Self-consistency test for the exchange-only Kohn-Sham potential

The relationship, recently derived by Krieger, Li, and Iafrate [Phys. Lett. A 148, 470 (1990)], that ε_mσ, the exchange-only Kohn-Sham (KS) single-particle energy eigenvalue corresponding to the highest occupied orbital, exactly equals {ε}_mσHF, the expectation value of the Hartree-Fock (HF) single-particle Hamiltonian averaged over this Kohn-Sham orbital, is employed to test the accuracy of the local-spin-density (LSD) exchange-only potential as well as the recent results of Wang et al. [Phys. Rev. A 41, 78 (1990)]. For the eleven atoms with closed subshells from He to Xe we find that in the LSD approximation ε_mσ is only approximately equal to 60% of {ε}{} _mσHF, whereas the potential of Wang et al. yields ε_mσ{}{ε}{} _mσHF to within 0.5%, providing further evidence that it closely approximates the exact KS exchange-only potential.