-0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.0 0.2 0.4 0.6 0.8 N=6 N=10 N=14 N=16 Fig. 4 J=10 =10 ( =0.2) G/G$_{0}$ ω $_{l}$= ε $_{d}$- ε F F FIG. 4: Normalized conductance G/G 0 and several sizes N . The lower group of curves (thin lines, small points) is computed by means of Eq. (24), and the upper group (thick lines, big points) are obtained within the renormalization scheme described in the text. Notice that, unlike the strongly size-dependent unrenormalized curves, the renormalized curves are weakly size-independent even for the rather large values J = 10 and ξ = 10 used, which are less favorable for the renormalized procedure employed. So far, we have considered the dependence on the location of molecular level α relative to the electrode Fermi energy. We also employed this renormalization scheme to study the J - and ξ -dependence of the linear conductance away from resonance α = ε$_{F}$ . (Remember that G |$_{α}$ = ε$_{F}$ = G 0 for all ξ ’s and J ’s.) Results of this kind are depicted in Fig. 5, which includes both unrenormalized and normalized curves (thin and thick lines, respectively). They confirm that the size-dependence is stronger at larger ξ ’s, as already mentioned above. In addition, they reveal the interesting fact that the dependence of the Coulomb contact interaction J can be non-monotonic, as is the case of other previously published results [37]. As a general trend, we found that by increasing J the conductance G ( J ) gradually increases from the value G |$_{J}$ =0 , reaching its maximum at a Coulomb strength J$_{c}$ ∼ ξ , and decreases afterwards. This trend can be seen by inspecting Fig. 5, which also shows that the wider the electrode bandwidth (4 ξ ), the more pronounced is the conductance enhancement G ( J$_{c}$ ) /G ( J = 0). Within the NEGF-DFT approaches, the impact of electron correlations on the Green’s function of the isolated extended molecule is accounted for approximately, ˆ G$_{i}$ |$_{DF T}$ ≈ ˆ G$_{i}$ , by employing certain exchange-correlation (xc-)functionals. To determine the Green’s function VII. DISCUSSION 17