Understanding, controlling and programming cooperativity in self-assembled polynuclear complexes in solution

Deviations from statistical binding, that is cooperativity, in self-assembled polynuclear complexes partly result from intermetallic interactions Δ^M,M, whose magnitudes in solution depend on a balance between electrostatic repulsion and solvation energies. These two factors have been reconciled in a simple point-charge model, which suggests severe and counter-intuitive deviations from predictions based solely on the Coulomb law when considering the variation of △^M,M with metallic charge and intermetallic separation in linear polynuclear helicates. To demonstrate this intriguing behaviour, the ten microscopic interactions that define the thermodynamic formation constants of some twenty-nine homometallic and heterometallic polynuclear triple-stranded helicates obtained from the coordination of the segmental ligands Ll-L11 with Zn²⁺ (a spherical d-block cation) and Lu³⁺ (a spherical 4f-block cation), have been extracted by using the site binding model. As predicted, but in contrast with the simplistic coulombic approach, the apparent intramolecular intermetallic interactions in solution are found to be i) more repulsive at long distance (ΔE^Lu,Lu;_1-4>ΔE^Lu,Lu _1-2), ii) of larger magnitude when Zn²⁺ replaces Lu ³⁺ (ΔE^Zn,Lu_1-2>ΔE ^Lu,Lu_1-2) and iii) attractive between two triply charged cations held at some specific distance (ΔE^Lu,Lu _1-3<0). The consequences of these trends are discussed for the design of polynuclear complexes in solution.