Modelling ligand exchange in metal complexes with machine learning potentials

Abstract

Metal ions are irreplaceable in many areas of chemistry, including (bio)catalysis, self-assembly and charge transfer processes. Yet, modelling their structural and dynamic properties in diverse chemical environments remains challenging for both force fields and ab initio methods. Here, we introduce a strategy to train machine learning potentials (MLPs) using MACE, an equivariant message-passing neural network, for metal-ligand complexes in explicit solvents. We explore the structure and ligand exchange dynamics of Mg²⁺ in water and Pd²⁺ in acetonitrile as two illustrative model systems. The trained potentials accurately reproduce equilibrium structures of the complexes in solution, including different coordination numbers and geometries. Furthermore, the MLPs can model structural changes between metal ions and ligands in the first coordination shell, and reproduce the free energy barriers for the corresponding ligand exchange. The strategy presented here provides a computationally efficient approach to model metal ions in solution, paving the way for modelling larger and more diverse metal complexes relevant to biomolecules and supramolecular assemblies.

Fig. 1. Training data and active learning workflow: (a) training subsets for Mg²⁺ in aqueous solution, (b) training subset for Pd²⁺ in acetonitrile (MeCN), (c) scheme of the active learning workflow used to train the machine-learning potentials (MLPs).

Fig. 2. Comparison of the ground-truth and MACE prediction of energies and forces for cluster systems at 300 K: (a) Mg²⁺ solvated in 51 water molecules modelled at ωB97X-D3BJ/def2-TZVP level of theory, (b) Pd²⁺ solvated in 30 MeCN molecules modelled at TPSS0-D3BJ/def2-TZVP level of theory.

Fig. 3. Simulation boxes, radial distribution functions g(r) and coordination numbers N(r) of the metal complexes in solution. (a) Mg²⁺ in aqueous solution, (b) Pd²⁺ in MeCN.

Fig. 4. Potential of mean force (PMF) profiles of the two ligand exchange processes for (a) [Mg(H₂O)₆]²⁺ (the solvent molecule exchanged is coloured blue) and (b) [Pd(MeCN)₄]²⁺, where the black dot indicates the energy at the TS.