Theoretical study of the electrical conduction in the single molecule parallel circuit based on the frontier orbital theory

Abstract

In electronic devices, when the number of paths connecting the source and drain electrodes increase, the conductance of the device should also increase. This is true in the macroscopic case, but this is not always the case on the nanoscale. Kirchhoff’s superposition law tells us that when the number of paths is doubled, the conductance is also doubled. However, as far as the path in a sense of molecular graph theory goes, things are not so simple. When the number of paths in a molecule gets doubled, two situations will arise: the conductance gets more than doubled or even gets smaller. Our theoretical study with the non-equilibrium Green’s function method has revealed that the distinction of these situations has a close relation to the aromaticity of the ring formed as a result of doubling the path. We will see how helpful it is to characterize the molecular transmission features relying on the frontier orbital theory and orbital interactions. Some discrete mathematical aspects of the relation between the atom connectivity and electron conductivity are also described.