Efficient linearization of the augmented plane-wave method

We present a detailed analysis of the $\mathrm{APW}+\mathrm{lo}$ basis set for band-structure calculations. This basis set consists of energy independent augmented plane-wave (APW) functions. The linearization is introduced through local orbitals evaluated at the same linearization energy as the APW functions. It is shown that results obtained with the $\mathrm{APW}+\mathrm{lo}$ basis set converge much faster and often more systematically towards the final value. The $\mathrm{APW}+\mathrm{lo}$ thereby allows accurate treatment of systems that were previously unaccessible to linearized APW. Furthermore, it is shown that $\mathrm{APW}+\mathrm{lo}$ converges to the same total energy as LAPW provided the higher angular momenta l are linearized, either by adding extra local orbitals or treating them by LAPW. It is illustrated that the APW basis functions are much closer to the true form of the eigenfunctions than the LAPW basis functions. This is especially true for basis functions that have a strong energy dependence inside the sphere.