A Correlated Source-Sink-Potential Model Consistent with the Meir-Wingreen Formula

We model a molecular device as a molecule attached to a set of leads treated at the tight-binding level, with the central molecule described to any desired level of electronic structure theory. Within this model, in the absence of electron-phonon interactions, the Landauer-Büttiker part of the Meir-Wingreen formula is shown to be sufficient to describe the transmission factor of the correlated device. The key to this demonstration is to ensure that the correlation self-energy has the same functional form as the exact correlation self-energy. This form implies that nonsymmetric contributions to the Meir-Wingreen formula vanish, and hence, conservation of current is achieved without the need for Green's Function self-consistency. An extension of the Source-Sink-Potential (SSP) approach gives a computational route to the calculation and interpretation of electron transmission in correlated systems. In this picture, current passes through internal molecular channels via resonance states with complex-valued energies. Each resonance state arises from one of the states in the Lehmann expansion of the one-electron Green's function, hole conduction derived from ionized states, and particle conduction from attached states. In the correlated device, the dependence of transmission on electron energy is determined by four structural polynomials, as it was in the tight-binding (Hückel) version of the SSP method. Hence, there are active and inert conduction channels (in the correlated case, linked to Dyson orbitals) governed by a set of selection rules that map smoothly onto the simplest picture.