Effect of Magnetic Anisotropy on the 1H NMR Paramagnetic Shifts and Relaxation Rates of Small Dysprosium(III) Complexes

We present a detailed analysis of the 1H NMR chemical shifts and transverse relaxation rates of three small Dy(III) complexes having different symmetries (C3, D2 or C2). The complexes show sizeable emission in the visible region due to 4F9/2 → 6HJ transitions (J = 15/2 to 11/2). Additionally, NIR emission is observed at ca. 850 (4F9/2 → 6H7/2), 930 (4F9/2 → 6H5/2), 1010 (4F9/2 → 6F9/2), and 1175 nm (4F9/2 → 6F7/2). Emission quantum yields of 1–2% were determined in aqueous solutions. The emission lifetimes indicate that no water molecules are present in the inner coordination sphere of Dy(III), which in the case of [Dy(CB-TE2PA)]+ was confirmed through the X-ray crystal structure. The 1H NMR paramagnetic shifts induced by Dy(III) were found to be dominated by the pseudocontact mechanism, though, for some protons, contact shifts are not negligible. The analysis of the pseudocontact shifts provided the magnetic susceptibility tensors of the three complexes, which were also investigated using CASSCF calculations. The transverse 1H relaxation data follow a good linear correlation with 1/r6, where r is the distance between the Dy(III) ion and the observed proton. This indicates that magnetic anisotropy is not significantly affecting the relaxation of 1H nuclei in the family of complexes investigated here.


INTRODUCTION
The lanthanide ions are a unique group of elements within the periodic table characterized by their similar chemical properties.In spite of being chemically very similar, the Ln(III) ions present very different optical and magnetic properties that are associated with their own specific electron configuration.Furthermore, the 4f orbitals are shielded from the environment by the external 5s 2 and 5p 6 electrons, 1 and therefore do not significantly participate in the formation of chemical bonds. 2 As a result, the coordination environment of the Ln(III) ion has a relatively minor impact on the optical and magnetic properties of the complex.Some Ln(III) complexes form highly luminescent complexes that emit in the visible [i.e., Eu(III) and Tb(III)] or nearinfrared regions [i.e., Pr(III), Nd(III), Ho(III), Er(III), or Yb(III)].Concerning their magnetic properties, complexes of Gd(III) are widely used in clinical practice as contrast agents for magnetic resonance imaging.The [Xe]4f 7 electron configuration of Gd(III) originates a symmetrical 8 S electronic ground state, which makes this ion very efficient in promoting relaxation of active NMR nuclei in its vicinity.In MRI, the shortening of relaxation times of 1 H water nuclei promoted by Gd(III) is used to generate contrast.Other paramagnetic Ln(III) ions induce relaxation rate enhancements in neighboring NMR nuclei, though the shorter electron relaxation times (∼10 −13 s) 3 result in longer T 1 and T 2 relaxation times.In contrast to Gd(III), all other Ln(III) ions form complexes affording observable NMR signals.
Chemists have taken advantage of this feature since the early times of NMR, as paramagnetic lanthanide complexes with Ln(III) ions other than Gd(III) were found to induce significant paramagnetic chemical shifts without causing extensive line broadening.Thus, small Ln(III) complexes were routinely used as shift reagents to aid the analysis of NMR spectra of different substrates. 4he use of Ln(III) complexes as shift reagents has declined over the years as the increasing magnetic field strength of NMR spectrometers has provided enhanced spectral resolution.Nevertheless, Ln(III)-based paramagnetic tags are widely used for protein structure determination, as the paramagnetic shifts induced by the Ln(III) ions are dominated by the dipolar (pseudocontact) contribution, 5−7 which encodes structural information.−15 The latter can be visualized directly in an MRI experiment, thanks to the paramagnetic effect that shifts 1 H NMR signals of the probe well out of the region where endogenous signals are observed.In paraCEST probes, contrast is generated by the saturation of an NMR signal of protons exchanging with bulk water.The paramagnetism of the metal ion shifts this signal far from that of bulk water. 16−32 The theory relies on the point-dipole approximation and assumes that relaxation is isotropic.Recent studies reported unusual relaxation trends across the lanthanide series and suggested that the anisotropic contribution to relaxation may not be negligible, at least for nonsymmetrical systems. 33n this work, we present a detailed analysis of the 1 H NMR spectra of three Dy(III) complexes that provide different coordination environments.We have selected Dy(III) as a representative example of a Ln(III) ion that provides large pseudocontact shifts, actually the largest among the lanthanide series according to Bleaney's theory, 34 as well as strong relaxation enhancement effects. 35Furthermore, the splitting of the 6 H 15/2 ground state of Dy(III) can be analyzed using luminescence measurements, which can potentially provide rich electronic structure information.The three selected ligands form well-characterized Ln(III) complexes.The metal ion in the [Dy(PYTA)] − complex is ten-coordinated by the ligand both in the solid state and in aqueous solution, with a D 2 symmetry. 36−39 Finally, the Ln(III) complexes with H 2 CB-TE2PA 40,41 display C 2 symmetry and contain eight-coordinate metal ions for Ln = Eu−Lu (Chart 1).
In this work, the 1 H NMR spectra of these complexes were measured and assigned in D 2 O solutions, which allowed determining their magnetic susceptibility tensors responsible for the pseudocontact shifts, as well as estimating the contact shift contributions to the different 1 H NMR signals using density functional theory (DFT).A detailed photophysical study was also performed to gain information on the electronic structure of the complexes and the splitting of the 6 H 15/2 ground state.The 1 H NMR spectra were subsequently measured at different magnetic fields (5.88, 7.05, 9.40, and 11.75 T).The T 2 relaxation times obtained from line-width analysis were used to test the traditional relaxation theory, 29 as expressed by the Solomon-Bloembergen equations for the dipolar relaxation and the equations describing the Curie-spin (CS) relaxation mechanism.We demonstrate that for this series of symmetrical complexes, relaxation is dominated by the isotropic contribution.The X-ray structure of the [Dy(CB-TE2PA)] + complex is also reported.(7); Dy(1)-N(2), 2.464 (7); Dy(1)-N(3), 2.613 (7); Dy(1)-N(4), 2.598 (7); Dy(1)-N(5), 2.539 (7); Dy(1)-N(6), 2.537 (7).

X-ray
−44 The two 1,4,7triazacyclodecane units of CB-cyclam unit adopt irregular [2233] conformations, 45 as observed previously for the La(III) and Eu(III) analogues.−48 2.2.Photophysical Properties.The magnetic anisotropy of Dy(III) complexes is related to the splitting of the 6 H 15/2 manifold caused by the ligand field. 49Absorption and emission spectroscopy can potentially provide detailed information on the electronic energy levels of Dy(III). 50Thus, we carried out a photophysical study to gain information on the electronic structure of the complexes investigated in this work.
The three complexes investigated here display similar lifetimes in H 2 O solution, with values close to 20 μs (Table 1).−61 Lifetimes are shorter in H 2 O than in D 2 O, as a result of the more efficient quenching effect of solvent O−H oscillators compared with O−D oscillators. 62,63The number of water molecules coordinated to the Dy(III) ion (q) can be estimated with an uncertainty of ±0.3 water molecules from these lifetimes using q = 24k obs − 1.3, with k obs = 1/τ Hd 2 O (in μs −1 ). 64The values of q determined by this method (0.0 ± 0.3, Table 1) confirm the absence of coordinated water molecules in these complexes, in agreement with the corresponding X-ray crystal structures.Hydration numbers of Dy(III) complexes can be also estimated from lifetimes determined in H 2 O and D 2 O, using the relationship q = 2.61Δk obs , with Δk obs = 1/τ Hd 2 O − 1/τ Dd 2 O , in μs −1 . 63The results again confirm the absence of water molecules in the inner coordination sphere (Table 1).However, the three complexes display significant differences in the lifetimes measured in D 2 O (Table 1), which range from ∼27 μs for [Dy(CB-TE2PA)] + to ∼40 μs for [Dy(PYTA)] − .
Considering the relative weakness of the NIR emission bands, they were neglected in the calculation of the luminescence quantum yields (QYs), which were determined using the visible part only.The overall QYs measured in aqueous solutions are in the range 1−2% and roughly double

Inorganic Chemistry
in D 2 O.These values are similar to those determined for Dy(III) complexes lacking coordinated water molecules (0.1− 3% in H 2 O), [57][58][59][60][61]65 with the exception of a complex with bistetrazolate-pyridine ligand, which shows a considerably higher ϕ Hd 2 O value of 7.1%.66 Figure 3 presents a comparison of the high-resolution emission spectra obtained for the three complexes at 77 K in the region of the 4 F 9/2 → 6 H 15/2 transition (Figure 3). The sectra recorded for the three complexes show remarkable differences in the number and energy of the different components, as well as in the overall shape of the spectrum.This indicates that the crystal field splitting of the 6 H 15/2 and 4 F 9/2 levels is significantly different in these Dy(III) complexes.The emission spectrum recorded for [Dy(PYTA)] − shows nine components that can be clearly identified, while the 6 H 15/2 multiplet splits into eight Kramers doublets by the effect of the crystal field.This suggests the emission spectrum contains contributions from hot emission bands, due to emission from different Kramers doublets of the 4 F 9/2 multiplet.This situation is even more obvious in the spectrum of [Dy(NO3PA)], which shows at least nine components.The thermal energy at 77 K is ∼53 cm −1 , and thus different Kramers doublets of the excited 4 F 9/2 manifold may have significant populations even at this temperature. Meurements at a lower temperature (4 K) would be required for a more detailed analysis.An alternative reason for the presence of hot emission bands is that they arise from the population of excited Kramers doublets of the 4 F 9/2 manifold from deactivation of the 4 I 15/2 manifold.This appears to be reasonable, since weak emission peaks due to 4 I 15/2 → 6 H J transitions are observed in the emission spectra.
Theoretical CASSCF calculations reported previously for [Dy(NO3PA)] predicted an overall splitting of the 6 H 15/2 multiplet <300 cm −1 for the equilibrium geometry, though relatively small structural changes impacted significantly the energy of the Kramers doublets. 68Our calculations performed at the CASSCF/QDPT level (see Computational Details section below) provide a similar result, with an overall splitting of 266 cm −1 (Figure S4, Supporting Information).The splitting of the groups of Kramers doublets is also similar to that reported by Parker. 68The energies of the eight Kramers doublets are shown in Figure 3, taking as a reference the component of the emission spectrum with the lowest energy at 484.2 nm.The emission spectrum displays several components on the high-energy side, out of the range marked by the splitting of the 6 H 15/2 level.This again suggests that hot emission bands provide a significant contribution to the overall emission spectrum.A similar conclusion was achieved previously from the analysis of the emission spectra of Dy(III) 69 and Yb(III) 70 complexes.In the case of [Dy(CB-TE2PA)] + , the splitting of the 6 H 15/2 multiplet obtained with CASSCF/QDPT calculations also suggests that two components on the high-energy side arise from hot transitions.For [Dy(PYTA)] − , the emission spectrum shows a broad feature on the low energy side, which makes it difficult to locate the position of the Kramers doublet of the 6 H 15/2 multiplet with the lowest energy.Nevertheless, CASSCF/QDPT calculations provide an overall splitting of 251 cm −1 for this complex, which again suggests that hot emission bands (arising from thermally populated Kramers doublets of the 4 F 9/2 multiplet) are present in the high-energy side of the spectrum.Nevertheless, the emission spectra indicate that the different coordination numbers and coordination polyhedra of the three complexes have an important impact on the crystal field splitting of the 6 H 15/2 multiplet.Noteworthy, a large splitting of the 6 H 15/2 manifold of about 500 cm −1 was observed for [Dy-(DOTA)] − , 71 which indicates that the splitting of the Kramers doublets is rather sensitive to variations of the coordination environment.
2.3. 1 H NMR Spectra.The 1 H NMR spectra of the three complexes were recorded in D 2 O solution at pH ∼ 7.0 (Figure 4).The 1 H NMR spectrum of the axially symmetrical [Dy(NO3PA)] complex displays the nine signals expected for an effective C 3 symmetry in the chemical shift range +26 to −29 ppm (at 298 K).The spectrum was partially assigned previously by Parker et al. 68 The full attribution of the spectrum was achieved using line-width analysis (Table 2), which allows identifying the axial and equatorial protons.Axial protons are generally closer to the paramagnetic center and thus provide broader signals. 35  A second set of paramagnetically shifted signals corresponding to a minor species present in solution is also observed.This minor species was attributed to a complex with a nine-coordinated metal ion in which one of the carboxylates remains uncoordinated. 36The integration of the 1  All three complexes investigated here adopt chiral point groups, and thus they exist in solution as racemic mixtures.For [Dy(NO3PA)], racemization requires a change in the rotation of the pendant arms and the inversion of the macrocyclic ring, as discussed for [Ln(DOTA)] − derivatives. 73,74However, we did not observe any spectral changes that could be associated with the dynamics of the racemization process, even in the 1 H NMR spectra recorded at high temperatures (see below).For [Dy(PYTA)] − and [Dy(CB-TE2PA)] + , racemization requires full detachment of the acetate or picolinate pendant arms, and thus they are not likely to affect the 1 H NMR spectra.
The paramagnetic chemical shifts of Dy(III) complexes are generally dominated by the pseudocontact contribution, which can be expressed as 5 r z x y r x y r Equation 1 assumes that the reference frame coincides with the orientation of the magnetic susceptibility tensor, whose axial and rhombic contributions are given by Δχ ax and Δχ rh , respectively.Furthermore, x, y and z represent the Cartesian coordinates of a nucleus i relative to the location of the paramagnetic metal ion [Dy(III)] placed at the origin; and r 2 = x 2 + y 2 + z 2 .In eq 1, the axial and rhombic parts of the magnetic susceptibility tensor as defined as The three complexes investigated here present comparable Dy(III)•••H distances, as demonstrated by the DFT calculations presented below.However, the chemical shift range of these complexes increases as the symmetry of the complex decreases, which probably reflects an increased anisotropy of the magnetic susceptibility.Alternatively, significantly different contact contributions may be responsible for the different paramagnetic shifts observed for the three complexes.
The [Dy(NO3PA)] complex is axially symmetrical, as it possesses a symmetry axis C n with n ≥ 3.Under these circumstances, the rhombic term in eq 1 vanishes, 75 which simplifies the analysis of the paramagnetic shifts.For axial symmetry, eq 1 can be rewritten in polar coordinates as follows: 5 r 12 (3 cos 1) Thus, a plot of the pseudocontact shifts versus the geometric term (3 cos 2 θ − 1)/r 3 should give a straight line passing through the origin with slope Δχ ax /12π.A plot of the observed paramagnetic shifts versus the geometric factors obtained using DFT shows a reasonable linear correlation (Figure S5, Supporting Information), affording a small Δχ ax value (Table 3).This value is in very good agreement with that reported by Parker using 1 H NMR data recorded in D 2 O (−5.3 × 10 −32 m 3 ). 27he paramagnetic shifts observed for the [Dy(PYTA)] − and [Dy(CB-TE2PA)] + complexes were analyzed using eq 1, with Cartesian coordinates obtained using DFT calculations.A reasonable fit was obtained using this approach, which neglects contact contributions to the paramagnetic shifts.However, we noticed that the shifts calculated for some protons with eq 1 experience rather large deviations with respect to the observed chemical shifts, up to 22 ppm for [Dy(PYTA)] − and 31 ppm for [Dy(CB-TE2PA)] + (Table 4, see also Table S1, Supporting Information).
The contact NMR shifts induced by paramagnetic Ln(III) ions are related to a through-bond delocalization of unpaired spin density of the metal ion to the observed nucleus.The spin  density at the observed nucleus is given by the scalar hyperfine coupling constant A/ℏ, while the contact shift δ C can be approximated by eq 2, 17,76 where ⟨S z ⟩ is the spin expectation value of the lanthanide ion, 35 γ I is the nuclear gyromagnetic ratio, k is the Boltzmann constant, and β is the Bohr magneton.
Contact shifts are generally negligible for 1 H nuclei placed five or more bonds away from the metal center but can be significant for nuclei close to the paramagnetic ion in terms of the number of bonds. 34,77In the particular case of Dy(III), pseudocontact shifts are expected to be roughly proportional to Bleaney's constant C j = −100 determined for this ion, while the contact contribution is proportional to ⟨S z ⟩ (28.565 for Dy(III)). 17Contact contributions are considered to be negligible for complexes of Yb(III), where C j /⟨S z ⟩ = 8.5, but significant for Dy(III) (C j /⟨S z ⟩ = −3.5). 21n estimate of the contact shifts was obtained by performing DFT calculations for the Gd(III) analogues, which provide straightforward access to the values of A/ℏ. 25,78,79The results of these calculations for [Dy(CB-TE2PA)] + are presented in Table 4, while those obtained for [Dy(PYTA)] − are presented in the Supporting Information (Table S1).Contact shifts were subsequently obtained from the A/ℏ values using eq 2 and ⟨S z ⟩ = 22.0. 25The results evidence that contact contributions are small for axial protons of CH 2 groups but sizeable for equatorial protons, representing up to ∼−21 ppm for H4eq in [Dy(PYTA)] − , and H4eq and H10eq in [Dy(CB-TE2PA)] + .The different contact contributions observed for axial and equatorial protons reflect the Karplus-like variation of the hyperfine coupling constant with the dihedral H-C-N-Dy angle. 78nce contact shifts were estimated, we analyzed the pseudocontact shifts using eq 1.The agreement between experimental and calculated shifts is very good, improving considerably with respect to the analysis neglecting contact shifts, as demonstrated by the agreement factor AF j , defined as 80

AF
( ) / ( ) Here, the sum runs over the different proton signals observed for a given complex.The analysis performed by neglecting contact contributions affords AF j values of 0.149 and 0.169 for [Dy(CB-TE2PA)] + and [Dy(PYTA)] − , respectively, which decrease significantly to 0.091 and 0.098 upon considering the contact shifts.Similar agreement factors have been obtained for Dy(III) complexes and are considered to be satisfactory. 77hese results confirm that our DFT calculations provide at least rough estimates of the contact contributions and that the geometry of the complex obtained by DFT provides a reasonable approximation to the actual structure.Of note, the theoretical calculation of contact shifts for Ln(III) complexes with DFT is a difficult task. 81Furthermore, it has been recently demonstrated that dynamic effects may affect significantly the pseudocontact shifts; a recent study demonstrated that an idealized structure of [Dy(NO3PA)] provides an incomplete description of the system. 82he values of Δχ ax and Δχ rh obtained for [Dy(CB-TE2PA)] + and [Dy(PYTA)] − (Table 3) define rhombic magnetic susceptibility tensors, as would be expected, The values for the complexes with PYTA 4− and CB-TE2PA 2− were obtained including contact shifts.The principal magnetic axes in [Dy(NO3A)] and [Dy(CB-TE2PA)] + match the position of the C 3 and C 2 symmetry axes, respectively.For [Dy(PYTA)] − , the z axis bisects the ethylenediamine units, and the x axis contains the pyridyl N atoms.considering the symmetry of the complexes.In the case of [Dy(PYTA)] − , the axial contribution is still dominant, while for [Dy(CB-TE2PA)] + , the rhombic term is ca. 2.6 times larger than Δχ ax . The Δχ ax value obtained for [Dy(NO3PA)] is about 5 times lower than those reported for Dy(III) DOTA derivatives, 83 which highlights the small magnetic anisotropy of the former.The values Δχ ax and Δχ rh reported for Dy(III)-DOTA derivatives are, however, close to those obtained here for [Dy(CB-TE2PA)] + and [Dy(PYTA)] − .84 2.4. 1 H NMR Relaxation.Once the structures of the complexes in solution were established using paramagnetic 1 H NMR spectroscopy, we envisaged to investigate 1 H relaxation.The spectra presented above display rather broad 1 H NMR signals, which makes the accurate determination of T 1 relaxation times difficult.However, transverse relaxation times T 2 can be obtained from the linewidths, which can be measured with good accuracy by fitting the experimental spectrum using Lorentzian−Gaussian functions.The paramagnetic contribution to the transverse relaxation rates receives contributions from the dipolar and Curie-spin mechanisms.The dipolar contribution T 2 D is the result of a through-space interaction between the observed nucleus and the unpaired electron spins, originating from the fluctuating magnetic field associated with electron relaxation, eq 7: 17,30 T r Here, μ 0 /4π is the magnetic permeability of a vacuum, γ I is the nuclear gyromagnetic ratio, μ eff is the effective magnetic moment of the paramagnetic ion, β is the Bohr magneton, ω I is the Larmor frequency of the nucleus, ω S is the Larmor precession frequency for an electron, and r is the distance between the observed nuclei and the paramagnetic center.The correlation time τ C depends on the rotational correlation time, τ R , and the electronic relaxation time T 1e : The Curie-spin (CS) mechanism is also a dipolar effect arising from the interaction of the nuclear spin and the static magnetic moment of the electrons, associated with the difference in population of the electron spin levels due to the Boltzmann distribution: 85 T H kT r Inspection of eq 9 evidences that the Curie-spin mechanism is expected to become more important as the applied magnetic field (H 0 ) increases, particularly in the case of Ln(III) ions with high μ eff values.Different authors have taken advantage of the dependence of the CS contribution with H 0 2 to estimate relative Ln•••H distances, with plots of 1/T i (i = 1 or 2) versus H 0 2 generally showing good linear correlations. 35,36,86,87quations 7−9 were also used to analyze 19 F relaxation rates in lanthanide complexes. 29It is important to mention that magnetic anisotropy may play a key role in the relaxation of 1 H nuclei of small lanthanide complexes, with the anisotropic and isotropic parts providing similar contributions. 88Part of the motivation of the present work was to test the traditional relaxation theory (eqs 7−9) using a well-characterized set of complexes having different magnetic anisotropies.This is the case of the complexes investigated here, as demonstrated by the data reported in Table 3.
The linewidths of the 1 H NMR signals of the complexes investigated here were obtained at four different magnetic fields (5.9, 7.05, 9.4, and 11.7 T) at 298 K. Furthermore, we also obtained a set of linewidths at 9.4 T and five different temperatures.We hypothesized that the variable field data would aid the fit of the relaxation data to eqs 7−9, allowing to discriminate the contributions of the dipolar and CS mechanisms.We have chosen a set of very rigid complexes, so that line broadening due to exchange effects provides negligible contributions to the linewidths.The measured linewidths are large (35−3600 Hz), and thus diamagnetic effects (∼4 Hz) were neglected.
The relaxation rates obtained from line-width data display reasonably good linear correlations when plotted against 1/r 6 , with distances taken from DFT calculations (Figures S6−S8, Supporting Information).These results suggest that classical relaxation theory provides a reasonably good description of 1 H relaxation in this family of complexes.We also note that R 2 displays a linear dependence with the square of the applied magnetic field (Figures S9−S11, Supporting Information), as expected according to eq 6.The plots of 1/T 2 versus the Dy••• H distances also evidence that relaxation is faster upon increasing the magnetic field strength (Figure 5).The relaxation rates increase upon decreasing the temperature, which is mainly the combined effect of the 1/T 2 dependence of the Curie-spin mechanism and the increased value of τ R due to slow rotational motion at lower temperatures.
The transverse relaxation rates were fitted to eqs 7−9, assuming that both T 1e and τ R display an Arrhenius dependence with temperature with activation energies E R and E V , respectively. 89,90The fits are shown in Figure 5, while the fitted parameters are given in Table 5. Due to the relatively large number of parameters, we had to fix μ eff to the common value of 10.64 BM. 91 Furthermore, the value of E v was fixed to 1 kJ mol −1 for [Dy(NO3PA)] and [Dy(PYTA)] − , as otherwise, small negative values were obtained.This has been observed previously very often when investigating the relaxation properties of Gd(III) complexes. 89,92,93Values of E v close to 1 kJ mol −1 were reported for the lanthanide aqua ions. 3he values of τ R obtained from the fits of the data are very reasonable, considering the size of the complexes, 94 with the slightly longer value of τ R being observed for the complex with the highest molecular weight.One should note that the values of τ R obtained from 1 H NMRD studies on Gd(III) complexes are expected to be somewhat shorter due to the local mobility (internal motion) of the coordinated water molecule. 86The values of E R are also close to those determined from 1 H NMRD studies on Gd(III) complexes (∼20 kJ mol −1 ).For [Dy(CB-TE2PA)] + , the fit of the data afforded a rather high value of E V (11.9 kJ mol −1 ), as well as a high value of E R .These values should be taken with some care, as these parameters are strongly correlated.It is, however, possible that the extreme rigidity of this complex results in a higher activation energy for the modulation of T 1e .
The values of T 1e obtained for the three complexes are relatively similar, increasing from 196 fs for [Dy(NO3PA)] to 375 fs for [Dy(CB-TE2PA)] + .Very similar values were reported for the Dy(III) aqua-ion [Dy(H 2 O) 8 ] 3+ (299 fs) 3 and for the [Dy(DOTA)] − complex (∼250 fs). 35This suggests that T 1e is rather insensitive to the coordination environment around the metal ion.The short values of T 1e suggest that electron relaxation may originate from changes in the metal coordination environment caused by fast molecular vibrations.

CONCLUSIONS
The purpose of this work was to analyze 1 H NMR relaxation in a series of well-characterized Dy(III) complexes.Luminescence measurements and the X-ray crystal structure of [Dy(CB-TE2PA)] + were reported here for the sake of completeness.The selected complexes display different coordination numbers and thus coordination polyhedra, which results in markedly different magnetic anisotropies, which were obtained using 1 H NMR measurements.The analysis of the transverse relaxation rates evidences that the traditional relaxation theory describes reasonably well the relaxation in these complexes, as evidenced by the linear dependence of 1/T 2 with 1/r 6 .This indicates that anisotropic relaxation does not provide a significant contribution for the complexes investigated here.We note that the effect of anisotropy is expected to be small while being one order of magnitude smaller than the average susceptibility. 95his situation is observed for the studied complexes, as Δχ ax and Δχ rh represent <15% of χ iso (∼151 × 10 −32 m 3 ).In the case of [Dy(NO3PA)], Δχ ax is particularly small compared with χ iso (<4%).However, we do not exclude that anisotropic relaxation may play a role in Ln(III) complexes with very large magnetic anisotropies.[Dy(CB-TE2PA)] + was prepared in a microwave apparatus, following the procedure reported for the Eu(III) complex, 40 and the resulting complex was then redissolved in either H 2 O or D 2 O. NMR measurements were recorded using complex concentrations of ∼30 mM. 1 H NMR spectra were recorded in Bruker DPX 250 (5.87 T), Bruker Avance 300 (7.05 T), Bruker ARX400 (9.40 T), and Bruker Avance 500 (11.75 T) spectrometers.Linewidths were measured with the deconvolution tool of MestRe Nova, 96 using Lorentzian− Gaussian functions (Figure S13, Supporting Information).Single crystals of [Dy(CB-TE2PA)](PF 6 )•2.5H 2 O were obtained by slow evaporation of an aqueous solution of the complex in the presence of excess KPF 6 .

EXPERIMENTAL AND COMPUTATIONAL SECTION
4.2.Luminescence Measurements.Spectroscopic measurements were performed with 10 × 10 mm 2 Quartz Suprasil certified cells (Hellma Analytics).UV/Vis absorption spectra were recorded on a Lambda 950 UV/VIS/NIR absorption spectrometer from PerkinElmer.Steady-state emission spectra were recorded on an Edinburgh Instruments FLP920 working with a continuous 450 W Xe lamp and a red sensitive R928 photomultiplier from Hamamatsu in Pelletier housing for visible detection (230 to 900 nm) or a Hamamatsu R5 509-72 photomultiplier cooled at 77 K for the Vis-NIR part.A 330 nm high pass cutoff filter was used to eliminate the

Inorganic Chemistry
second-order artifacts for the visible part, and an 850 nm high pass cutoff filter for the NIR part.Luminescence lifetimes were measured on the same instrument working in the multichannel spectroscopy mode and using a Xenon flash lamp as the excitation source.The decay curves were corrected for the intensity profile of the lamp by measuring the diffraction signals of a scattering sample of colloidal silica.Errors in the luminescence lifetimes are estimated to be ±10%.Luminescence quantum yields were measured according to conventional procedures, with diluted solutions (optical density < 0.05 at the excitation wavelength), using Rhodamine 6G in water (φ = 76.0%). 67igh-resolution emission spectra were recorded at 77 K using a nitrogen-cooled Oxford Instruments cryostat with 0.05 nm slits at the emission, except for [Dy(CB-TE2PA)] + , for which slits of 0.1 nm were used due to the weaker intensity.

X-ray Diffraction Measurements.
A crystal of [Dy(CB-TE2PA)](PF 6 )•2.5H 2 O was analyzed by X-ray diffraction.Crystallographic data and structure refinement parameters are shown in Table S2 (Supporting Information).Crystallographic data were collected on a Bruker D8 Venture diffractometer with a Photon 100 CMOS detector at 100 K with Mo Kα radiation (λ = 0.71073 Å) generated by an Incoatec high brilliance microfocus source equipped with Incoatec Helios multilayer optics.APEX3 97 software was used for collecting frames of data, indexing reflections, and the determination of lattice parameters, while SAINT 98 was used for the integration of the intensity of reflections and SADABS 99 for scaling and empirical absorption correction.The structure was solved by dual-space methods using the program SHELXT. 100 All non-hydrogen atoms were refined with anisotropic thermal parameters by full-matrix leastsquares calculations on F 2 using the program SHELXL-2014. 101ydrogen atoms of the compound were inserted at calculated positions and constrained with isotropic thermal parameters.CCDC 2257994 contains supplementary crystallographic data, which can be obtained free of charge from the Cambridge Crystallographic Data Centre via www.ccdc.ac.uk/data_request/cif. 4.4.Computational Details.The geometries of the Dy(III) complexes were optimized using Gaussian 16, 102 employing the hybrid-meta GGA functional TPSSh, 103 in combination with the small-core quasi-relativistic effective core potential proposed by Dolg et al. 104 (28 electrons, 1s-3d, in the core for Dy) and the associated ECP28MWB_GUESS basis set, which possesses a (42s26p20d8f)/ [3s2p2d1f] contraction scheme.The standard Def2-TZVPP basis set was used for the ligand atoms. 105Solvent effects were incorporated using the polarized continuum model (IEF-PCM variant). 106,107requency calculations were employed to confirm that the optimized geometries corresponded to true energy minima.
Complete active space self-consistent field (CASSCF) 108 calculations were carried out using the ORCA program package (version 5.0.3). 109,110The active space included the nine electrons of Dy(III) distributed over the seven 4f orbitals [CASSCF (9,7)].The state average CASSCF calculation included 21 sextet, 224 quartet, and 490 doublet roots.In these calculations, we used the SARC2-DKH-QZVP 111 basis set for Dy and its associated SARC2-DKH-QZVP/JK auxiliary basis set to accelerate the calculations with the resolution of identity and chain of spheres (RIJCOSX) 112,113 method.For ligand atoms, we used the DKH-def2-TZVPP 105 basis set and auxiliary basis sets generated by ORCA with the Autoaux 114 procedure.Relativistic effects were taken into account with the Douglas−Kroll−Hess (DKH2) method 115,116 using a finite nucleus model. 117SOC effects were incorporated using quasi-degenerate perturbation theory (QDPT). 118,119Solvent effects were included using the SMD solvation model. 120ASSOCIATED CONTENT * sı Supporting Information The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.inorgchem.3c01959.
Absorption and emission spectra, additional NMR data, and computational data (PDF)
H NMR signals indicates that the abundance of the minor species is ca.10%.Finally, the [Dy(CB-TE2PA)] + complex shows 17 signals in the 1 H NMR spectrum, in line with an effective C 2 symmetry in solution.These resonances are observed in the chemical shift range +190 to −175 ppm.

Figure 5 . 1 H
Figure 5. 1 H NMR transverse relaxation rates measured for Dy(III) complexes at different magnetic field strengths and temperatures (D 2 O, pH ∼ 7.0) versus the Dy•••H distances obtained with DFT calculations.The solid lines represent the fits of the data, as explained in the text.
a b c Estimated error ± 10%.d Calculated according to ref 64. e Calculated according to ref 63.

Table 2 .
a See Chart 1 for labeling.Diamagnetic contributions taken from the shifts of the Lu(III) analogue, ref 38.b Geometric factors obtained with DFT calculations (see computational methods).

Table 3 .
Magnetic Susceptibility Tensors Determined from the Analysis of the Paramagnetic Shifts of Dy(III) Complexes (288 K) a

4.1. General. All
38lvents and reagents used were purchased from commercial sources and were used as supplied.Ligands H 3 NO3PA,38H 2 CB-TE2PA,40and H 4 PYTA 36 were synthesized according to previously reported procedures.The Dy(III) complexes [Dy-(PYTA)] − and [Dy(NO3PA)] were prepared by mixing equimolar amounts of ligand and Dy(NO 3 ) 3 •6H 2 O in either D 2 O or H 2 O and adjustment of the pH to ∼7.0 using a diluted NaOH solution.

Table 5 .
Parameters Obtained from the Fits of Relaxation Data for Dy(III) Complexes a a Fixed during the fitting procedure.