Title: Multi-radius Soler-Williams Augmented Plane Waves (SAPMR) and multi-radius Soler-Williams Linearized Augmented Plane Waves (SLAPWMR)

Abstract: In this work we present a new basis set for electronic structures (Density Functional Theory (DFT)) calculations. It extends Soler Williams Linearized Augmented plane Wave (SLAPW) basis sets by allowing variable radii for the different angular momentum channels and wave vectors. This allows to match additional derivatives of the wave function at the Muffin Tin (MT) radius without having to resort to additional higher derivative terms. This should lead to low wave vector basis set and low linearization energy errors. We dub these basis sets SAPWMR and SLAPWMR. Similarly Local orbital (LO and lo) basis wave functions are suggested with a variable radius. Full Potential Hamiltonian calculations (FLAPW) are extended to FSLAPWMR full potential calculations in the appendix.