A Simple Thermodynamic Model for Quantitatively Addressing Cooperativity in Multicomponent Self-Assembly Processes—Part 1: Theoretical Concepts and Application to Monometallic Coordination Complexes and Bimetallic Helicates Possessing Identical Binding Sites

Abstract

A thermodynamic model has been developed for quantitatively estimating cooperativity in supramolecular polymetallic [M_mL_n] assemblies, as the combination of two simple indexes measuring intermetallic () and interligand () interactions. The usual microscopic intermolecular metal–ligand affinities () and intermetallic interaction parameters (u^MM), adapted to the description of successive intermolecular binding of metal ions to a preorganized receptor, are completed with interligand interactions (u^LL) and effective concentrations (c^eff), accounting for the explicit free energy associated with the aggregation of the ligands forming the receptor. Application to standard monometallic pseudo-octahedral complexes [M(L)_n(H₂O)_(6-n)] (M=Co, Ni, Hf, L=ammonia, fluoride, imidazole, n=1–6) systematically shows negative cooperativity (u^LL<1), which can be modulated by the electronic structures, charges, and sizes of the entering ligands and of the metal ions. Extension to the self-assembly of more sophisticated bimetallic helicates possessing identical binding sites is discussed, together with the origin of the positively cooperative formation of [Eu₂(L3)₃].