Elimination of the linearization error and improved basis-set convergence within the FLAPW method

We analyze in detail the error that arises from the linearization in linearized augmented-plane-wave (LAPW) basis functions around predetermined energies $E_l$ and show that it can lead to undesirable dependences of the calculated results on method-inherent parameters such as energy parameters $E_l$ and muffin-tin sphere radii. To overcome these dependences, we evaluate approaches that eliminate the linearization error systematically by adding local orbitals (LOs) to the basis set. We consider two kinds of LOs: (i) constructed from solutions $u_l(r,E)$ to the scalar-relativistic approximation of the radial Dirac equation with $E>E_l$ and (ii) constructed from second energy derivatives $\partial^2 u_l(r,E) / \partial E^2$ at $E=E_l$. We find that the latter eliminates the error most efficiently and yields the density functional answer to many electronic and materials properties with very high precision. Finally, we demonstrate that the so constructed LAPW+LO basis shows a more favorable convergence behavior than the conventional LAPW basis due to a better decoupling of muffin-tin and interstitial regions, similarly to the related APW+lo approach, which requires an extra set of LOs to reach the same total energy, though.