanded in the same plane-wave representation. {} 1996 The American Physical Society.