nuclear charge distribution is used together with the rms radii taken from Ref. [56], with the exception of the uranium ion, for which the rms value is taken from work [16]. The calculations have been performed in both Feynman and Coulomb gauges for the photon propagator describing the electron-electron interaction. The results agree very well with each other, thus providing an accurate check of the numerical procedure. In Table VIII we compare our values of the screened SE and VP corrections, calculated in the Kohn- Sham, core-Hartree, and Coulomb potentials (as zeroth-order approximation), with other theoretical results. As one can see from the table, our values for the screened SE and VP corrections in the Coulomb potential are in perfect agreement with the corresponding results of works [4, 57] and [5], respectively. As to comparison with the related values from Ref. [9], some deviation can be stated for both screened SE and VP contributions. This discrepancy is especially noticeable for the 2 p$_{1}$$_{/}$$_{2}$ and 2 p$_{3}$$_{/}$$_{2}$ screened SE terms. The reason of this disagreement is unclear for us. In Table IX we present our results for the total screened QED correction to the ionization energies of the 2 s , 2 p$_{1}$$_{/}$$_{2}$ , and 2 p$_{3}$$_{/}$$_{2}$ valence states as well as to the energy differences 2 p$_{j}$ − 2 s , calculated in the Kohn-Sham potential. The corresponding results obtained in the core- Hartree potential are rather close to the Kohn-Sham ones. Therefore, for the conservative estimation of the theoretical uncertainty of the ionization energies due to the higher-order contributions we consider the difference between the values obtained in the Coulomb and Kohn-Sham potentials and assign the uncertainty to be 30% of this difference. The related uncertainty for the energy differences 2 p$_{j}$ − 2 s is determined to be the maximum of the error bars for the 2 p$_{j}$ and 2 s states. 27