Green’s function ˆ G of the embedded molecule as ˆ G $_{−}$1 ≃ ˆ G $_{−}$1 i, 0 − ˆ Σ$_{i,corr}$ − ˆ Σ 0 ,L − ˆ Σ 0 ,R , (13) ˆ G $_{−}$1 ≃ ˆ G $_{−}$1 i − ˆ Σ 0 ,L − ˆ Σ 0 ,R , (14) Γ$_{x}$ = i [ Σ r 0 ,x − ( Σ r 0 ,x ) † ] , Σ < 0 ,x = if$_{x}$ Γ$_{x}$ , (15) Σ > 0 ,x = − i (1 − f$_{x}$ ) Γ$_{x}$ . provided that one is able to accurately compute the matrix Green’s function ˆ G$_{i}$ of an iso- lated, but still sufficiently large extended molecule. In view of the physical motivation behind it, we shall refer to the approximation involved in Eqs. (13) and (14) as the approx- imation of a sufficiently large extended molecule. This concept plays a central role for all the subsequent considerations of the present paper. According to Eq. (14), to compute the full matrix Green’s function ˆ G of a sufficiently large extended molecule, in addition to ˆ G$_{i}$ , one only needs Γ$_{x}$ and ˆ Σ 0 ,x ( x = L, R ). More precisely, what one only needs is the retarded self-energy Σ r 0 $_{,x}$, because all the other quantities can be expressed in terms of it as follows [16, 25] Consequently, the hard part to calculate the current is to obtain the matrix Green’s function ˆ G$_{i}$ of the isolated extended molecule. [As shown below, it even suffices to compute the retarded block G r $_{i}$, cf. Eqs. (17) and (16).] By inserting Eqs. (3), (5), (6), and (15) into Eq. (1), one can express the steady-state current through a sufficiently large extended molecule as In the absence of correlations G r,a → G r,a 0 , Eq. (16), which reduces to the familiar Landauer formula, is an exact result probably first deduced in Ref. 26 and often discussed later, e. g. [16, 18, 25, 27, 28]. Although similar to the uncorrelated case, Eq. (16) does account for electron correlations, because ( G $^{r,a}$) $_{−}$1 − ( G r,a 0 ) $_{−}$1 ≃ − Σ$_{i,corr}$ = 0 . It becomes similar to Eq. (10) of Ref. 16, deduced for proportionate coupling, if one approximates Σ ≃ Σ 0 there, in the spirit of the present paper. It is also similar to Eq. (17) of Ref. 25; if the correction factor used there is set to unity ( Λ = 1), that equation coincides with the present Eq. (16). The physical motivation of the coincidence of these two equations is clear: as seen I ≃ e h ∫ d ε Tr [ f$_{L}$ ( ε ) − f$_{R}$ ( ε )] Γ$_{L}$ ( ε ) G $^{r}$( ε ) Γ$_{R}$ ( ε ) G $^{a}$( ε ) . (16) 7