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Rationalization of Anomalous Pseudocontact Shifts and Their Solvent

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Sep 8, 2017 - Solvent Dependence in a Series of C3‑Symmetric Lanthanide ... decades to explain paramagnetic NMR pseudocontact shifts, and has been ...

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Rationalization of Anomalous Pseudocontact Shifts and Their Solvent Dependence in a Series of C3‑Symmetric Lanthanide Complexes Michele Vonci,† Kevin Mason,‡ Elizaveta A. Suturina,§ Andrew T. Frawley,‡ Steven G. Worswick,§ Ilya Kuprov,*,§ David Parker,*,‡ Eric J. L. McInnes,*,† and Nicholas F. Chilton*,† †

School of Chemistry, The University of Manchester, Oxford Road, Manchester M13 9PL, U.K. Department of Chemistry, Durham University, South Road, Durham DH1 3LE, U.K. § School of Chemistry, The University of Southampton, Highfield, Southampton SO17 1BJ, U.K. ‡

S Supporting Information *

ABSTRACT: 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 [LnL1] (Ln = Eu, Tb, Dy, Ho, Er, Tm, and Yb; L1: 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 L1. 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 [LnL1]. 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.


angular momentum J and the Landé factor gJ, its value depends only on the electronic configuration of the lanthanide ion.

Complexes of lanthanide (Ln) ions are widely used in biochemical and medical applications of NMR spectroscopy including, for example, magnetic resonance imaging and structural and functional study of biological systems.1−6 A cornerstone of this area has been the interpretation of chemical shift data via Bleaney’s theory of magnetic anisotropy.7,8 This theory states that for remote nucleiwhere the Fermi contact term δc is vanishingly small, as discussed by others9the paramagnetic chemical shift is dominated by the pseudocontact (dipolar) shift (δpc) and can be simply related to the crystal field (CF), the geometry, and a factor that relates to the identity of the specific Ln ion. For an axially symmetric complex, δpc is approximated by eq 1. Here, θ and r are the polar coordinates of the NMR active nucleus with respect to the principal axes of the magnetic susceptibility tensor χ, B02 is the second rank axial CF parameter of the Hamiltonian eq 2 (where Ô qk are the Steven’s operator equivalents and ⟨J||k||J⟩ are the operator equivalent factors) and CJ = gJ2J(J + 1)(2J − 1)(2J + 3)⟨J||k = 2||J⟩ is Bleaney’s constant. Since CJ is a function of the total © 2017 American Chemical Society

δpc = − Ĥ =

CJβ 2 ⎛ 3 cos2 θ − 1 ⎞ 0 ⎟B 2 ⎜ ⎠ 30(kT )2 ⎝ r3



∑ Bkq⟨J || k || J ⟩Ôk


k ,q

The crucial assumptions made by Bleaney were (i) that the total CF splitting is ≪ kT, and (ii) that J is a good quantum number. If these assumptions hold, only second order terms of temperature (T) are required to accurately describe the magnetic susceptibility. Furthermore, it is often assumed that the axial CF parameter and the geometric part

3 cos2 θ − 1 r3

do not

vary across an isostructural series of complexes, in which case the relative order of δpc for a given nucleus in an isostructural Received: July 7, 2017 Published: September 8, 2017 14166

DOI: 10.1021/jacs.7b07094 J. Am. Chem. Soc. 2017, 139, 14166−14172


Journal of the American Chemical Society

Figure 1. (Left) Structure of [LnL1] and assignment of the three pyridyl (py) H atoms. (Center) Schematic representation of the δpc values for the pyH3−5 resonances of [DyL1], [TmL1], and [YbL1] (in D2O, 298 K). (Right) NMR spectra (absolute shifts, δ) of [DyL1] in D2O (blue), MeOD (green), and DMSO-d6 (red) solution (298 K).

χ⊥), extremely responsive to seemingly trivial geometric changes in the first coordination sphere, ultimately controlling the sign and magnitude of the pseudocontact paramagnetic NMR shift. This is not the first time that the tricapped trigonal prismatic geometry has been implicated in anomalous pseudocontact shifts;16−18 however, we rationalize the origins of such effects for the first time in terms of the underlying electronic structure of the lanthanide complexes.

series of lanthanide complexes should follow CJ, or in other words, there should be a linear relationship between the experimentally determined values of δpc and CJ (CJ values for some LnIII = Tb −158; Dy −181; Ho −71.2; Er +58.8; Tm +95.3; and Yb +39.2).7 While this simplistic description has been proven correct in many cases,10,11 it has been found to be invalid in some recent works,12−14 failing to reproduce even the trends in experimental shifts across isostructural series of Ln complexes. Discrepancies are often attributed to the many approximations given above, without specifying the main source. In certain cases, the “culprit” seems clear, as in the case reported by Piguet and co-workers where a sudden structural variation across the Ln series leads to abrupt change in the value of B02.15 A relevant example, recently reported by some of us, concerns the behavior of the [LnL1] family.12 This set of complexes constitutes the archetypal 9-coordinate system in C3 symmetry, with the smallest CF splitting known for a lanthanide coordination complex, (Ln = Eu, Tb, Dy, Ho, Er, Tm and Yb; L1 = 1,4,7-tris[(6-carboxypyridin-2-yl)methyl]1,4,7-triazacyclononane, Figure 1, left). In this family, the Ln ions adopt a tricapped trigonal prismatic {N6O3} coordination geometry, via an N3-macrocycle (providing the axial N-donors) with pendant pyridyl arms (providing the capping equatorial Ndonors), and carboxylate substituents on the pyridyl groups (providing the axial O-donors). For these complexes, despite the CF being relatively weak, the relative order and magnitude of the δpc of the three unique pyridyl 1H nuclei (pyH3−5) do not correlate with the value of Bleaney’s constant. On the basis of CJ alone and assuming a constant value of B02, the expected order of the pseudocontact shifts for the pyridyl protons should be Dy < Tb < Ho < Yb < Er < Tm, while experimentally, the order is found to be Tb < Ho < Er < Yb < Dy < Tm. In this series and two closely related isostructural series based on triazacyclononane, it was shown, with the aid of two/three nuclei plots devised by Reuben/Geraldes, that resonances from the pyridyl protons located some 5.4 to 6.3 Å from the metal center were not subject to any significant contact shift.12 Here, we provide a detailed explanation of the origin of the peculiar paramagnetic NMR behavior of [LnL1], including the origin of a new and significant solvent dependence (D2O, MeOD and DMSO-d6). We demonstrate how the delicately balanced CF provided by the L1 ligand renders the sense of magnetic anisotropy, i.e., easy axis (χ∥ > χ⊥) or easy plane (χ∥
g⊥) for the ground and first excited doublet, respectively (Figure 3 and Table S4). Upon decreasing α by only 1° from the reference geometry, hence increasing θ to a value closer to the magic angle, the two lowest doublets swap order, resulting in an easy plane ground state and an easy axis first excited state (Figure 3 and Table S4). This change coincides with the change in sign of the calculated room temperature magnetic susceptibility anisotropy, although this necessarily results from contributions due to all Boltzmannpopulated excited doublets at 298 K. Furthermore, decreasing α consolidates this trend with the two lowest Kramer’s doublets progressively moving further apart and an increased easy plane character of the ground doublet; the opposite trend is observed for increasing α from the reference geometry. Interestingly, the optimized reference geometry is very close to the minimum overall CF splitting of the J = 15/2 multiplet (Figure 3), corresponding to a CF which does not favor any particular magnetic states and thus gives a near-isotropic magnetic susceptibility. In terms of the CF Hamiltonian eq 2, we observe that only the second rank axial term B02 changes sign as a function of α and that it has by far the largest variation of all the 0,±3,±6 terms CF parameters (Figure 4, Table S5; only B02, B0,±3 4 , B6 are allowed in C3 symmetry). Therefore, it is clear why an anomalous trend is observed for the pseudocontact shifts of [LnL1]: B02 is very sensitive to very minor changes in geometry in this ligand system and cannot be assumed to be a constant. Our analysis shows the extreme sensitivity of the magnetic anisotropy, even at room temperature, of [DyL1] toward tiny variations in ligand torsion angles, on the order of a few degrees. As a consequence, any attempt to reproduce the solution phase pseudocontact NMR shifts in this family of complexes using DFT-optimized structures is a lottery, depending on the choice of lanthanide, DFT functional and solvent model. However, by developing a magnetostructural correlation of the magnetic susceptibility tensor with the torsion angle α, we are able to empirically determine the solution structure of [DyL1] in this solvent system (D2O); in 14169

DOI: 10.1021/jacs.7b07094 J. Am. Chem. Soc. 2017, 139, 14166−14172


Journal of the American Chemical Society

Figure 5. Determination of α and corresponding θ at which the CASSCF-SO calculated anisotropy of the susceptibility tensor χ∥ − χav (black squares) matches the experimental value extracted from NMR data in D2O (blue line), MeOD (green line), DMSO-d6 (red line) for [DyL1]. Reference geometry calculated at the M06/SMD level for H2O.

Hence, we hypothesize that the experimentally observed solvent dependence of δpc is due to changes in the anisotropy of the magnetic susceptibility. Under the assumption that for [DyL1] the contact contribution is negligible and hence the paramagnetic shift is dominated by δpc,13 we can find the latter by plotting the experimental δpc of protons as a function of the structural part of eq 3: the slope then gives the magnetic susceptibility anisotropy (χ∥ − χav) for [DyL1] in each solvent system (Figure S7). Then, we can correlate these against the calculated angular dependence of χ∥ − χav to determine the structure of [DyL1] in each solvent (Figure 5). We determine α = 38.8, 37.9, and 37.5° for D2O, MeOD and DMSO-d6, respectively, corresponding to polar angles for the O-donors of θ = 52.0, 53.3, and 53.8°, respectively. Hence, our results indicate that the O-donor atoms become more axial as the polarity, and H-bonding ability, of the solvent increases.32 This suggests that solvating water molecules “tug” on the oxygen atoms at the “open face” of the molecule more strongly than MeOD and DMSO-d6. The role that tiny structural distortions have on the magnetic anisotropy of [DyL1] is further exemplified by the variable temperature NMR signal of pyH3−5 in MeOD in the 205−300 K range (Figure S9); the experimental anisotropy χ∥ − χav becomes more negative as the temperature is decreased. By interpolating the ab initio susceptibility anisotropy dependence on α, it is possible to construct the surface S(α,T) mapping the variation of the magnetic anisotropy with α and T (Figure S10). Plotting the experimental values of the magnetic anisotropy on the surface S(α,T) we observe that the anisotropy changes less than it should as a function of temperature if α remained constant; therefore, there must be a small structural relaxation with temperature on the order of Δα ∼ 0.2° to account for the experimental results. Independent confirmation of the solvent effect on the electronic structure is possible with the complementary technique of luminescence spectroscopy for [DyL1] and

Figure 4. (Top) Ab initio CF parameters as a function of α (and corresponding polar angle at the O-donors, θ) for [DyL1]. (Bottom) Percentage variation of ab initio CF parameters with respect to the with q ≠ 0, we give reference geometry. For the Bqk and B−q k (Bkq)2 + (Bk−q)2 to remove the arbitrary choice of xy reference axes. The data for α = 40.4° correspond to the reference DFT optimized structure in H2O (M06/SMD).

order to match the experimental magnetic susceptibility anisotropy χ∥ − χav and thus δpc, we determine that α = 38.8° (Figures 5 and S7). We now turn to the solvent dependence of the pseudocontact shifts in [DyL1]. Experimentally, we find that the measured δpc for pyH3−5 become more positive, and have a larger spread, on moving from D2O to MeOD to DMSO-d6 (Figures 1 and S1). Unsurprisingly, given the results above, optimized structures obtained with M06/SMD for MeOH and DMSO solvent parametrizations do not lead to δpc values that agree with experiment (Table S6). In order to generalize our approach across all three solvents, and hence determine the solution structures, we adopt a few sensible approximations. First, we have tested and can show that the dependence of the magnetic anisotropy on the polar angle of the O-donors (θ, mapped through systematic variation of α) is practically identical when starting from DFT optimized geometries with MeOD, DMSO-d6 and D2O solvent parametrizations (Figure S8). Second, we have tested and observe that the structural part in eq 3 varies very little across the D2O, MeOD and DMSO-d6 optimized structures (≤3%, Table S7), or for variation in α (within a sensible range) for a given solvent (≤3%, Table S8). 14170

DOI: 10.1021/jacs.7b07094 J. Am. Chem. Soc. 2017, 139, 14166−14172


Journal of the American Chemical Society [EuL1] in H2O, MeOH, and DMSO solutions. The 4F9/2 → 6 H15/2 emission lines of [DyL1] show slight differences in fine structure due to the modified CF splitting in different solvents (Figure S11), however, the small CF splitting and low resolution of the spectra prevents any reliable assignment. On the other hand, the solvent dependence of the emission lines for [EuL1] is very informative. These spectra feature the usual 5 D0 → 7F0,1,2,3,4 emission bands in the 570−720 nm region (Figure S12), and the fine structure due to the CF splitting of each of the 7Fn spin−orbit multiplets clearly differs between solvents. The 5D0 → 7F1 transition is particularly diagnostic, because in C3 symmetry the 7F1 multiplet splits into a doublet (MJ = ± 1) and a singlet (MJ = 0), the ordering and separation of which depending only on the second rank axial CF parameter B02; the doubly degenerate level being higher in energy for negative values of B02.31 The luminescence spectra for this transition shows the 7F1 splitting increasing as H2O < MeOH < DMSO (Figure 6); circularly polarized luminescence

tensor shows the same extreme sensitivity to small variations of the polar angle θ of the O-donor atoms that we observe for [DyL1], implying a subsequent sensitivity of the δpc values (Figure S16). Such behavior suggests that the hypersensitivity of the electronic structure toward geometrical changes is consistent across the entire [LnL1] series. However, the overall paramagnetic shifts for [EuL1] and [ErL1] are very small in these three solvents and cannot be approximated with total confidence as being solely due to the pseudocontact term;13 this issue is a consequence of their small magnetic moments and minimal magnetic anisotropy, respectively. The same is true for [TbL1] and [HoL1] in D2O, where the susceptibility is also very close to isotropic. In all the other cases ([TmL1] and [YbL1] in each solvent, [TbL1] and [HoL1] in MeOD and DMSO-d6), the δpc have a linear correlation with the structural part of eq 3, showing that the pseudocontact term is indeed dominant, allowing extraction of the experimental susceptibility anisotropy (Figure S7).13 Variation of solvent for these complexes shows that δpc of pyH3−5 has the same strong dependence as observed for [DyL1] (Figure S17), even including a change in sign of the δpc values for [TmL1] and [YbL1] on moving from D2O to MeOD, which implies that the susceptibility anisotropy switches from easy plane in D2O to easy axis in MeOD and DMSO-d6. This is in contrast with [DyL1], which shows easy plane anisotropy in all solvents (Figure S7). The same analysis for [TbL1] and [HoL1] in MeOD and DMSO-d6 reveals an easy plane anisotropy, similarly to [DyL1]. In all cases, the fitted values of α show the same trend as the [DyL1] and [EuL1] analogues: α decreases, and as a consequence θ for the O-donor atoms increases, going from D2O to MeOD to DMSO-d6 (Figure S16). The fitted angles, and hence the structure, vary depending on the lanthanide and solvent, meaning that the CF is not the same across the series. The changes in CF across the [LnL1] series are very subtle and yet crucial in order to understand the experimental pseudocontact shifts. Rather than just a small change in magnitude of the CF along the series, like the ∼±15% change reported by Bertini et al. across a series of Ln-bound calbindin protein samples,10 we observe that the B02 CF term can in fact change sign in response to a change of solvent, even when that solvent is not coordinated to the metal. Such hypersensitivity of the electronic structure for lanthanide chelates may be more common than currently surmised, and a careful study of anomalous experimental results may provide further examples of delicately balanced CFs, such as those defined herein.

Figure 6. Luminescence spectrum of [EuL1] in H2O (blue), MeOH (green), and DMSO (red) in the region of the 5D0 → 7F0 and 5D0 → 7 F1 emission lines (λexc = 272 nm, 295 K, 30 μM solutions). Experimental data (open circles), deconvolution of the bands with two Gaussians (dotted lines), and fitted spectra (solid lines). Due to the poor resolution of the spectra in H2O and MeOH, the Gaussian fitting in these solvents was performed by fixing the line width of the individual contributions to that of the better resolved spectrum in DMSO.

does not increase the resolution of these spectra (Figure S13). Fitting the emission lines with a two component Gaussian model gives the expected 1:2 ratio (Table S9), and shows that the sign of B02 is negative in all three solvents (Table S10). In the same way that we have fit α to the experimental magnetic anisotropy of [DyL1], we can fit α to the experimental CF splitting of the 7F1 multiplet observed by luminescence spectroscopy for [EuL1] (Figure S14). The solvent-dependent trend in α, and correspondingly in θ, agrees with that of [DyL1], with increasingly larger values of θ going from H2O to MeOH to DMSO (Figures S14 and S15). Thus, the independent techniques of NMR and luminescence spectroscopy for two different lanthanides reveal the same structural sensitivity toward solvent. For the remaining late lanthanide complexes of the series, namely [TbL1], [HoL1], [TmL1], and [YbL1], the ab initio calculated room temperature anisotropy of the susceptibility

CONCLUSION Our magnetostructural correlation has allowed us to explain the anomalous trend in D2O of [DyL1] having the same sign of δpc as [TmL1] and [YbL1] as well as the variation of δpc for [LnL1] (Ln = Tb, Dy, Ho, Tm, Yb) across solvents, including the change in sign of δpc from D2O to MeOD for [TmL1] and [YbL1]. We have shown that the deviations from simple interpretations using Bleaney’s theory for [LnL1] are due to the very peculiar nature of the tricapped trigonal prismatic ligand L1, resulting in hypersensitivity of the electronic structure to minimal variations in the position of the O donor atoms. In this case, the structural part of Bleaney’s eq (eq 1) is approximately constant and it is the second rank axial CF parameter B02 that can vary dramatically, including changing sign, upon minimal variation of the coordination geometry. 14171

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Journal of the American Chemical Society Thus, we conclude that B02 cannot be considered a constant in this series of complexes. We have shown that significant variations in the NMR pseudocontact shifts in different solvents are due to small structural variations, likely owing to solvent polarity and/or hydrogen bonding propensity, and have independently confirmed this with luminescence spectroscopy. These results have important consequences for the design of magnetic resonance shift agents and responsive optical probes. The ease of modulation of the size and sign of B02 associated with this ligand type could be exploited in developing probes that respond to small physicochemical perturbations, e.g., from changes in the local environment, such as medium polarity.

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S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/jacs.7b07094. Paramagnetic NMR shift data for [LnL1], DFT structural examination, CASSCF-SO results, extraction of magnetic anisotropy, luminescence data and fitting, computational methods, NMR methods, optical methods (PDF)


Corresponding Authors

*i.kuprov@soton.ac.uk *david.parker@durham.ac.uk *eric.mcinnes@manchester.ac.uk *nicholas.chilton@manchester.ac.uk ORCID

Michele Vonci: 0000-0002-0880-3225 Elizaveta A. Suturina: 0000-0003-4407-1882 David Parker: 0000-0001-5281-5146 Nicholas F. Chilton: 0000-0002-8604-0171 Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS We thank the EPSRC for funding (EP/N007034/1 and EP/ N006909/1); NFC thanks the Ramsay Memorial Trust for a Research Fellowship.


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