Structural evolution of paramagnetic lanthanide compounds in solution compared to time- and ensemble-average structures

Anisotropy in the magnetic susceptibility strongly influences the paramagnetic shifts seen in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) experiments. A previous study on a series of C₃-symmetric prototype MRI contrast agents showed that their magnetic anisotropy was highly sensitive to changes in molecular geometry, and concluded that changes in the average angle between the lanthanide-oxygen (Ln-O) bonds and the molecular C₃ axis due to solvent interactions had a significant impact on the magnetic anisotropy and, consequently, the paramagnetic shift. However, this study, like many others, was predicated on an idealised C₃-symmetric structural model, which may not be representative of the dynamic structure in solution at the single-molecule level. Here, we address this by using ab initio molecular dynamics simulations to simulate how the molecular geometry, in particular the angles between the Ln-O bonds and the pseudo-C₃ axis, evolves over time in solution, mimicking typical experimental conditions. We observe large-amplitude oscillations in the O-Ln-₃ angles, and complete active space self-consistent field spin-orbit calculations show that this leads to similarly large oscillations in the pseudocontact (dipolar) paramagnetic NMR shifts. The time-averaged shifts show good agreement to experimental measurements, while the large fluctuations suggest that an idealised structure provides an incomplete description of the solution dynamics. Our observations have significant implications for modelling the electronic and nuclear relaxation times in this and other systems where the magnetic susceptibility is exquisitely sensitive to the molecular structure.