Exploring the Dynamic Coordination Sphere of Lanthanide Aqua Ions: Insights from r²SCAN-3c Composite-DFT Born–Oppenheimer Molecular Dynamics Studies

Born-Oppenheimer molecular dynamics (BOMD) simulations were performed to investigate the structure and dynamics of the first hydration shells of five trivalent lanthanide ions (Ln³⁺) at room temperature. These ions are relevant in various environments, including the bulk aqueous solution. Despite numerous studies, accurately classifying the molecular geometry of the first hydration sphere remains a challenge. To addres this, a cluster microsolvation approach was employed to study the interaction of Ln³⁺ ions (La, Nd, Gd, Er, and Lu) with up to 27 explicit water molecules. Electronic structure calculations were performed with the composite r²SCAN-3c method. The results demonstrate that this method offers an optimal balance between precision and computational efficiency. Specifically, it accurately predicts average Ln-O distances (MAE = 0.02 Å) of the first hydration sphere and preferred coordination numbers (CN) for the different lanthanide cations as compared to reported data in bulk. Highly dynamic first hydration shells for the examined Ln³⁺ ions were found, with noticeable and rapid rearrangements in their coordination geometries, some of which can be recognized as the tricapped trigonal prism (TTP) and the capped square antiprism (CSAP) for CN = 9, and as the square antiprism (SAP), the bicapped trigonal prism (BTP), and the trigonal dodecahedron (DDH) for CN = 8. However, ca. 70% of the nonacoordinated configurations did not meet the criteria of TTP or CSAP structures. For CN = 8, the percentage of configurations that could not be assigned to SAP, BTP, or DDH was lower, around 30%. The theoretical EXAFS spectra obtained from the BOMD simulations are in good agreement with the experimental data and confirm that model microsolvated environments accurately represent the near-solvation structure of these trivalent rare-earth ions. Moreover, this demonstrates that the faster dynamics of the first hydration shell can be studied separately from the dynamics of water exchange in the bulk aqueous solution.