Variational collapse of the optimized effective potential method with an orbital-dependent exchange-correlation functional based on second order perturbation theory

It is well known, that second-order perturbation theory (PT2) breaks down when the gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied MO (LUMO) becomes too low. It is demonstrated that when the local Kohn–Sham (KS) potential vs is approximated by an expansion in a set of basis functions, exact HOMO–LUMO degeneracy occurs, if a finite orbital basis set is used. Numerical evidence is given for the He atom, which until now stood out as a ‘safe’ simple case. Variational collapse of the optimized effective potential (OEP) method with the PT2 functional in a finite orbital basis may be expected to be a common phenomenon. We also show variational breakdown with a non-perturbative functional when the HOMO–LUMO gap is used to regulate the contribution of virtual orbitals.