Ab initio electron propagator methodology may be applied to the calculation of electrical current through a molecular wire. A new theoretical approach is developed for the calculation of the retarded and advanced Green functions in terms of the electron propagator matrix for the bridge molecule. The calculation of the current requires integration in a complex half plane for a trace that involves terminal and Green’s-function matrices. Because the Green’s-function matrices have complex poles represented by matrices, a special scheme is developed to express these “matrix poles” in terms of ordinary poles. An expression for the current is derived for a terminal matrix of arbitrary rank. For a single terminal orbital, the analytical expression for the current is given in terms of pole strengths, poles, and terminal matrix elements of the electron propagator. It is shown that Dyson orbitals with high pole strengths and overlaps with terminal orbitals are most responsible for the conduction of electrical current.

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Indeed, if the real part of the self-energy is not small, the partitioning becomes questionable. If it is really large, one should introduce a so-called extended molecule that includes such a large interaction (Ref. 8). Small interaction of the extended molecule with the rest of the leads is assumed to be small (Refs. 26, 27, and 29).

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