A simple thermodynamic model for quantitatively addressing cooperativity in multicomponent self-assembly...

A thermodynamic model has been developed for quantitatively estimating cooperativity in supramolecular polymetallic [M(m)L(n)] assemblies, as the combination of two simple indexes measuring intermetallic (I(c)MM) and interligand (I(c)LL) interactions. The usual microscopic intermolecular metal-ligand affinities (f(i)(M,L)) and intermetallic interaction parameters (uMM), adapted to the description of successive intermolecular binding of metal ions to a preorganized receptor, are completed with interligand interactions (uLL) 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 (uLL < 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].