Computational Explorations of Th⁴⁺ First Hydrolysis Reaction Constants: Insights from <i>Ab Initio</i> Molecular Dynamics and Density Functional Theory Calculations

The fundamental hydrolysis behavior of tetravalent actinide cations (An⁴⁺) with a high charge is crucial for understanding their solution chemistry, particularly in nuclear fuel reprocessing and environmental behavior. Using Th⁴⁺ as a reference of the An⁴⁺ series, this work employed both the periodic model and the cluster model to calculate the first hydrolysis reaction constant (p<i>K</i>_a1) of the Th⁴⁺ aqua ion and conducted a detailed evaluation of these approaches. In the periodic model, <i>ab initio</i> molecular dynamics (AIMD) simulations of Th⁴⁺ in the explicit solvation environment are conducted, using metadynamics and constrained molecular dynamics to calculate p<i>K</i>_a1 values. Metadynamics simulations with sufficient sampling yielded a value of 5.02, aligning with the experimental values (4.12-4.97). Moreover, AIMD results reveal further Grotthuss-type proton transfers and changes in the solvent structures, which are important for accurately modeling the hydrolysis process. In the cluster model, density functional theory calculations are performed on isolated hydrate clusters to obtain p<i>K</i>_a1 values, describing solvation effects through the cluster-continuum model. Based on insights from the periodic models, particularly regarding further proton transfer, the cluster model was modified and tested using different functionals and similar cations (La³⁺and Ac³⁺). The p<i>K</i>_a1 values obtained in the cluster model also show good agreement with the experimental values. The current computational approaches provide a comprehensive understanding of Th⁴⁺ hydrolysis and a reference framework for studying the hydrolysis of other lanthanide and actinide ions.