Green function of conjugated oligomers: the exact analytical solution with an application to the molecular conductance

The exact analytical expression of the Green function of oligomers M–M–…–M and M1–M2–M1–…–M2–M1, where M, M1, and M2 are monomers of arbitrary π electronic structure described by the tight-binding Hamiltonian, is derived for the first time. This result makes possible to address relevant spectral and electron transport properties of large linear molecules on the basis of realistic exactly solvable models. The power of the approach is exemplified by obtaining a number of explicit relations between the transport related quantities, in particular, through molecule tunneling decay constant, and the molecular electronic structure for a wide family of potential molecular wires.