Transfer-Learned Machine-Learning Potentials with Embedded Correlated Wavefunction Accuracy for Ca²⁺–CO₃²⁻ Ion Pairing in Aqueous Solution

Understanding microscopic mechanisms of Ca²⁺-CO₃²⁻ ion pairing in aqueous solution is essential for modeling CO₂ mineralization in seawater, yet this process challenges conventional DFT-based molecular dynamics simulations due to the high computational cost required for long sampling times and the limited accuracy of DFT electron exchange and correlation. We develop a transfer-learned machine-learning potential (MLP) initially trained on DFT-revPBE+D3(BJ) data and further refined with embedded correlated wavefunction (ECW) theory using MP2 and coupled-cluster methods. The ECW-informed MLP reaches near-chemical accuracy while enabling fully converged sampling of the free-energy surface governing Ca²⁺-CO₃²⁻ association and dissociation. The resulting landscape reveals how water polarization and solvent fluctuations mediate transitions between contact, solvent-shared, and solvent-separated ion pairs, providing a predictive framework for aqueous carbon dioxide mineralization and demonstrating the general applicability of the ECW-MLP approach.