Decay of the molecular wire conductance with length: the role of spectral rigidity

In the tunnelling regime, the conductance of a metal-molecular wire-metal tunnel junction decreases exponentially with the length of the wire. Complementary to the homo-lumo gap of this molecular wire, we demonstrate on a series of simple tight binding molecular wires that this decay is also controlled by a new parameter ρ, the level repulsion of the wire electronic spectrum. ρ is the first moment of the statistical description of the molecular wire electronic energy levels distribution over the complete energy range. When connected between two electrodes, the effective mass of the tunnel electron is proportional to ρ−2.