Modified Augmented-Plane-Wave Method for Calculating Energy Bands

The orthogonalized-plane-wave (OPW) expansion converges poorly for ionic crystals and also for $d$-bands in transition metals even when modified by the addition of an atomiclike $d$ function to the basis set. The augmented-plane-wave (APW) expansion converges rapidly, but requires the crystal potential to be approximated by an unphysical spherical muffin-tin potential. We here develop a modified APW expansion and compare its convergence with the other methods. The modified APW converges with the rapidity of the usual APW but, like the OPW, is applicable to nonspherical potentials.