Nuclear- and Electron-Spin Relaxation Rates in Symmetrical Iron

6301

J. Phys. Chem. 1995, 99, 6301-6308

Nuclear- and Electron-Spin Relaxation Rates in Symmetrical Iron, Manganese, and Gadolinium Ions Sandip K. Sur and Robert G. Bryant* Chemistry Department, University of Virginia, McCormick Road, Charlottesville, Virginia 22901 Received: April 8, 1994; In Final Form: November 9, 1994@

Measurements of water 'H spin-lattice relaxation rates as a function of magnetic field strength are reported for aqueous solutions of iron(II1) and manganese(I1) and X-band EPR measurements are reported for manganese(II), iron@), and gadolinium(II1) solutions that provide an improved understanding of what controls nuclear- and electron-spin relaxation in these electronically symmetric paramagnetic centers. The electronspin relaxation rates of the iron(II1) and gadolinium(II1) aquo ions are higher than in other symmetrical complexes of these metal centers, which appears to be caused by intramolecular motions of the coordinated water molecules. The water proton relaxation rate at low magnetic field strengths in aqueous manganese(I1) and iron(II1) solutions increases with increasing perchloric acid concentration, which results in part from an increase in the metal-proton hyperfine coupling constant. In the iron(II1) case, the additional relaxation efficiency is interpreted in terms of a change in the orientation of the coordinated water molecule that brings the protons closer to the metal center. The gadolinium(II1) electron relaxation rate decreases with increasing perchloric acid and glycerol concentration, which is interpreted in terms of a change in the number of coordinated water molecules changing from 9 to 8. Electron-spin relaxation rates estimated from electronspin resonance line widths of iron(II1) and Gd(II1) ions in symmetric complexes such as [FeF6I3- or [FeClJ are long and demonstrate that construction of complex species with long electron-spin relaxation times that will be efficient water proton spin relaxation agents should be possible using iron(II1) centers.

Nuclear magnetic relaxation of water protons is crucial to contrast control and interpretation of magnetic resonance images.' The nuclear-spin relaxation process and its regulation by paramagnetic metal ions is of general interest in its own right and raises several interesting structural and dynamical questions. Of particular interest are the metal complexes of half-filled d or f orbitals that have S electronic ground-state configurations because the electron relaxation times in these complexes are relatively long and permit the development of high nuclear-spin relaxation rates in the solvent water protons. Thus, complexes of gadolinium(II1) are used as contrast agents for medical magnetic imaging. Manganese(I1) complexes are nearly as efficient but suffer from lower chemical stability. However, iron(III), which is isoelectronic with manganese(I1) and may be of lower toxicity, is generally thought to be a poor relaxation agent because the iron(II1) ion changes the water proton spin-lattice relaxation rate relatively little compared with manganese(II)ion. These observations are generally understood in terms of the Solomon, Bloembergen, and Morgan equation^,^-^ which are thoroughly discussed elsewhere5-' but reproduced here for convenience. The paramagnetic contribution from fistcoordination-sphere water molecules to the water proton spinlattice relaxation rate is

where rexis the mean residence time of the water in the first coordination sphere, PM is the probability that a proton is in the first coordination sphere, which is given by q[M]/[H20], where q is the number of coordinated water molecules, the square brackets indicating molar concentration, and @

where y1 and ys are the nuclear and electron magnetogyric ratios, W I and u sare the Lamor frequencies for the nuclear and electron spins, h is Planck's constant divided by 2x, T M - H is the distance from the metal center to the proton of a coordinated water molecule, S is the spin of the paramagnetic ion, A is the electron-proton hyperfine coupling constant, and the correlation times are -1 zck-1 -- trot

+",, + -1

k = 1, 2

(3) (4)

where rrotis the rotational correlation time of the intermoment vector and SI and zs2 are the electron-spin longitudinal and transverse relaxation times respectively. The electron-spin relaxation times depend on the magnetic field strength.*-'O The present work is focused on low-molecular-weight complexes so that the rotational correlation time is generally near 40 ps, while the chemical exchange times of either the whole solvent molecule or the labile protons are longer and may usually be neglected in eqs 3 and 4. The model usually assumed for the electron relaxation rate is

Abstract published in Advance ACS Abstracts, April 1, 1995.

0022-365419.512099-6301$09.00/0

tSk-l

0 1995 American Chemical Society

6302 J. Phys. Chem., Vol. 99, No. 17, 1995

Sur and Bryant

90

where ZSOis the electron-spin relaxation time at zero field and is a measure of the strength of the interaction causing the electron relaxation, which is usually identified with fluctuations in the zero-field splitting. tVis the correlation time for these fluctuations, and OS is the electron Larmor frequency. The outersphere or translational contributions to the water proton relaxation rate were computed assuming an unmodified translational diffusion coefficient for water in the vicinity of these ions and Freed’s theory,l1-l3 as discussed by Lester and Bryant.I4 In the iron case, the electron relaxation rate estimate was included as a component of the calculation. These values were subtracted from the observed relaxation rates, and the remainder of the relaxation was analyzed using eqs 1-6. The electron relaxation time contribution to the effective correlation time for the electron-nuclear coupling is of major interest and ranges from several nanoseconds to tens of picoseconds for the aquo complexes of Mn(II), Gd(III), and Fe(1II). A key question is why is the electron relaxation time of the hexaaquoiron(1II) complex so different from that of the hexaaquomanganese(I1) complex and, in general, how to make electron relaxation times longer so that they do not become limiting factors in eqs 3 and 4 when the metal center is coordinated to a complex ligand with a larger rotational correlation time. We address here nuclear- and electron-spin relaxation in the aquo complexes as a function of several variables including viscosity and co-solvent activity and examine electron-spin relaxation in several symmetrical complexes that shed light on the processes controlling these relaxation rates. Experimental Section

FeC136H20, Fe(C104)36H20, and NH4F were purchased from Strem Chemicals, Inc., Newburyport, MA. Anhydrous potassium fluoride and sodium fluoride were purchased from Eastman Kodak Co. Analytical grade acetonitrile, glycerol, and MnSOqH20 were obtained from Mallinckrodt, Paris, KY. Lithium chloride, MnCly6Hz0 were Baker Analyzed reagent grade chemicals. Perchloric acid (70 wt % aqueous), triflic acid, and sodium 3-(trimethylsilyl)propionate (TSP) were purchased from Aldrich Chemical Co. Deuterated water was obtained from Cambridge Isotope Laboratory, Cambridge, MA. Water used in all experiments was routinely taken from a Bamsted Millipore filtration system with both ionic and organic sections that used house-deionized water as the feed. The hexafluoroferrate(II1) complex was prepared typically by dissolving 0.023 g of Fe(C104)3*6H20 in about 15 mL of deionized water in a 25-mL volumetric flask to form a yellow solution. A solution made by dissolving 1.85 g of m F in 5 mL of deionized water was added dropwise with stimng to the yellow iron(II1) perchlorate solution until the yellow color disappeared. The resulting solution was diluted to the mark with deionized water to yield a 2.0 mM solution at pH 7.0. Addition of the yellow iron(III) perchlorate solution to the NI&F solution yields a precipitate. Precipitation was also observed when alkali-metal fluorides were used in place of ammonium fluoride. All EPR measurements were carried out at ambient laboratory temperature on a Bruker ESP-300 spectrometer at X-band using 1OO-kHzmagnetic field modulation with a modulation amplitude of 0.05-5 G. Microwave power was set at 10 mW. DPPH (2,2’-diphenyl-l-picrylhydrazyl)was used to calibrate the magnetic field assuming a g factor of 2.0036. The pH’s of the

t

75

E 60

U

45

30

15

0 0.01

0.10

1.00

10.00

100.00

’H Larmor Frequency (MHz) Figure 1. ‘H relaxivity, Le., the nuclear magnetic relaxation rate per mM of metal, plotted as a function of magnetic field strength expressed as the proton Larmor frequency for aqueous solutions of manganese(I1) and iron(II1) at 298 K. (A) A, 0.10 mM manganese(I1) chloride in 2.80 M perchloric acid; (B) A, 0.1 mM aqueous manganese(I1)chloride at pH 6.6; (C) W, 0.5 mM iron(II1) perchlorate in 2.80 M perchloric acid; (D) 0,0.5 mM iron(II1) perchlorate in 0.28 M perchloric acid; (E) 0,2.0 mM iron(II1)perchlorate in water at pH 3.1; (F) 2.0 mM [FeF# in 2.0 M ammonium fluoride at pH 7. The ordinate of the

+,

graph is relaxivity per mM of metal; the concentrations listed are those of the solutions actually measured. solutions were measured either using a Orion Model 720A or a Coming Model 240 pH meter. The ’H nuclear magnetic relaxation rates were measured over a range of magnetic field strengths corresponding to proton Larmor frequencies between 0.01 and 30 MHz using a fieldcycling spectrometer described elsewhere.I6 ‘H NMR spectra of aqueous solutions of iron(III) perchlorate (10 mM) and manganese@) sulfate (20 mM) in perchloric acid were measured as a function of temperature on a Varian Unity Plus NMR spectrometer operating at 499.91 MHz. The chemical shifts of the water protons were measured with respect to internal TSP protons taken as 0.0 ppm. The proton spinlattice relaxation times were measured at 500 MHz using the standard inversion-recovery sequence. Results and Discussion

Figure 1 shows the nuclear magnetic relaxation dispersion (NMRD) profiles for the water protons in aqueous solutions of iron@) and manganese(I1) at several pH values. The iron(1II) solutions are notoriously complex in the dilute acid range because of hydrolysis of the coordinated water and the formation of bridged p-hydroxo and di-p-hydroxo species, among other^.'^ The addition of acids with coordinating counterions such as hydrochloric acid’* may seriously complicate the solution chemistry because of anions substituting for water in the first coordination sphere. For example, the data of Koenig and coworkers on the hexaaquomanganese(II) ion relaxivity, presented in several place^'^-^^ but which appear to be the same data set, are complicated by the presence of 0.1 M acetate ion. This concentration is sufficient to cause formation of acetatomanganese(I1) complexes and reduce substantially the effective concentration of the hexaaquomanganese(I1) ion22 and to compromise the quantitative discussions. We have used the sulfate salt and no supporting electrolyte to minimize coordination problems at the expense of imprecisely controlling the pH of the unbuffered solution. However, hydrolysis of manganese(I1) is minimal below pH 7J2,” Similarly, this group has reported relaxivities for iron(1II) solutions in hydrochloric acid, but while the hydrochloric acid may minimize hydrolysis and associated problems, the iron(III) forms complexes with chloride

Relaxation Rates in Symmetrical Fe, Mn, and Gd 400

300

;

7

s-

6

s

r

n I

I

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J. Phys. Chem., Vol. 99, No. 17, 1995 6303

though they differ somewhat from those utilized by Bertini and co-workers recently.27 Of particular importance to the analysis of the data in Figure 1 are the changes observed in the values of the proton-electron hyperfine coupling constant derived from the chemical shift data and summarized in Table 1. When the perchloric acid concentration is raised in either the Mn(II) or the Fe(III) solution, the value of the hyperfine coupling constant increases. Although these changes in the hyperfine coupling constant are only about 20%, they enter the relaxation equations as the square and thus have a substantial effect on the low magnetic field relaxation rates as discussed below. The results in Table 1 reduce the number of adjustable parameters required to compute the relaxation rates shown in Figure 1. The solid lines through the data of Figure 1 were computed using the parameters summarized in Table 2, and represent best fits to eqs 1-4. In the manganese(I1) case, the only parameters adjusted were the intermoment distance, the rotational correlation time, and zso. The magnetic field dependence for the electron relaxation time is not detectable from the water proton spin-lattice relaxation data because the electron relaxation time is much longer than the rotational correlation time which dominates eq 3. Any dispersion in the electron relaxation time will only make its contribution to the effective correlation time smaller. Therefore, no attempt was made to determine a value for z, although the value of a few picoseconds is consistent with the spirit of the model and has been suggested earlier.4,27The increase in the proton-manganese@) hyperfine coupling constant on the addition of high concentrations of perchloric acid is clearly reflected in the increased water proton relaxation rate at low field shown in curve A compared with curve B of Figure 1. The changes in the high-field portion of the dispersion curves for manganese(I1) ion are small by comparison. We assume that the rotational correlation time increases in direct proportion to the increase in viscosity. Thus, in the 2.8 M perchloric acid solutions, we assume that the rotational correlation time increases by 15.4% and leave only QO and the intermoment distance to be determined from the shape of the relaxation dispersion curve. This approach yields a decrease of 14% in zso, and the intermoment distance increases from 2.75 to 2.82 A. An interesting point about the value of the intermoment distance for the hexaaquomanganese(I1) complex is that the value of 2.75 8, is shorter than implied by X-ray data obtained on crystalline salts. The values reported for the Mn-0 distance range from 2.18 to 2.22 8,.28,29The oxygen-proton distance reported for water in ice30*31 ranges from 0.97 to 1.00 A; for the gas phase, the value is 0.957 These values place the maximum metal-proton distance at 2.90 A. The value of 2.75 A for the Mn-proton distance requires that, within the spirit of the point-dipole approximation, the water molecule dipole not point directly at the metal. The intermoment distance in the aquo complex may change as a consequence of the plane of the water molecule, tilting away from the direction of the metal-oxygen bond. If the water molecule were coordinated on average so that the electric dipole moment of the water molecule pointed directly at the metal, then the metal-hydrogen distance is maximum and the tilt angle, 8, is zero. But if coordination were at the tetrahedral orientation at the same metal-oxygen distance, the hydrogen atoms would be closer to the metal center and the tilt angle would then be approximately 70". When this distance change is raised to the sixth power, a factor of approximately 7 increase ,in the relaxation rate may result. Applying this analysis to the manganese distance of 2.75 8, suggests that the plane of the

;;w 10

5 0

2.62.0 3.03.2 3.4 3.6 3.0

lOOO/T, K-' Figure 2. 'H chemical shifts and relaxivities as a function of reciprocal temperature at 500 MHz for 10 mh4 iron(II1) perchlorate and 20 mM manganese(I1) sulfate. (a) Proton chemical shifts relative to TSP for (e)iron(II1) ion in 2.8 M perchloric acid, (B) iron(II1) ion in 0.28 M perchloric acid, (A)manganese(I1) ion in 2.8 M perchloric acid, and ( 0 )manganese(I1) ion, no added perchloric acid, pH 6.6. (b) Water proton relaxation rates for 10 mM iron(II1) ion: (A) UT2 for 2.8 M perchloric acid solutions, (0)1/T2for 0.28 M perchloric acid solutions, and (B) UTI for 2.8 M perchloric acid solutions. (c) Water proton relaxation rates for 20 mM manganese(I1) ion: (A) 1/T2 for 2.8 M perchloric acid solutions, (0)1/T2 for no perchloric acid added at pH 6.6, and (B) 1/Tl for 2.8 M perchloric acid solutions.

ion, which also compromise the quantitative analysis of the relaxation data. We have attempted to minimize these complications using perchloric acid or triflic acid which are very weak coordinating ligands. The W-visible absorption spectra of iron in solutions of these acids are consistent with octahedral complex formation by the solvent once the pH is sufficiently 10w.I~ Two of the parameters that enter eqs 1-4 are the mean residence time, re,, and the hyperfine coupling constant, which may be obtained from separate measurements of the chemical shift and line widths of the water resonances as a function of temperature. Such measurements were reported for iron by Luz and S h ~ l m a nand , ~ ~the results were used to discuss water proton spin relaxation in aqueous iron(II1) systems. Since we have used different conditions and wish to minimize the number of adjustable parameters in the fit to the data in Figure 1, we have repeated these measurements at a proton Larmor frequency of 500 MHz, which affords a larger dynamic range than the earlier 60-MHz measurements. The data for manganese(I1) and iron@) are summarized in Figure 2 where the solid lines drawn were computed using the standard equations of Swift and C ~ n n i c k , *and ~ the parameters are summarized in Table 1. These results are similar though not identical to those reported earlier for iron(III) in dilute acid.23,25The value of the exchange rate is different from that reported earlier for iron(III) by a factor of nearly 2 at 298 K, which may result from the sensitivity of the system to changes in pH or counterion. These values obtained for the manganese(I1) system are in reasonable agreement with earlier reports of the hyperfine coupling and the exchange rates based on proton NMR

Sur and Bryant

6304 J. Phys. Chem., Vol. 99, No. 17, 1995

TABLE 1: Kinetic Parameters for Exchange of Protons between the First Coordination Sphere of the Aquo Ions and Bulk Water manganese(I1) iron(II1) parameter 0 M HC104 2.8 M HC104 0.28 M HClOi 2.8 M HC104 31 f 2 22 f 3 M ,kT mol-' 2941 1 30 f 2 A P , J mol-' K-' -1.8 f 1.0 0.8 & 1.0 -23 i 3 -52 iz 4 (5.6 f 2.0) x lo-' (4.1 f 1.0) x lo-* (6.7 f 4.0) x lo-' (2.4 f 1.0) x 2,298, s 20 f 5 20 f 5 E,, kT mol-' 24 f 2 23 f 2 A/h, MHz 0.82 i 0.02 0.99 f 0.02 1.29 f 0.04 1.60 f 0.03 TABLE 2: Best-Fit Relaxation Parameters for Aqueous Solutions of Manganese(I1) and Iron(1II) Ions

2.90 2.77 2.90 2.90 2.75 2.82 2.87 2.62 2.7 1 2.51

33 x 10-9 60 10-9 66 x 4 6 f 10 3 2 f 10

24 10-9 41 x 10-9 io x 10-9

O f 10 53 f 10

3.8 10-7 6.7 x 10-7 5.6 10-7

33 38 30 59 30 35 49 53 42 49

Manganese(I1) 2.2 2.0 2.9 2.2 2.8 2.4 Iron(II1) 13 0.090 0.090 5.3 5.0 0.107 0.083 5.8

water molecule is tipped by an angle of approximately 46 f 10" from the symmetry axis of the metal center. This possibility is curious but supported in part by simulations which indicate that water molecule orientations adjacent to charged cations may not generally be perfectly symmetric.33 We are led to this consideration essentially by the high relaxation rate observed and the assumption that the water molecule coordination number is 6. With the assumptions discussed above concerning the change in rotational correlation time with increasing perchloric acid concentration, at 2.8 M perchloric acid, this analysis suggests that the tip angle decreases to 32 f 10". The data for the iron(II1) solutions shown in curves C-E of Figure 1 also show a clear increase in the low magnetic field relaxation rate as the perchloric acid concentration is raised. Curve E for iron(II1) perchlorate at pH 3.1 demonstrates the low relaxivity that results from hydrolysis of the iron species and the complex intercomplex association reactions that then result. Curve D obtained in 0.28 M perchloric acid eliminates the majority of the hydrolysis problems, and the relaxivity is substantially higher. As for manganese(II), the proton relaxivity is higher in the 2.8 M perchloric acid solution, although unlike the manganese(I1) case, the whole curve is displaced to higher values. Analysis of the iron(II1) data is complicated by the absence of a clear low field inflection that permits unambiguous definition of the electron relaxation time. No distinguishable separate inflection point is discernible from these data, which requires that the correlation time for the hyperfine term is nearly degenerate with that for the dipolar term in eq 2; that is, the value of zsois near that for the rotational correlation time of the complex. As a result, the magnetic field dependence of the electron relaxation times must be included in the analysis, which adds an additional parameter to the discussion, namely, The determination of the iron(II1) parameters is, therefore, less certain than in the manganese(I1) case; the parameters that were varied in fitting the data were the intermoment distance, the rotational correlation time of the complex, the value of SO, and the value of zv. The value of zv is actually reasonably constrained by the recent observations by the Florence that there is an increase in the water relaxivity at higher magnetic fields than shown here. Their value for zy near 5 ps is consistent with the present data but not well tested by it. The value of

0.82 0.78 0.68 0.82 0.99 0.00

0.43 1.29 1.60

6 6 6 6 6 6

refs 19-21 ref 59 at 35 "C, ref 27 at 15 O C , ref 27 this work, pH 6.6 this work, 2.8 M HC104

6 6 6 6

ref 21 ref 25, with 1.0 M HC104 this work, 0.28 M HC104 this work, 2.8 M HC104

ZSO is determined only by the fact that the iron relaxation dispersion is not perfectly symmetric, declining more rapidly at lower fields than expected if the electron relaxation rate were unimportant. Therefore, that the value of SO obtained from the fit is somewhat greater than the rotational correlation time is qualitatively reasonable based only on inspection of Figure 1. The value of the rotational correlation time obtained for the hexaaquoiron(1II) complex is 40% larger than for the manganese(I1) case, which is not unreasonable based on the increase in charge. The hyperfine coupling contribution to the low-field relaxivity in the iron(II1) solutions has sometimes been However, in the present case, we have measured the hyperfine coupling constant independently and compute the size of the contribution. The values in Table 2 yield a hypefine contribution to the total relaxivity at low magnetic field strengths of approximately 4.4 s-I or a contribution of 16% for the 0.28 M perchloric acid solution. The excellent fits of these data using the values of the hyperfine coupling constants obtained from the chemical shift data cast doubt on the recent suggestion that the relaxation rates and the chemical shifts measure different hyperfine couplings in the iron(II1) system.25 Using the same approach as for manganese(II), we increase the correlation time by the ratio of the viscosities and fix it in the determination of the parameters associated with the 2.8 M perchloric acid data. The increase in the relaxation rate from the hyperfine contribution adds only 2.4 s-l to the low-field portion of the relaxation dispersion profile. The remainder of the increase, including that for the high-field portion of the dispersion profile, must derive from a change in the intermoment distance, which appears to decrease from a value of 2.71 to 2.51 8, when the perchloric acid concentration is changed from 0.28 to 2.8 M. We note that the value reported by the Florence group of 2.62 8, is between the values in Table 2 and is at an intermediate concentration. Using a metal-oxygen d i ~ t a n c e ~ ~ - ~ ~ of 1.99 8, and an oxygen-proton distance of 0.96 A, the metalproton distance in Table 2 yields a value of 0 f 10" for the tip angle of the plane of the water molecule in the 0.28 M perchloric acid sample. However, in the 2.8 M perchloric acid solution, the value is 53 f 10". Qualitatively, a change in the intermoment distance at constant coordination number requires that the angle between

Relaxation Rates in Symmetrical Fe, Mn, and Gd

J. Phys. Chem., Vol. 99, No. 17,1995 6305

TABLE 3: EPR Parameters of Metal Ion Complexes in Various Solvents and CosolutesO 552.

metal AHpp,G Fe(II1)

1120.0 1218.0 1124.0 1081.0 1124.0 1193.0 1410.0 597.2 1183.0 1486 49.2 46.4 10.8 12.2 16.0 Mn(I1) 20.0 23.2 28.1 21.6 21.0 21.2 34.2 42.5 15.0 3 1.5 Gd(II1) 520.0 502.0 475.7 396.4 324.3 261.3 270.3 290.0 a

ns

comment

0.058 0.054 0.058 0.061 0.058 0.055 0.047 0.110 0.055 0.044 1.330 1.410 6.070 5.370 4.100 3.00 2.83 2.33 3.03 3.13 3.09 1.92 1.54 4.37 2.08 0.13 0.13 0.14 0.17 0.20 0.25 0.24 0.23

aq solution, ref 38 0.1 M in D20, pH 1.4, this work 0.1 M in H20, pH 1.4, this work 0.1 M in 0.28 M aq perchloric acid, this work 0.1 M in 1.4 M aq perchloric acid, this work 0.1 M in 2.8 M aq perchloric acid, this work 0.1 M in 5.6 M aq perchloric acid, this work 0.1 M in 12 M aq hydrochloric acid, this work 0.6 M in 7 M aq nitric acid, this work 0.1 M iron(II1) perchlorate in acetonitrile, this work 4 mM iron(II1) chloride in acetonitrile, this work 4 mM iron(II1) chloride in acetonitrile, LiCl, this work 2 mM in 2 M ammonium fluoride in HzO, this work 2 mM in 2 M ammonium fluoride in D20,this work 3 mM with 2 M NHIF, 24 wt % aq glycerol, this work aq solution, ref 23 1.25 mM in H20 at pH 6.0, this work 1.25 mM in DzO at pH 6.0, this work 1 mM in 0.28 M aq perchloric acid, this work 1 mM in 1.4 M aq perchloric acid, this work 1 mM in 2.8 M aq perchloric acid, this work I mM in 5.6 M aq perchloric acid, this work 1 mM in 6.3 M aq perchloric acid, this work 3 mM in acetonitrile containing LiC1, this work 5 mM in 24 wt % aq glycerol, this work 100 mM aq solution, ref 60 10 mM (aq) at pH 5.6, this work 10 mM in 0.28 M aq perchloric acid, this work 10 mM in 1.4 M aq perchloric acid, this work 10 mM in 2.8 M aq perchloric acid, this work 10 mM in 4.2 M aq perchloric acid, this work 10 mM in 4.9 M aq perchloric acid, this work 10 mM in 5.6 M aq perchloric acid, this work

All data at room temperature.

the plane of the water molecule and the symmetry axis of the aquo complex must change. The iron(II1) case is substantially different in this instance from the manganese(II) case, where the high-field relaxation rate changes with perchloric acid may be accounted for by changes in the correlation time resulting from the viscosity changes when the perchloric acid concentration is raised. At present, we do not have a firm understanding of the basis for this difference between iron(II1) and manganese(I1). Although changes in the water molecule coordination geometry in metal complexes may be a general feature contributing importantly to the relaxation efficiency of a particular complex, this iron(II1) example appears to be the f i s t reasonably clear experimental demonstration of the effect. This hypothesis is consistent with theoretical discussions of iron solutions where water molecule coordination geometry is examined by molecular dynamics ~ i m u l a t i o n s .We ~ ~ also note that diffraction studies of iron(III) salts also suggest a variability in the water molecule ~ r i e n t a t i o n . ~ ~ The EPR spectra of these ions are readily obtained. Neglecting effects of inhomogeneous broadening from unresolved hyperfine coupling, the EPR line widths provide an estimate of the electron-spin relaxation time based on the relation that ts2 = 2/(yeAHpp2/3)where AHppis the width measured between the extrema of the derivative mode EPR spectrum. The results are summarized in Table 3 and are useful as a qualitative guide. The value of the t s 2 shown for the iron(II1) supports the conclusion that the effective correlation time characterizing the electron-nuclear coupling has a significant contribution from the electron relaxation rate. For the manganese@) ion, however, the electron relaxation rate is too long to make a significant contribution to the correlation time for the electron-nuclear coupling. A very interesting feature of the iron(II1) proton relaxation is the fact that the electron relaxation time is short in spite of

* 3.3

3.4

3.5

3.6kG

H-

Figure 3. Electron paramagnetic resonance spectra of iron(II1) complexes obtained at X-band and room temperature. (A) 2.0 mM iron(II1) chloride in acetonitrile saturated with lithium chloride, (B) 2.0 mM iron(II1) perchlorate in a 2.0 M aqueous ammonium fluoride at pH 7, (C) 2.0 m M iron(II1) perchlorate in water at pH 2.5, and (D) 100 mM iron(II1) perchlorate in water at pH 1.53.

the fact that the complex is octahedral, which is of such high symmetry that long electron relaxation times are expected, like those observed in the isoelectronic manganese(I1) solutions. However, some octahedrally coordinated iron(II1) complexes may have long electron relaxation time^.^^.^^ The EPR spectra of [FeF6I3- ion in water and iron(1n) ion in acetonitrile solution are shown in Figure 3. The narrow EPR lines correspond to electron relaxation times of 6.0 and 1.4 ns, respectively, i.e., as long as usually associated with manganese(U) systems of similar structure and symmetry and much longer than found for the hexaaquoiron(III) complex. The EPR line widths in the [FeF6l3ion correspond to electron 232 values that are similar to those recently reported for ion in zeolites.40 Thus, with these complexes, the effective electronic symmetry is high at the iron(II1) center, and the fluctuation spectrum that drives the electron relaxation is less intense or of higher frequency than for the aquo ion case so that the long relaxation times anticipated for octahedral symmetry are achieved. We conclude that there is nothing inherent in the iron@) electronic structure that should prevent construction of an efficient relaxation agent because of the limitations caused by the electron relaxation times. We will show below that other high symmetry environments for iron(111) may have remarkably long electron relaxation times and correspondingly efficient relaxation effects on the solvent protons. NMRD plots for the iron(1II) ion in 2 M ammonium fluoride solution and in acetonitrile are shown in Figure 1, curve F, and Figure 4, curve C. The equilibrium constants reported for the aqueous iron-fluoride system are such that in this 2 M fluoride ion solution, the iron(II1) is predbminately distributed between the hexafluoroferrate(II1) and the aqnopentafluoroferrate(II1) complexes.38 Thus, the relaxation effects observed represent a superposition of effects from these two species. The hexafluoro species should contribute outersphere or translational contributions only unless there were significant coordination of HF, thought to be unlikely at these pH value^.^^,^^ The low-field outersphere contribution associated with a distance of closest approach of 3.7 hl is approximately 3.3 mh4-' s-I.l4 The remaining contribution to the 'H relaxation would be associated with scalar and dipolar contributions from the aquopentafluoro complex. If we assume that the water molecule geometry

Sur and Bryant

6306 J. Phys. Chem., Vol. 99, No. 17, 1995

-

-0.01 1

1

0.1

10

I 100

H Larmor Frequency (MHz)

Figure 4. 'H nuclear magnetic relaxivity plotted as a function of magnetic field strength expressed as the proton Larmor frequency for acetonitrile solutions. (A) M, 2.0 mM manganese(I1) chloride and saturating concentration of lithium chloride; (B) A, 1.0 mM iron(II1) chloride and saturating concentration of lithium chloride; (C) A, 1.0 mM iron(II1) chloride in acetonitrile; (D) 0 , the IH spin-lattice relaxation rate for metal-free but not degassed acetonitrile. The ordinate for this curve has units of s-'. TABLE 4: Best-Fit Proton Relaxation Parameters for Acetonitrile Solutions of Manganese(II) and Iron(III) Ions ~~~

metal Fe(II1) only Fe(II1) withLiCl Mn(I1) withLiCl

~

~

b, trot,SI, 109D, A ps ns m2 s-]

4.0 37 3.9 3.7 52 5.9 3.0 39 5.6

4.2 2.6 2.3

comment [FeClJ and [Fe(CH3CN)6I3+ [FeCIJ [MnCl#

corresponds to a metal-hydrogen bond distance of 2.7 8, and the effective correlation time for the dipolar interaction is 40 ps, then estimating the fraction of the total iron(II1) as the aquopentafluoro complex as 0.46, the contribution from the single coordinated water to the relaxation rate is about 2.5 s-l per mM iron(II1). These estimates do not account for the total observed relaxation rate without adding a Contribution from hyperfine effects. Using an electron relaxation derived from the EPR line width of 0.2 ns, this remaining contribution to the water proton relaxation rate corresponds to a hyperfine coupling constant to the putative water proton of 2.7 MHz. This estimate is somewhat larger than the entries in Table 2 or earlier estimates of electron-proton hyperfine coupling constants for iron(II1) and rests on the assumptions of the appropriate correlation times and intermoment distances which may, of course, be in error. Nevertheless, the hyperfine contribution appears to provide a nonnegligible contribution to the total relaxivity at low field strengths for this system. Solutions of iron(II1) in acetonitrile provide interesting comparisons. The observable EPR line in acetonitrile solutions of iron(II1) chloride are narrow and correspond to an electron of iron(II1) perchlorate relaxation time of 1.3 n ~ . ~Solutions ' in acetonitrile give EPR line widths of 1486 G, corresponding to an electron relaxation time of 44 ps, which is more than 2 orders of magnitude shorter than that for the chloride. The long electron relaxation times and high paramagnetically induced nuclear magnetic relaxation rates are provided by tetrahedral iron(II1) complexes. The addition of high concentrations of chloride ion to the acetonitrile solution causes the formation of [FeClJ that has an EPR spectrum with g = 2.02 and line width corresponding to an electron relaxation time of 1.4 ns.40,41The NMR dispersion data from this solution, shown in Figure 4, were analyzed using the relaxation equations for outer-coordination-sphere relaxation. l 3 The parameters describing the lines in Figure 4 are summarized in Table 4. The curve drawn corresponds to a relative translational diffusion constant of 2.6

2.9

I 3.0 3.1 3.2 3.3 3.4 3.5

1000/T, K

.'

Figure 5. NMR line widths obtained at 9.4 T on a GE Omega 400 NMR spectrometer as a function of reciprocal temperature for 5.0 mM iron(II1) in aqueous 2.0 M ammonium fluoride. (A) I9F line width; ( 0 )water proton line width. x m2 s-I and a distance of closest approach of 3.7 A, which are reasonable values based on earlier work.I4 The similar tetrachloromanganate(I1) ion EPR spectra in acetonitrile saturated with lithium chloride are also narrow and correspond to electron relaxation times of 4.4 ns and AM,,(II)of 80 G; the chlorine hyperfine couplings are not The interesting feature of these solutions is that unlike the heraaquoiron(II1) ion, these species have long electron relaxation times similar to the manganese(I1) complexes. The fluorine and proton NMR line widths in aqueous ammonium fluoride solutions of iron(II1) are shown in Figure 5 plotted as a function of reciprocal temperature. As mentioned above, the fluoride ion association constants reported imply that there is a distribution of species with the predominant contributions being from the aquopentafluoro- and the hexafluoroiron(II1) complexes. The dependence of the fluoride ion line width on temperature is characteristic of an exchange rate limitation on the paramagnetic contribution to the line width; Le., the relaxation rate increases substantially with increasing temperature. Although detailed analysis of these data is not attempted because of the distribution of species, we estimate that an average fluoride ion exchange rate with the iron(II1) complexes is approximately lo3 s-' at 298 K, with an approximate species average activation energy of 9.6 kcdmol. These values are reasonable when compared with other iron(111) exchange lifetimes reported.43 Though the electron relaxation rates are long, the efficiency of the fluoride ion relaxation is limited by slow exchange of the ligand with the metal center. Unlike the aquo species where 'H exchange may be much faster than oxygen exchange, the fluoride must exchange by breaking the metal-ligand bond. The proton Nh4R line widths in these solutions have the opposite temperature dependences; Le., the line width decreases with increasing temperature. The mixture of species includes significant concentrations of the pentafluoroaquoferrate(II1) ion that may contribute to the total 'H relaxation rate by a first-coordination-sphereprocess. However, the water proton relaxation rates are low. The first-coordinationsphere contribution would have a similar temperature dependence to that of the fluoride ion if the water exchange event limited the spin relaxation rate. In the hexaaquo complex, however, the proton exchange is not limiting the water proton relaxation rate.2?.44.45In this case, the temperature dependence for the water relaxation would reflect the temperature depen-

Relaxation Rates in Symmetrical Fe, Mn, and Gd

J. Phys. Chem., Vol. 99, No. 17,1995 6301

1 .a

1.5 1.2 0.9

0.3 I 0

I

3

6

9

12

15

!I *rlo Figure 6. EPR line widths obtained at X-band for 10 mM gadolinium chloride at ambient room temperature: (A) 0, aqueous perchloric acid solutions; (B) 0, aqueous glycerol solutions; (C) W, aqueous sucrose; (D) A, 5 mM manganese(I1) ion in aqueous glycerol solutions; (E) A, 3.0 mM [FeF6I3-ion in aqueous glycerol solutions. dence of the rotational and translational mobility of the solvent and the metal complex. The low activation energy of approximately 2 kcal/mol is consistent with this hypothesis. Gadolinium(II1) ion is similar to iron(II1) ion in that while it is an S state ion, the electron-spin relaxation times for the aquo complex are not very long; in addition, the electron relaxation time has an unusual dependence on solution viscosity and the concentration of cosolutes or cosolvents. The gadolinium relaxation problem will be discussed in greater detail elsewhere;46however, the EPR line widths for Gd(II1) are shown as a function of concentration for aqueous perchloric acid and aqueous glycerol solutions in Figure 6. The EPR line width decreases with increasing concentrationsof glycerol even though the viscosity increases substantially over the range shown. Were the usual models for electron-spin relaxation for such highly symmetrical complexes entirely operative, the electron-spin relaxation rate and EPR line width should increase with increasing viscosity," opposite to the observed dependence. Similar changes in the EPR line widths are observed in the Gd(II1) spectrum with increasing concentrations of perchloric acid as shown in Figure 6. In contrast, the EPR line width of the hexafluoroferrate(II1) ion in aqueous glycerol solutions is a linear function of the solution viscosity over the range of Figure 6. The decrease in gadolinium ion electron relaxation rates observed with increasing concentrations of glycerol or perchloric acid is unusual and suggests an increase in the symmetry of the metal center. A reasonable hypothesis for the increased symmetry is that the decrease in the water activity, which attends the higher concentrations of perchloric acid or glycerol, induces a change in the coordination number for the gadolinium(II1) ion from 9 to 8.47-50 By hypothesis, the 8-coordinate species has a higher symmetry and a longer electron relaxation time than the 9-coordinate specie^.^' An interesting feature of the glycerol data is that the electron relaxation rate as measured by the EPR line width becomes a very weak function of the viscosity in violation of the usual linear dependence on viscosity anticipated by the standard relaxation equations and the Stokes-Einstein-Debye relations. Other metal systems have demonstrated this behavior such as [Gd(DOTA)]-, [Gd(DTPA)]*-, and [Mn111(TPPS4)]-.52,53 This observation may result from some unique solvent structure around the metal complex such as a clathrate which may decouple the local rotational or collisional frequencies from the bulk solution properties; however, there is no evidence that this has occurred in the present cases. Altematively, the electron

relaxation may be dominated by intramolecular motions that are relatively insensitive to the bulk dynamical properties of the solution. The electron relaxation problem is similar to the nuclear electric quadrupole relaxation problem in solutions. An important recent result from studies of the quadrupole relaxation problem is that for some species that are similar to those considered here, Le., hexaaquosodium(1) ion, the fluctuations of the field gradient at the nucleus are apparently dominated by fluctuations in the orientation of the fist-coordination-sphere water molecule^.^^-^^ Since the problem is essentially identical to that of the electron relaxation problem in the aquo ions of Fe(II1) and Gd(III), similar fluctuations of the coordinated water molecule orientations should be important. As mentioned earlier, the wagging and tilting of the coordinated water molecule electric dipole moment represent vibrational motions of low frequency that affect the zero-field splitting at the metal center but may be only weakly coupled to the bulk transport properties of the solution. This hypothesis that coordinated water molecule motions may make a dominant contribution to the electron-spin relaxation rate of the aquo ion is consistent with the present observations of both EPR and NMR relaxation rates. It seems reasonable to adopt this idea as a tentative explanation for the observations that the aquo complexes of the tripositive ions have short electron-spin relaxation times. A consequence of this situation is that local steric constraint of the coordinated ligand motion, including coordinated water, should decrease the amplitude of the fluctuations and lengthen the electron relaxation time. In a polydentate system, making the structure of the complex more rigid should also increase the frequency of such fluctuations, which would lengthen the electron relaxation time, other things being equal. Acknowledgment. We acknowledge helpful discussions with many people including particularly Prof. Harold Friedman at the State University of New York, Stony Brook, Prof. George L. McLendon and Dr. Scott D. Kennedy at the University of Rochester, and Prof. Jack Freed at Come11 University. This work was supported by the National Institutes of Health (GM39309), the University of Rochester, and the University of Virginia. References and Notes (1) Mansfield, P.; Morris, P. G. NMR Imaging in Biomedicine; Academic: New York, 1982. (2) Solomon, I. Phys. Rev. 1955, 99, 559. (3) Bloembergen, N. J. Chem. Phys. 1957, 27, 572. (4) Bloembergen, N.; Morgan, L. 0. J . Chem. Phys. 1961, 34, 842. (5) Bertini, I.; Luchinat, C. NMR of Paramagnetic Molecules in Biological Systems; BenjaminKummings: Menlo Park, CA, 1986. (6) Banci, L.; Bertini, I.; Luchinat, C. Nuclear and Electron Relaration; VCH: Weiheim, New York, Basel, Cambridge, 1991. (7) Koenig, S. H. J. Mugn. Reson. 1978, 31, 1. (8) Gregson, A. K.; Dodrell, D. M.; Pegg, D. T. Aust. J . Chem. 1978, 31, 469. (9) Poupko, R.; Baram, A,; Luz, A. Mol. Phys. 1974, 27, 1345. (IO) Kowalewski, J.; Nordenskiold, L.; Benetis, N.; Westlund, P. 0. Prog. Nucl. Magn. Reson. Spectrosc. 1985, 17, 141. (11) Polnaszek, C. F.; Bryant, R. G. J . Am. Chem. SOC. 1984,106,428. (12) Polnaszek, C. F.; Bryant, R. G. J . Chem. Phys. 1984, 81, 4038. (13) Freed, J. H. J . Chem. Phys. 1978, 68, 4034. (14) Lester, C. C.; Bryant, R. G. J . Phys. Chem. 1990, 94, 2843. (15) Martin, R. B. J. lnorg. Biochem. 1991, 44, 141. (16) Hernandez, G. H.; Brittain, H. G.; Tweedle, M. F.; Bryant, R. G. Inorg. Chem. 1990, 29, 985. (17) Cotton, F. A,; Wilkinson, G. Advanced Inorganic Chemistry, A Comprehensive Text; Wiley: New York, 1980; p 758. (18) Koenig, S. H.; Baglin, C. M.; Brown, R. D., I11 Mugn. Reson. Med. 1985, 2, 283. (19) Koenig, S . H.; Brown, R. D., I11 Mugn. Reson. Med. 1984, 1,478. (20) Koenig, S. H.; Baglin, C.; Brown, R. D., 111; Brewer, C. F. Magn. Reson. Med. 1984, I , 496.

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