On the relationship between NMR chemical shifts of thermally polarized and hyperpolarized ⁸⁹Y complexes and their solution structures

Abstract

Recently developed dynamic nuclear polarization (DNP) technology offers the potential of increasing the NMR sensitivity of even rare nuclei for biological imaging applications. Hyperpolarized ⁸⁹Y is an ideal candidate because of its narrow NMR linewidth, favorable spin quantum number (I=½) and long longitudinal relaxation times (T₁). Strong NMR signals were detected in hyperpolarized ⁸⁹Y samples of a variety of yttrium complexes. A dataset of ⁸⁹Y NMR data composed of 23 complexes with polyaminocarboxylate ligands was obtained using hyperpolarized ⁸⁹Y measurements or ¹H,⁸⁹Y-HMQC spectroscopy. These data were used to derive an empirical equation that describes the correlation between the ⁸⁹Y chemical shift and the chemical structure of the complexes. This empirical correlation serves as a guide for the design of ⁸⁹Y sensors. Relativistic (DKH2) DFT calculations were found to predict the experimental ⁸⁹Y chemical shifts to a rather good accuracy.

Graphical abstract

The ⁸⁹Y NMR chemical shifts measured for a wide range of Y³⁺ complexes can be estimated from a set of empirical contributions associated to the different types of donor atoms coordinated to the metal ion. This correlation will serve as a guide for the design of Magnetic Resonance Imaging sensors based on hyperpolarized ⁸⁹Y.

Introduction

Magnetic resonance imaging (MRI) is a technique widely used in medical diagnosis that is based on the same fundamental principles as NMR. Traditional MRI scanners detect the NMR signal of water proton nuclei present in the body, image contrast being achieved by using adequate pulse sequences that take advantage of differences in proton densities and longitudinal and transverse relaxation times among tissues.^[1] MRI provides 3D images of the body with very high resolution, but is traditionally regarded as a rather insensitive technique.^[2] In an external magnetic field B₀, the extent to which a nuclear spin becomes polarized is described by:^[3]

$$P=\frac{(N^{+}-N^{-})}{(N^{+}-N^{-})}$$ [1]

Where N⁺ and N^- denote the number of nuclear spins parallel (“spin up”) and anti-parallel (“spin down”) with respect to B₀. The polarization at Boltzmann equilibrium (P₀) is given by:^[4]

$$P_0=\mathit{tan}h\left(\frac{\gamma \hslash B_0}{2k_{B}T}\right)\approx \frac{\gamma \hslash B_0}{2k_{B}T}$$ [2]

Where γ is the gyromagnetic ratio of the nucleus under study, k_B is the Boltzman constant and other symbols have their usual meaning. Eq. 2 shows that spin polarization increases with field so the tendency has been for human MRI scanners to move to higher fields over the years to gain sensitivity. Eventually, this becomes cost prohibitive so alternative ways to increase NMR sensitivity are being explored. One method is to use hyperpolarized (HP) materials that exist, at least temporarily, in a non-equilibrium hyperpolarized state where (N⁺-N^-) is increased several orders of magnitude over thermal equilibrium. Dynamic nuclear polarization (DNP), one of the more popular methods to produce hyperpolarized materials, has been used to amplify the sensitivity of ¹³C and ¹⁵N nuclei to a level where common metabolites can be imaged by MRI. For example, ¹³C polarization levels as high as 50% have been achieved using DNP at low temperatures and high fields.^[5] The experimental protocol involves doping the ¹³C material with a stable free radical such as trityl or nitroxide, freezing the sample in a solvent that forms a glass, and irradiating the sample with continuous microwave irradiation at a frequency close to the corresponding electron resonance frequency.

Recently Sherry et al. reported the use of DNP methods to hyperpolarize a variety of ⁸⁹Y complexes.^[6-9] Yttrium exists in nature 100% as the stable isotope, ⁸⁹Y. The predominant chemical form of yttrium is the diamagnetic, trivalent ion, Y³⁺. ⁸⁹Y has a much smaller nuclear magnetic moment than ¹³C so its NMR sensitivity is only 0.668 relative to ¹³C.^[10] Consequently, it is quite difficult and time consuming to acquire an ⁸⁹Y NMR spectrum at Boltzmann spin levels except for highly concentrated samples. However, ⁸⁹Y³⁺ has a nuclear spin quantum number of I=½, exhibits narrow NMR linewidths and long longitudinal relaxation times (T₁) so it is an attractive nucleus for hyperpolarization. In addition, yttrium is not naturally present in the human body so there is zero background signal. The effective ionic radius of Y³⁺ (1.019 Å for CN8) is similar to that of Gd³⁺ (1.053 Å)^[11] so any ligand used to complex Gd³⁺ will also form stable complexes with Y³⁺.^[12,13] Y³⁺ complexes can be also used as models for investigating the solution behaviour of the corresponding paramagnetic lanthanide complexes.^[14]

Only a single ⁸⁹Y NMR report existed before 1970 likely due to the extremely low NMR sensitivity of this nucleus.^[15] In the late 1970s the first T₁ values for some ⁸⁹Y complexes were found to be unusually long.^[16] In 2007, three ⁸⁹Y complexes, Y-DOTP, Y-DOTA, Y-DTPA, plus YCl₃ were hyperpolarized using DNP methods and NMR signals were obtained on complexes at concentrations of only 5-15 mM after a single scan.^[6] The enhanced signals showed that yttrium complexes could be polarized to levels reasonable for imaging. Furthermore, the various ⁸⁹Y complexes displayed a wide range of chemical shifts. This observation in combination with the long relaxation times of these complexes makes them potentially attractive as probes for various physiological parameters such as pH or redox environment. This preliminary study triggered our interest in conducting hyperpolarization experiments on a broader range of ⁸⁹Y complexes. We report here ⁸⁹Y NMR spectra of both thermally polarized and hyperpolarized samples of the diverse group of Y³⁺ complexes shown in Scheme 1 and Scheme 2. Subsequently, density functional theory (DFT) calculations were conducted to better understand the factors that affect the observed ⁸⁹Y NMR chemical shifts and eventually establish empirical correlations between NMR chemical shifts and the number and types of donor atoms in each complex, which might serve as a guide for designing new ⁸⁹Y complexes as biosensors.

Scheme 1.

Complexes with macrocyclic ligands investigated in this work.

Scheme 2.

Complexes with non-macrocyclic ligands investigated in this work.

Results and Discussion

Structure of the Y³⁺ complexes

Establishing a correlation between the observed ⁸⁹Y NMR chemical shifts and the coordination environment around the metal ion requires an accurate determination of the structure in solution of the concerned complexes. Given the similar coordination properties of Y³⁺ and the lanthanide ions (Ln³⁺) we sought to expand the family of structurally characterized Y³⁺ complexes by taking advantage of our recent studies on Ln³⁺ complexes. Thus, we have included in our studies a series of macrocyclic-based ligand complexes, [Y(Me2DO2PA)]⁺, [Y(CB-TE2PA)]⁺, [Y(P2C14Et4)]³⁺, [Y(P2C14Py4)]³⁺ and [Y(BP18C6)]⁺ (Scheme 1), where the structures of the corresponding Ln³⁺ complexes have been established by X-ray diffraction in the solid state and/or by analysis of the Ln³⁺-induced paramagnetic ¹H NMR shifts in aqueous solution.^[17-25] The X-ray structure obtained using single crystals with formula [Y(P2C14Et4)](NO₃)₃·6H₂O confirm that the [Y(P2C14Et4)]³⁺ complex retains the ten-coordinate structure observed for the Ln³⁺ series along the whole lanthanide series (Figure 1).^[20,25] Similarly, the [Y(Me2DO2PA)]⁺ and [Y(CB-TE2PA)]⁺ complexes adopt eight-coordinate structures in the solid state very similar to those established for the corresponding complexes with the Ln3⁺ ions (Figures 2 and 3).^[18,19,21] The family of Y³⁺ complexes with macrocyclic ligands investigated in this work also includes [Y(DOTA)(H₂O)]^-, [Y(DOTAM)(H₂O)]³⁺ and [Y(DO3A)(H₂O)₂]. The structure of [Y(DOTA)(H₂O)]^- in the solid state has been established by X-ray diffraction,^[26,27] while the structure of Ln³⁺ complexes of these ligands have been also investigated both in the solid state and in solution.^[28-33] The Gd³⁺ complex of DO3A was shown to be present in solution as a hydration equilibrium involving an eight-coordinated [Gd(DO3A)(H₂O)] complex and a nine-coordinated bis-hydrated [Gd(DO3A)(H₂O)₂] complex. The speciation in solution was found to be dominated by the bis-hydrated form, which results in an overall hydration number of 1.8-1.9 at 25 °C.^[34,35]

Figure 1.

View of one of the complex cations present in crystals of [Y(P2C14Et4)](NO₃)₃·6H₂O. Water molecules, anions and hydrogen atoms (except those of the hydroxyl groups) have been omitted for simplicity. Bond distances (Å): Y1-O1, 2.435(2); Y1-O2, 2.442(2); Y1-N1, 2.562(2); Y1-N2, 2.628(3); Y1-N3, 2.657(3).

Figure 2.

View of one of the complex cations present in crystals of [Y(CB-TE2PA)](PF₆)·H₂O. Water molecules, anions and hydrogen atoms have been omitted for simplicity. Bond distances (Å): Y1-O1, 2.275(4); Y1-O3, 2.259(4); Y1-N1, 2.590(5); Y1-N2, 2.526(5); Y1-N3, 2.607(5); Y1-N4, 2.520(4); Y1-N5, 2.459(5); Y1-N6, 2.470(5).

Figure 3.

View of one of the complex cations present in crystals of [Y(Me2DO2PA)](PF₆)·H₂O. Water molecules, anions and hydrogen atoms have been omitted for simplicity. Bond distances (Å): Y1-O1, 2.272(2); Y1-N1, 2.565(2); Y1-N2, 2.569(3); Y1-N3, 2.425(2).The complex presents a crystallographically imposed C₂ symmetry.

The chemical formula of all Y³⁺ complexes with non-macrocyclic ligands included in this study are shown in Scheme 2. The number of inner-sphere water molecules in some of the complexes was assigned on the basis of available crystallographic data and solution studies performed on the Ln³⁺ analogues ([Y(EGTA)(H₂O)]^-,^[36,37] [Y(DTPA)(H₂O)]^2-,^[38] [Y(TTHA)]^3-39]). In other cases the complexes present variable hydration numbers in the solid state so the exact number of water molecules coordinated to Y³⁺ cannot be predicted in a straightforward manner. For instance, the sodium salt of [Y(EDTA)(H₂O)₃]^- was found to contain three coordinated water molecules, while the structurally related [Y(DCTA)(H₂O)₂]^- complex was reported to be bis-hydrated in the solid state.^[40] The number of coordinated water molecules in these complexes was assessed by using DFT calculations, which provided theoretical ⁸⁹Y NMR shifts using different plausible coordination numbers. The comparison of experimental and calculated shifts allowed an unequivocal assignment of the hydration state (see below). Most ligands included in this study are known to form 1:1 complexes with the trivalent Ln³⁺ ions, except for NTA^3- and NTPA^3-, which can form both 1:1 and 1:2 complexes, or HIDA^2- and IMDA^2-, which form 1:2 and 1:3 complexes, respectively.^[10]

⁸⁹Y NMR chemical shifts

⁸⁹Y NMR spectra of hyperpolarized samples of Y³⁺-EDTA and Y³⁺-EGTA are illustrated in Figure 4. These spectra demonstrate that one can obtain high quality ⁸⁹Y NMR spectra relatively easily. The ⁸⁹Y chemical shifts of seven complexes measured on hyperpolarized samples are listed in Table 1. Thermally polarized ⁸⁹Y spectra have been reported previously for Y³⁺-(DTPA), Y³⁺-EGTA, Y³⁺-(NTA)₂, Y³⁺-EDTA and Y³⁺-TTHA, and their chemical shifts agree well with those measured from spectra of hyperpolarized samples.^[10,41]

Figure 4.

NMR spectra of hyperpolarized (a) Y³⁺-EDTA (6.1 mM) and (b) Y³⁺-EGTA (7.7 mM) at pH 7.4 collected at 9.4T using a single 20° pulse.

Table 1.

⁸⁹Y chemical shifts and T₁ values for seven hyperpolarized Y³⁺ complexes.^[a]

Y3+ complex	Concentration (mM)	Chemical shift (ppm)	T1 (s)
EGTA	7.7	68.6	474 ± 13
(NTA)2	7.2	73.0	534 ± 118
DTPA	6.2	76.0	227 ± 5
DO3A	7.2	103.5	247 ± 91
EDTA	6.1	133.5	310 ± 4
DOTA	12.5	111.3	446 ± 7
TTHA	7.7	96.9	245 ± 90
		103.2	230 ± 14

^a∼0.2M samples dissolved in H₂O/glycerol (3/1) plus 15 mM OX63 were frozen at 1.4K and polarized for 3 h in an Oxford DNP HyperSense system. The samples were quickly dissolved in a buffer and transferred to a 10 mm NMR tube for data collectionusing a 9.4T magnet. ⁸⁹Y spectra were collected using 20° pulses every 20 s over a period of 300-600 s and the resulting data were fitted to standard decay curve for polarized samples. All chemical shifts are reported relative to YCl₃ set to 0 ppm.

Another set of ⁸⁹Y NMR shifts was obtained using ¹H,⁸⁹Y heteronuclear shift correlation through scalar coupling (¹H,⁸⁹Y-HMQC). This technique allows a much faster acquisition compared with conventional pulse-acquisition ⁸⁹Y NMR measurements, which are very time-consuming due to the long T₁ relaxation times of ⁸⁹Y (Table 1). ¹H,⁸⁹Y-HMQC spectroscopy allows an indirect ¹H detection of ⁸⁹Y, thereby overcoming this problem.^[42] The representative example of the ¹H,⁸⁹Y-HMQC spectrum of [Y(P2C14Et4)]³⁺ is shown in Figure 5. Several cross-peaks relating the ⁸⁹Y NMR signal of the complex at 25.7 ppm and aliphatic protons of the ligand situated at a three-bond distance are observed. A weak correlation involving the pyridyl proton H2, situated four bonds away the metal ion, is also evident. The strongest correlations involve H4_ax, H5_ax, H7_eq and H7_ax, which according to the X-ray crystal structure present H-C-N-Y or H-C-O-Y dihedral angles of 80.6, 78.4, 104.1 and 136.9°. However, no cross-peaks are observed in the case of protons H4_eq ad H5_eq, which are characterized by dihedral angles of 162.2 and 163.5°. These results suggest that the intensity of the scalar coupling between ¹H and ⁸⁹Y follows a Karplus-like relationship, as observed for the ¹H scalar coupling constants responsible for the contact shifts induced by paramagnetic Ln³⁺ ions.^[19]

Figure 5.

¹H,⁸⁹Y-HMQC NMR spectrum of [Y(P2C14Et4)]³⁺ recorded in D₂O solution(4.7 mM).

The ⁸⁹Y NMR chemical shift data of the complexes investigated in this work are compiled in Table 2. The yttrium chemical shifts of our data set composed of 23 polyamino-polycarboxylate complexes vary over 270 ppm. Particularly surprising are the shifts of [Y(Me2DO2PA]⁺ (245.8 ppm) and [Y(CB-TE2PA)]⁺ (218.5 ppm) and the negative chemical shift of [Y(BP18C6)]⁺ (-23.6 ppm), which expand the ⁸⁹Y NMR chemical shift range of polyaminocarboxylate complexes by ∼200 ppm with respect to the window of ⁸⁹Y NMR shifts reported previously (∼70 ppm).^[10,41]

Table 2.

Measured chemical shifts and predicted chemical shifts from (3) of Y³⁺ complexes with the numbers of coordinated amine nitrogen atoms (n_Nam), pyridine nitrogen atoms (n_Npy), carboxylate oxygen atoms (n_Oc), ether oxygen atoms (n_Oe), amide oxygen atoms (n_Oa) and water oxygen atoms (n_Ow).

Y3+ complex	δexp (ppm)	δcalc (ppm)	nNam	nNpy	nOc	nOe	nOh	nOa	nOw
[Y(DOTA)(H2O)]- (1)	111.3	107.0	4	0	4	0	0	0	1
[Y(DOTAM)(H2O)]3+ (2)	123.0[a]	125.1	4	0	0	0	0	4	1
[Y(DO3A)(H2O)2] (3)	103.5	93.4	4	0	3	0	0	0	2
[Y(P2C14Et4)]3+ (4)	25.7	29.8	4	2	0	0	4	0	0
[Y(P2C14Py4)]3+ (5)	78.6	76.0	4	6	0	0	0	0	0
[Y(DOTA-(gly)4)(H2O)]- (6)	121.6	125.1	4	0	0	0	0	4	1
[Y(DOTAM-2C)(H2O)]- (7)	120.9	125.1	4	0	0	0	0	4	1
[Y(DOTAM-3C)(H2O)]- (8)	118.7	125.1	4	0	0	0	0	4	1
[Y(DOTAM-5C)(H2O)]- (9)	117.8	125.1	4	0	0	0	0	4	1
[Y(Me2DO2PA)]+ (10)	244.7	231.0	4	0	0	0	0	0	0
[Y(CB-TE2PA)]+ (11)	218.5	231.0	4	0	0	0	0	0	0
[Y(BP18C6)]+ (12)	-23.6	-15.3	2	0	0	4	0	0	0
[Y(TTHA)]3- (13)	103.2	120.6	4	0	5	0	0	0	0
[Y(IMDA)3]3- (14)	98.7[b]	94.7	3	0	6	0	0	0	0
[Y(DTPA)(H2O)]2- (15)	76.0, 82.2,[b] 83.0[c]	81.1	3	0	5	0	0	0	1
[Y(EDTA)(H2O)2]- (16)	133.5, 129.6[b]	135.7	2	0	4	0	0	0	2
[Y(DCTA)(H2O)2]- (17)	132.7[b]	135.7	2	0	4	0	0	0	2
[Y(HEDTA)(H2O)2] (18)	78.6[b]	76.0	2	0	3	0	1	0	3
[Y(DPTA)(H2O)2]- (19)	130.0[b]	135.7	2	0	4	0	0	0	2
[Y(EGTA)(H2O)]- (20)	68.6, 69.4,[c]68.5[b]	52.0	2	0	4	2	0	0	1
[Y(HIDA)2]- (21)	57.0[b]	48.6	2	0	4	0	2	0	1
[Y(NTA)2]3- (22)	73.0, 76.5[b]	162.8	2	0	6	0	0	0	0
		55.2	2	0	6	0	0	0	1
[Y(NTPA)2]3- (23)	90.5[b]	162.8	2	0	6	0	0	0	0
		55.2	2	0	6	0	0	0	1
[Y(NTA)] (24)	62.6[b]	82.5	1	0	3	0	0	0	4
		-25.1	1	0	3	0	0	0	5
[Y(NTPA)] (25)	44.0[b]	82.5	1	0	3	0	0	0	4
		-25.1	1	0	3	0	0	0	5
[Y(H2O)8]3+ (26)	0.0	2.5	0	0	0	0	0	0	8
SNam	SNpy	SOc	SOe	SOh		SOa		SOw
68.1+6.4	85.7+5.4	94.0+5.8	95.7+4.9	97.3+4.9		89.5+5.4		107.6+6.2

^aData from reference [45].

^bData from reference [10].

^cThermally polarized data (this work).

The sensitivity of the ⁸⁹Y NMR chemical shift to the ligand field produced by the chelate has been examined before for a series of organometallic complexes,^[43] but few studies have attempted to relate ⁸⁹Y chemical shifts with coordination number and identity of donor atoms in ligands that could potentially serve as reporter molecules in biological systems. An empirical relationship between the number of coordinated oxygen and nitrogen atoms and ¹³⁹La chemical shifts was reported previously.^[44] In that study, each negatively charged oxygen atom contributed 30 ppm to the chemical shift of ¹³⁹La, while each ligand nitrogen atom contributed 50 ppm. This same empirical relationship does not hold for yttrium(III) complexes because the range of NMR chemical shifts observed for the two trivalent ions is quite different. Nevertheless, if one makes the same assumption that each ligand nitrogen atom contributes equally and each oxygen atom contributes equally to the ⁸⁹Y chemical shift, the ⁸⁹Y chemical shifts of some of the yttrium(III) complexes listed in Table 2 are rather poorly predicted. An inspection of the ⁸⁹Y chemical shift data reported in Table 2 shows that generally ten-coordinated complexes (i. e. [Y(BP18C6)]⁺ and [Y(P2C14Et4)]³⁺) give signals at higher fields, while the⁸⁹Y resonances of eight-coordinate complexes are more deshielded and nine coordinated complexes give signals in an intermediate range. Furthermore, the replacement of inner sphere water molecules in [Y(EDTA)(H₂O)₂]^- for ligands with different oxygen donor atoms as lactate affects drastically the value of the ⁸⁹Y NMR chemical shift (Figure S8, Supporting Information). This supports the use of different shielding constants for ligands having oxygen donor atoms of water, hydroxyl or carboxylate groups. In the other hand, the ⁸⁹Y NMR chemical shifts measured for thermally polarized samples of complexes [Y(DOTAM-2C)]^-, [Y(DOTAM-3C)]^- and [Y(DOTAM-5C)]^- are very similar to that of [Y(DOTA-(gly)₄)]^- (Table 2, Figure S9, Supporting Information). The varying lengths of the 4 side chains of the ligand have an effect on the inversion of the population of the twisted square antiprismatic (TSAP) and square antiprismatic (SAP) diastereomers. Therefore, it turns out that chemical shifts are mainly dependent of contribution from the coordinated atoms rather than other structural factors. Thus, we attempted to fit the experimental ⁸⁹Y NMR data to an empirical relationship of the form:

$${\delta }^{\text{calc}}{(}^{89}\mathrm{Y})=A-({\mathrm{S}}_{\text{Nam}}\cdot n_{\text{Nam}}+{\mathrm{S}}_{\text{Npy}}\cdot n_{\text{Npy}}+{\mathrm{S}}_{\text{Oc}}\cdot n_{\text{Oc}}+{\mathrm{S}}_{\text{Oh}}\cdot n_{\text{Oh}}+{\mathrm{S}}_{\text{Oe}}\cdot n_{\text{Oe}}+{\mathrm{S}}_{\text{Oa}}\cdot n_{\text{Oa}}+{\mathrm{S}}_{\text{Ow}}\cdot n_{\text{Ow}})$$ [3]

where A is an empirical constant that can be regarded as the chemical shift of Y³⁺ in the absence of any ligand, S_Nam, S_Npy, S_Oc, S_Oh, S_Oe, S_Oa and S_Ow represent the shielding contribution of amine, pyridine, carboxylate, hydroxyl, ether, amide and water donor atoms and n_Nam, n_Npy, n_Oc, n_Oh, n_Oe, n_Oa and n_Ow are the number of donor atoms of each class. The use of different shielding constants for similar donor atoms such as amide or carboxylate oxygen atoms is justified by the different chemical shifts observed for [Y(DOTA)(H₂O)]^- (111 ppm) and [Y(DOTAM)(H₂O)]³⁺ (123 ppm),^[45] which indicate that oxygen atoms of carboxylate groups provide a slightly more important contribution to the shielding of the ⁸⁹Y NMR resonance than amide oxygen atoms. The best fit of the data provided A = 863 ± 48 ppm and the shielding constants reported in Table 2.

The shielding effect of an amine nitrogen atom (S_Nam = 68.1 ppm) is considerably smaller than that of pyridyl nitrogen atoms (S_Npy = 85.7 ppm). Oxygen donor atoms of organic ligands provoke a rather similar shielding effects (94.0-97.3 ppm), while the shielding contribution of water molecules in significantly higher (S_Ow = 107.6 ppm). Figure 6 shows a plot of experimental versus calculated ⁸⁹Y NMR shifts obtained with equation (3) for 21 complexes. The shifts of NTA^3- and NTPA^3- complexes were found to deviate considerably from the predicted values, and were omitted from Figure 6. The reasons for this discrepancy are likely related to the presence of hydration equilibria in solution, as discussed below. Nevertheless, the error between the calculated versus experimental data for the 21 complexes is relatively small, ±6.9 ppm.

Figure 6.

Plot of experimental ⁸⁹Y chemical shifts versus those predicted by equation (3). The straight line is theidentity line.

Given the good agreement between the observed and calculated ⁸⁹Y NMR shifts for most systems, the noticeable deviations from the experimental and calculated data of [Y(NTA)₂]^3- and [Y(NTPA)₂]^3- are intriguing. In the case of [Y(NTA)₂]^3-, equation (3) predicts a shift of 55.2 ppm assuming the presence of a coordinated water molecule and 162.8 ppm if the complex lacks inner-sphere water molecules. The experimental shifts (73.0 ppm) is closer to the value calculated for the q = 0 species. In the case of [Y(NTPA)₂]^3- the donor atoms of the ligands are identical to those of [Y(NTA)₂]^3-, leading to the same calculated values. However, the experimental value is quite different (90.5 ppm). We interpret these data in terms of hydration equilibria involving a non-hydrated species and a complex species containing one coordinated water molecule. The calculated ⁸⁹Y NMR shifts suggest that the major species in solution corresponds to the hydrated complex, the population of the q = 0 species being estimated as ∼15 and ∼30% for [Y(NTA)₂]^3- and [Y(NTPA)₂]^3-, respectively. Similar hydration equilibria involving complex species containing four and five coordinated water molecules are probably present in solutions of the [Y(NTA)] and [Y(NTPA)] complexes (Table 2).

The [Y(TTHA)]^3- complex presents at least two species in solution at about neutral pH, as two signals at 103.2 ppm and 96.9 ppm are observed in the hyperpolarized ⁸⁹Y NMR spectrum at pH 6.9 (Table 1). The Ln³⁺ complexes of TTHA^6- form different structures in the solid state depending upon the size of the metal ion.^[46] The smallest Ln³⁺ ions form nine-coordinated complexes through binding of four amine nitrogen atoms and five oxygen atoms of carboxylate groups, the remaining carboxylate unit remaining uncoordinated. For the largest Ln³⁺ ions ten-coordinate species were observed in the solid state thanks to the coordination of the four amine nitrogen atoms and the six carboxylate oxygen atoms. Additionally, dinuclear [Ln₂(HTTHA)₂]^4- species containing nine-coordinated metal ions were also reported, with the metal coordination environment being fulfilled by three amine nitrogen atoms, four carboxylate groups of one of the ligands and two carboxylate groups of a neighboring ligand unit. The chemical shift values calculated with equation (3) for the nine- and ten-coordinated [Y(TTHA)]^3- species are 120.6 ppm and 26.6 ppm, respectively. The calculated value for the dinuclear [Ln₂(HTTHA)₂]^4- species is 94.7 ppm. The latter value is in excellent agreement with the NMR signal observed at 96.9 ppm. Thus, most likely the Y³⁺-TTHA complex is present in solution as a mixture of a mononuclear and a dinuclear species giving ⁸⁹Y NMR signals at 103.2 and 96.9 ppm, respectively. A minor amount of ten-coordinate [Y(TTHA)]^3- species might be responsible for the 17.5 ppm difference between the experimental and calculated shifts of [Y(TTHA)]^3-.

DFT calculations

Aiming to have a deeper insight on the origin of the ⁸⁹Y NMR chemical shifts observed for polyaminocarboxylate complexes, we turned our attention to theory. Prior to calculation of ⁸⁹Y NMR chemical shifts using DFT methods, we first performed geometry optimizations of 16 Y³⁺ complexes with polyaminocarboxylates using the TPSSh functional and a quasirelativistic pseudopotential that includes the inner 28 electrons in the core (see computational details below). For those complexes containing coordinated water molecules, we explicitly included two second-sphere water molecules hydrogen-bonded to each coordinated water molecule, as the inclusion of second-sphere water molecules was found to be critical for an accurate calculation of Gd³⁺-O_waterdistances and ¹⁷O hyperfine coupling constants in Gd³⁺ complexes of polyaminocarboxylates.^[47,48] The optimized geometries of all Y³⁺ complexes together with the calculated bond distances of the Y³⁺ coordination environments are shown in Figures S10-S11, Supporting Information). The quality of the optimized structures was assessed by comparison of the calculated bond distances of the metal coordination environment with crystallographic data (Tables S1-S3, Supporting Information).

Since Y³⁺ is a relatively heavy atom, relativistic effects are expected to play an important role on the ⁸⁹Y NMR shifts.^[49] Thus, the absolute shielding constants were obtained using relativistic DFT calculations at the TPSSh/DKH2/TZVP level. A plot of the isotropic nuclear shielding values (σ_iso) versus the observed ⁸⁹Y NMR shifts provides a rather good linear correlation (Figure 7). Furthermore, the chemical shifts obtained using the σ_iso value calculated for [Y(H₂O)₈]³⁺ are also in reasonable agreement with the experimental values (Table 3). Besides, these calculations allowed us to assess the hydration number of those complexes for which the number of coordinated water molecules was uncertain. One of such cases is [Y(DO3A)(H₂O)_q], for which the ⁸⁹Y NMR shift calculated for the bis-hydrated complex (103.4 ppm, Table 3) is virtually identical to the experimental one (103.5 ppm). On the contrary, the mono-hydrated complex yields a calculated chemical shift of 181.8 ppm, a value that deviates ∼78 ppm from the experimental one. For [Y(EDTA)(H₂O)_q]^-, the DFT calculations predict ⁸⁹Y NMR shifts of 20.5 and 119.4 ppm for the tris- and bis-hydrated forms, the latter value being in reasonably good agreement with the experimental one (135.7 ppm). However, for [Y(NTA)₂(H₂O)_q]^3- the chemical shifts calculated for both the q = 1 (24.3 ppm) and q = 0 (101.8 ppm) species deviate considerably from the experimental value (73.0 ppm), suggesting that a hydration equilibrium exists in solution involving a mono- and a bis-hydrated species. The presence of hydration equilibria in solution was ascertained using absorption spectroscopy for different Eu³⁺ complexes, and therefore it is likely that some Y³⁺ complexes will show similar behavior.^[50,51]

Figure 7.

Plot of the experimental ⁸⁹Y NMR shifts versus the isotropic nuclear shielding values calculated in aqueous solution (COSMO) at the TPSSh/DKH2/TZVP level.

Table 3.

Isotropic ⁸⁹Y nuclear shielding values (σ_iso), diamagnetic (σ^d) and paramagnetic (σ^p) contributions to σ_iso and ⁸⁹Y NMR shifts calculated in aqueous solution (COSMO) at the TPSSh/DKH2/TZVP level.

Y3+ complex	σiso	σd	σp	δcalc
[Y(DOTA)(H2O)]- (1)	2843.6	4469.5	-1625.8	96.4
[Y(DOTAM)(H2O)]3+ (2)	2827.6	4464.8	-1637.6	112.4
[Y(DO3A)(H2O)2] (3)	2836.6	4464.9	-1628.3	103.4
[Y(P2C14Et4)]3+ (4)	2899.6	4521.6	-1622.0	40.4
[Y(Me2DO2PA)]+ (10)	2727.2	4461.4	-1734.2	212.8
[Y(CB-TE2PA)]+ (11)	2729.9	4494.0	-1764.2	210.1
[Y(BP18C6)]+ (12)	2977.3	4547.7	-1570.4	-37.3
[Y(TTHA)]3- (13)	2871.1	4489.1	-1618.0	68.9
[Y(IMDA)3]3- (14)	2852.3	4378.4	-1526.1	87.7
[Y(DTPA)(H2O)]2- (15)	2894.9	4446.1	-1551.2	45.1
[Y(EDTA)(H2O)2]- (16)	2820.6	4386.6	-1565.9	119.4
[Y(DCTA)(H2O)2]- (17)	2810.8	4440.9	-16300	129.2
[Y(DPTA)(H2O)2]- (19)	2810.9	4407.4	-1596.5	129.1
[Y(EGTA)(H2O)]- (20)	2898.0	4437.5	-1539.5	42.0
[Y(HIDA)2]- (21)	2882.8	4406.6	-1523.8	57.2
[Y(H2O)8]3+ (26)	2940.0	4060.5	-1120.6	0.0

The calculated σ_iso values provide a rather good linear correlation with the calculated electron density at the Y³⁺ nucleus (Figure S12, Supporting Information). The σ_iso values can be broken down into the diamagnetic (σ^d) and paramagnetic (σ^p) contributions, which were obtained using each nucleus as the gauche origin for separation (Table 3).^[52] The diamagnetic contribution arises from the magnetic field at the nucleus produced by the diamagnetic current density caused in the electrons by the external magnetic field.^[53] Excluding the aquated ion, for the series of complexes listed in Table 3 the diamagnetic contribution varies by up to ∼169 ppm. The σ^d values calculated for the complexes with polyaminocarboxylate ligands are larger than that calculated for [Y(H₂O)₈]³⁺, which shows that the diamagnetic contribution provides a shielding effect to the ⁸⁹Y NMR shifts. The analysis of the natural electron configurations obtained for Y³⁺ in this series of complexes with Natural Bond Orbital (NBO) analysis provides some insight into the nature of this shielding effect (Table S4, Supporting Information). The natural electron configurations reveal significant changes in the 5s and 4d populations depending upon the metal coordination environment. The 5s populations are relatively small and vary from 0.162 for [Y(EDTA)(H₂O)₂]^- to 0.186 for [Y(IMDA)₃]^3-, while the calculated 4d populations present values in the range 0.82-1.08. The 5p populations are smaller (< 0.014) than the 5s and 4d populations, as would be expected. Plots of the diamagnetic shielding contribution versus the calculated 4d, 5s and 5p populations (Figure S13, Supporting Information) reveal linear trends that indicate increasing shielding effects upon increasing the population of the Y³⁺ valence orbitals.

The paramagnetic contribution accounts for the mixing of certain excited states with the electronic ground state in the presence of a magnetic field. The calculated σ^p values for complexes with polyaminocarboxylate ligands are more negative than that obtained for [Y(H₂O)₈]³⁺, indicating that the paramagnetic contribution results in a deshielding effect in the family of Y³⁺ complexes investigated here. The σ^p term generally becomes more important as the HOMO-LUMO gap is reduced (Figure S14, Supporting Information). This is expected as smaller HOMO-LUMO gaps tend to decrease the energy differences between all occupied and unoccupied orbitals.^[54]

Conclusions

This study showed that Y³⁺ complexes with polyaminocarboxylate ligands provide a rather wide range of ⁸⁹Y NMR chemical shifts that expands ∼270 ppm, which represents an expansion of about 200 ppm with the chemical shift range observed previously. The ⁸⁹Y NMR chemical shifts can be obtained either using hyperpolarized samples or ¹H,⁸⁹Y-HMQC NMR experiments to overcome the long acquisition times required for traditional ⁸⁹Y NMR experiments due to the long relaxation times. The ⁸⁹Y NMR chemical shift values were found to change considerably depending upon the coordination number of the complex and the nature of the donor atoms of the ligand. A relativistic DFT study was conducted to rationalize the origin of the ⁸⁹Y NMR chemical shifts. These calculations can predict the observed chemical shifts to a rather good accuracy. The breakdown of the calculated isotropic shielding constants revealed that the calculated ⁸⁹Y NMR chemical shifts are a subtle balance of the two contributions. Generally increased 4d, 5s and 5p populations and large HOMO-LUMO gaps have a shielding effect on the ⁸⁹Y chemical shifts. However, these general trends do not allow a prediction of the chemical shifts without performing the DFT calculations. Thus, we proposed an empirical relationship that provides calculated chemical shifts to an accuracy of about ±6.9 ppm with respect to the experimental ones. This empirical expression will be useful for the rational design of ⁸⁹Y NMR imaging probes for hyperpolarized imaging. Furthermore, the ⁸⁹Y NMR chemical shifts are also useful to gain information on the solution structure of the corresponding complexes with Ln³⁺ ions.

Experimental and Computational Section

General

All chemicals used were of the highest available purity and were not purified further. Solvents used were available commercially and used as received. Hexahydrated yttrium nitrate was obtained from Aldrich. Syntheses performed under microwave radiation were carried out with a Monowave Anton Paar 300 instrument (30 bar/850W). Elemental analyses were performed in a Carlo-Erba EA 1108 microanalyzer. Attenuated total reflection infrared (ATR-FTIR) spectra were recorded on a FP-6100 Jasco spectrometer. ESI-MS experiments of complexes [Y(P2C14Et4)](NO₃)₃·6H₂O and [Y(P2C14Py4)](NO₃)₃·6H₂O were performed on an microTOF(focus) mass spectrometer (Bruker Daltonics, Bremen, Germany). Ions were generated using an ApolloII (ESI) source and ionization was achieved by electrospray. ESI-MS analyses of the remaining complexes were done either at HT Laboratory (San Diego, CA) or at core facilities at UT Southwestern Medical Center at Dallas. The pH values were direct readings as measured on an Orion 720A+ (Thermo Corporation, city, state) or an Ultra Basic 5 pH meter (Denver Instruments, city state).

NMR spectroscopy

One dimensional ¹H NMR spectra of compounds [Y(P2C14Et4)](NO₃)₃·6H₂O, [Y(P2C14Py4)](NO₃)₃·6H₂O, [Y(Me2DO2PA)]Cl and [Y(CB-TE2PA)]Cl were recorded at 25°C on a BRUKER Avance III HD 500 spectrometer equipped with an indirect 5mm triple resonance broad band (TBI) ¹H/ {BB} /¹³C probe. Spectra were performed according BRUKER's pulse programs with standard pulse sequences using delay times of 2s, a 30° pulse and 16 scans. The ⁸⁹Y chemical shifts were obtained using Heteronuclear Multiple Quantum Coherence ¹H-⁸⁹Y (HMQC) experiments with a delay for evolution of long range couplings of 41.66 ms and a 2s delay for relaxation time. For example, in an HMQC experiment the raw data set consisted of 48 fid of 1024 (F2) * 98(F1) complex data points each zero filled to 1k in the F1 dimension prior to Fourier transform with a spectral width of 31846 Hz and 4504 Hz in the F1 and F2 dimensions, respectively. ¹H Chemical shifts were expressed in ppm relative to TSP as external reference, in 99.97% D₂O, and TMS for others solvents. ⁸⁹Y chemicals shifts were expressed in ppm relative to Yttrium nitrate, hexahydrate 1M, pH = 4.3 as external reference. The one dimensional ⁸⁹Y spectrum reference was recorded with a 50 s delay relaxation time, 976 scans, and a spectral window of 5980 Hz. ¹H,¹³C, and thermally polarized ⁸⁹Y NMR spectra of all other complexes were recorded using a Bruker Avance III 400 MHz spectrometer and a 5 mm sample probe. Hyperpolarized ⁸⁹Y NMR spectra were collected at a field strength of 9.4 T at 25° on an Oxford unshielded 89 mm magnet with Varian 10 mm low gamma probe. Both hyperpolarized and thermally polarized ⁸⁹Y NMR spectra were referenced to YCl₃ at 0 ppm.

Hyperpolarization Experiments

Hyperpolarization of [Y(EDTA)(H₂O)₂]^- (0.158 M), [Y(EGTA)(H₂O)]^- (0.200 M), [Y(TTHA)]^3- (0.200 M), [Y(NTA)₂]^3- (0.187 M), [Y(DTPA)(H₂O)₂]^- (0.160 M), [Y(DOTA)(H₂O)]^- (0.397 M), and [Y(DO3A)(H₂O)₂] (0.187 M) were generated following a reported method.^[7] After 4.16 mL of hyperpolarized [Y(EDTA)(H₂O)₂]^- solution was ejected from the HyperSense, 1 mL was transferred to a 10mm NMR tube to acquire the ⁸⁹Y NMR data. Hyperpolarized ⁸⁹Y spectra of [Y(TTHA)]^3- were collected at pH 4.8 and 6.9 in buffer solutions.

Crystal Structure Determinations

X-ray diffraction data for compound [Y(P2C14Et4)](NO₃)₃·6H₂O were collected at 173 K on a Bruker Smart-CCD- 6000 using Cu-Kα radiation. All data were corrected by Lorentz and polarization effects. Empirical absorption corrections were also applied.^[55] Complex scattering factors were taken from the program package SHELX-97.^[56] The structure was solved by direct methods using SIR-92,^[57] which revealed the position of all non-hydrogen atoms. The structure was refined on F² by a full-matrix least-squares procedure using anisotropic displacement parameters for all non hydrogen atoms. The hydrogen atoms bonded to carbon atoms were located in their calculated positions and refined using a riding model. For compounds [Y(Me2DO2PA)]Cl and [Y(CB-TE2PA)]Cl single-crystal X-ray diffraction data were collected with a Xcalibur 2 CCD 4-circle Diffractometer (Oxford Diffraction) fitted with a graphite monochromatedMoKα radiation (λ = 0.71073 Å). Data were collected at 170 K and 298 K. Unit cell determination and data reduction, including interframe scaling, Lorentzian, polarization, empirical absorption, and detector sensitivity corrections, were carried out using attached programs of CrysAlis software (Oxford Diffraction).^[58] Structures were solved by direct methods and refined by full matrix least-squares method on F² with the SHELXL97⁵⁶ suite of programs. The hydrogen atoms were identified at the last step and refined under geometrical restraints and isotropic U-constraints.

Crystal data and structure refinement details are given in Table S5 (Supporting Information). CCDC 1484094, 1484140 and 1484139 contain the supplementary crystallographic data for this paper. These data can be obtained free of charge from The Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/data_request/cif. Molecular graphics were generated by using USCF Chimera (version 1.8).^[59]

Preparation of the complexes

Yttrium complexes derived from ligands EDTA, EGTA, TTHA, DTPA, DO3A, NTA, DOTA, DOTA-(gly)₄, DOTAM-2C, DOTAM-3C, DOTAM-5C, were synthesized following reported procedures^[7,60]. MS(ESI^-, H₂O): m/z 377.00 (100%) [Y(EDTA)]^-; 465.07 (100%) [Y(EGTA)-4H]^-; 579.20 (30%) [Y(H₂TTHA)]^-; 601.13 (100%) [Y(HTTHA)+Na]^-; 467.00 (52%) [Y(NTA)₂-4H]^-; 511.07 (88%) [Y(NTA)₂+2Na]^-; 489.00 (100%) [Y(NTA)(HNTA)+Na]^-; 489.5 (100%) [Y(DOTA)]^-; 238.4 (100%) [Y(DTPA)]^2-/2;773.53 (100%) [Y(DOTAM-2C)]^-; 829.60 (100%) [Y(DOTAM-3C)]^-; 941.73 (100%) [Y(DOTAM-5C)]^-.MS (ESI⁺): m/z741.87 (100%)[Y(HDOTA-(Gly)₄)+Na]⁺; 455.20 (100%) [Y(DO3A)+Na]⁺; 571.20 (80%)[Y(DO3A)+3Na+2Cl]⁺.

General procedure for the syntheses of [Y(P2C14Et4)](NO₃)₃·6H₂Oand [Y(P2C14Py4)](NO₃)₃·6H₂O

A solution of Y(NO₃)₃·6H₂O (0.04 mmol) in methanol (5 mL) was added to a stirred solution of the appropriate ligand (0.04 mmol) in the same solvent (10 mL). The solution was allowed to concentrate and the crude products were recrystallized in water. By slow concentration of the water solutions, crystalline products were obtained, which were filtered off and air-dried.

[Y(P2C14Et4)](NO₃)₃·6H₂O

Yield: 67%;¹H NMR (500 MHz, D₂O, pD = 7.46, 25 °C): δ=8.00 (t, ³J = 7.8 Hz, 2H, py), 7.51 (d, ³J = 7.8 Hz, 4H, py), 4.68 (d, ²J = 16.3 Hz, 4H, –CH_2eq-py), 4.17 (td, ²J = 10.9 Hz, ³J = 6.7 Hz, 4H, –CH_2ax-OH), 3.88 (m, 4H, –CH_2ax-py), 3.86 (m, 4H, –CH_2eq-OH), 3.59 (d, ³J = 9.9 Hz, 4H, –CH_2eq-(ethyl)), 3.26-3.19 (m, 4H, –CH_2ax-N), 2.68 (td, ²J = 10.9 Hz, ³J = 6.7 Hz, 4H, –CH_2eq-N), 2.57 ppm (d, ³J = 9.9 Hz, 4H, –CH_2ax-(ethyl));IR (ATR): ν=1607 (s), 1457 (s) (C=C) and (C=N)_py, 2868 (m), 2763 (m) (OH), 1329 (s), 827 (m), 736 (m) (NO₃^-); MS (ESI⁺): m/z 589.22 (100%) [Y(P2C14Et4)-2H]⁺, 737.19 (4%) [Y(P2C14Et4)+Na+2(NO₃)-H]⁺; elemental analysis calcd (%) forC₂₆H₅₄N₉O₁₉Y: C 35.3, H, 6.2 N; 14.2; found: C 35.1, H 6.4, N 14.3.

[Y(P2C14Py4)](NO₃)₃·6H₂O

Yield: 66%;¹H NMR (500 MHz, D₂O, pD = 7.46, 25°C): δ=8.46 (t, ³J = 7.9 Hz, 2H, py), 7.97 (d, ³J = 7.9 Hz, 4H, py), 7.56 (t, ³J = 7.7 Hz, 4H, -(py)₄), 7.27 (d, ³J = 7.7 Hz, 4H, -(py)₄), 7.07 (t, ³J = 6.6 Hz, 4H, -(py)₄), 6.87 (m, 4H, -(py)₄), 4.74 (d, ³J = 16.6 Hz, 4H, -(CH_2eq-py)₄), 4.59 (d, ³J = 17.5 Hz, 4H, –CH_2eq-py), 4.03 (d, ³J = 16.6 Hz, 4H, -(CH_2ax-py)₄), 3.78 (d, ³J = 17.5 Hz, 4H, –CH_2ax-py), 3.18 (d, ³J = 10.0 Hz, 4H, –CH_2eq-(ethyl)), 2.43 ppm (d, ³J = 10.0 Hz, 4H, –CH_2ax-(ethyl)); IR (ATR): ν=1602 (s), 1457 (s) (C=C) and (C=N)_py, 1324 (s), 817 (m), 828 (m), 760 (m) (NO₃^-); MS (ESI⁺): m/z903.3 (70%) [Y(P2C14Py4)(NO₃)₂]⁺, 420.6 (100%) [Y(P2C14Py4)(NO₃)]²⁺; elemental analysis calcd (%) forC₄₂H₅₈N₁₃O₁₅Y: C 47.0, H 5.4, N 17.0;found: C 47.0, H 5.7, N 16.8.

[Y(Me2DO2PA)]Cl

This complex was synthesized following a reported procedure.^[18] To a solution of Me2DO2PA·4HCl (0.050 mg, 0.081 mmol) and Et₃N (66 mg, 0.649 mmol) in MeOH (4 mL) was added a solution of YCl₃.6H₂O (37 mg, 0.122 mmol) in MeOH (3 mL). The mixture was heated to reflux during 72h and then concentrated to dryness. The residue was stirred in CH₃CN (2 mL) at room temperature during 24h. The precipitate was filtered and rinsed with CH₃CN (2mL) and Et₂O (2mL) to yield 34 mg of a white solid. Addition of an excess of KPF₆ to a solution of the complex gave single crystals suitable for X-ray diffraction analysis. Yield 71%; ¹H NMR (500 MHz, D₂O, pD = 7.46, 25°C): δ=8.31 (m, 2H, py), 8.07 (d, ³J = 7.5 Hz, 2H, py), 7.91 (d, ³J = 9.0 Hz, 2H), 4.86 (d, ²J = 16.5 Hz, 2H, –CH₂py), 4.29 (d, ²J = 16.5 Hz, 2H, –CH₂py), 3.69 (s br, 4H, –CH₂-cyclen), 3.4 – 2.7 (m, 10H, –CH₂-cyclen), 2.33 (d, ²J = 14.5 Hz, 2H, –CH₂-cyclen), 2.10 ppm (s, 6H, -CH₃). ¹³C NMR (125.77 MHz, D₂O, pD = 7.46, 25°C): δ=174.22, 158.99, 152.13 (quaternary C); 145.74, 129.87, 127.06 (tertiary C); 58.47, 56.17 (secondary C); 47.76 ppm (primary C).

[Y(CB-TE2PA)]Cl

This complex was prepared following the previously reported procedure.^[21] A mixture containing H₂CB-TE2PA·4HCl (50 mg, 0.078 mmol), DIPEA (80 mg, 0.624 mmol) and YCl₃·6H₂O (47 mg, 0.156 mmol) in n-butanol (10 mL) was heated at 150°C during 4h under microwave radiation. The solvent was evaporated and the solid was washed four times with THF. The complex was obtained as a brown solid (28 mg). Addition of an excess of KPF₆ to a solution of the complexgave single crystals suitable for X-ray diffraction analysis. Yield: 58%; ¹H NMR (500 MHz, D₂O, pD = 5.65, 25 °C): δ=8.21 (t, ³J = 7.9 Hz, 2H, py), 7.96 (d, ³J = 7.9 Hz, 2H, py), 7.82 (d, ³J = 7.9 Hz, 2H, py), 5.11 (d, ²J = 15.3 Hz, 2H, –CH_2ax-py), 4.15 (d, ²J = 15.3 Hz, 2H, –CH_2eq-py), 3.7-3.6 (m, 4H), 3.10-3.01 (m, 2H), 2.96-2.80 (m, 6H), 2.72-2.69 (m, 2H), 2.50-2.41 (m, 2H), 2.4-2.25 (m, 4H), 2.0- 1.9 (m, 2H), 1.3 ppm (m, 2H). ¹³C NMR (75.47 MHz, D₂O, pD = 5.65, 25 °C): δ=175.80, 159.56, 151.96 (quaternary C); 145.62, 129.08, 126.00 (tertiary C); 71.52, 62.22, 62.10, 60.74, 55.91, 55.62, 26.88 ppm (secondary C).

Computational details

Geometry optimizations were performed in aqueous solution employing DFT within the hybrid meta-GGA approximation with the TPSSh exchange-correlation functional,^[61]and the Gaussian 09 package (Revision D.01).^[62]In these calculations we used the quasi-relativistic effective core potential ECP28MWB of Preusset al.^[63] and the related (8s7p6d2f1g)/[6s5p3d2f1g]-GTO valence basis set for Y,^[63,64] in combination with the standard 6-31G(d,p) basis set for the ligand atoms. No symmetry constraints have been imposed during the optimizations. The default values for the integration grid (75 radial shells and 302 angular points) and the SCF energy convergence criteria (10^-8) were used in all calculations. The stationary points found on the potential energy surfaces as a result of the geometry optimizations have been tested to represent energy minima rather than saddle points via frequency analysis. Bulk solvent effects (water) were included with the polarizable continuum model using the integral equation formalism (IEFPCM)^[65] variant as implemented in Gaussian 09. The universal force field radii (UFF)^[66] scaled by a factor of 1.1 were used to define the solute cavities.

The calculations of the ⁸⁹Y NMR shielding tensors were carried out using the ORCA program package (Version 3.0.1)^[67] using the own nucleus as the origin of this gauche origin. Relativistic effects were considered by means of the second order Douglas-Kroll-Hess (DKH2) method,^[68] with the all-electron scalar relativistic TZVP-DKH basis set of Pantazis et al for Y.^[69]The geometries of the complexes optimized with the Gaussian code as described above were employed. The RIJCOSX approximation^[70] was used to speed up the calculations of NMR parameters using the Def2-TZVPP/JK^[71] auxiliary basis set as constructed automatically by ORCA. The convergence tolerances and integration accuracies of the calculations were increased from the defaults using the available TightSCF and Grid5 options. Solvent effects (water) were taking into account by using the COSMO solvation model as implemented in ORCA.^[72] Chemical shifts were calculated as δ = (σ^ref-σ) using [Y(H₂O)₈]³⁺ as a reference. Natural electron configurations were obtained with the NBO 6.0 program developed by Weinhold.^[73]