Incorporating a neural network into the AMOEBA polarizable force field for ligand field effects of Cu2+ ions.

Characterizing the solvation of open-shell transition metal ions remains a challenge for classical force fields due to ligand field electronic effects. Here, we present AMOEBA + NN, a machine-learning-augmented polarizable potential, to investigate Cu2+ solvation in NH3 and H2O and mixed environments. The model, trained on quantum-mechanical (QM) association energies, accurately reproduces the Cu2+ energy landscape across diverse coordination geometries. Molecular dynamics simulations demonstrate that AMOEBA + NN successfully captures the electronically driven Jahn-Teller (JT) distortion. Evidence from radial distribution functions (RDFs) and geometry optimizations reveals characteristic axial elongation, which is absent in conventional classical descriptions. Kinetic analysis shows a highly dynamic Cu2+-NH3 environment with a rapid ligand exchange (residence time of 66.52 ps), contrasting with the H2O system where binding is two to three orders of magnitude more stable. Furthermore, the calculated hydration free energy of -477.59 ± 0.50 kcal mol-1 shows excellent agreement with experimental data (within 1.31 kcal mol-1). This work provides a unified, computationally efficient framework for describing the structural, dynamic, and thermodynamic observables of transition metal coordination.