Understanding Single-Molecule Parallel Circuits on the Basis of Frontier Orbital Theory

In electronic devices, as the number of paths connecting source and drain electrodes increases, the conductance of the device will also increase. However, this is not always the case on the nanoscale. According to the current superposition law at work in the macroscopic electrical circuits, doubling the number of paths should double the conductance, but when such paths are examined on the basis of the frontier orbital theory for nanoscale electrical circuits, more complex scenarios arise. When the number of paths in a molecule is doubled, the conductance may get more than doubled, remain unchanged, or even be reduced. We propose a classification of conducting systems falling into each of these scenarios with the help of aromaticity. The present work involves a theoretical study using the nonequilibrium Green's function that shows that these varying outcomes are closely related to the presence or absence of aromatic rings. This work serves to characterize molecular conductance characteristics based on frontier orbital theory, orbital interactions, and a local transmission concept. Some discrete mathematical aspects of the relationship between atom connectivity and electron conductivity are also described.