1302.3130 (Gregor Michalicek et al.)

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

Gregor Michalicek, Markus Betzinger, Christoph Friedrich, Stefan Blügel

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 convergence behavior of the so constructed LAPW+LO basis is superior to that of the related APW+lo approach in cases where the linearization error is large.

View original: http://arxiv.org/abs/1302.3130