Graphs that predict exciton delocalization

The field of molecular excitons and related supramolecular systems has largely focused on aggregates where nearest neighbour couplings dominate. We propose that radically different states can be produced by moving beyond that paradigm. In practice, accomplishing this task remains an open challenge because it requires the development of ways to couple network molecules more densely. In the present work, we suggest why it would be worthwhile. We describe a merger of work developed in the field of discrete mathematics with concepts and needs for the field of molecular excitons. We discuss the reasons for exciton localization and posit how systems where the spectrum contains a gap can be robust to disorder, and thus maintain coherence or delocalization. We propose that certain kinds of structures (expander graphs) specifying how molecules are coupled to each other show such a gap and thus resilience to decoherence. We review the relevant background known from graph theory. This perspective suggests a fascinating scope of new properties possible by demonstrating expander graph inspired excitonics. This article is part of the discussion meeting issue 'Excitonic frontiers'.