in the definition of Λ [cf. Eq. (13) of Ref. 25], this factor accounts for the renormalization of the electrode self-energies and should approach unity if the extended molecule becomes sufficiently large [29]. Eq. (16) seems odd for the correlated case, as it only contains the retarded Green’s function [notice that G a = ( G $^{r}$) $^{†}$] but not the lesser Green’s function [cf. Eq. (1)]. However there is no contradiction. G < needed in Eq. (1), can be expressed in terms of G r only if the bare embedding self-energies Σ$_{x,}$ 0 of Eq. (15) are used instead of the dressed ones Σ$_{x}$ in Eq. (3), and this is legitimate only for a sufficiently large extended molecule. For smaller sizes, both (nonequilibrium) G r and G < are needed to compute the current. The retarded Green’s function block G r of the sufficiently large extended molecule cou- pled to electrodes can be obtained from that of the isolated one G r i from a Dyson equation similar to Eq. (2) ( G $^{r}$) − 1 ≃ ( G r $_{i}$) − 1 − Σ r 0 ,L − Σ r 0 $_{,R}$. (17) In view of Eq. (17), the retarded Green’s function G r i of an isolated but sufficiently large molecular cluster represents the crucial quantity, which is needed to compute the current from Eq. (16). For real molecules, G r i can be obtained, e. g., within diagrammatic schemes to approximate the self-energy Σ r $_{i,corr}$. One of these schemes are the ADC-approximations widely employed for accurate electronic structure calculations [30–32]. Another scheme is based on the GW approximation, which was proposed long time ago for metallic solids [11] and used in several recent studies of small molecules [33, 34] and nanotransport [5–10]. It is certainly of interest to attempt to use such schemes for real systems, where exact results are not available, but applying them here in conjunction with Eqs. (13) and (16) is less useful conceptually. They represent certain mathematical approximations, which can be justified by comparing their predictions with experiments, but their validity in physically unclear. By constrast, our approximation possesses a precise physical content. Electrons can be strongly correlated in the molecule, but if interactions responsible for these correlations remain localized within a restricted spatial domain, the larger the extended molecule, the more accurate are the results; they should become exact in the limit of an infinite extended molecule [25, 35]. Our present goal is to document the approximation of a sufficiently large extended molecule, and, to facilitate the interpretation of the results, we do not use any further approximation. Therefore, we shall employ a simple model of a correlated molecule, which 8