Precision of total energy and orbital energies with the expansion method for the optimized effective Kohn-Sham potential

For functionals that depend on the Kohn-Sham orbitals, the optimized effective potential method (OEP) of density functional theory (DFT) seeks a lowest energy solution by finding that particular local potential vs for which a stationary value of the energy is obtained, δE/δvs=0. We assess the performance of a particular method of solution, namely the expansion of vs, or the rest term vs-v0, in a finite set of expansion functions, using the exact exchange functional (EXX) as the simplest realistic orbital dependent functional. Here, v0 is a fixed local potential having the long-range asymptotics −1/r. For some prototype small systems the interdependence of the basis sets for the Kohn-Sham orbitals and for the potential has been investigated, as well as the effect of the reference potential v0. We specifically address the numerical precision with which the total energy EEXX and the orbital energies {εiEXX} can be obtained. The EXX solution is obtained both with and without explicitly imposing the 'HOMO condition' that the energy εH of the highest occupied molecular orbital be equal to the expectation value of the Fock operator. The potential expansion method yields reliable total energies even without the use of a reference potential (v0=0). However, the reliability of the calculated orbital energies remains a serious problem. Without the HOMO condition even the use of reference potentials with correct asymptotics cannot prevent an uncontrolled shift of the orbital energies. Imposing the HOMO condition solves this problem. But even with this condition imposed, the accuracy of other orbital energies is, typically, many orders of magnitude lower than that for the total energy.