accounts for molecular electron correlations, which are included via the Green’s function G r i of a sufficiently large extended molecule. Because our method is based on the exact Green’s function G r i (whose counterpart for real molecules is a Green’s function computed by accu- rately including electron correlations within appropriate ab initio methods), it is clear that it will provide more reliable results than NEGF-DFT’s. 

To give support to the intuitive physical reason underlying the concept of a sufficiently large extended molecule, we have presented numerical results deduced within a non-trivial correlated model. Based on them, we argue that the present approach is able to provide results, which are interesting for the transport in correlated molecular systems. To this aim, the essential prerequisite is the ability to accurately compute the Green’s function G r i of the isolated extended molecule. Fortunately, this can be regarded as a feasible com- putational task. Such Green’s functions were already obtained by means of the Lanczos algorithm within the ADC [30–32]. The information contained in G r i [ionization energies and electro-affinities, and pole strengths, see Eq. (18)] can be directly compared with ex- perimental results, which can be obtained from appropriate experimental investigations of the isolated molecule. Encouragingly, accurate ADC schemes were successfully applied for correlated medium size molecules (e. g., benzene), comparable to those of interest for molec- ular electronics [49]. Importantly, although these methods are much more accurate than the currently considered GW, the computational effort is not much larger; it scales as N 5 o within ADC(2) and as ≈ N 4 o within GW, where N$_{o}$ is the number of atomic orbitals [55]. 

The difference between the present approach and the usual NEGF-approaches to cor- related transport [5–10, 28] can be discussed by inspecting the parenthesis of the r.h.s. of Eq. (11). In our case, this parenthesis becomes negligibly, and the difficulty to acount for correlations is to accurately tackle a sufficiently large extended molecule. If we considered the true (small) molecule and neglected that parenthesis, we would make an approxima- tion similar to the so-called elastic cotunneling approximation [56–58]. Then, the current would be (rather poorly) approximated by Eq. (16) [28]. This amounts to take N = 3 [59], which as seen by inspecting Figs. 3, 4, and 5, is not a good approximation. Our ap- proach goes beyond the elastic cotunneling approximation, it accounts for all higher-order processes within the extended molecule. Other NEGF-approaches to correlated transport [5–10, 18, 28] (which are also beyond the elastic cotunneling) adopt a different standpoint: they consider the true (small) molecule linked to electrodes and the evaluate the aforemen- 

