Solution structure of Ln(III) complexes with macrocyclic ligands through theoretical evaluation of ¹H NMR contact shifts

Herein, we present a new approach that combines DFT calculations and the analysis of Tb^III-induced ¹H NMR shifts to quantitatively and accurately account for the contact contribution to the paramagnetic shift in Ln^III complexes. Geometry optimizations of different Gd ^III complexes with macrocyclic ligands were carried out using the hybrid meta-GGA TPSSh functional and a 46 + 4f⁷ effective core potential (ECP) for Gd. The complexes investigated include [Ln(Me-DODPA)] ⁺ (H₂Me-DODPA = 6,6′-((4,10-dimethyl-1,4,7,10- tetraazacyclododecane-1,7-diyl)bis(methylene))dipicolinic acid, [Ln(DOTA)(H ₂O)]^- (H₄DOTA = 1,4,7,10-tetraazacyclododecane- 1,4,7,10-tetraacetate), [Ln(DOTAM)(H₂O)]³⁺ (DOTAM = 1,4,7,10- tetrakis[(carbamoyl)methyl]-1,4,7,10-tetraazacyclododecane), and related systems containing pyridyl units (Ln = Gd, Tb). Subsequent all-electron relativistic calculations based on the DKH2 approximation, or small-core ECP calculations, were used to compute the ¹H hyperfine coupling constants (HFCCs) at the ligand nuclei (A_iso values). The calculated A_iso values provided direct access to contact contributions to the ¹H NMR shifts of the corresponding Tb^III complexes under the assumption that Gd and Tb complexes with a given ligand present similar HFCCs. These contact shifts were used to obtain the pseudocontact shifts, which encode structural information as they depend on the position of the nucleus with respect to the lanthanide ion. An excellent agreement was observed between the experimental and calculated pseudocontact shifts using the DFT-optimized geometries as structural models of the complexes in solution, which demonstrates that the computational approach used provides (i) good structural models for the complexes, (ii) accurate HFCCs at the ligand nuclei. The methodology presented in this work can be classified in the context of model-dependent methods, as it relies on the use of a specific molecular structure obtained from DFT calculations. Our results show that spin polarization effects dominate the ¹H A_iso values. The X-ray crystal structures of [Ln(Me-DODPA)](PF₆)·2H₂O (Ln = Eu or Lu) are also reported.