“Hidden Frustration” in Molecule-based K₄ and Diamond Lattices Revealed by the Line Graph Transformation

Abstract

In the graph theory, it is known that the line graphs of the K₄ and diamond lattices are the hyper-kagome and pyrochlore lattices, respectively. The hyper-kagome and pyrochlore lattices are possible frustration lattices, because they consist of a triangular or tetrahedral component. In the present article, we describe the crystal structures and physical properties of a molecule-based K₄, (–)-NDI-Δ, and a molecule-based diamond, bpBDTDA. The line graph transformation reveals a spin frustration in (–)-NDI-Δ, which results in a spin liquid ground state, and a bond frustrations in bpBDTDA, which induces a stepwise and inhomogeneous lattice dimerization.