Graph-theoretical exploration of the relation between conductivity and connectivity in heteroatom-containing single-molecule junctions

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Abstract
In this study, we employ the Sachs graph theory to formulate the conduction properties of a single-molecular junction consisting of a molecule in which one carbon atom of an alternant hydrocarbon is replaced with a heteroatom. The derived formula includes odd and even powers of the adjacency matrix, unlike the graph of the parental structure. These powers correspond to odd- and even-length walks. Furthermore, because the heteroatom is represented as a self-loop of unit length in the graph, an odd number of passes of the self-loop will change the parity of the length of the walk. To confirm the aforementioned effects of heteroatoms on conduction in an actual sample, the conduction behavior of meta-connected molecular junctions consisting of a heterocyclic six-membered ring, whose conductive properties have already been experimentally determined, was analyzed based on the enumerated number of walks.
Funding Information
  • Japan Society for the Promotion of Science London (JP17K14440, JP17H03117, JP21K04996, JP20H04643, JP19H04700)
  • Ministry of Education, Culture, Sports, Science and Technology
  • Core Research for Evolutional Science and Technology (JPMJCR15P5)
  • JST-Mirai Program (JPMJMI18A2)

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