Can optimized effective potentials be determined uniquely?

The computational difficulties in the linear-combination-of-atomic-orbital (LCAO) optimized effective potential (OEP) method were addressed. It was proven that in the limit of an infinite basis set, an exchange potential of the OEP method can be uniquely determined up to an additive constant by the OEP equation alone. Hence, evidence was obtained indicating that the said difficulties are primarily due to the incompleteness of the orbital basis set.