J. Phys. Chem. C 2007, 111, 5633-5639
5633
Understanding Paramagnetic Relaxation Phenomena for Water-Soluble Gadofullerenes Sabrina Laus,† Balaji Sitharaman,‡ EÄ va To´ th,*,†,§ Robert D. Bolskar,*,| Lothar Helm,*,† Lon J. Wilson,*,‡ and Andre´ E. Merbach† Laboratoire de Chimie Inorganique et Bioinorganique, Ecole Polytechnique Fe´ de´ rale de Lausanne, EPFL-BCH; CH-1015 Lausanne, Switzerland, Department of Chemistry, The Richard E. Smalley Center for Nanoscale Science and Technology, and the Center for Biological and EnVironmental Nanotechnology MS 60, Rice UniVersity, Houston, Texas 77251-1892, Centre de Biophysique Mole´ culaire, CNRS, rue Charles Sadron, 45071 Orle´ ans, France, and TDA Research Incorporated, 12345 West 52nd AVenue, Wheat Ridge, Colorado, 80033 ReceiVed: January 19, 2007
Water-soluble, endohedral gadofullerenes exhibit considerably higher relaxivities than clinically used Gd3+chelates and are currently explored as potential magnetic resonance imaging (MRI) contrast agents. The relaxivities of Gd@C60(OH)x (x ≈ 27) and Gd@C60[C(COOHyNa1-y)2]10 were previously found to vary with pH because of pH-dependent aggregation. By relaxometric measurements, we proved that aggregation can be suppressed by salt addition (75-100 equiv of sodium phosphate). In the aim of better understanding paramagnetic relaxation mechanisms in water-soluble gadofullerenes, we recorded variable-temperature and multiple-field 17O and 1H relaxation rates for Gd@C60(OH)x and Gd@C60[C(COOHyNa1-y)2]10 in both aggregated and disaggregated state (monomers). In the aggregated solutions, the 17O T1 and T2 values are very different. This proves the confinement of water molecules in the interstices of the aggregates which is more important for the OH than for the malonate derivative. The rapid exchange of these water molecules with bulk contributes to the high relaxivity of the aggregated gadofullerenes. After disruption of the aggregates into distinct gadofullerene molecules, the temperature-dependent proton relaxivities could be described as the sum of an outer-sphere and an inner-sphere-like mechanism. The inner-sphere-like term originates from proton exchange between the bulk and protonated OH or COOH sites. The relaxivity peak observed between 10 and 300 MHz in the nuclear magnetic relaxation dispersion (NMRD) profile evidences that the malonate groups are at least partially protonated at pH 7.4. The rotational correlation times are long (∼1.2 ns) and identical for the two gadofullerenes. The larger relaxivity of Gd@C60(OH)x as compared to Gd@ C60[C(COOHxNa1-x)2]10 at frequencies above 20 MHz is related to the larger number of protonated sites.
Introduction Derivatized, water-soluble endohedral metallofullerenes have been proposed for a variety of biomedical purposes, including contrast agent applications of the gadolinium-containing fullerenes in magnetic resonance imaging (MRI).1-4 Nowadays, MRI is one of the most powerful techniques in medical diagnosis. Its prominence is closely related to the successful use of paramagnetic contrast agents, essentially stable Gd3+ poly(aminocarboxylate) complexes which lead to an improved image contrast, thus better delineating diseased tissues.5 These paramagnetic compounds increase the relaxation rate of water protons by providing new relaxation pathways.6 Much effort has been recently devoted to the rational development of highly efficient MRI contrast agents. The gauge of efficiency of an MRI contrast agent is its proton relaxivity, r1, defined as the paramagnetic longitudinal relaxation rate enhancement of water protons by unity of concentration (mM) of the paramagnetic center. Gadofullerenes have shown promising results both in phantom and in vivo MRI studies.2,3,7 Water-soluble gadofullerenes with OH substitutes or malonate functions (Gd@C60(OH)x (x ≈ 27) and Gd@C60[C(COOHyNa1-y)2]10, respectively, Figure 1) ex* To whom correspondence should be addressed. † Ecole Polytechnique Fe ´ de´rale de Lausanne. ‡ Rice University. § CNRS. | TDA Research, Inc.
Figure 1. Depiction of Gd@C60(OH)x C60[C(COOHyNa1-y)2]10 (bottom).
(top)
and
Gd@
hibit relaxivities that are up to 20 times higher than that of Gd3+chelates in current clinical use and have been therefore proposed by several groups as a new generation of MRI contrast media.1-4 The high relaxivity values of the gadofullerenes have been attributed to a large number of exchangeable protons and water molecules close to the paramagnetic center and to slow tumbling arising from self-aggregation. In addition to remarkable relax-
10.1021/jp070458o CCC: $37.00 © 2007 American Chemical Society Published on Web 03/28/2007
5634 J. Phys. Chem. C, Vol. 111, No. 15, 2007 ivities, another important feature of gadofullerenes is the incorporation of the toxic Gd3+ ion inside the fullerene carbon cage, which prevents metal ion release and thus represents a safe alternative to coordination compounds, as long as the number of hydroxyl groups is not too large.8 Moreover, watersoluble gadofullerenes exhibit strongly pH-dependent relaxivities. For this reason, they represent the current tendency to develop paramagnetic agents4,9,10 which are reporters of the biochemical environment and may offer a way to distinguish tumors from healthy tissues on the basis of their different pH. In addition, these high-relaxivity compounds also provide a versatile scaffold for attachment of any (bio)chemical function for targeting purposes.11 In a previous study on salt-free water-soluble gadofullerene solutions, we have shown that the presence of a relaxivity hump in the nuclear magnetic relaxation dispersion (NMRD) profiles at magnetic fields common for MRI (0.7-1.4 T, proton Larmor frequency of 30-60 MHz) as characteristic of slow rotational motion.4 This slow rotation was explained in terms of selfaggregation,12 which is a common phenomenon for aqueous solutions of water-soluble fullerenes.13-15 Actually, previous studies have shown that intermolecular aggregation occurs for a variety of functionalized fullerenes with alcohol,13 malonate,15-17 quaternary ammonium,15,18 sulfonate,19 and cyclodextrin substituents.20 On the basis of a combination of proton relaxivity and dynamic light-scattering studies, we have also shown that the aggregates formed in aqueous solutions of Gd@C60(OH)x and Gd@C60[C(COOHyNa1-y)2]10 can be disrupted by addition of salts.21 For instance, increasing the NaCl concentration in a Gd@C60(OH)x solution from 0 to 150 mM results in a decrease of the hydrodynamic diameter from 810 to 121 nm and a concomitant drop in the relaxivity from 83.2 to 31.6 mM-1 s-1 (37 °C, 60 MHz). Upon addition of salt, the aggregates are broken up into smaller and more rapidly tumbling entities which leads to a dramatic decrease in relaxivity. Phosphate salts proved to be a particularly efficient way to destroy the aggregates. The disruption of gadofullerene aggregates in the presence of salt might have important implications for biological or biomedical applications, although we have also demonstrated that saltinduced disaggregation is a relatively slow process in vitro with half-lives about 30-40 min. This implies that a salt-free gadofullerene contrast agent solution injected into the blood stream will be mainly present in aggregated (high relaxivity) form during the time frame of a typical MRI examination. A similar aggregation of a water-soluble gadofullerene has been reported for [Gd@C82O6(OH)16(NHCH2COOH)8]x.22 It was revealed that the aggregation of the gadofullerene studied is pH-dependent. According to the authors, the self-aggregation is dominated by hydrogen-bonding effects at pH 7 and below. Under alkaline conditions (pH 9), the aggregation follows a crystal-growth mechanism, resulting in the formation of large and rigid particles.22 In the aggregated gadofullerene solutions, there is a distribution of species of various sizes, which makes it difficult to obtain a correct and quantitative analysis of the experimental waterproton relaxation rates. The objective of the present study was to measure and analyze proton relaxation rates for OH- and malonate-derivatized Gd@C60 fullerenes in the totally disaggregated state. Under such conditions, the microscopic parameters that we calculate from the relaxation rates can be attributed to a single, nonaggregated species, and this can provide insight into the mechanisms that are involved in the paramagnetic relaxation of gadofullerenes. To this end, proton relaxivities have been first determined for both gadofullerenols and malonated
Laus et al. gadofullerenes at varying phosphate concentration to establish the experimental conditions that allow for full destruction of the aggregates. Then, multiple magnetic field and variabletemperature 17O transverse and longitudinal relaxation rates have been measured and variable-temperature NMRD profiles have been recorded for both aggregated and disaggregated forms under physiological pH. Finally, the NMRD profiles of the disrupted aggregates of Gd@C60(OH)x and Gd@ C60[C(COOHyNa1-y)2]10 have been analyzed with the traditional Solomon-Bloembergen-Morgan (SBM) equations to yield parameters describing proton exchange and rotation. Experimental Section Sample Preparation. Gd@C60(OH)x (x ≈ 27) and Gd@ C60[C(COOHyNa1-y)2]10 were synthesized and characterized as previously reported.1,4 The absence of free, nonencapsulated Gd3+ was verified as already described.4 The Gd3+ content of the samples was assessed by ICP-AES measurements. The preparation of the solutions for the inductively coupled plasmaatomic emmission spectroscopy (ICP-AES) analysis first involved digestion by 65% HNO3. The solution was carefully heated until a solid residue was obtained, and then any remaining carbonaceous material was further digested using 30% H2O2. This solution was again carefully heated until a solid residue was obtained, which was then dissolved in 2% HNO3. The Gdcontent of the fullerene derivatives used in this study was 2.68% (m/m) for Gd@C60(OH)x and 1.54% (m/m) for Gd@ C60[C(COOHxyNa1-y)2]10. The difference between measured and theoretically calculated Gd-content is due to empty fullerene derivatives. Stock solutions of the gadofullerenes were prepared by weight and then were diluted to the desired concentration. The pH of all solutions was adjusted to 7.4 by addition of phosphate buffer or known amounts of perchloric acid (for aggregated solutions) and was measured with a glass electrode calibrated with Metrohm buffers. The Gd concentrations of the gadofullerene solutions were as follows: Gd@C60(OH)x: 0.499 mM (1H NMRD, variable phosphate concentration study, cphosphate ) 0-100 mM), 0.519 mM (1H NMRD, disaggregated solution, cphosphate ) 100 mM), 0.499 mM (1H NMRD, aggregated solution), 0.01026 mol kg-1 of solvent H2O (17O NMR, disaggregated solution, cphosphate ) 1 M, 1 M phosphate as an external diamagnetic reference), 0.01046 mol kg-1 (17O NMR, aggregated solution); Gd@C60[C(COOHyNa1-y)2]10: 0.665 mM (1H NMRD, variable phosphate concentration study, cphosphate ) 0-100 mM), 0.701 mM (1H NMRD, disaggregated solution, cphosphate ) 100 mM), 0.665 mM (1H NMRD, aggregated solution), 0.00996 mol kg-1 (17O NMR, disaggregated solution, cphosphate ) 1 M, 1 M phosphate as an external diamagnetic reference), 0.00831 mol kg-1 (17O NMR, aggregated solution). All solutions for 17O NMR were enriched to 1% with 17O-enriched water (Isotrade GmbH) to improve sensitivity. 17O NMR Spectroscopy. Transverse and longitudinal 17O relaxation rates and chemical shifts were measured between 275 and 366 K for aqueous gadofullerene solutions. The data were recorded on Bruker DRX and ARX 400 (9.4 T, 54.2 MHz) and Bruker Avance-200 spectrometers (4.7 T, 27.1 MHz). Bruker VT 3000 temperature control units were used to maintain a constant temperature, which was measured by a substitution technique.23 The samples were sealed in glass spheres, fitting into 10-mm NMR tubes, to eliminate susceptibility corrections to the chemical shifts.24 Longitudinal relaxation rates, 1/T1, were obtained by the inversion recovery method, and transverse
Relaxation for Water-Soluble Gadofullerenes relaxation rates, 1/T2, were measured by the Carr-PurcellMeiboom-Gill spin echo technique.25,26 Proton Relaxivity. 1/T1 NMRD measurements were performed on a Stelar Spinmaster FFC fast field cycling relaxometer covering a continuum of magnetic fields from 2.35 × 10-4 to 0.47 T (corresponding to a proton Larmor frequency range of 0.01-20 MHz) and equipped with a VTC90 temperature control unit. The temperature was fixed by a gas flow. At higher fields, the 1H relaxivity measurements were performed on Bruker Minispecs mq30 (30 MHz), mq40 (40 MHz), and mq60 (60 MHz) and on Bruker 1.18 T (50 MHz), 2.35 T (100 MHz), and 4.70 T (200 MHz) cryomagnets connected to a Bruker Avance-200 console. In each case, the temperature was measured by a substitution technique. The least-squares fits of the NMRD relaxation data were performed with the Visualiseur/ Optimiseur programs working on a Matlab platform.27,28 Molecular Dynamics (MD) Simulations. Three classical molecular dynamics simulations have been performed on a PC using the program Tinker.29 In each simulation, one derivatized fullerene containing a gadolinium ion has been put into a periodic water box with 462 (Gd@C60(OH)x simulations), respectively 441 (Gd@C60[C(COOHyNa1-y)2]10 simulations), TIP3P-water molecules. Radial distribution functions for gadolinium-OH and gadolinium-COOH protons, as well as GdHwater and Gd-Owater, have been calculated from 70-ps trajectories using the routine Radial coming with Tinker. Results and Discussion In the literature, diverse relaxivity values have been reported for a given gadofullerene species (e.g., for Gd@C82(OH)x Shukla et al. published 47 mM-1 s-1 (25 °C, 9.4 T),30 Wilson and coworkers published 20 mM-1 s-1 (40 °C, 0.47 T),31 and Mikawa et al. published 81 mM-1 s-1 (25 °C, 1.0 T)3). We have recently proposed that the different states of aggregation resulting from different salt contents could account for this discrepancy.21 The synthetic methods used for derivatization of gadofullerenes involve various salts, and some may remain in the sample after purification. In this way, the relaxivity of different gadofullerene samples could be influenced by the differing amount and nature of these salts from one preparation to another. Similarly, the relaxivity of gadofullerene preparations produced by the same synthetic route can also vary from batch to batch; for example, we have reported relaxivities of 83.2 mM-1 s-1 and 24.0 mM-1 s-1 for a previous batch of Gd@C60(OH)x and Gd@ C60[C(COOHyNa1-y)2]10, respectively (37 °C, 60 MHz),21 in contrast to the values of 97.7 mM-1 s-1 and 14.8 mM-1 s-1 presented in this work for new batches. Prior to a comprehensive NMRD study, it was necessary to systematically determine for each batch the salt concentration needed to fully disrupt the aggregates. Relaxivity values were thus measured for the gadofullerenes with varying amounts of sodium phosphate as the disaggregating agent.21 As Figure 2 shows, above a certain sodium phosphate concentration the relaxivities reach a minimum plateau which we interpret to mean that the gadofullerenes cannot be further disrupted and are therefore present in a monomeric form (vide infra). The variation of the relaxivity from batch to batch is much smaller in the disaggregated state than in the aggregated state (11.2 mM-1 s-1 and 6.2 mM-1 s-1 compared to 13.1 mM-1 s-1 and 4.6 mM-1 s-1 for previous and new batches of Gd@C60(OH)x and Gd@C60[C(COOHyNa1-y)2]10, respectively, 37 °C, 60 MHz). On the other hand, it appears that the number of phosphate equivalents needed to reach maximum disaggregation depends on the nature of the functional groups: >100 equiv for Gd@C60(OH)x and >75 equiv for Gd@C60[C(COOHyNa1-y)2]10.
J. Phys. Chem. C, Vol. 111, No. 15, 2007 5635
Figure 2. 1H relaxivities of Gd@C60(OH)x (9) (cGd(III) ) 0.499 mM) and Gd@C60[C(COOHyNa1-y)2]10 (2) (cGd(III) ) 0.665 mM) at variable sodium phosphate concentration, pH 7.4, 25 °C, 60 MHz. The curves are tendency lines to guide the eyes. 17O NMR Measurements. The large number of water molecules in the proximity of the fullerene surface, in addition to slow tumbling, has been often evoked to account for the high relaxivities of gadofullerenes.1,2 With the aim of better understanding the role of close water molecules in the relaxation processes of gadofullerenes, we have performed 17O longitudinal and transverse relaxation rate measurements for Gd@C60(OH)x and Gd@C60[C(COOHxNa1-x)2]10. In contrast to a previous 17O NMR study,4 here we have measured relaxation rates in both aggregated and disaggregated solutions (see Figure 3). Since the relaxation rates obtained at 9.4 and 4.7 T are very similar, we present only the high field data. For the aggregated systems, the transverse relaxation rates are significantly higher than the longitudinal ones, whereas this difference strongly diminishes or vanishes for the disaggregated solutions (Figure 3). In general, the split between 1/T1 and 1/T2 gives information on the nature of the water molecules in the vicinity of the paramagnetic center. For traditional Gd3+ poly(amino carboxylate) complexes, identical values of 1/T1 and 1/T2 imply a purely outer-sphere relaxation, that is, the interaction between the water-oxygen nuclei and the paramagnetic center is governed by random translational motion.32 The large difference between 1/T1 and 1/T2 for the aggregated gadofullerene systems clearly indicates that certain water molecules are confined to the interstices inside the fullerene aggregates. The diffusion of such confined water molecules to the exterior of the assembly is slower than the mutual translational diffusion between bulk water molecules and paramagnetic centers. For both systems, the temperature dependence of 1/T2 (Figure 3a and 3c) shows no maximum and even no inflection point which allows us to conclude, that for both aggregates, exchange between confined water molecules and bulk water molecules is considerably faster than exchange between a first-sphere water molecule of a traditional Gd3+ poly(amino carboxylate) complex and the bulk. The confinement of water molecules inside the aggregates is in full agreement with a previous SANS and SAXS (SANS: small-angle neutron scattering, SAXS: small-angle X-ray scattering) study of sulfonate-derivatized C60 where 2500 water molecules were found to be present in each aggregate formed by seven fullerenes.19,33 A quantitative analysis of the transverse 17O relaxation rates is not possible at this time since we lack not only the number of water molecules involved in the exchange between the confined and bulk state but also an appropriate theory for electron-spin relaxation of gadofullerenes. The difference between the transverse and longitudinal 17O relaxation rates is much larger for Gd@C60(OH)x (Figure 3a and 3b) than for Gd@C60[C(COOHyNa1-y)2]10 (Figure 3c and 3d). On the basis of this result, we hypothesize that, for the Gd@C60(OH)x aggregates, there are more water molecules
5636 J. Phys. Chem. C, Vol. 111, No. 15, 2007
Laus et al.
Figure 3. Temperature dependence of longitudinal (9) and transverse (2) 17O relaxation rates at B ) 9.4 T. Left: Gd@C60(OH)x (a) in the aggregated form (cGd(III) ) 0.01046 mol kg-1) and (b) in the disaggregated form (cGd(III) ) 0.01026 mol kg-1, cphosphate ) 1 M); right: Gd@C60[C(COOHyNa1-y)2]10 (c) in the aggregated form (cGd(III) ) 0.00831 mol kg-1) and (d) in the disaggregated form (cGd(III) ) 0.00996 mol kg-1, cphosphate ) 1 M).
confined or they are more tightly bound and remain in a more restricted space. This is also consistent with the observation that higher phosphate equivalents are needed to disrupt the gadofullerenol aggregates (>100 equiv vs >75 for Gd@C60(OH)x and Gd@C60[C(COOHyNa1-y)2]10, respectively. Given the similar size of the two aggregated compounds at physiological pH (DH ∼ 450 nm),12 this result implies that aggregates of gadofullerenols are held together by stronger forces than those of the malonate derivatives. The present findings about aggregated fullerenes also have consequences concerning the water proton relaxivities. In the case of Gd@C60(OH)x, the stronger interaction between molecules can make the macromolecular assemblies more rigid. Moreover, the number of water molecules confined in the interstices of the aggregates, and thus in the vicinity of the paramagnetic center, can be also significantly greater than for the malonate derivative. Both of these effects could contribute to a considerably higher proton relaxivity for aggregated Gd@C60(OH)x as compared to Gd@C60[C(COOHyNa1-y)2]10.4 Proton Relaxivity Measurements. Fully understanding the relaxation mechanisms that lead to the remarkable relaxivities of gadofullerenes remains a challenge. In a previous study, we measured and analyzed variable-field proton relaxivities for Gd@C60[C(COOHyNa1-y)2]10, however, only in the aggregated state.4 Thus, the microscopic parameters obtained in the fit (the rotational correlation time τR and the exchange rate kex, for example) could not be attributed to one single species. Moreover, for Gd@C60(OH)x no sensible fit of the NMRD data could be obtained. In this work, we have recorded and analyzed NMRD profiles for disaggregated solutions (containing individual metallofullerene molecules) of both Gd@C60[C(COOHyNa1-y)2]10 and Gd@C60(OH)x for the first time. In the disaggregated state, we propose that the observed relaxivities originate from an “outer-sphere” effect because of the translational diffusion of water molecules in the surroundings of the paramagnetic gadofullerene and from an “inner-spherelike” contribution related to the exchange of protons between the protonation sites on the malonate or OH groups and the bulk. In the case of gadofullerenes, we do not speak about an
inner-sphere mechanism for water molecules in the same sense as for Gd3+ chelates; in our case, no water molecules are directly bonded to the paramagnetic ion which is encapsulated within the fullerene cage. However, the residence time of the protons on the malonate and OH groups is sufficiently long so that the correlation time for the interaction between the 1H nuclear spin and the Gd3+ electron spin is modulated by the rotational motion of the individual gadofullerenes. This paramagnetic relaxation effect is then transmitted to the bulk via chemical exchange between these OH and COOH protons and bulk water protons. The inner-sphere-like contribution to proton relaxivity is proportional to the number of hydroxyl and carboxylate protons on the derivatized fullerenes. We assumed that on average 27 protons are available on each gadofullerenol molecule since all hydroxyl functions are protonated at pH 7.4 (pK ) 9.8 and 18 for phenol and tert-butanol, respectively).34,35 In reality, for the gadofullerenol we can expect a pK higher than that of the phenol, since the anion of the phenol is stabilized by mesomerism, whereas the geometry of fullerenol hinders this stabilization. For the malonate gadofullerene derivative, the number of protonated carboxylate functions is more difficult to establish. Given the protonation constants for malonic acid, pK1 ) 1.9 and pK2 ) 6.2, in a first approximation, one could consider that practically all of the 20 carboxylate functions are deprotonated at pH 7.4. However, a complete deprotonation of all carboxylates would mean that only the outer-sphere contribution to relaxivity is active and no relaxivity hump should be found at frequencies between 10 and 100 MHz. The presence of such a hump (vide infra) shows that at least some carboxylates must be protonated at the pH of the experiment. The protonation of carboxylate functional groups at pH 7.4 is conceivable if one considers that the fullerene cage bears 20 protonating sites and therefore behaves as a polyelectrolyte. The acid-base properties of ionizable groups in macromolecules will differ significantly from those of isolated protonable functions on individual molecules because of electrostatic interactions between the close sites. Therefore, the pK values of the gadofullerene derivative will differ strongly from those of the malonic acid and can span over several logarithmic units.30 In addition
Relaxation for Water-Soluble Gadofullerenes
Figure 4. Radial distribution functions, g(r), from classical molecular dynamics simulations. (a) Gd@C60(OH)27: Gd-hydroxyl protons (black), Gd-Hwater (blue), Gd-Owater (red) and (b) Gd@C60[C(COOH)2]10 (full lines) and Gd@C60[C(COOH)(COO-)]10 (dashed lines): Gd-carboxylate protons (black), Gd-Hwater (blue), Gd-Owater (red).
to the electrostatic effects between neighboring protonable sites, hydrogen-bonding interactions can also contribute to the increased pK values as compared to isolated protonable functionalities.36 For example, a remarkably higher pK value of a copolymer functionalized with acrylic acids has been observed upon hydrogen-bonding interaction.37 As a consequence of the significant increase in the pK values induced by both of the above cited interactions, we will assume that 10 carboxylate sites are protonated on each gadofullerene molecule. The measurement of the protonation state of the malonate gadofullerene derivative is not so simple in the disaggregated form. In the disaggregated gadofullerene solution, a very high concentration of phosphate is present whose protonation can “hide” the protonation of the malonate. To calculate the inner-sphere-like and the outer-sphere contributions to the overall water proton relaxivity, reasonable gadolinium-proton distances have been estimated. This task is complicated by the fact that the gadolinium is not in the center of the C60-cage.38-40 The amplitude of the displacement from the center was shown by extended X-ray absorption fine structure (EXAFS) to be 1.4 Å (Eu@C60) and by density functional theory (DFT) to be 1.2 ( 0.1 Å (La@C60).35,41-43 Moreover, a static view of endohedral fullerenes does not reflect reality. Ab initio molecular dynamics simulations on La@C60 have shown that the metal diffuses very fast at room temperature, tangentially to the carbon cage, and completes one entire round in only ∼1.1 ps.35 Such fast dynamic processes are completely averaged on the NMR time scale. Estimations of Gd-H distances have been obtained from classical molecular dynamics simulations. Figure 4 shows radial distribution functions, g(r), for Gd@C60(OH)27 in aqueous solution. For Gdhydroxyl protons, a broad distribution between 4.6 and 7.2 Å is observed. A mean distance of rGdH ) 5.8 Å was calculated from the 1/r6-weighted distances. The distance of closest
J. Phys. Chem. C, Vol. 111, No. 15, 2007 5637 approach for water protons can be estimated from g(r) for Gdwater protons (Figure 4a) to be aGdH ) 6.0 Å. For the malonate derivative, two simulations have been performed: one with fully protonated carboxylated groups, Gd@C60[C(COOH)2]10, and one with one carboxylate group deprotonated per malonate, Gd@C60[C(COOH)(COO-)]10. Radial distribution functions lead to large peaks between 6 and 8.5-9 Å for both simulations (Figure 4b). Interestingly, from these simulations, it follows that water protons can approach the gadolinium as close as the carboxylate protons. The weighted mean gadolinium-carboxylate proton distance from the MD simulations is about 7 Å for both simulations. Such a long distance can, however, not explain the relaxivity hump between 10 and 100 MHz, even if protonation of all carboxylate groups is assumed. We therefore fixed rGdH at 6 Å, the same value as for the distance of closest approach for water protons. Given the large number of parameters involved in the analysis of the 1H NMRD data, the fullerene-water mutual diffusion constant, DGdH298 and its activation energy, EDGdH, were fixed at 2 × 10-9 m2 s-1 and 25 kJ mol-1, respectively.44 To analyze the NMRD profiles, the magnetic field and temperature dependences of the electron spin relaxation of Gd3+ in gadofullerenes must be known. We have previously shown that considering a scalar coupling between electron spins on Gd3+ (S ) 7/2) and the fullerene cage (S ) 1/2) does not provide understanding of the electron spin relaxation and, in particular, does not agree with the experimental EPR data.4 An all-electron relativistic density functional study by Lu et al. showed that the electronic structure of Gd@C60 is characterized by a nearly complete transfer of the three outmost valence electrons of gadolinium to the C60-cage.43 Following this study, the gadolinium 4f spins are nearly intact and antiferromagnetically coupled with that on C60. In our previous analysis of the 1H NMRD data for Gd@C [C(COOH Na 4 60 y 1-y)2]10 aggregates, 45 we used the Florence computer program of Bertini et al. which was developed for slowly rotating systems by taking into account both transient and static contributions to the zero-field splitting, the main interaction for electron spin relaxation of Gd3+. Disaggregated, single-molecule gadofullerenes are much smaller (
