Bleaney's long-standing theory of magnetic anisotropy has been employed with some success for many decades to explain paramagnetic NMR pseudocontact shifts, and has been the subject of many subsequent approximations. Here, we present a detailed experimental and theoretical investigation accounting for the anomalous solvent dependence of NMR shifts for a series of lanthanide(III) complexes, namely [LnL] (Ln = Eu, Tb, Dy, Ho, Er, Tm, and Yb; L: 1,4,7-tris[(6-carboxypyridin-2-yl)methyl]-1,4,7-triazacyclononane), taking into account the effect of subtle ligand flexibility on the electronic structure. We show that the anisotropy of the room temperature magnetic susceptibility tensor, which in turn affects the sign and magnitude of the pseudocontact chemical shift, is extremely sensitive to minimal structural changes in the first coordination sphere of L. We show that DFT structural optimizations do not give accurate structural models, as assessed by the experimental chemical shifts, and thus we determine a magnetostructural correlation and employ this to evaluate the accurate solution structure for each [LnL]. This approach allows us to explain the counterintuitive pseudocontact shift behavior, as well as a striking solvent dependence. These results have important consequences for the analysis and design of novel magnetic resonance shift and optical emission probes that are sensitive to the local solution environment and polarity.

A detailed analysis of paramagnetic NMR shifts in a series of isostructural lanthanide complexes relavant to PARASHIFT contrast agents reveals unexpected trends in the magnetic susceptibility anisotropy that cannot be explained by the commonly used Bleaney's theory. Ab initio calculations reveal that the primary assumption of Bleaney's theory—that thermal energy is larger than the ligand field splitting—does not hold for the lanthanide complexes in question, and likely for a large fraction of lanthanide complexes in general. This makes the orientation of the magnetic susceptibility tensor differ significantly between complexes of different lanthanides with the same ligand: one of the most popular assumptions about isostructural lanthanide series is wrong.

Ytterbium and yttrium complexes of octadentate ligands based on 1,4,7,10-tetraazacyclododecane with a coordinated pyridyl group and either tricarboxylate (L) or triphosphinate (L) donors form twisted-square-antiprismatic structures. The former crystallizes in the centrosymmetric group P2/c, with the two molecules related by an inversion center, whereas the latter was found as an unusual kryptoracemate in the chiral space group P2. Pure shift NMR and EXSY spectroscopy allowed the dynamic exchange between the (RRR)-Δ-(δδδδ) and (RRR)-Λ-(λλλλ) TSAP diastereomers of the [Y.L] complex to be detected. The rate-limiting step in the exchange between Δ and Λ isomers involves cooperative ligand arm rotation, which is much faster for [Ln.L] than for [Ln.L]. Detailed analysis of NOESY, COSY, HSQC, and HMBC spectra confirms that the major conformer in solution is (RRR)-Λ-(λλλλ), consistent with crystal structure analysis and DFT calculations. The magnetic susceptibility tensors for [Yb.L] and [Yb.L], obtained from a full pseudocontact chemical shift analysis, are very different, in agreement with a CASSCF calculation. The remarkably different pseudocontact shift behavior is explained by the change in the orientation of the pseudocontact shift field, as defined by the Euler angles of the susceptibility tensor.

Lanthanide ions accelerate nuclear spin relaxation by two primary mechanisms: dipolar and Curie. Both are commonly assumed to depend on the length of the lanthanide-nucleus vector, but not on its direction. Here we show experimentally that this is wrong - careful proton relaxation data analysis in a series of isostructural lanthanide complexes (Ln = Tb, Dy, Ho, Er, Tm, Yb) reveals angular dependence in both Curie and dipolar relaxation. The reasons are: (a) that magnetic susceptibility anisotropy can be of the same order of magnitude as the isotropic part (contradicting the unstated assumption in Guéron's theory of the Curie relaxation process), and (b) that zero-field splitting can be much stronger than the electron Zeeman interaction (Bloembergen's original theory of the lanthanide-induced dipolar relaxation process makes the opposite assumption). These factors go beyond the well researched cross-correlation effects; they alter the relaxation theory treatment and make strong angular dependencies appear in the nuclear spin relaxation rates. Those dependencies are impossible to ignore - this is now demonstrated both theoretically and experimentally, and suggests that a major revision is needed of the way lanthanide-induced relaxation data are used in structural biology.