Minimal attenuation for tunneling through a molecular wire

The electronic transmission coefficient through a finite-length molecular wire decreases exponentially when its length increases for energy chosen in its gap. It is demonstrated that the damping factor in the exponential depends on the full wire electronic structure and not only on the gap width as obtained from a WKB calculation of this factor. The gap remains in controlling the minimum of the damping factor. However, this minimum is far from being reached on known molecular wires. An optimization procedure is proposed to define molecular wires with a very small damping in the tunneling regime.