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.