## I. INTRODUCTION 

Intensive experimental and theoretical work done in the last decade led to significant advances in the field of electric transport through molecules and nanostructures [1, 2]. From the theoretical side, ab initio approaches — mostly based on ground state density- functional theory (DFT) calculations combined with the Keldysh nonequilibrium Green’s functions (NEGF) — contributed to a qualitative understanding of some trends impor- tant for molecular electronics [3, 4]. However, intrinsic limitations of the DFT-approaches make it impossible to quantitatively describe electronic transport in correlated molecular systems. There is a broad consensus in attributing the rather large quantitative discrep- ancies between the calculated and measured currents to the notorious fact that the DFT substantially underestimates the excitation energies, in particular the HOMO-LUMO gap. In order to more appropriately account for electron correlation effects on nanotransport, several studies, which also used the NEGF, focused their attention on other methods, e. g., the so-called GW approximation [5–10], a method proposed long time ago for metals [11]. 

The theory of electric transport through correlated molecular systems (i. e., which cannot be described within a single-particle picture) is confronted with problems, which are not encountered in the absence of electron correlations. A basic issue is that of partitioning the real system into electrodes and the molecule [12]. In the uncorrelated case, the electric current can be computed exactly within the Landauer approach. Being exact, the result is partition-independent, and therefore the specification of the electrode-molecule interfaces used in calculations is not important. For physical reasons, the current through a correlated molecular system should also be partition-independent. Excepting for a few models, the calculations on the transport in correlated systems are not exact. The various approximation schemes employed do not necessarily satisfy this partition invariance. 

We are not aware of a systematic study addressing this issue. In most cases, the reported results are from calculations carried out for the largest extended molecule that can be tackled, wherein besides the molecule itself the largest possible electrode portions linked to it are included. The main concern of the most elaborate theoretical approaches of the correlated molecular transport developed so far is not the partition invariance or, alternatively, the independence on the size N of the extended molecule. One is merely interested whether the employed approximate approach is current conserving or not, i. e., whether the calculated 

