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

Abstract

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.

Figures (3)

• Figure 1: Workflow combining accurate electronic structure, MLPs and enhanced sampling: Schematic of the framework used in this work, using MLPs to access converged thermodynamics in solution at various levels of electronic structure theory. To obtain the CCSD(T) level model a $\Delta$-learning approach uses gas phase clusters to correct the periodic MP2 model to CCSD(T) level. In general the models are 'self-consistently' converged to ensure reliable predictions of the density and PMF (generically labelled 'Property' in the middle panel) and adequate sampling of configuration space. Finally efficient implementations of the MLPs are used in tandem with enhanced sampling simulations to resolve the thermodynamics of complex potential (free) energy surfaces.
• Figure 2: Ion pair association free energy, enthalpy and entropy from OPES simulations: Comparison of cWFT MLPs (CCSD(T), MP2 and RPA) and DFT MLPs (revPBE0-D3, revPBE-D3) for (top) the standard ion pair association free energy at 300 K (middle) enthalpy and (bottom) entropy of ion pair association. The experimental range from literature kellermeierEntropyDrivesCalcium2016plummerSolubilitiesCalciteAragonite1982 is shaded in blue for each quantity. Error bars on the cWFT and DFT results are the standard error on the mean of 6 independent OPES simulations. All results have also been corrected for finite size effects, as described in Section \ref{['si-fig:finitesize']} of the SI. Convergence of the OPES simulations is also shown in Figure \ref{['si-fig:opes_convergence']} of the SI, as well as the full temperature dependance of the ion pair association free energy used to obtain the enthalpy and entropy in Figure \ref{['si-fig:dgdt']} of the SI.
• Figure 3: CaCO3 ion pair dissociation pathways and ion solvation: Left panel: Ion pairing pathways for a selection of models at 300 K: revPBE-D3, revPBE0-D3 and CCSD(T). The minimum free energy path in each case is plotted in white. Above is the potential of mean force, aligned to the analytic solution for point charges in a dielectric medium (grey dashed line). The bidentate contact ion pair (1), monodentate contact ion pair (2), solvent-shared ion pair (3) and solvent separated ion pair (4) are labelled for the revPBE0-D3 case, along with representative snapshots above. In the snapshots, calcium, carbon, oxygen and hydrogen are coloured blue, green, red and white, respectively. Right panel: Free energy as a function of water coordination number for a calcium (top) and carbonate (bottom) ion in water for revPBE-D3, revPBE0-D3 and CCSD(T) models. Representative snapshots are shown alongside (only a small region of the full simulation cell is shown).