Li-like ions in the range of the nuclear charge number Z = 10 − 92. Employing the extended Furry representation, one partially takes into account the higher-order electron-electron in- teraction effects, that are beyond the considered order of the perturbative expansion. This approach can accelerate the convergence of the QED perturbation theory with respect to the interelectronic-interaction effects, especially for small values of Z , where the convergence of the perturbative expansion becomes slower. The Dirac equation in the extended Furry representation can be written as where V$_{nuc}$ is the Coulomb potential of the extended nucleus and V$_{scr}$ is a local screening potential, which partially accounts for the interaction between the valence electron and the closed core electrons. We employ here the Kohn-Sham screening potential derived within the density-functional theory [58], This potential was successfully utilized in our previous QED calculations for the g factor and hyperfine splitting of Li-like ions [59–61]. Here, ρ$_{t}$ denotes the total radial charge density distribution of the core electrons ( b ) and the valence electron ( a ) where n$_{b}$ is the number of the core electrons. The Kohn-Sham potential is constructed for the lithiumlike ground state, namely, for the (1 s $^{2}$)2 s state. In order to estimate the sensitivity of the result on the choice of the potential we consider also the core-Hartree potential, which is just a Coulomb potential generated by the core electrons. The screening potentials are generated self-consistently by solving the Dirac equation (14) until the energies of the core and valence states become stable on the level of 10 − $^{9}$. The asymptotic behavior of the Kohn-Sham potentials at large distances is restored by introducing the Latter correction [62]. The complete gauge invariant set of diagrams which have to be considered are shown in Fig. 2. They are referred to the SE ( a − c ) and VP ( d − f ) diagrams. The counterterm associated with the extra interaction term V$_{scr}$ is represented graphically by the symbol ⊗ . The formal expressions for these diagrams are derived from the first principles of QED employing the two-time Green-function method [63]. 23 ρ$_{t}$ ( r ) = ∑ b [ G 2 $_{b}$( r ) + F 2 b ( r )] + [ G 2 $_{a}$( r ) + F 2 $_{a}$( r )] , ∫ ∞ 0 d r ρ$_{t}$ ( r ) = n$_{b}$ + 1 , (16) V$_{scr}$ ( r ) = α ∫ ∞ 0 d r ′ 1 r$_{>}$ ρ$_{t}$ ( r $^{′}$) − 2 3 α r ( 81 32 π $_{2}$rρ$_{t}$ ( r ) ) 1 / 3 . (15) [ − i α · ∇ + β + V$_{nuc}$ + V$_{scr}$ ] | n 〉 = ε$_{n}$ | n 〉 , (14)