Article pubs.acs.org/IC
Water Exchange on [Ln(DO3A)(H2O)2] and [Ln(DTTA−Me)(H2O)2]− Studied by Variable Temperature, Pressure, and Magnetic Field NMR Shima Karimi and Lothar Helm* Laboratoire de Chimie Inorganique et Bioinorganique, Ecole Polytechnique Fédérale de Lausanne, EPFL-BCH, CH-1015 Lausanne, Switzerland S Supporting Information *
ABSTRACT: Water exchange kinetics of [Ln(L)(H2O)2]x complexes (Ln = Pr, Nd, Dy, Tm, and Yb; L = DO3A and DTTA−Me) were studied by 17O NMR spectroscopy as a function of temperature, pressure, and frequency and by 1H nuclear magnetic relaxation dispersion. Water exchange rate constants of both complexes show a maximum at dysprosium. Water exchange on negatively charged complexes of the acyclic DTTA−Me ligand is much faster than on the neutral complexes of the macrocyclic DO3A. Small activation volumes |ΔV⧧| < 1 cm3 mol−1 measured for water exchange on [Ln(DO3A)(H2O)2] indicate an interchange type of mechanism (I) for the lanthanide complexes studied. In the case of [Ln(DTTA− Me)(H2O)2]−, a change in mechanism is detected from a dissociative mechanism (D, ΔV⧧ = 7 cm3 mol−1) for complexes with larger ions (Pr to Gd) to an interchange mechanism (Id, I; ΔV⧧ = +1.8 and +0.4 cm3 mol−1) for complexes with smaller ions (Dy and Tm).
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INTRODUCTION Complexes of lanthanide(III) ions have been shown to behave as effective NMR shift and relaxation probes, allowing them to be used in structural studies of biomolecules and also as contrast agents (CAs) to enhance the contrast between healthy and pathological tissues in medical diagnoses by magnetic resonance imaging. Clinically approved CAs contain only one water molecule in their first coordination sphere.1,2 The structures and water exchange rates of these complexes have already been well-studied for DOTA3,4 and DTPA,5 which are the two important chelators used in MRI contrast agents. However, this is not the case for [Ln(L)(H2O)2]x complexes with a hydration number of two. There are a few studies with the lanthanide ions Gd3+6−12 and Eu3+,13−16 but no systematic study over the lanthanide series has been done so far. In this study of [Ln(L)(H2O)2]x complexes, we focus on DO3A and DTTA−Me (Scheme 1) as representatives of macrocyclic and acyclic ligands, respectively. In spite of the high relaxivity values obtained with compounds using Gd3+ complexes of DO3A and DTTA−Me, these compounds cannot be considered as new leads in the synthesis of contrast agents due to their insufficient thermodynamic and kinetic stabilities. The lack of these important requirements limits their use as CAs to in vitro studies. For a better understanding of the relationship among structure, exchange rate constant, and the mechanism of water exchange, we conducted a comprehensive study of the water exchange kinetics of selected Ln3+ complexes using 17O NMR spectroscopy performed as a function of temperature, pressure, © XXXX American Chemical Society
Scheme 1. Structure of the Ligands
and frequency and 1H nuclear magnetic relaxation dispersion (NMRD). Mechanistic conclusions based on the activation parameters are drawn, and comparisons are made with other lanthanide ion complexes.
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THEORY AND DATA TREATMENT H NMR Relaxation. The measured longitudinal proton relaxation rate, 1/T1,obs, is the sum of the diamagnetic and paramagnetic contribution expressed in eq 1, where r1 is the proton relaxivity (mM−1 s−1): 1
Received: February 16, 2016
A
DOI: 10.1021/acs.inorgchem.6b00363 Inorg. Chem. XXXX, XXX, XXX−XXX
Article
Inorganic Chemistry 1 1 1 1 = + = + r1[Ln] T1,obs T1,d T1,p T1,d
1/2 ⎤ ⎡⎡ τ ⎞ 1⎛ J(ω) = Re⎢⎢1 + ⎜iωτLnH + LnH ⎟ ⎥ ⎢⎣⎢⎣ Te ⎠ ⎥⎦ 4⎝
(1)
The paramagnetic contribution is divided into inner and outer sphere components: r1 = r1IS + r1OS
1/2 ⎡ ⎛ τLnH ⎞ ⎢1 + ⎜iωτ + ⎟ LnH ⎢⎣ Te ⎠ ⎝
(2)
3/2 ⎤⎤ τLnH ⎞ 1 ⎛ τLnH ⎞ ⎥⎥ 4⎛ + ⎜iωτLnH + ⎟ + ⎜iωτLnH + ⎟ 9⎝ Te ⎠ 9⎝ Te ⎠ ⎥⎦⎥⎦
Inner sphere relaxivity refers to the relaxation enhancement due to solvent molecules directly coordinated to the paramagnetic ion and is obtained by eq 3,17 where T1,m and τm are the longitudinal relaxation time and the residence lifetime of the bound water, respectively, and q is the number of bound water molecules. q 1 1 r1IS = 1000 55.5 T1,m + τm (3)
OS = r1,Cu
The correlation times and the diffusion constant are supposed to obey an Arrhenius law with respect to temperature variation: ⎡E ⎛ 1 1 ⎞⎤ ⎟⎥ τR = τR298 exp⎢ R ⎜ − ⎣ R ⎝T 298.15 ⎠⎦ ⎡E ⎛ 1 1 ⎞⎤ 298 DLnH = DLnH exp⎢ LnH ⎜ − ⎟⎥ ⎣ R ⎝ 298.15 T ⎠⎦
(4)
2 2 2 2 ⎤ 7Te 3Te 1 2 ⎛ μ0 ⎞ γI μB μeff ⎡ ⎜ ⎟ ⎥ ⎢ = + 2 2 2 2 6 T1,d 15 ⎝ 4π ⎠ rLnH ⎣ 1 + ωs Te 1 + ωI Te ⎦
1 T1,Cu
=
2 ⎤ 6τR 1 ⎛ μ0 ⎞ ωI μB μeff ⎡ ⎜ ⎟ ⎥ ⎢ 2 2 5 ⎝ 4π ⎠ (3kT )2 rLnH 6 ⎣ 1 + ωI τR ⎦ 4
(10)
O NMR Relaxation. The analysis of the temperature and pressure dependence of 17O water nuclear relaxation is a welldefined procedure for the evaluation of water exchange dynamics. Cossy obtained the following for dilute and fast exchanging lanthanide systems (except Gd3+):30
4
1 1 − = PmΔωm 2τm T2 T1
(6)
where γI is the nuclear gyromagentic ratio, μB is the Bohr magneton, J is the total angular quantum number, ge is the electron g factor, μeff is the effective magnetic moment of the Ln3+ ion (μeff2 = ge2J(J + 1)), ωS and ωI are the electron and nucleus Larmor frequencies, respectively, and rLnH is the electron spin−proton distance. The correlation time for dipolar relaxation is governed by the electron spin relaxation time Te which is, for lanthanides (except Gd3+), much shorter than τm and τR, the rotational correlation time for the reorientation of the electron spin− proton vector.25 The outer sphere relaxivity refers to relaxation enhancement due to solvent molecules in the second coordination sphere and bulk solvent and is given as the sum of the dipolar and Curie relaxations. The dipole−dipole relaxation is described by eq 7, developed by Freed26,27 and Ayant.28 The Curie relaxation has been described by Fries29 (eq 8), where NA is the Avogadro constant, aLnH is the distance of closest approach of an unbound water proton to the metal center, DLnH is the mutual diffusion of bulk water and the complex, τLnH is the correlation time for translational diffusion such that τLnH = aLnH2/DLnH, and J(ω) is the spectral density function. OS = r1,d
(9)
17
(5) 2
(8)
1 ⎤ ⎡ 1 + 4 (iωτLnH)1/2 ⎥ ⎢ J(ω) = Re ⎢ 1 + (iωτLnH)1/2 + 4 (iωτLnH) + 1 (iωτLnH)3/2 ⎥ ⎦ ⎣ 9 9
The longitudinal relaxation rate of inner sphere water protons is considered to be the sum of the dipolar (1/T1,d) and Curie (1/T1,Cu) contributions (eqs 4−6).17,18 In the case of lanthanide ions, with the exception of Gd3+, the latter can become significant18,19 at high magnetic field strengths because of their large quantum number and subpicosecond electronic relaxation time.20−24 Because the water protons have negligible scalar coupling to the electron spins, the relaxation due to scalar coupling can be neglected.20 1 1 1 = + T1,m T1,d T1,Cu
2 ωI 2μB 4 μeff 4 NA 96π ⎛ μ0 ⎞ ⎜ ⎟ [3J(ωI)] 405 ⎝ 4π ⎠ aLnHDLnH (3kBT )2
(11)
where Pm and Δωm are the molar fraction of bound water and the chemical shift difference between bound and free solvent in the absence of chemical exchange, respectively. If the lanthanide concentration is high and the solution cannot be considered dilute, one obtains (see Supporting Information): ⎤ ⎡⎛ 1 1 1 1 ⎞ − = Pm⎢⎜ − ⎟ + PA 2Δωm 2τm ⎥ ⎥⎦ ⎢⎣⎝ T2m T2 T1 T1m ⎠
(12)
1/T1 and 1/T2 are the measured longitudinal and transverse O relaxation rates, respectively, and 1/T1m and 1/T2m are the corresponding relaxation rates of water in the first coordination shell of paramagnetic lanthanide ions. Despite Cossy showing that 1/T1m ≈ 1/T2m for Ln3+ aqua ions,30 we included it in the calculation with the consideration that both are the sums of contributions due to dipole−dipole (1/Ti,d), Curie (1/Ti,Cu), and quadrupolar (1/Ti,q) mechanisms (see Supporting Information). The temperature variation of Δωm is expressed in eq 13, where ω0 is the 17O nucleus resonance frequency (in rad s−1) and B1 and B2 are the constants described by Lewis31 and Bleaney,32 respectively. 17
2 NA 32π ⎛ μ0 ⎞ ⎜ ⎟ γ 2μ 2 μ 2 [3J(ωI) + 7J(ωS)] 405 ⎝ 4π ⎠ aLnHDLnH I B eff
⎛B B ⎞ (ΔωmT)p = ω0⎜ 1 + 22 ⎟ ⎝T T ⎠
(7) B
(13) DOI: 10.1021/acs.inorgchem.6b00363 Inorg. Chem. XXXX, XXX, XXX−XXX
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Inorganic Chemistry
Figure 1. 17O NMR shifts in [Ln(DO3A)(H2O)q] (●, dashed line) and [Ln(DTTA−Me)(H2O)q]− (■, solid line), pH 5.7, [Ln3+] ∼ 100 mM, B0 = 18.8 T, and T = 25 °C.
On the basis of our experimental data, a linear variable pressure dependence of Δωm is also considered (eq 14),33 where P is the pressure and P1 is the proportionality factor. (ΔωmP)T
=
(Δωm0)T (1
+ PP 1 )
The pressure dependence of the exchange rate constant is described by36 ln(kexp )T = ln(kex0 )T −
(14)
2 4πcs ⎛ μeff ⎞ 3 ⎜ ⎟ × 10 T ⎝ 2.84 ⎠
Δβ is the compressibility of activation, which is usually very small for aqueous complexes; hence, it has been neglected in the present study. k0ex refers to the rate constant at zero pressure.36 Number of Inner Sphere Water Molecules. In a UV− visible study on [Eu(DO3A)(H2O)q], Tóth et al. found a hydration equilibrium of q = 1.8 ± 0.1.18 In a luminescence study, Zhang et al. found a similar value of q = 1.8 ± 0.2 for [Tb(DO3A)(H2O)q].37 To investigate the possible change in the number of inner sphere water molecules (q) along the series, 1H nuclear magnetic relaxation dispersion (NMRD) and 17 O chemical shift data were investigated. Because only one inner sphere water molecule for [Ln(L)(H2O)q]x compounds (Ln = Dy, Tm, and Yb) was considered when analyzing the NMRD data, the model would not give a reasonable fit of the experimental data or would lead to unreasonable parameters (Te > 1 ps and τR > 250 ps). Furthermore, because the observed 17O chemical shifts are linearly proportional to the hydration number of the Ln3+ ions and arise from the contact and pseudocontact shifts,38 one can write
(15)
where c is the concentration of the paramagnetic solute in mol L−1, T is the absolute temperature, and s is dependent on the shape of the sample and its position in the magnetic field s = 1/ 3 for a cylinder parallel to the main field.34 Moreover, it has to be highlighted that a concentration change is expected as the pressure changes. Hence, the consideration of density variation with pressure is necessary for an accurate calculation of the BMS shift. The temperature dependence of the water exchange rate constant is described by the Eyring equation35 shown in eq 16, where P and T are the experimental pressure and temperature, respectively. (k298 ex )p is the exchange rate constant at 298 K, and P ∼ 0.1 MPa. ΔS⧧ and ΔH⧧ are the entropy and enthalpy of activation, respectively, for the water exchange process. R is the perfect gas constant, and h and kB are the Planck and Boltzmann constants, respectively.
δm =
⎡ ΔH ⧧ ⎛ 1 1 ⎞⎤ ⎜ exp⎢ − ⎟⎥ 298.15 T ⎠⎦ ⎣ R ⎝ 298.15
(19) (20) D
where F and G are ligand-dependent parameters and C and ⟨Sz⟩ are lanthanide ion-dependent parameters. When δm for a particular ligand is available for different lanthanides, eq 20 can be written in two linear forms.38
(kex298)p T
δm
(16)
C
The variation of the reaction rate constant with pressure is related to the activation volume36 (ΔV⧧) by eq 17. ΔV⧧ is the difference in volume between the transition state and the reactants. ⎛ ∂ ln(kex ) ⎞ ΔV ⎜ ⎟ =− ⎝ ∂P ⎠T RT
δobs − δA , fm = [Ln 3 +]/[H 2O] qfm
δm = ⟨Sz⟩(qF ) + C D(qG)
⎛ ΔS ⧧ kT ΔH ⧧ ⎞ ⎟ (kexT )p = B exp⎜ − h RT ⎠ ⎝ R =
(18)
⧧
It has to be noted that, because the samples for variable pressure 17O NMR measurements were in cylindrical tubes, the contribution of the bulk magnetic susceptibility (BMS) shift for paramagnetic species has to be evaluated. The BMS shift contribution (ωBMS) can be calculated using eq 15: ωBMS =
P 2Δβ ⧧ P ΔV ⧧ + RT RT
D
=
⟨Sz⟩ CD
(qF ) + qG
δm CD = qF + (qG) ⟨Sz⟩ ⟨Sz⟩
(21)
(22)
According to eqs 21 and 22, a change in the number of inner sphere water molecules along the series results in a break in the plots of δm due to the change in the slope and intercept.38 As
⧧
(17) C
DOI: 10.1021/acs.inorgchem.6b00363 Inorg. Chem. XXXX, XXX, XXX−XXX
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Figure 2. 1H NMRD profiles at 298 K (top), 17O NMR temperature dependence of ln[(1/T2 − 1/T1)/Pm] (middle), and chemical shifts (Δωm) (bottom) of the [Ln(DO3A)(H2O)2] complexes (Ln = Pr, Nd, Dy, Tm, and Yb; pH 5.7; [Ln3+] ∼ 100 mM; B0 = 9.4 (●); and B0 = 18.8 T (■)). Lines correspond to the best fit of the experimental data using the parameters listed in Table 1. The dashed, dotted, and dash-dotted lines in the 1H IS OS NMRD profiles show the contributions rIS 1,d, r1,Cu, and r1 , respectively, to r1.
Figure 3. 1H NMRD profiles at 298 K (top), 17O NMR temperature dependence of ln[(1/T2 − 1/T1)/Pm] (middle), and chemical shifts (Δωm) (bottom) of the [Ln(DTTA−Me)(H2O)2]− complexes (Ln = Pr, Nd, Dy, Tm, and Yb; pH 5.7; [Ln3+] ∼ 100 mM; B0 = 9.4 (●); and B0 = 18.8 T (■)). Lines correspond to the best fit of the experimental data using the parameters listed in Table 2. The dashed, dotted, and dash-dotted lines in IS OS the 1H NMRD profiles show the contributions rIS 1,d, r1,Cu, and r1 , respectively, to r1.
shown in Figure 1, no break is observed, suggesting that q is constant along the series. Hence, in this study, the number of
inner sphere water molecules is considered to be constant (q = 2) for all [Ln(L)(H2O)q]x complexes. We furthermore assume D
DOI: 10.1021/acs.inorgchem.6b00363 Inorg. Chem. XXXX, XXX, XXX−XXX
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Inorganic Chemistry
Figure 4. 17O NMR pressure dependence of the ln[(1/T2 − 1/T1)/Pm] of [Ln(DO3A)(H2O)2] (left) and [Ln(DTTA−Me)(H2O)2]− (right) complexes (Ln = Pr, Nd, Dy, and Tm; pH 5.7; [Ln3+] ∼ 100 mM; B0 = 9.4 T; T = 22 °C). Lines correspond to the best fit of the experimental data using the parameters listed in Tables 1 and 2.
Table 1. Parameters Obtained from the Nonlinear Least Squares Fit of 1H and 17O NMR Data for [Ln(DO3A)(H2O)2] Complexesa ΔH⧧ k298 ex ΔS⧧ ΔV⧧ τ298 R,O ER rLnH Te a
(kJ mol−1) (106 s−1) (J mol−1 K−1) (cm3 mol−1) (ps) (kJ mol−1) (Å) (ps)
Pr3+
Nd3+
Gd3+13
Dy3+
Tm3+
Yb3+
23 ± 1 1.6 ± 0.1 −50 ± 2 −0.4 ± 0.2 107 ± 4 22 ± 1 3.43 ± 0.6 0.5 ± 0.2
40 ± 1 2.9 ± 0.1 +12 ± 2 −0.5 ± 0.2 105 ± 3 22 ± 1 3.41 ± 0.4 0.6 ± 0.2
33.3 ± 1.6 11 ± 1 +1.4 ± 0.5
29 ± 1 16.6 ± 0.3 −9 ± 3 −0.5 ± 0.3 98 ± 3 21 ± 1 3.28 ± 0.1 0.6 ± 0.1
13 ± 1 3.2 ± 0.1 −77 ± 3 −0.9 ± 0.5 93 ± 2 23 ± 1 3.12 ± 0.1 0.4 ± 0.1
12 ± 1 2.2 ± 0.1 −83 ± 3
97 ± 1 20.5 ± 0.3
96 ± 3 24 ± 1 3.11 ± 0.3 0.5 ± 0.3
Reported errors correspond to one standard deviation obtained by statistical analysis. For a full list of parameters, see the Supporting Information.
Table 2. Parameters Obtained from the Nonlinear Least Squares Fit of 1H and 17O NMR Data for [Ln(DTTA−Me)(H2O)2]− Complexesa ΔH⧧ k298 ex ΔS⧧ ΔV⧧ τ298 R,O ER rLnH Te a
(kJ mol−1) (106 s−1) (J mol−1 K−1) (cm3 mol−1) (ps) (kJ mol−1) (Å) (ps)
Pr3+
Nd3+
Gd3+
Dy3+
Tm3+
Yb3+
26 ± 1 3.5 ± 0.1 −31 ± 1 +7.0 ± 0.2 152 ± 4 24 ± 1 3.37 ± 0.5 0.5 ± 0.1
49 ± 1 5.8 ± 0.1 +49 ± 1 +6.8 ± 0.2 156 ± 4 21 ± 1 3.36 ± 0.7 0.6 ± 0.1
40 ± 1 22.7 ± 0.7 +29 ± 3 +7.0 ± 2 150 ± 1 20 ± 1
36 ± 1 40.6 ± 0.9 +21 ± 2 +1.8 ± 0.2 149 ± 6 26 ± 2 3.28 ± 0.1 0.7 ± 0.2
13 ± 1 26.7 ± 0.8 −60 ± 2 +0.4 ± 0.4 146 ± 3 23 ± 1 3.16 ± 0.1 0.4 ± 0.1
13 ± 1 13.9 ± 0.1 −64 ± 3 133 ± 1 23 ± 1 3.12 ± 0.1 0.5 ± 0.1
Reported errors correspond to one standard deviation obtained by statistical analysis. For a full list of parameters, see the Supporting Information.
quadrupole coupling constant of pure water (7.58 MHz).39 The other relaxation mechanisms contributed less than 15% to the overall relaxation of bound water molecules. The Ln−O distances were fixed to the values reported by D’Angelo for lanthanide aqua ions.40 From these fits, we obtained rotational correlation times τR,O for the rotational diffusion of the Ln−O vectors. In the second round, we performed a simultaneous fit of ln[(1/T2 − 1/T1)/Pm] (17O), Δωm (17O), and r1 (1H), including inner sphere (17O, 1H) and outer sphere (1H) contributions to relaxation. Dipolar and Curie relaxations for both 1H and 17O were considered. The quadrupolar relaxation for 17O relaxation is canceled in the difference 1/T2 − 1/T1. The correlation time of the Ln−H vectors (τR,H) is equal to or shorter than the correlation time of the Ln−O vectors (τR,O) due to the internal rotation of inner sphere water molecules.41 In the first test, τR,O was fixed to values obtained from the
that the coordination number remains constant with temperature and pressure variation. The small absorption band at ∼580.6 nm found for [Eu(DO3A)(H2O)2]18 could be due to the presence of a steric isomer where q is also equal to 2, similar to the SAP/TSAP isomers found for DOTA complexes.10 Variable Temperature Data. The dipolar and Curie relaxation rates used to calculate inner sphere contributions to 1 H relaxivity or 17O relaxation depend on the distance between the electron spin and the corresponding nuclear spin as rLnX−6. The only relaxation mechanism independent of the distance is the quadrupolar relaxation, which is the dominant contribution to 1/T1 of 17O. No experimental information is available for Ln−O and Ln−H distances for the compounds studied. To overcome this lack of information, we adopted the following strategy. In the first round of fitting, we fitted 17O 1/T1 for all [Ln(L)(H2O)2]x solutions. For these fits, we used the E
DOI: 10.1021/acs.inorgchem.6b00363 Inorg. Chem. XXXX, XXX, XXX−XXX
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⧧ Table 3. Water Exchange Rate Constants (k298 ex ), Activation Volumes (ΔV ), and Exchange Reaction Mechanisms for Different Lanthanide Complexes
[Ln(H2O)8/9]3+30 6 k298 ex (10 s−1)
Pr3+ Nd3+ Eu3+ Gd3+ Tb3+ Dy3+ Ho3+ Er3+ Tm3+ Yb3+ a
ΔV⧧ (cm3 mol−1)
>40 >50 804 496 386 191 118 81 41
−3.3 −5.7 −6.0 −6.6 −6.9 −6.0
(Ia) (Ia) (Ia) (Ia) (Ia) (Ia)
[Ln(DTPA-BMA) (H2O)]46 6 k298 ex (10 s−1)
ΔV⧧ (cm3 mol−1)
0.53 0.66 0.43 1.61 3.53 5.98
−0.8 (Ia) +8.5 (D) +7.3 (D) +9.8 (D) +7.3 (D) +9.4 (D)
[Ln(L3) (H2O)],51a
[Ln(DTTA-Me) (H2O)2]−b
[Ln(PDTA)(H2O)2]−45 ΔV⧧ (cm3 mol−1)
6 k298 ex (10 s−1)
6 −1 k298 ex (10 s )
0.022 0.0059 0.0013 −1.5 (Ia) −7.6 (Ia, A) −5.5 (Ia, A)
102 24 6.6 0.057
−6.5 (Ia, A) −1.2 (Ia) +7.4 (Id, D)
0.56 0.35 0.28
0.17
6 k298 ex (10 s−1)
[Ln(DO3A)(H2O)2]b
ΔV⧧ (cm3 mol−1)
6 k298 ex (10 s−1)
1.6 2.9
ΔV⧧ (cm3 mol−1) −0.4 (I) −0.5 (I)
3.5 3.8
+7.0 (D) +6.8 (D)
22.7
+7.0 (D)
11
40.6
+1.8 (Id, I)
16.6
−0.5 (I)
26.7 13.9
+0.4 (I)
3.2 2.2
−0.9 (I)
L3 = DOTA−4AmCe, studied in CD3CN. bStudied in this work.
magnitude, ranging from 0.4 to 0.7 × 10−12 s, and are independent of the chelating ligand. A magnetic field dependence of relaxivity is observed at proton frequencies of 200 MHz and higher, indicating that the Curie mechanism contributes significantly to the relaxation
previous fit, and the program was allowed to adjust the τR,H/ τR,O ratio, which should be in the range of 0.6−1.41 The fit gave values between 0.8 and 1 with an error of ∼0.2. We therefore decided to fix this ratio to one. The Ln−H distance (rLnH), which is a sixth-power weighted mean of the four Ln−H distances in [Ln(L)(H2O)2]x, was fitted. As a last approximation, we considered a unique rate constant for the exchange of the two water molecules in the q = 2 complexes. Moreover, the following parameters were fixed: aLnH = 3.6 × 10−10 m and −10 2 −1 D298 m s . The diffusion constant is assumed to LnH = 25 × 10 obey the Arrhenius law.
rates
(
1 T1,Cu
)
∝ B0 2 . As already mentioned for this mechanism,
the rotational correlation time (τR,H) is the characteristic time which allows, in principle, the calculation of τR,H. In the case of the light lanthanides, the Curie mechanism contributes only up to 20% to the overall relaxation; therefore, the rotational correlation times obtained are subject to large errors if determined by NMRD data alone. Water Exchange. Surprisingly, water exchange reactions on lanthanide complexes other than Gd3+ have not been studied extensively. Besides some slow-exchanging tetraamide complexes that are of interest as PARACEST agents for MRI,44 to our knowledge only [Ln(PDTA)(H2O)2]−45 and [Ln(DTPA− BMA)(H2O)]46 have been studied so far (Table 3). Water exchange on lanthanide aqua ions has been studied for the heavy Ln3+, from gadolinium to ytterbium,47 which are all eight-coordinated. For those aqua ions, a very fast water exchange has been found, which decreases monotonically with the ionic radius (Table 3). The lower limits detected for k298 ex for the light lanthanide ions Pr3+ and Nd3+48 as well as rate constants from complex formation with SO42−49 suggest a 3+ maximum of k298 in the ex for water exchange on [Ln(H2O)q] 47 middle of the lanthanide series. Through the use of negative activation volumes, an associative interchange mechanism has been assigned to all measured exchange reactions on aqua ions of heavy lanthanides. For lanthanide poly(aminocarboxylate) complexes, water exchange is in general notably slower compared to that of the aqua ions.47 For gadolinium complexes with DTPA or DOTA, water exchange rate constants are about 2 orders of magnitude slower compared to that of [Gd(H2O)8]3+.7,50 For water exchange on [Ln(DTPA−BMA)(H2O)], the measured rate constants increase from neodymium to holmium, which has been rationalized by an increase in steric compression on the bound water molecule, leading to a decrease of the energy barrier in the dissociative reaction (Table 3).46 The very slow exchanging [Ln(DOTA−4AmCe)(H2O)] chelates were studied in acetonitrile solution, showing a minimum of k298 ex at Eu3+.51 For [Ln(PDTA)(H2O)2]−, which has two water
■
RESULTS AND DISCUSSION The experimental data and calculated curves are shown in Figures 2−4, and the corresponding fitted parameters are reported in Tables 1 and 2. It has to be noted that, for [Sm(DTTA−Me)(H2O)2]− and [Sm(DO3A)(H2O)2], the chemical shifts were too small (Δωm ≤ 0.1 ppm) to enable the determination of the water exchange rate by 17O NMR measurements even at the high magnetic field of 18.8 T and a high concentration of metal ion chelate (100 mM). Proton Relaxivity. As shown in Figures 2 and 3, the proton relaxivity of the lanthanide complexes (other than Gd3+) is quite low (0.013−0.18 mM−1 s−1 at 20 MHz and 25 °C) compared to that of the Gd analogue [Gd(DO3A)(H2O)2] (6.0 mM−1 s−1 at 20 MHz and 25 °C).42 This has already been observed in the case of lanthanide aqua ions18, where the relaxation rates decrease by 2 orders of magnitude from 5 mM−1 s−1 for [Gd(H2O)8]3+ to 0.05 mM−1 s−1 for [Yb(H2O)8]3+ at 20 MHz and 25 °C. In the case of Gd3+, the electronic relaxation is several orders of magnitude slower compared to that of the other lanthanide ions, leading to high nuclear spin relaxation rates. The relaxation increase measured on bulk water molecules is mostly due to the inner sphere contribution; the outer sphere contribution can go up to 25% at high magnetic fields. For proton frequencies lower than 200 MHz, the NMRD profile is field independent, indicating that the relaxation mechanism is dipolar and the short, field independent electronic relaxation ⎛ ⎛μ 2⎞ ⎞ time43 is the dominating correlation time, ⎜r1 ≅ c ⎜ eff 6 ⎟Te⎟, ⎝ rLnH ⎠ ⎠ ⎝ allowing the calculation of Te. One should, however, keep in mind that the fitted Te strongly depends on rLnH. The values obtained for the lanthanides studied are of the same order of F
DOI: 10.1021/acs.inorgchem.6b00363 Inorg. Chem. XXXX, XXX, XXX−XXX
Article
Inorganic Chemistry molecules in the first coordination sphere, k298 decreases ex toward the smaller Ln3+ ions.45 This decrease is accompanied by a change in the mechanism from associatively activated to dissociatively activated.45 Water exchange rate constants measured on DO3A and DTTA−Me complexes both show a maximum of k298 ex around dysprosium (Figure 5). Water exchange on complexes of the
explanation can be found in a change of coordination geometry similar to that found for the DOTA4 and DOTMA57 complexes. Nothing is known so far concerning geometrical isomers of lanthanide DO3A complexes in solution, which is probably due to their fast rate compared to that of DOTA, arising from a missing carboxylate arm.4 For DOTA and DOTMA, it is known that water exchange rate constants vary considerably between square-antriprism (SAP) or twisted square-antiprism (TSAP) structured complexes.57,58 We also would like to stress that the pressure variation as used for the determination of ΔV ⧧ could displace the SAP/TSAP equilibrium and therefore lead to errors in the activation volumes, even if no marked change was detected on the chemical shifts measured. Water exchange on [Ln(DTTA−Me)(H2O)2]− also varies by more than a factor of 10 between Pr and Yb complexes on one side and the Dy chelate on the other side. In this case, a change in mechanism is detected from dissociative for the larger ions (Pr to Gd, ΔV⧧ ∼ +7 cm3 mol−1) to interchange for the smaller ones (Dy and Tm, ΔV⧧ = +1.8 to +0.4 cm3 mol−1). This seems contradictory because there should be less space for an incoming water molecule in the case of the smaller ions. Two explanations are possible for this surprising result. The first is a change in coordination geometry. From the absence of the formation of ternary complexes, it has been concluded that the two water molecules in [Gd(DTTA)(H2O)2]− are nonadjacent,59 even if this structure has not been confirmed by DFT calculations.56 A nonadjacent arrangement could explain the dissociative character of the water exchange on [Ln(DTTA)(H2O)2]−. A water molecule has to leave the first coordination sphere in at least a considerable amount before it can be replaced by an incoming one. Chelates with smaller cations could favor a configuration with adjacent water molecules which then exchange via an interchange mechanism. The second explanation takes into account that the exchange of the two water molecules happens at different rates: one water molecule can exchange much faster than the other. A decrease in the ionic radius of Ln3+ could have an influence on the ratio of water exchange rates and lead to smaller apparent values of ΔV⧧. It should be noted that we measure changes in the relaxation of bulk water induced by the exchange with water bound to paramagnetic species by NMR, and we cannot distinguish by this method the different binding sites on the chelates.
Figure 5. Water exchange rate constants (k298 ex ) of [Ln(DO3A)(H2O)2]− (●, dashed line) and [Ln(DTTA−Me)(H2O)2] (■, solid line) complexes. [Ln3+] ∼ 100 mM, T = 25 °C.
acyclic DTTA−Me ligand is much faster than water exchange on the macrocyclic DO3A. It has been found previously that increasing the negative charge of the complex generally accelerates water exchange in a dissociative exchange reaction.3 The higher negative charge weakens the electrostatic attraction between the 3+ lanthanide ion and the negatively charged oxygen atom of the water molecule and favors dissociation. Concerning [Ln(DO3A)(H2O)2], small activation volumes of |ΔV⧧| < 1 cm3 mol−1 indicate an interchange type of mechanism for all lanthanide complexes studied. It has been found previously that DO3A complexes of lanthanides can form ternary complexes with bidentate anions in which the two inner sphere water molecules are replaced.52−55 These formations of ternary complexes and recent results from DFT structure calculations56 show that the two inner sphere water molecules are adjacent in [Ln(DO3A)(H2O)2]. One water molecule is farther from the negative carboxylate groups (Figure 6), which perhaps allows the approach of the incoming water molecule in the interchange mechanism. The relatively constant ΔV⧧ measured for [Ln(DO3A)(H2O)2] along the lanthanide series is a bit surprising in view of the 10-fold increase and decrease in k298 ex from Pr to Dy and from Dy to Yb, respectively (Table 1 and Figure 5). A possible
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CONCLUSION A systematic study of the water exchange kinetics of selected Ln3+ complexes with DO3A and DTTA−Me as representatives for macrocyclic and acyclic ligands, respectively, is reported. The number of inner sphere water molecules is found to be constant at q = 2 for all [Ln(L)(H2O)q]x complexes studied. Water exchange rate constants measured on the DO3A and DTTA−Me complexes both show a maximum around dysprosium. Moreover, a water exchange is observed on negatively charged complexes of the DTTA−Me ligand faster than that on the complexes of DO3A. Variable pressure studies suggested an interchange type of mechanism for [Ln(DO3A)(H2O)2] complexes, as small activation volumes of |ΔV⧧|
