Conductance of molecular wires connected or bonded in parallel

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Abstract
The conductance superposition law of molecules connected in parallel between the two electrodes of a tunnel junction is discussed. For molecules directly adsorbed between the electrodes, a linear superposition law is found with corrections coming from the interaction between the molecules through the surface of the electrodes. For molecules connected to the electrodes via molecular wires (the molecular connection nodes being located inside the tunnel junction), a quadratic law is found. These two superposition regimes are illustrated on realistic conjugated oligomer molecular circuits.