Tunneling across molecular wires: an analytical exactly solvable model

On the basis of the Landauer approach and Green function technique we have developed an exactly solvable analytical model that gives a quick and reliable estimate of (ohmic) tunnel conductance in metal–molecular heterojunctions. The model covers conjugated oligomers of types M–M–⋯–M and M 1–M 2–M 1–⋯–M 2–M 1 connecting metal pads in molecular contacts. Based on a realistic Hamiltonian for these kinds of oligomers we obtain an analytical expression for the tunnel conductance: (2 e 2/ h) g 0( E F ) g mol 0( E F )e −2 δ( E F ) N , where N is the number of the structural units M (or M 1). The pre-exponential factor g 0( E F ) depends on the metal and metal–molecule coupling characteristics only, whereas g mol 0( E F ) and the exponential decay constants are explicit functions of the Green function matrix elements of monomers M (or M 1 and M 2). This formula provides, for the first time, an analytical relationship between a realistic description of the molecular electronic structure and the heterojunction resistance. The results obtained from this formula are of immediate use for probing currents through single molecules, e.g. by scanning tunneling microscope (STM) techniques as well as for measurements of electron transfer rates in donor/bridge/acceptor systems.