energies Σ$_{x}$ from the bare self-energies Σ 0 $_{,x}$. This renders more significant the quantity in the parenthesis of the r.h.s. of Eq. (12), which was neglected to derive the approximate Eqs. (16) and (24). To make those parentheses negligible, one has to reduce the renormal- ization at the ends of the extended molecule due to electron correlations, and for this one has to sufficiently increase its size N . As illustrated by Figs. 3a and b, for larger ξ ’s, the unitary limit can be reasonably reproduced by using the smallest possible size N = 4 only for weak Coulomb interactions of the order of the bare hybridization J ∼ Γ. Unfortunately, such Coulomb strengths are of little interest. They are too weak, and the correlation effects they bring about are negligible. The counterpart of Fig. 2b, the linear conductance G = G ( α ) for J ∼ Γ is not significantly different from that for J = 0. For ξ = 10, a Coulomb strength J = 2Γ = 0 . 4 solely yields a slight change of the half-width at half maximum from Γ = 0 . 2 to 0.22, and for ξ = 5 and J = 2Γ = 0 . 8 the change in the half-width is only a bit larger (from Γ = 0 . 4 to 0.485). The impact of the stronger but still realistic Coulomb contact interaction of Fig. 2b ( J = 4) is also significant at larger ξ . For ξ = 10 it increases the half-width at half maximum of the curve G = G ( α ) from Γ = 0 . 2 to 0 . 43, whereas for ξ = 5 the increase is from Γ = 0 . 4 to 0 . 80. However, the corresponding values of J/ Γ = 20 and J/ Γ = 10, respectively, are much larger than that of Fig. 2b ( J/ Γ = 2). At these values of J/ Γ, the curves of Figs. 3a and b exhibit a notable N -dependence. However, for the smallest extended molecule ( N = 4) the computed conductance still amounts a significant fraction of the exact conductance ( ∼ 45% and ∼ 55%, respectively). For N = 8, which corresponds to include three and four layers in the left and right electrodes, these fractions are increased to ∼ 67% and ∼ 80%, respectively. In view of the state-of-the art in the field of molecular electronic transport, characterized by large differences between theory and experiments, these values suggest that, although less accurate than for organic electrodes, achieving a semi-quantitative description based on ab initio quantum-chemical calculations is possible even in the case of metallic electrodes with moderately strong Coulomb contact repulsion. As alternative to the approximation of a sufficiently large extended molecule, one can start from the exact Dyson equation (8) and attempt to use renormalized electrode self- VI. A SIMPLE RENORMALIZATION SCHEME 15