Metallo-supramolecular binary necklaces with multiple symmetries

Inspired by the binary necklace problem in combinatorial mathematics, we designed and constructed a series of metallo-supramolecular polygons via coordination-driven self-assembly (CDSA) of an anisotropic tetratopic terpyridine ligand with Zn(II) ions. Such anisotropic units with two different orientations serve as two types of “beads” in the assembly process, resulting in supramolecular “necklaces” that, in theory, exhibit numerous isomers. Through combinatorial analysis, molecular modelling, and experimental validation, we identified three predominant hexameric isomers with distinct symmetrical characteristics. The experimental distribution of these isomers agreed well with their formation probabilities resolved from the binary necklace problem. Notably, detailed structural analysis by scanning tunneling microscopy imaging confirmed the pivotal role of entropy in determining the isomeric distribution. Upon heating under diluted conditions, such three hexameric isomers were transformed into a single pentameric structure as the dominant species, which aligns with the theoretical predictions of binary necklace problem and minimized strain energy. This transformation was corroborated with theoretical modelling and experimental study, highlighting the critical influence of symmetry and entropy in directing the thermodynamic pathway of CDSA. This work provides a notable example of mathematically rationalized supramolecular chemistry, offering profound insights into the thermodynamic aspects of CDSA.