  The finite basis optimized effective potential (OEP) method within density
functional theory is examined as an ill-posed problem. It is shown that the
generation of nonphysical potentials is a controllable manifestation of the use
of unbalanced, and thus unsuitable, basis sets. A modified functional
incorporating a regularizing smoothness measure of the OEP is introduced. This
provides a condition on balanced basis sets for the potential, as well as a
method to determine the most appropriate OEP potential and energy from
calculations performed with any finite basis set.
