Computational insight into a mechanistic overview of water exchange kinetics and thermodynamic stabilities of bis and tris-aquated complexes of lanthanides

Abstract

A thorough investigation of Ln³⁺ complexes with more than one inner-sphere water molecule is crucial for designing high relaxivity contrast agents (CAs) used in magnetic resonance imaging (MRI). This study accomplished a comparative stability analysis of two hexadentate (H₃cbda and H₃dpaa) and two heptadentate (H₄peada and H₃tpaa) ligands with Ln³⁺ ions. The higher stability of the hexadentate H₃cbda and heptadentate H₄peada ligands has been confirmed by the binding affinity and Gibbs free energy analysis in aqueous solution. In addition, energy decomposition analysis (EDA) reveals the higher binding affinity of the peada⁴⁻ ligand than the cbda³⁻ ligand towards Ln³⁺ ions due to the higher charge density of the peada⁴⁻ ligand. Moreover, a mechanistic overview of water exchange kinetics has been carried out based on the strength of the metal–water bond. The strength of the metal–water bond follows the trend Gd–O47 (w) > Gd–O39 (w) > Gd–O36 (w) in the case of the tris-aquated [Gd(cbda)(H₂O)₃] and Gd–O43 (w) > Gd–O40 (w) for the bis-aquated [Gd(peada)(H₂O)₂]⁻ complex, which was confirmed by bond length, electron density (ρ), and electron localization function (ELF) at the corresponding bond critical points. Our analysis also predicts that the activation energy barrier decreases with the decrease in bond strength; hence k_ex increases. The ¹⁷O and ¹H hyperfine coupling constant values of all the coordinated water molecules were different, calculated by using the second-order Douglas–Kroll–Hess (DKH2) approach. Furthermore, the ionic nature of the bonding in the metal–ligand (M–L) bond was confirmed by the Quantum Theory of Atoms-In-Molecules (QTAIM) and ELF along with energy decomposition analysis (EDA). We hope that the results can be used as a basis for the design of highly efficient Gd(III)-based high relaxivity MRI contrast agents for medical applications.