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Towards the Prediction of Water Exchange Rates in MRI Contrast Agents: A DFT Study Martín Regueiro-Figueroa, and Carlos Platas-Iglesias J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.5b01728 • Publication Date (Web): 22 May 2015 Downloaded from http://pubs.acs.org on May 26, 2015

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The Journal of Physical Chemistry

Towards the Prediction of Water Exchange Rates in MRI Contrast Agents: A DFT Study Martín Regueiro-Figueroa,† and Carlos Platas-Iglesias,*,† †

Departamento de Química Fundamental, Universidade da Coruña, Campus da Zapateira, Rúa da Fraga

10, 15008 A Coruña, Spain. AUTHOR EMAIL ADDRESS [email protected]

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Abstract We present a theoretical investigation of Gd-Owater bonds in different complexes relevant as contrast agents in MRI. The analysis of the Ln-Owater distances, electron density (ρBCP) and electron localization function (ELF) at the bond critical points of [Ln(DOTA)(H2O)]- and [Ln(DTPA-BMA)(H2O)] indicates that the strength of the Ln-Owater bonds follows the order DTPA-BMA > DOTA (M isomer) > DOTA (m isomer). The ELF values decrease along the 4f period as the Ln-Owater bonds get shorter, in line with the labile capping bond phenomenon. Extension of these calculations to other Gd3+ complexes allowed us to correlate the experimentally observed water exchange rates and the calculated ρBCP and ELF values. The water exchange reaction becomes faster as the Gd-Owater bonds are weakened, which is reflected in longer bond distances and lower values of ρBCP and ELF. DKH2 calculations show that the two coordinated water molecules may also have significantly different 17O hyperfine coupling constants (HFCCs).


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Introduction Magnetic Resonance Imaging (MRI) is a powerful technique used by radiologists for medical diagnosis. MRI uses the 1H NMR signal of water molecules present in the body to obtain high-resolution 3D images of tissues and organs. Image contrast may be improved by the administration of the so called contrast agents (CAs), which are paramagnetic probes that enhance the image contrast by preferentially influencing the longitudinal and/or transverse relaxation times of water molecules in the vicinity of the complex.1-4 Most of the commercially available CAs are gadolinium(III) complexes with poly(aminocarboxylate) ligands ensuring a high stability to prevent the release of the toxic metal ion in vivo.5 CAs used in clinical practice contain a water molecule coordinated to the metal ion that exchanges rapidly with the bulk water, although some stable Gd3+ complexes containing two coordinated water molecules have been also proposed.6-11 The presence of two water molecules in the Gd3+ coordination sphere increases the efficiency of the CA, which is often evaluated in vitro in terms of its relaxivity, defined as the longitudinal relaxation rate enhancement of water proton nuclei per mM concentration of gadolinium ions.1 Indeed, the inner-sphere contribution to relaxivity is proportional to the number of water molecules present in the coordination sphere of the paramagnetic ion (often denoted as q). Additionally, the inner-sphere contribution depending also on four correlation times: the residence time of a water proton in the inner coordination sphere (τm), the rotational correlation time of the Gd···H vector (τR), and the longitudinal and transverse electronic relaxation times of the metal ion (T1e and T2e).12-15 The residence time of a water molecule in the inner coordination sphere of Gd3+ complexes (τm = 1/kex, where kex is the water exchange rate) covers a range of about four orders of magnitude from the longest determined for dota-tetraamide derivatives (τm298 = 8-20 µs as estimated for the Eu3+ complex of DOTAM)16 to the shortest measured for the aqua ion17 and the Gd3+ complex of BPEDP5- (τm298 ~ 1.31.4 ns, Scheme 1).18,19 It is well known that LnIII DOTA-like complexes exist in solution as two diastereoisomeric forms (m=minor and M=major) that differ by the layout of their acetate arms: the M


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isomer has a square antiprismatic geometry, whereas the m isomer has a twisted square antiprismatic coordination.20 The water exchange could be studied on both isomers for the Eu3+ complexes of dotatetraamides.16,21 Water exchange on these complexes is sufficiently slow that 1H and 17O NMR signals of bound water could be observed. It was found that the water exchange at 298 K is independent of the chelating ligand, and that water exchange on the m isomer is about two orders of magnitude faster than on the M isomer.22 Among the different factors that have been identified to accelerate the water exchange of the coordinated water molecule in Gd3+ complexes are: i) increasing the negative charge of the complex,17 and ii) increasing the steric compression around the water coordination site.23-25 Both effects facilitate the departure of the coordinated water molecule in a dissociative process, which is the most common mechanism responsible for the water exchange reaction in nine-coordinate Gd3+ complexes.1 Indeed, a few examples of Gd3+ complexes with associatively activated water exchange have been reported,26,27 the most prominent being the family of HOPO complexes developed by Raymond.28 The residence time of water molecules in the inner coordination sphere of Gd3+ is among the most important parameters that determine the relaxivity of a CA, particularly if the rotational correlation time is simultaneously optimized.29 The aim of this work is to develop a simple methodology based on DFT to rationalize and predict the water exchange rates of potential Gd3+-based MRI contrast agents. For this purpose we have investigated the Gd3+ complexes with the ligands shown in Chart 1. Complexes [Gd(DTPA)(H2O)]2-

(gadopentetate

dimeglumine,

Magnevist),

[Gd(DTPA-BMA)(H2O)]

(gadodiamide, Omniscam) and [Gd(DOTA)(H2O)]- (gadoterate meglumine, Dotarem) are currently used as CAs in clinical practice.30 The Eu3+ complex of DOTAM is known to provide very slow water exchange rates,16 while the complexes of EGTA4- and BPEDP6- are among the Gd3+ chelates endowed with a very fast water exchange rate,18,31 which in the case of [Gd(HBPEDP)(H2O)]2- is ca. 140 times faster than that of [Gd(BPEDA)(H2O)]-.32 Finally, in the last decade intense efforts have been made to optimize the proton relaxivity of MRI CAs by increasing the number of water molecules coordinated to the Gd3+ ion.6-11 Thus, we have also investigated complexes [Gd(DTTA)(H2O)2]-, [Gd(DO3A)(H2O)2] ACS Paragon Plus Environment

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and [Gd(AZZTA)(H2O)2]- as representatives of potential MRI CAs containing two coordinated water molecules. For the latter two complexes the mean residence time of the two coordinated water molecules was determined using 17O NMR and/or 1H NMRD measurements.9,33 However, it is not yet known if the two coordinated water molecules contribute to the same extent to the observed NMR chemical shifts and relaxation rates, or if on the contrary the two water molecules have very different residence times in the Gd3+ coordination sphere. Chart 1. Chemical structure of the ligands discussed in this work.

Besides the analysis of the molecular structures of these complexes obtained using DFT calculations, we also report wave function analyses based on the atoms-in-molecules theory of Bader.34 Recent computational studies performed on the Ln3+ aqua-ions and some Ln3+ chelates have shown to provide ACS Paragon Plus Environment

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valuable information regarding the preferred coordination numbers and the exchange rates of coordinated water molecules.35,36

Computational Methods All calculations were performed employing DFT within the hybrid meta-GGA approximation with the TPSSh exchange-correlation functional,37 and the Gaussian 09 package (Revision D.01).38 The TPSSh functional was shown to provide more accurate bond distances of the metal coordination sphere in lanthanide complexes than the popular B3LYP functional.39 In previous papers we have shown that mixed cluster/continuum approaches with the explicit inclusion of two second-sphere water molecules is required to obtain accurate metal-OH2 distances and 17O hyperfine coupling constants of both Gd3+ and Mn2+

complexes

relevant

as

MRI CAs.40-42

Thus,

full

geometry optimizations

of the

[Gd(DTPA)(H2O)]2-·2H2O, [Ln(DTPA-BMA)(H2O)]·2H2O, [Ln(DOTA)(H2O)]-·2H2O, (Ln = La-Lu, except Pm), [Eu(DOTAM)(H2O)]3+·2H2O, [Gd(BPEDA)(H2O)]-·2H2O, [Gd(HBPEDP)(H2O)]2-·2H2O, [Gd(EGTA)(H2O)]-·2H2O,

[Gd(DTTA)(H2O)2]-·4H2O,

[Gd(DO3A)(H2O)2]·4H2O

and

[Gd(AZZTA)(H2O)2]-·4H2O were performed in aqueous solution by using the large-core relativistic effective core potential (LCRECP) of Dolg et al. and the related (7s6p5d)/[5s4p3d]-GTO valence basis set for the lanthanides,43 and the standard 6-31G(d,p) basis set for C, H, N, O and P atoms. This LCRECP includes 46+4fn electrons in the core for the lanthanide, leaving the outermost 11 electrons (5s, 5p, 5d and 6s) to be treated explicitly. LCRECPs provide good results in DFT studies that focus on the structure, dynamics and estimates of relative energies of Ln3+ complexes, as the 4f orbitals do not significantly contribute to bonding due to their limited radial extension as compared to the 5d and 6s shells.44,45 Since LCRECP calculations include the 4f electrons in the core, they were conducted on a pseudo-singlet state configuration. 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. For comparative purposes, we have ACS Paragon Plus Environment

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carried out geometry optimizations of the Gd3+ complexes using the small-core RECPs of Dolg et al. (SCRECP),46 which include 28 electrons in the core for the lanthanides, and the associated ECP28MWB_GUESS basis set.47 Isotropic

17

O

and

1

H

HFCCs

(Aiso

values)

in

the

[Gd(DTTA)(H2O)2]-·4H2O,

[Gd(DO3A)(H2O)2]·4H2O and [Gd(AZZTA)(H2O)2]-·4H2O systems were calculated in aqueous solution using the TPSSh functional in combination with the all-electron second order Douglas-Kroll-Hess (DKH2) method as implemented in Gaussian09.48,49 In these calculations we used the all-electron scalar relativistic basis set of Pantazis and Neese for Gd50 and the EPR-III basis sets of Barone51 for the ligand atoms. Bulk solvent effects (water) were evaluated by using the polarizable continuum model (PCM), in which the solute cavity is built as an envelope of spheres centred on atoms or atomic groups with appropriate radii. In particular, we used the integral equation formalism (IEFPCM)52 variant as implemented in Gaussian 09. The universal force field radii (UFF)53 scaled by a factor of 1.1 were used to define the solute cavities. Wave function analysis was carried out by computing the electron localization function (ELF),54 the electron density (ρ) and its Laplacian (∇2ρ) at the bond critical points (BCPs)34 with the computer program Multiwfn 3.2.55 The binding energies (BEs) of the coordinated water molecule were calculated at the TPSSh/LCRECP/6-31G(d,p) level, and they include Basis Set Superposition Error (BSSE) corrections obtained with the standard Counterpoise method56 with calculations performed in the gasphase.57 Molecular graphics were generated using USCF Chimera (version 1.8).58

Results and Discussion The [Ln(DTPA-BMA)(H2O)]·2H2O and [Ln(DOTA)(H2O)]-·2H2O systems. The optimized structures of the [Gd(DTPA-BMA)(H2O)]·2H2O and [Gd(DOTA)(H2O)]-·2H2O complexes optimized using the LCRECP approximation and a slightly different basis set to describe the ligand atoms (6-31G(d)) have been presented in a earlier contribution.40 These calculations have been extended to the whole series of lanthanide(III) complexes (Ln3+ = La3+-Lu3+, except Pm3+) to gain insight into the factors 7 ACS Paragon Plus Environment


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that lead to significantly different water exchange rates for these complexes. For the [Ln(DOTA)(H2O)]-·2H2O complexes our calculations provided the expected m and M diastereoisomers as minimum energy conformations, which provide twisted and regular square antiprismatic geometries, respectively.20 The water molecule is capping the square face of the coordination polyhedra defined by the four oxygen atoms of the acetate groups coordinating to the metal ion. The distance between the metal ion and the oxygen atoms of the coordinated water molecule calculated for the M isomer of [Gd(DOTA)(H2O)]-·2H2O (2.494 Å) is in good agreement with the experimental value determined using X-ray diffraction (2.456 Å).59 The optimized geometry of [Gd(DTPA-BMA)(H2O)]·2H2O is shown in Figure 1. The coordination polyhedron is best described as a monocapped square antiprism, where the basal plane is defined by the amine nitrogen atoms N1, N2 and N3 and oxygen atom O5, while the upper plane is delineated by O1, O2, O3 and O4. The two least squares planes defining the coordination polyhedron are virtually parallel (3.7º). The mean twist angle of the two square planes (40.1º) is close to the ideal value expected for a square antiprism (45º). The oxygen atom of the coordinated water molecule is capping the upper plane. Previous studies have shown that LCRECP calculations provide somewhat longer bond distances of the metal coordination environment than computations based on the SCRECP approach.60-62 Our results are in line with these studies, as SCRECP calculations give bond distances typically 0.04-0.06 Å shorter than the LCRECP counterparts (see Figure 1 and Figures S1-S7, Supporting Information). However, the values of the electron localization function (ELF), the electron density (ρ) and its Laplacian (∇2ρ) obtained with LC and SC calculations for Gd complexes are very similar (see below). Thus, considering the important computational effort required to carry out geometry optimizations using small-core calculations

we

have

studied

the

whole

series

of

[Ln(DTPA-BMA)(H2O)]·2H2O

and

[Ln(DOTA)(H2O)]-·2H2O systems (Ln = La to Lu, except Pm) using the LC approach.


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Figure 1. Optimized geometry of the [Gd(DTPA-BMA)(H2O)]·2H2O complex obtained with DFT calculations performed in aqueous solution at the TPSSh/LCRECP/6-31G(d,p) level. Hydrogen atoms, except those of water molecules, are omitted for simplicity. Bond distances (Å) of the Gd3+ coordination environment (values obtained with the SCRECP are given within parentheses): Gd-O1w 2.482 (2.447); Gd-O1 2.375 (2.320); Gd-O2 2.517 (2.436); Gd-O3 2.520 (2.441); Gd-O4 2.380 (2.342); Gd-O5 2.352 (2.298); Gd-N1 2.761 (2.699); Gd-N2 2.648 (2.577); Gd-N3 2.801 (2.746).

The Ln-Ow distances of the [Ln(DTPA-BMA)(H2O)]·2H2O and [Ln(DOTA)(H2O)]-·2H2O systems calculated along the lanthanide series provide insight into the different lability of the coordination water molecules in these systems. Indeed, the La-Ow distances calculated for the complex of DTPA-BMA3and the two isomers of the complex with DOTA4- are very similar, differing by less than 0.011 Å (Figure 2). However, the Ln-Ow distances diverge as the ionic radius of the Ln3+ ion decreases across the series, and by the center of the lanthanide series the Gd-Ow distance calculated for the m isomer of


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[Gd(DOTA)(H2O)]-·2H2O (2.514 Å) is significantly longer than that found for the M isomer (2.494 Å). The Gd-Ow distance is shorter in the case of the complex of DTPA-BMA3- complex (2.482 Å).

Figure 2. Distances between the metal ion and the oxygen atom of the coordinated water molecule obtained with DFT calculations for the [Ln(DTPA-BMA)(H2O)]·2H2O and [Ln(DOTA)(H2O)]-·2H2O systems (Ln = La-Lu, except Pm). The solid lines represent quadratic fits of the data according to y = a + bx + cx2 with R2 > 0.998.

Different experimental63 and theoretical64,65 studies showed that the Ln-donor bond distances generally decrease quadratically along the series. The Ln-Ow distances obtained for [Ln(DTPABMA)(H2O)]·2H2O and [Ln(DOTA)(H2O)]-·2H2O complexes indeed follow quadratic trends with respect to the number of 4f electrons of the Ln3+ ion (Figure 2), providing the fitting parameters shown ACS Paragon Plus Environment

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in Table 1. Parameters a and c do not change significantly for the three series of complexes investigated, but both b and the normalized parameter b* become more negative following the sequence DOTA (m isomer) – DOTA (M isomer) – DTPA-BMA. Thus, an increased constraint for the coordination of the water molecule to the Ln3+ ions across the 4f period is reflected in more negative b and b* values.

Table 1. Results of the quadratic fits (y = a + bx + cx2) of the Ln-Ow distances calculated for [Ln(DTPA-BMA)(H2O)]·2H2O and [Ln(DOTA)(H2O)]-·2H2O complexes. DOTA (m)

DOTA (M)

DTPA-BMA

a(σ)

2.613(1)

2.603(1)

2.602(2)

102 b(σ)

-1.75(3)

-1.93(5)

-2.14(6)

104 c(σ)

4.7(2)

4.6(3)

5.1(4)

103 b* = b/a

-6.714

-7.435

-8.222

104 c* = c/a

1.780

1.753

1.966

102 c/b

-2.65

-2.36

-2.39

R2

0.9994

0.9989

0.9986

The analysis of the Ln-Ow distances indicates that the coordinated water molecule is more tightly bound to the metal ion in the [Ln(DTPA-BMA)(H2O)]·2H2O complexes than in the [Ln(DOTA)(H2O)]-·2H2O analogues, and that the inner-sphere water molecule is more labile in the m isomer than in the M one. If the water exchange reaction is to follow a dissociatively activated mechanism, which requires the rupture of the Ln-Ow bond to give an eight-coordinated transition state, one would expect that the residence time of the coordinated water molecule increases as the Ln-Ow distances become shorter and the b* parameter more negative.


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Figure 3. Electron density (ρ) and electron localization function (ELF) at the Ln-Ow critical points calculated for the [Ln(DTPA-BMA)(H2O)]·2H2O and [Ln(DOTA)(H2O)]-·2H2O systems (Ln = La-Lu, except Pm). The solid lines are simply a guide for the eye.


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The strength of the Ln-Ow bonds was further investigated by calculating the electron density (ρ) and electron localization function (ELF) at the critical points of the concerned bonds. Larger values of the ρBCP and ELF indicate stronger bonds. Our results (Figure 3) show that both ρBCP and ELF follow the trend DTPA-BMA > DOTA (M isomer) > DOTA (m isomer) along the whole 4f period from La to Lu. The ρBCP values obtained for DTPA-BMA and the M isomer of DOTA show saturation behavior along the lanthanide series, while in the case of the m isomer of DOTA ρBCP increases at the beginning of the series, reaches a maximum and then decreases. This suggests that the interaction between the inner-sphere water molecule and the metal ion is significantly weakened by the end of the lanthanide series for the m isomer of DOTA complexes. Interestingly, the m isomers of DOTA of the smallest lanthanide ions were found to lose their inner-sphere water molecule.20 The ELF values obtained for the three series of geometries decrease along the whole 4f period, which is in line with a weakening of the Ln-Ow bonds in spite of the fact that they become shorter. This is in agreement with the shorter and weaker capping bond phenomenon discovered in previous studies.35,36 Besides, this is also in line with the acceleration of the water exchange reaction in [Ln(DTPA-BMA)(H2O)] complexes across the 4f period,66 as weaker Ln-Ow bonds are expected to provide faster water exchange rates in dissociatively activated processes. The relationship between strength of the Ln-Ow bonds and water exchange rates. The results presented in the previous section encouraged us to extend our studies to different Gd3+ (or Eu3+) complexes containing one coordinated water molecule. Thus, we performed geometry optimizations of the

[Gd(DTPA)(H2O)]2-·2H2O,

[Eu(DOTAM)(H2O)]3+·2H2O,

[Gd(BPEDA)(H2O)]-·2H2O,

[Gd(HBPEDP)(H2O)]2-·2H2O and [Gd(EGTA)(H2O)]-·2H2O systems. In the case of DOTAM we have chosen Eu3+ instead of Gd3+ as in the former case the exchange rates of the coordinated water molecule could be measured for the two isomers (m and M) independently. Given the similar ionic radius and coordination chemistry of Eu3+ and Gd3+, it is expected that the water exchange rates of coordinated water molecules in these complexes are very similar. The optimized geometries of the [Eu(DOTAM)(H2O)]3+·2H2O systems are very similar to those of the DOTA4- complexes, and do not 13 ACS Paragon Plus Environment


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deserve additional discussion (see Supporting Information for details). Furthermore, the optimized structure of [Gd(DTPA)(H2O)]2-·2H2O is very similar to that of the complex with the bisamide derivative

described

above

(see

Figure

1).

Concerning

the

[Gd(BPEDA)(H2O)]-·2H2O,

[Gd(HBPEDP)(H2O)]2-·2H2O complexes, they present similar geometries (Figure 4, see also Supporting Information). The bond distances reported in Figure 4 and Figures S1-S7 (Supporting Information) confirm that calculations using the SC approximation provide slightly shorter lanthanide-donor distances than those employing the SC approach.

Figure 4. Optimized geometry of the [Gd(HBPEDP)(H2O)]2-·2H2O complex obtained with DFT calculations performed in aqueous solution at the TPSSh/LCRECP/6-31G(d,p) level. Hydrogen atoms, except those of water molecules, are omitted for simplicity. Bond distances (Å) of the Gd3+ coordination environment (values obtained with the SCRECP are given within parentheses): Gd-O1w 2.553 (2.520); Gd-O1 2.447 (2.432); Gd-O2 2.273 (2.190); Gd-O3 2.428 (2.388); Gd-O4 2.441 (2.406); Gd-N1 2.947 (2.833); Gd-N2 2.863 (2.832); Gd-N3 2.660 (2.636); Gd-N4 2.711 (2.658).


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The assignment of a coordination polyhedron to describe the metal coordination environments in [Gd(BPEDA)(H2O)]-·2H2O, [Gd(HBPEDP)(H2O)]2-·2H2O is not straightforward. Thus, we performed continuous shape measures [S(A)] with the assistance of the SHAPE program.67 The shape measure S(A) equals 0 for a structure fully coincident in shape with the reference polyhedron, while the maximum allowed value of S(A) is 100. The analysis of the coordination polyhedra in these complexes provides

shape

measures

for

a

spherical-relaxed

capped

cube

of

2.96

and

2.57

for

[Gd(BPEDA)(H2O)]-·2H2O, [Gd(HBPEDP)(H2O)]2-·2H2O, respectively, while a hula-hoop gives shape measures of 3.96 and 3.90, respectively.68 The remaining reference polyhedra considered in the analysis of the metal coordination environments give even higher S(A) values [S(A) = 4.4 – 30]. Thus, the metal coordination environment these complexes can be described as a distorted capped cube, where two of the quasi-parallel quadrangular faces are defined by O1-N1-N2-N3 and O2-O3-O1w-N4. One of the oxygen atoms of a picolinate moiety (O4) is capping the latter plane. It is worth mentioning that the Gd-O4 distance is considerably shorter than the Gd-Ow one, in spite of the fact that the water molecule resides in one of the eight vertex of the cube and not in a capping position. Thus, in spite of the geometrical description of the coordination polyhedron in these complexes it is clear that the water molecule provides a rather weak interaction with the Gd3+ ion. The optimized structure of [Gd(EGTA)(H2O)]-·2H2O provides a coordination environment very similar to those reported in the solid state for the Er3+ complex and in a recent computational study.69,6 Shape measures indicate that the coordination polyhedron can be best described as a monocapped square antiprism [S(A) = 0.87], while a tricapped trigonal prism gives only a slightly higher S(A) value (1.43). In any of the two descriptions the coordinated water molecule occupies a capping position. The analysis of the Gd-Ow distances shows that longer distances are related to shorter residence times of the coordinated water molecule (Table 2), in line with the results obtained for [Gd(HP-DO3A)] using ab initio molecular dynamics simulations.70 Besides, the binding energies of the coordinated water molecule generally decrease as the water exchange rate becomes faster (Table S6, Supporting Information). Furthermore, while binding energies provide a rather poor linear correlation with the ACS Paragon Plus Environment

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measured water exchange rates plotted in a logarithmic scale (R2 ~ 0.87, Figure S9, Supporting Information), the ρBCP and ELF values calculated at the critical points of the Gd-Ow bonds correlate reasonably well (R2 ~ 0.95, Figure 5). The linear correlation observed with respect to logkex is not surprising, as water exchange rates often obey the Eyring equation, which presents an exponential dependence of kex with the term ∆S‡/R - ∆H‡/RT, with ∆S‡ and ∆H‡ being the entropy and enthalpy of activation. Our attempts to correlate the water exchange rate with the strength of the Gd-Ow bonds, as estimated by the ρBCP and ELF values, obviously neglect any possible role of entropy changes. In spite of this simplification, the results shown in Figure 5 clearly show that faster water exchange rates are characterized by weaker Gd-Ow bonds. This suggests that the rate of the water exchange reaction is mainly controlled by the energy cost of breaking the Gd-Ow bond to reach an eight-coordinate transition state. This is in line with different kinetic studies have shown that the T∆S‡ term represents less than 30% of the activation free energy ∆G‡ at 298K.17 The nature of the bonding between the Ln3+ ion and the water molecule can be characterized by the values of ρBCP and its Laplacian (∇2ρBCP). As a general rule, ρBCP values above 0.20 a. u. and negative ∇2ρBCP values indicate a covalent bond, while ρBCP < 0.10 a. u. and positive ∇2ρBCP values are characteristic of ionic bonds.71 The data shown in Table 2 provide ρBCP values of ca. 0.03-0.04 a.u. with the Laplacian being small and positive. This is characteristic of a predominantly electrostatic nature of the Ln-OW interaction, as would be expected. Interestingly, the ρBCP and ELF values obtained with the large-core and small core RECPs are very similar (Table 2 and Table S5, Supporting Information), providing correlations with logkex with comparable quality (Figure S8, Supporting Information). Furthermore, the two core sizes give also similar values of the Laplacian of the electron density (∇2ρ) at the bond critical points (Table 2 and Table S5, Supporting Information). These results show that wave function analyses performed using both LC and SC calculations provide very similar results.


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Table 2. Calculated Gd-Ow distances (Å), electron density (ρ, a.u.), electron localization function (ELF) at the critical points of the Gd-Ow bonds for [GdL(H2O)q]n+/-·yH2O complexes (q = 1 , 2; y = 2, 4), and water exchange rates of the coordinated water molecule (kex298, ×106 s-1) reported in the literature. L

Gd-Ow

q/y

ρBCP

ELF

∇2ρBCP

kex298

kex298 (cald.)i

EGTA

2.540

1/2

0.0350

0.0968

0.1406

31a

50(4)

DTPA

2.501

1/2

0.0372

0.0979

0.1569

3.3b

19(9)

DTPA-BMA

2.482

1/2

0.0398

0.1072

0.1648

0.45b

1.0(0.6)

BPEDP

2.553

1/2

0.0337

0.0929

0.1353

700c

204(67) d

DOTAM (M)

2.377

1/2

0.0489

0.1158

0.2249

0.0083

DOTAM (m)

2.444

1/2

0.0429

0.1108

0.1855

0.327d

0.122(0.047)

DOTA (M)

2.494

1/2

0.0382

0.1034

0.1581

4.1e

3.7(1.5)

DOTA (m)

2.514

1/2

0.0367

0.1012

0.1492

BPEDA

2.514

1/2

0.0371

0.1014

0.1509

5.0f

8.5(3.0)

DO3A (M)

2.499

2/4

0.0381

0.1016

0.1586

10g

5.3(0.2)

0.0368

0.1001

0.1512

0.0391

0.1043

0.1637

0.0374

0.0984

0.1566

15.6(6.3)

0.0383

0.0979

0.1655

16.2(11.4)

0.0334

0.0925

0.1337

248(78)

2.510 AAZTA

2.484

2/4

2.505 DTTA

2.483

2/4

2.558 a

Ref. 20.

b

Ref. 9.

c

Ref. 10a.

d

10.8(4.7)

12.2(2.2) 11h

Data for the Eu3+ complex from Ref. 8.

contributions of the M and m isomers was not considered.

f

Ref. 21.

0.0049(0.0027)

g

2.1(0.6)

e

Ref. 9. The different

Average value for the two

coordinated water molecules, Ref. 22. h Average value for the two coordinated water molecules, Ref. 5. i Average values obtained using the linear correlations of ρBCP and ELF data, with standard deviations within parentheses.


17


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Page 18 of 32

Figure 5. Plot of the water exchange rates measured for Gd3+ complexes versus the electron density (ρ) and electron localization function (ELF) at the critical points of the Gd-Ow bonds. Note the logarithmic scale of the x axis and the break introduced in the y axis for better visualization. The solid lines correspond to the linear least-square fits of the data: ρBCP = 0.05941 – 0.00316 logkex298 and ELF = 0.13532 – 0.00503 logkex298.

The linear correlations shown in Figure 5 were used to estimate the water exchange rates of the coordinated water molecules in the complexes investigated in this work. The results given in Table 2 correspond to the average values of the data obtained using ρBCP and ELF values. The calculated kex298 data follow reasonably well the trend evidenced by the experimental data. In the case of [Eu(DOTAM)(H2O)]3+ the kex298 value present a good quantitative agreement with the experimental ACS Paragon Plus Environment

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data, the water exchange rate calculated for the m isomer being ~25 times faster than that of the M isomer. For [Gd(DOTA)(H2O)]- the water exchange determined experimentally did not take into account the contributions of the two diastereoisomers present in solution. According to our calculations the exchange rate in the m isomer is about 3 times faster than in the M form. The agreement between the experimental and calculated water exchange rates of [Gd(DTPA-BMA)(H2O)] is excellent, even when in our analysis we have considered only one of the four isomers of this complex present in solution (the cis isomer).72 This is in line with a previous computational study, which showed that the distance between the metal ion and the coordinated water molecule assumes similar values in all the isomers.73 Water exchange rates in bis-hydrated complexes. Recent computational studies have introduced the concept of labile capping bonds,24,25 which can become weaker across the lanthanide series even if they are shorter. Given the results reported in the previous section, it is reasonable to expect that Gd3+ complexes containing two coordinated water molecules have two significantly different Gd-Ow distances, and therefore water exchange rates. In particular, this is expected in those cases where one of the water molecules occupies a capping position while the second one is located in one of the vertexes of the polyhedron. To address this issue, we have performed geometry optimizations of the [Gd(DO3A)(H2O)2]·4H2O system, which presents a monocapped square antiprismatic coordination polyhedron. The Gd-Ow distance involving the water molecule placed in the capping position (2.510 Å) is somewhat longer than that occupying a position in the upper plane of the square antiprism (2.499 Å). As a result, the ρBCP and ELF values obtained for the two water molecules are significantly different. The water exchange rate of the water molecule in the capping position, estimated using the linear relationships obtained for the q = 1 complexes, is about twice the value for the water molecule at one of the vertexes of the polyhedron. These results therefore suggest that the two coordinated water molecules in Gd3+-DO3A derivatives might have significantly different water exchange rates. This is in line with some experimental studies, which showed that monodentate binding of acetate, fluoride and hydrogenphosphate to Gd3+ DO3A-trisamide derivatives resulted in a marked increase of the rate of


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Page 20 of 32

water exchange, which was explained by coordination of the anion in one of the positions of the polyhedron, leaving the water molecule in the capping position.74

Figure 6. Optimized geometry of the [Gd(AZZTA)(H2O)2]-·4H2O complex obtained with DFT calculations performed in aqueous solution at the TPSSh/LCRECP/6-31G(d,p) level. Hydrogen atoms, except those of water molecules, are omitted for simplicity. Bond distances (Å) of the Gd3+ coordination environment: Gd-O1w 2.484; Gd-O2w 2.505; Gd-O1 2.421; Gd-O2 2.416; Gd-O3 2.430; Gd-O4 2.374; Gd-N1 2.718; Gd-N2 2.799; Gd-N3 2.614.

Geometry optimizations were also performed for the [Gd(DTTA)(H2O)2]-·4H2O and [Gd(AZZTA)(H2O)2]-·4H2O systems as representatives of Gd3+ complexes containing two inner-sphere water molecules. The optimized geometry of the [Gd(AZZTA)(H2O)2]-·4H2O complex is shown in Figure 6 (see Supporting Information for [Gd(DTTA)(H2O)2]-·4H2O). Each coordinated water molecule is involved in hydrogen-bonding interaction with two second-sphere water molecules, which in turn ACS Paragon Plus Environment

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form hydrogen bonds with oxygen atoms of the carboxylate groups. The analysis of the coordination polyhedral using the SHAPE program45 indicates that two coordination polyhedral, capped square antiprism

and

muffin,

provide

very

similar

shape

measures

(1.76

and

1.37

for

[Gd(AZZTA)(H2O)2]-·4H2O; 1.20 and 1.37 for [Gd(DTTA)(H2O)2]-·4H2O). In spite of the description of the coordination polyhedron, it is clear that the two coordinated water molecules present very different Gd-Ow distances (Table 2 and Figure 6), which in the case of the DTTA complex differ by up to 0.075 Å). The subsequent estimation of the water exchange rates using the calculated ρBCP and ELF values (Table 2) confirms that the two coordinated water molecules are endowed with very different water exchange rates. As a result, the water exchange rates determined experimentally for these complexes likely reflect averaged values of the actual water exchange rates of the two coordinated water molecules.

Table 3. Calculated hyperfine coupling constants (Aiso, MHz) for [Gd(DTTA)(H2O)2]-·4H2O, [Gd(DO3A)(H2O)2]·4H2O and [Gd(AZZTA)(H2O)2]-·4H2O complexes (TPSSh/DKH2/Neese/EPR-III). L

Gd-Ow (Å)

17

DO3A (M)

2.499

0.528

0.094/0.089

2.510

0.518

0.072/0.066

2.484

0.550

0.092/0.068

2.505

0.502

0.045/0.088

2.483

0.599

0.072/0.055

2.558

0.367

0.063/0.059

AAZTA

DTTA

1

O

H

HFCCs of the coordinated water molecules in bis-hydrated complexes. In a recent paper we reported a computational study of the 17O and 1H hyperfine coupling constants (HFCCs) of the coordinated water molecules in different Gd3+ complexes relevant as MRI contrast agents.28 We have shown that the 17O HFCCs on inner-sphere water molecules are very sensitive both to the Gd-O distances and the orientation of the coordinated water molecule plane with respect to the Gd-O vector. We therefore have extended

these

studies

to

the

bis-hydrated

complexes


[Gd(DTTA)(H2O)2]-·4H2O, 21


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Page 22 of 32

[Gd(DO3A)(H2O)2]·4H2O and [Gd(AZZTA)(H2O)2]-·4H2O to analyze whether the two coordinated water molecules are characterized by significantly different HFCCs or not.

The

17

O

HFCCs

calculated

for

the

two

coordinated

water

molecules

of

[Gd(DO3A)(H2O)2]·4H2O and [Gd(AZZTA)(H2O)2]-·4H2O are rather similar, being within the range 0.50 - 0.55 MHz. These values are close to those generally obtained both from 17O NMR measurements and DFT calculations for Gd3+ complexes containing one coordinated water molecule (0.37-0.57 MHz).9,28,75 The Aiso values calculated for [Gd(DO3A)(H2O)2]·4H2O are close to those obtained experimentally (0.56-0.67 MHz, 3.5 – 4.2 ×106 rad s-1).22 The 17O HFCCs of the two coordinated water molecules of [Gd(DTTA)(H2O)2]-·4H2O differ significantly (~0.23 MHz) as a consequence of the rather different Gd-Ow distances. Even so, both values are comparable to those reported for different Gd3+ monohydrated complexes. The HFCCs obtained for different DTTA4- derivatives containing two coordinated water molecules (0.59-0.62 MHz) are very close to the Aiso value calculated for the water molecule with the shortest Gd-Ow distance.76,77 Finally, as expected the calculated 1H isotropic HFCCs for the systems investigated in this work are very small.7879

Conclusions In summary, we have shown that DFT calculations and wave function analyses provide insight into the water exchange rates of nine-coordinated Gd3+ complexes relevant as contrast agents in MRI. The water exchange reaction in these complexes follows a dissociatively activated mechanism whose rate determining step is likely to be the departure of the inner-sphere water molecule to give an eightcoordinate transition state. In particular, our calculations have shown that: (i) Fast water exchange rates are related to weaker Gd-Ow bonds, which is reflected in longer bond distances and lower electron density (ρ) and electron localization function (ELF) values at the bond critical points. (ii) The water exchange rates of the two water molecules in Gd3+ complexes with q = 2 might be significantly different. In the case of DO3A-like systems the water molecule occupying the capping 22 ACS Paragon Plus Environment

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position is considerably more labile than that placed at one of the vertexes of the coordination polyhedron. (iii) The two coordinated water molecules in q = 2 complexes may have significantly different

17

O

HFCCs associated to different strengths of the Gd-Ow bonds. Acknowledgment. The authors are also indebted to Centro de Supercomputación de Galicia (CESGA) for providing the computer facilities. Supporting Information Available. Optimized geometries, bond distances, calculated ρBCP and ELF values, and optimized Cartesian coordinates for the systems investigated in this work. This material is available free of charge via the Internet at http://pubs.acs.org.

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O NMR Observation of Coordinated Water on

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For Table of Contents Only:

DFT calculations reveal that fast water exchange rates of Gd3+-based contrast agents are related to weaker Gd-Ow bonds, which is reflected in longer bond distances and lower electron density (ρ) and electron localization function (ELF) values at the bond critical points.


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Toward the Prediction of Water Exchange Rates in ... - ACS Publications

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