Some remarks about the APW method

$\bullet$ Note that the wavefunction in general will have discontinous derivatives on the boundary between the interstitial and atomic regions.

$\bullet$ In the APW method the augmenting function $R_l$ corresponds to the exact muffin-tin potential eigenstate of eigenenergy . Because of this energy dependence of the function $R_l$ the eigenvalue problem will be non-linear in energy and has to be solved iteratively. This is, however, computationally very costly. On the other hand, any eigenstate of a different eigenenergy will be poorly described without adapting . To overcome this problem linearized versions of the APW method have been developed, where the energy is set to a fixed value and the basis functions are modified to gain extra flexibility to cover a larger energy region around their linearization energy. These methods are the linearized APW method (LAPW) and the APW+ local orbitals (APW+lo).