attention on the following fact. To give support to the robustness of their theoretical results, many investigators mentioned that reasonable changes of the molecule-electrode distance d do not notably alter the calculated transport properties. Such a behavior can indeed be an indication for robust results, but it could also have a different origin. Within the IRLM, an increasing d makes both parameters β and J to decrease. The decrease of β always causes a conductance reduction. As already noted and visible by inspecting the renormalized curves of Fig. 5, depending on the range, a decrease in J could either suppress or enhance the conductance. Noteworthy, this effect brought about by a modification in J can be observed on the renormalized curves. For realistic values of J ( ∼ 1), the unrenormalized conductance increases with decreasing J . So, rather than indicating robust results, the aforementioned behavior could be related to the fact that the size of the extended molecule employed in the calculations is too small, and for that size there is a compensation of two opposite effects induced by the β - and J -variations. Of course, we do not expect that in all cases the largest extended molecule that can be tackled is sufficiently large to justify neglecting the influence of electron correlations on the self-energies at the contacts. In Sect. VI, we considered a renormalization scheme appropriate for the IRLM, for which the exact conductance on resonance is known. To avoid misunderstandings, we emphysize that this scheme represents an extra renormaliza- tion, which solely accounts for the fact that the parentheses of Eqs. (11) and (14) do not exactly vanish. The important renormalization (the exact intramolecular correlations of the isolated extended molecule) is already incorporrated in G r $_{i}$. Simple schemes similar to our, which underline the renormalization considered in the Landau Fermi liquid theory, work pretty well even in Kondo context (see, e. g., the supplementary material of Ref. 62). Cer- tainly, the renormalization scheme of Sect. VI cannot be applied in an identical form in general. However, we think that the possibility to renormalize the Green’s function G $^{r}$( ε ) of the embedded molecule by an ε -independent factor, which furthermore turned out to be (practically) independent on the model parameters, is interesting and deserves further attention. This (almost) constant factor can no more be determined from the unitary limit, as done in Sect. VI, but one may think to determine it by using general properties of the Green’s functions (e. g., sum rules or asymptotic behavior [19, 62]). The speculation on the existence of a (nearly) constant renormalization factor is also appealing from a different perspective. In the cases where the renormalization effect can be accounted for by an almost 22