Unveiling the Electronic Properties of the Strong Isotropic Molecular Materials through the Graph Theory

The strong isotropic lattices, honeycomb, K4, and diamond lattices, can be transformed into the spin frustration lattices, kagome, hyper-kagome, and pyrochlore lattices, respectively, by the line graph relation. This means that the strong isotropic lattices possess"hidden"electronic properties and phenomena. Here, I introduce several examples:the spin frustration in a honeycomb MOF, Cu3(L)2(L=HHTP and THQ), and a molecule-based K4, Rb3[(–)-NDI-Δ]2. I also describe the exotic band structure of a molecule-based honeycomb lattice, Rb3(p-TT), and the unusual phase transitions in a molecule-based diamond, bpBDTDA, which are considered to result from bond frustration.