From Accurate Quantum Chemistry to Converged Thermodynamics for Ion Pairing in Solution

Quantitative prediction of thermodynamic properties in solution is essential for translating atomistic simulations into reliable chemical insight. As an exemplar system, the behaviour of CaCO$_3$ in water has been widely studied to understand its mineralization in seawater, with potential implications for carbon-capture strategies. However, making accurate computational predictions has been a long-standing challenge, requiring both highly accurate electronic structure methods and extensive statistical sampling. Here, we combine advances in machine learning and electronic structure theory to fully resolve the ion pairing free energy of CaCO$_3$ with explicit solvation. We show that achieving quantitative agreement with experiment requires going beyond the standard density functional theory up to the "gold-standard" coupled cluster theory with single, double, and perturbative triple excitations [CCSD(T)]. We generate a set of systematically improvable models, enabling reliable insights into the initial association mechanism of Ca and CO$_3$ ions prior to nucleation while fully quantifying enthalpic and entropic effects. Our results demonstrate that CCSD(T)-level thermodynamic predictions of complex aqueous systems can now be routinely achieved.