II. THEORETICAL FRAMEWORK Within the Keldysh nonequilibrium Green’s function framework, it is possible to express the steady-state current I through a correlated molecule linked to electrodes, wherein elec- trons are supposed to be uncorrelated, by the formula [16–18] Above, the obvious ε -dependence of the integrand has been omitted for brevity. In Eq. (1), G $^{r}$, G $^{a}$, and G < stand for the nonequilibrium ( V = 0) exact retarded, advanced, and the lesser Green’s functions of the extended molecule, respectively, and Γ L and Γ R describe the coupling of the extended molecule to the left (L) and right (R) electrodes, respectively. The bold symbols are used to denote matrices, whose indices label the basis states of the extended molecule. These are site indices for the case considered below; in a realistic ab initio calculations, they would specify the molecular orbitals characterizing the extended molecule. As usual, each electrode is assumed to be in equilibrium; f$_{L,R}$ represent Fermi distribution functions characterized by chemical potentials µ$_{L,R}$ , which are imbalanced ( µ$_{L}$ − µ$_{R}$ = eV ) due to an applied voltage V responsible for the current flow. The Green’s functions G $^{r}$, G $^{a}$, and G < entering Eq. (1) are those of the extended molecule coupled to the electrodes. To compute these nonequilibrium Green’s functions one usually resorts to the Dyson equations [17–19] I = ie 2 h ∫ d ε Tr [ ( f$_{L}$ Γ$_{L}$ − f$_{R}$ Γ$_{R}$ ) ( G r − G $^{a}$) + ( Γ$_{L}$ − Γ$_{R}$ ) G $^{<}$] . (1) G r,a = G r,a 0 + G r,a 0 Σ $^{r,a}$Gr,a , (2) G$^{<}$ > = ( 1 + G $^{r}$Σ$^{r}$) G$^{<}$ > 0 ( 1 + Σ $^{a}$G$^{a}$) + G $^{r}$Σ$^{<}$ $^{>}$Ga → G $^{r}$Σ$^{<}$ $^{>}$Ga , (3) ˆ G =  $^{G}$$^{t}$ − G < G > − G ˜ t   ; ˆ Σ =   Σ t − Σ < Σ > − Σ ˜ t   , (4) which relate the exact Green’s functions (without subscript) to those of a noninteracting (uncorrelated) reference (subscript 0) by means of the self-energies Σ ’s. Uncorrelated elec- trons can refer either to free electrons or described within the SCF approximation. The expression at the right of the arrow in Eq. (3) applies to the case of a steady-state flow considered here [12]. The above nonequilibrium Dyson equations can be written in a more compact form by means of the block matrices [19] 4