Dynamic metal-ligand coordination in solution: a ligand-exchange relay mechanism for gold(i) sulfido complex...

Understanding dynamic metal-ligand interactions in polynuclear metal complexes is essential to control their structures and reactivities, yet the underlying mechanisms remain elusive because key intermediates are short-lived and often spectroscopically silent. Here we combine ab initio-accurate machine-learning interatomic potentials (MLPs) with on-the-fly probability enhanced sampling (OPES) in molecular dynamics (MD) simulations to resolve such solution-phase transformations. Using the interconversion of phosphine-ligated gold(i) sulfido complexes, [Au₁₀S₄(L)₄]²⁺ ⇌ 2 [Au₅S₂(L)₂]⁺ (L = LPh or LTh), as a prototypical system, we uncover a ligand-exchange relay mechanism mediated by (µ₄-S)-Au-(µ₃-S) motifs. Au-P bond cleavage triggers successive phosphine-exchange steps that relay electrophilic character across equatorial Au atoms, during which dynamic η ²-arene-Au interactions stabilize the electrophilic centers. Free-energy analysis shows that the decanuclear complexes are thermodynamically favored over the corresponding pentanuclear products and that the maximum barrier is lower for LPh-ligated than for LTh-ligated systems, approximately 130 vs. 167 kJ mol^-1, consistent with experimental observations. This ligand dependence arises from the P-P bite distance, which controls key Au-S contacts and thereby the relay-intermediate stability. These findings reveal ligand-exchange relay as a distinct dynamic coordination mode and demonstrate that MLP-driven enhanced-sampling simulations can resolve interconversions of polynuclear complexes with atomistic and free-energy resolution.