  This paper investigates the influence of the basis set on the GW self-energy
correction in the full-potential linearized augmented-plane-wave (LAPW)
approach and similar linearized all-electron methods. A systematic improvement
is achieved by including local orbitals that are defined as second and higher
energy derivatives of solutions to the radial scalar-relativistic Dirac
equation and thus constitute a natural extension of the LAPW basis set. Within
this approach linearization errors can be eliminated, and the basis set becomes
complete. While the exchange contribution to the self-energy is little affected
by the increased basis-set flexibility, the correlation contribution benefits
from the better description of the unoccupied states, as do the quasiparticle
energies. The resulting band gaps remain relatively unaffected, however; for Si
we find an increase of 0.03 eV.
