An efficient method for calculating the electronic structure of systems that need a very fine sampling of the Brillouin zone is presented. The method is based on the variational optimization of a single (i.e., common to all points in the Brillouin zone) basis set for the expansion of the electronic orbitals. Considerations from $\mathbf{k}\cdot \mathbf{p}-\mathrm{approximation}$ theory help to understand the efficiency of the method. The accuracy and the convergence properties of the method as a function of the optimal basis set size are analyzed for a test calculation on a 16-atom Na supercell.

• Received 18 January 2000

DOI:https://doi.org/10.1103/PhysRevB.62.15499