Stability constants of lanthanide-nitrate complexes in aqueous solutions: a theoretical study

Calculating stability constants for lanthanide-nitrate complexes in aqueous solution is challenging due to the complex free-energy landscapes of the participating species. In this work, we independently compare cluster-continuum solvation at a density functional theory level and condensed-phase approaches using universal machine learning interatomic potentials (MLIPs) for determining the stability constants of lanthanide-nitrate complexes in aqueous solutions. Within the cluster-continuum solvation framework at the B3LYP level of theory, reactions involving lanthanide coordination numbers of both 8 and 9 are found to be relevant. After an empirical linear free-energy correction, the cluster-continuum results fall on the same order-of-magnitude scale as the experimental stability constants. By contrast, condensed-phase simulations using MACE-MP0 MLIP underestimates lanthanide hydration numbers and provides potential of mean forces resulting in stability constants with large deviations from experiment, whereas MACE-MATPES-R2SCAN improves both hydration structure and the stability-constant scale but still does not quantitatively reproduce the detailed lanthanide trend. Across both approaches, nitrate binding is generally viewed as a labile coordination motif involving interconverting mono- or bidentate structures, with hydration-shell structure influencing which configurations are favored. Overall, the cluster-continuum calculations provide a practical semi-quantitative baseline for the experimental stability-constant scale, while the explicit-solvent MLIP benchmarks show clear progress from MACE-MP0 to MACE-MATPES-R2SCAN but also highlight the need for lanthanide-targeted training, or improved long-range and polarization treatments in condensed-phase simulations to obtain predictive thermodynamics for complex aqueous lanthanide chemistry.