Five thermodynamic describers for addressing serendipity in the self-assembly of polynuclear complexes in solution

Abstract

The thermodynamic self-assembly of any metallo-supramolecular complex [M_pmL_pn] in solution can be dissected into five additive free energy contributions. According to a hierarchical energetic order, the two microscopic describers f_inter and f_intra, which refer to the hetero-component metal–ligand connections, bring the main driving forces to the complexation process. Combined with the statistical factor ω of the self-assembly, which measures the changes in intrinsic rotational entropies accompanying the complexation process, these three parameters provide a satisfying description of the statistical binding leading to [M_pmL_pn] in solution. Deviations from statistics, i.e. cooperativity, has then two different origins. Firstly, the preorganization controlling the intramolecular connection events may vary along the assembly process, thus affecting f_intra. Secondly, the homo-component interactions brought by the specific location of the different components in the final assembly (M⋯M interactions: ΔE^M,M, and L⋯L interactions: ΔE^L,L), may additionally contribute to the total free energy change and affect f_inter. Beyond the determination of quantitative experimental values for these five parameters operating in various metal-containing assemblies, considerable efforts have been focused on their physico–chemical origins, with the ultimate goal of unravelling their chemical design. In this Feature Article, the bases are first considered leading to the emergence of the free additive thermodynamic model in metallo-supramolecular chemistry. A tutorial discussion of the current level of understanding of each microscopic thermodynamic describer follows, together with some selected practical applications in the field of polynuclear d-block and f-block complexes.