carrying out accurate ab initio quantum chemical calculations need not be very large. Partic- ularly attractive is the case of organic conducting electrodes, for which only a few electrode layers have to be included (cf. Sect. V A). Another advantage is that, without metal atoms, ab initio calculations are less demanding. For metallic electrodes, more electrode layers need be included (cf. Sect. V B), but one can still hope to a semi-quantitative description. Alternatively, simpler (tight-binding) models can be utilized to include metallic electrode layers and their coupling to the molecule as well, similar to the first four terms of Eq. (20). Regarding the case of metallic electrodes, it is still worth emphasizing the following aspect. Experimental data indicate that electric conduction through molecules typically occurs by non-resonant tunneling, characterized by a rather large energy offset | ε$_{F}$ − ε$_{HOMO}$ | (p-type conduction) or | ε$_{LUMO}$ − ε$_{F}$ | (n-type conduction) [41, 60], which represents the counterpart of the quantity | α − ε$_{F}$ | in the presently employed model. This fact is important because, based on our calculations, we can state that the size dependence of the transport properties is particularly pronounced near resonance ( | α − ε$_{F}$ | ≈ 0), but becomes much less significant away from resonance. This feature, which is visible if one inspects the unrenormalized curves of Fig. 4, is very encouraging: one can hope to obtain quantitatively correct results by using extended molecules with reasonable sizes even in the case of metallic electrodes. There is a general claim (e. g., Ref. 61) that whether the electron transport is correlated or not solely depends on value of the ratio between the characteristic Coulomb electron-electron interaction and the hybridization (in our case J/ Γ). By comparing the results of Sects. V A and V B among themselves, we found limitations of this rule of thumb [61]. Based on these results, one can conclude that the ratio J/ Γ alone is not sufficient to distinguish between significant and insignificant correlation effects on the transport. For large ξ ’s, significant effects arise at Coulomb strengths J substantially larger than Γ, while for ξ ∼ β values J ∼ Γ suffice. As mentioned from the very beginning, the main interest of the present work was not to analyze the physical properties of a simple model (i. e., IRLM), to which all our numerical results refer. Rather, we attempted to extract from them information, which is useful from the perspective of real systems of interest for molecular transport. Nevertheless, in spite of its simplicity, we emphasize that the IRLM incorporates a significant physical aspect, namely the Coulomb repulsion at the contacts. Concerning the physical relevance of the employed IRLM, we also want to draw the 21