Entropy directs the self-assembly of supramolecular palladium coordination macrocycles and cages

The self-assembly of palladium-based cages is frequently rationalized via the cumulative enthalpy (ΔH) of bonds between coordination nodes (M, i.e., Pd) and ligand (L) components. This focus on enthalpic rationale limits the complete understanding of the Gibbs free energy (ΔG) for self-assembly, as entropic (ΔS) contributions are overlooked. Here, we present a study of the M₂ ^linL₃ intermediate species (M = dinitrato(N,N,N',N'-tetramethylethylenediamine)palladium(ii), ^linL = 4,4'-bipyridine), formed during the synthesis of triangle-shaped (M₃ ^linL₃) and square-shaped (M₄ ^linL₄) coordination macrocycles. Thermochemical analyses by variable temperature (VT) ¹H-NMR revealed that the M₂ ^linL₃ intermediate exhibited an unfavorable (relative) ΔS compared to M₃ ^linL₃ (triangle, ΔTΔS = +5.22 kcal mol^-1) or M₄ ^linL₄ (square, ΔTΔS = +2.37 kcal mol^-1) macrocycles. Further analysis of these constructs with molecular dynamics (MD) identified that the self-assembly process is driven by ΔG losses facilitated by increases in solvation entropy (ΔS _solv, i.e., depletion of solvent accessible surface area) that drives the self-assembly from "open" intermediates toward "closed" macrocyclic products. Expansion of our computational approach to the analysis of self-assembly in Pd ^benL₂ cages (^benL = 4,4'-(5-ethoxy-1,3-phenylene)dipyridine), demonstrated that ΔS _solv contributions drive the self-assembly of both thermodynamic cage products (i.e., Pd₁₂ ^benL₂₄) and kinetically-trapped intermediates (i.e., Pd₈ ^cL₁₆).