0 10 20 30 40 50 60 70 0.0 0.2 0.4 0.6 0.8 N=4 N=8 N=12 N=16 Fig. 4 =10 G/G$_{0}$ ω $_{l}$= ε $_{d}$- ε F J 0 5 10 15 20 25 30 35 0.0 0.2 0.4 0.6 0.8 N=4 N=8 N=12 N=16 Fig. 4 =5 G/G$_{0}$ ω $_{l}$= ε $_{d}$- ε F J 0 3 6 9 12 15 18 21 0.0 0.2 0.4 0.6 0.8 N=4 N=8 N=12 N=16 Fig. 4 =3.33 G/G$_{0}$ ω $_{l}$= ε $_{d}$- ε F J 0 2 4 6 8 10 12 14 0.0 0.2 0.4 0.6 0.8 N=4 N=8 N=12 N=16 Fig. 4 =2 G/G$_{0}$ ω $_{l}$= ε $_{d}$- ε F J FIG. 5: Normalized conductance G/G 0 plotted versus J/ Γ for ξ = 10   5   3 . 33   2. All the curves were computed for the out-of-resonance situation | α − ε$_{F}$ | = Γ / 2  which corresponds to G/G 0 = 0 . 8 at J = 0. Notice that  the smaller the ξ -value  the stronger the size-dependence of thin curves computed from Eq. (24)  and the larger the departure from the practically N -independent renormalized curves  depicted by thin lines. ˆ G |$_{DFT}$ = ( ˆ G $_{−}$1 i |$_{DFT}$ − ˆ Σ 0  L − ˆ Σ 0  R ) − 1 of the extended molecule coupled to electrodes  those approaches employ the bare self-energies ˆ Σ 0  L and ˆ Σ 0 $_{ R}$. Because the isolated extended molecule is modeled by an effective Kohn-Sham effective Hamiltonian  the underlying picture is a one-particle picture  and therefore the Landauer-type formulae (16) and (24) with ˆ G r replaced by ˆ G $^{r}$|$_{DFT}$ follow as “exact” results (i. e.  without any other approximation as the DFT-approximation itself). We emphasize that Landauer-type expressions like those Eqs. (16) and (24) are not valid in general for correlated electron systems. As explained in Sect. II  they represent justi- fied approximations in the correlated case only when sufficiently large extended molecules are considered. The advantage of the approach based on this concept is its clear physical content. Eqs. (16) and (24) hold for electron correlations that can be strong within the molecule but are negligible at the ends of a sufficiently large extended molecule. This is the reason we employed in the Dyson equation (14) the bare self-energies ˆ Σ 0  L and ˆ Σ 0 $_{ R}$  as in the NEGF-DFT approach. However  at variance with the latter  our approach accurately 18