Superposition Rules for Molecular Circuits Embedded in a Single Molecule Bis-Terpyridine Breadboard Junction

Molecular electronics, which is governed by quantum mechanics, urgently requires establishing predictive frameworks and rules to combine molecular components and create miniaturized integrated circuits. To this end, we have recently demonstrated a bis-terpyridine based molecular breadboard with four conductance state formed by the superposition of five 2-5ring circuits. Here, we develop a generic analytical/statistical model to extract the conductance of the five embedded circuits in a bis-terpyridine based molecular breadboard junction. The model can be used to experimentally verify the rules for superposing the conductance of multiple molecular circuits, a key step towards building molecular circuitry. Further, our study provides a general framework to simulate and analyze break-junction conductance histograms of complex molecular junctions with more than two electrode anchoring groups.