  The optimized-effective-potential (OEP) method is a special technique to
construct local Kohn-Sham potentials from general orbital-dependent energy
functionals. In a recent publication [M. Betzinger, C. Friedrich, S. Bl\"ugel,
A. G\"orling, Phys. Rev. B 83, 045105 (2011)] we showed that uneconomically
large basis sets were required to obtain a smooth local potential without
spurious oscillations within the full-potential linearized augmented-plane-wave
method (FLAPW). This could be attributed to the slow convergence behavior of
the density response function. In this paper, we derive an incomplete-basis-set
correction for the response, which consists of two terms: (1) a correction that
is formally similar to the Pulay correction in atomic-force calculations and
(2) a numerically more important basis response term originating from the
potential dependence of the basis functions. The basis response term is
constructed from the solutions of radial Sternheimer equations in the
muffin-tin spheres. With these corrections the local potential converges at
much smaller basis sets, at much fewer states, and its construction becomes
numerically very stable. We analyze the improvements for rock-salt ScN and
report results for BN, AlN, and GaN, as well as the perovskites CaTiO3, SrTiO3,
and BaTiO3. The incomplete-basis-set correction can be applied to other
electronic-structure methods with potential-dependent basis sets and opens the
perspective to investigate a broad spectrum of problems in theoretical
solid-state physics that involve response functions.
