J. Phys. Chem. 1993,97, 6351-6354
6351
Water Proton Relaxation for Some Lanthanide Aqua Ions in Solution Ivano Bertini,’J Francesco Capozzi,* Claudio Luchinat,* Giuseppe Nicastro,t and Zhicheng Xiat Department of Chemistry, University of Florence, 501 21 Florence, and Institute of Agricultural Chemistry, University of Bologna, 401 27 Bologna, Italy Received: December 28, 1992
The nuclear magnetic relaxation dispersion (NMRD) profiles of water protons have been investigated between 0.01 and 600 MHz for lanthanide aqua complexes, where the lanthanide is Pr, Sm, Dy, Ho, Er, and Yb. The experimental profiles have been interpreted as due to contributions from proton-electron dipolar coupling and Curie relaxation mechanisms. For the former the correlation time is the electron relaxation time itself and for the latter the rotational correlation time of the aqua ion. This is the first time that a Curie contribution to longitudinal relaxation has been observed through its magnetic field dependence.. The electron relaxation times are confirmed to be magnetic field independent, very short, and substantially temperature independent. Their actual values are now proposed by taking into consideration crystal field effects. The mechanisms causing electron relaxation have been discussed.
Introduction Electron relaxation first and then nuclear relaxation have been fashionable in the 1960s to study the spin dynamics of electrons and nuclei. The main approach was the investigation of the EPR line widths and of the water lH-NMR line widths at one or two frequencies. The availability of relaxometers working between 0.01 and 50 MHz (for the proton) provided new insights into the field. We have been interested in a systematic investigation of electron and nuclear relaxation of paramagnetic metal ions in water solution as aqua ions or bound to macromolecules. When necessary, water-ethylene glycol mixtures have been used to control theviscosity and then thetumblimgrate. We haveextended the range of frequencies from 0.01 up to 600 MHz. In every case previous theories have been refined or new mechanisms have been proposed. Electron relaxation in copper(I1)-containing systems at room temperature in solutions has been ascribed either to Orbach (hexaaqua) or Raman types of mechanisms.lJ In hexaaquatitanium(II1) electron relaxation is due to an Orbach type mechanism, although an increase in nuclear transverse relaxation rate with magnetic field is observed above 50 MHz.’ In the case of V02+,the coupling between the magnetic moment of the metal nucleus and the unpaired electron is believed to provide electron relaxation, the coupling being modulated by solvent collisions. In the case of VO(H20)s2+, the correlation time for electron relaxation, T”, is about 1C12s, consistent with the collision model! In the case of Mn2+,Fe3+,Ni2+,and Gd3+,both as aqua ions and bound to macromolecules, the modulation of the zero-field splitting (ZFS) seems to be the most efficient relaxation mechanism. The value behaves in the same fashion for all systems including V 0 2 + and depends on We favor a model in which collisions modulate the ZFS in every case rather than a model based on the modulation of a static ZFS by rotation. In cobalt(11), very efficient electron relaxation, which is also magnetic field independent, indicates an Orbach type Such mechanism is operative every time there are closely spaced electronic levels with efficient spin-orbit coupling. The solidstate model of the Orbach mechanism is not straightforwardly applicable to solutions. Solid-state phonons can be substituted by solvent molecule oscillations or by concerted oscillations of
* Correspondence should be addressed to Prof. Ivano Bertini, Department of Chemistry, University of Florence, Via Gin0 Capponi, 7,50121, Florence, Italy. + University of Florence. University of Bologna.
*
0022-3654/93/2097-635 1$04.00/0
solute atoms, in this case by viewing solute molecules as microcrystals. In this respect the most fascinating systems are represented by the lanthanide ions, except Gd3+,which has very short electron relaxation times in solids and presumably in solution as guessed from nuclear relaxation measurements which, however, have been taken over a relatively narrow range of proton Larmor frequencies.10-l2 We report here on an investigation of some aqua complexes of lanthanides(II1) through water proton relaxation between 0.01 and 600 MHz. We confirm that electron relaxation times are very short and independent of magnetic field. Furthermore we quantitate for the first time a sizable contribution to nuclear longitudinal relaxation arising from the presence of large static magnetic moments induced by the magnetic field (Curie spin relaxation). Finally, we propose toevaluate the electronrelaxation times for the investigated lanthanides through a modification of the Solomon equation that takes into account the zero-field splitting of the J multiplets. The values are compared with previous estimates.
Experimental Section Lanthanide aqua ions were prepared by dissolving the corresponding oxide into a slight excess of perchloric acid, and the pH of the resulting solutions was adjusted to be in the range 1.0-3.0. In this range, pH does not affect the relaxation rate of the lanthanide ions, as previously reported.1° The same samples containing 50% D2O (v/v) were used for all relaxation measurements over the whole range of magnetic fields. Nuclear relaxation rate measurements from 0.01 to 50 MHz were performed with a Koenig-Brown relaxometer installed at the University of Florence thanks to an agreement between the latter and the IBM T.J. Watson Research Center at Yorlctown Heights, New York. The details of the apparatus and the data collection were given el~ewhere.~ The sample volumes were 0.5 mL. The samples contained the appropriate lanthanide ion concentrations to give water proton longitudinal relaxation rate values in the 1-10 s-l range. The temperature was controlled by surrounding the sample with circulating liquid freon, a perfluorinated hydrocarbon. The temperaturecanbe stabilizedto 10.2 OC in the range -10 to +35 OC. Water proton longitudinal relaxation time measurements at high field were performed using the inversion-recovery method with the following spectrometers: at 200 MHz, Bruker MSL 200, at 300 MHz, Bruker AC-P 300; at 600 MHz, Bruker AMX 600. The temperature was controlled using the standard variable-temperature equipment provided by spectrometer manufacturers. 0 1993 American Chemical Society
6352 The Journal of Physical Chemistry, Vol. 97, No. 24, 19'93 1
1
'
"~""1
'
'"'."I
'
..'"'I
'
Bertini et al.
' '
1.4
0.2 0.10
L
1
r
n
j - . - $. - 0.03 0.06
0.00 0.01
0.1
1
10
100
1000
R o t o n L a m Fr8quency (MHS) Figure 1. Water 'HNMRD profiles of somelanthanideaqua ions at 298 K. The solid lines represent the best fit results using eqs 4 and 5.
The relaxivity values, TlP-l, were obtained by subtracting the diamagnetic contributions of the solvent, T1d-l (equimolar La3+ solution blanks were indistinguishable from solvent), from the total relaxation rate of the solutions containing the lanthanide ions, TI-1, and by dividing the result by the (millimolar) metal ion concentration, as shown in eq 1:
-'
T1p-l
T1- ' - T Id = 1000[Ln3+]
(1)
In turn, TlP-lis related to the proton relaxation rate of the bound water according to eq 2:
Tip-' =fm(TIM + TM)-'
+ Tim-'
(2)
wherefm is the molar fraction of protons sensing the paramagnetic center (fm = 1C3n/55.5, n being the hydration number and 55.5 being the molarity of water), and TM is the residence time of water protons bound to the paramagnetic center. T ~ Mis- the ~ longitudinal paramagneticrelaxationrate of a bound water proton. Tlm-l is the outer sphere contribution to relaxivity, which can usually be neglected in the case of aqua ions.6
0.00 0.01
R o t o n L a m Fr8-
1000
(MRs)
Epow 2. Water lH NMRD profiles of somelanthanide aqua ions at 308 K. The solid lines represent the best fit results using eqs 4 and 5. dynamic and structural information from nuclear relaxation measurements by either making comparable contribution to TIM in eq 2 if it is too slow or contributing to the correlation time for nuclear relaxation if it is too fast. For lanthanide aqua ions, the chemical exchange rate of inner sphere water usually falls into the range 10-6-10-8 s from 1 7 0 N M R measurements,17J* while TIMvalues are longer than 2.0 X l(r 8. In fact, for most lanthanide ions, when the temperature is increased, nuclear relaxivity decreases. If chemicnl exchange were important, the contrary would be observed. On the other hand, chemical exchange cannot influence the correlation time, because of the veryshortelcctronicrelaxationtime(- 10-13s).1@12 Sophisticated parmagnetic shift measurements of 13C,1 7 0 , and lH for some lanthanide chelating agents point out that the contact hyperfine interaction between the metal and the hydrogencan beneglected.19 The enhanced relaxation rates for lanthanide ions are predominantly dipolar in origin. The basic equations describing the paramagnetic relaxation due to the dipoldpole interaction have been derived by Solomon in the 1950s." In the prescnt case the J quantum number substitutes the S quantum number:
Results and Discussion The water proton relaxivity values from 0.01 to 600 MHz for some lanthanide aqua ions at 278 and 308 K are reported in Figures 1 and 2. At first glance, the N M R D profiles are quite different from those of the well-studied 3d metal aqua ions: the latter show a dispersion near 7 MHz when the rotational correlation time dominates the correlation time for nuclear rela~ation?.~J~ or an increase in relaxation above 10 MHz when electron relaxation is magnetic field d~pendent.'~When the electron relaxation time is the correlation time and is fieldindependent, the profile is flat. In the present case the relaxivity values are constant from 0.01 to 50 MHz for all lanthanide ions. This indicates that the correlation time for nuclear relaxation is the electronic relaxation time, and that it is magnetic field independent at least in this range. A peculiar magnetic field dependence of nuclear relaxation is observed at high magnetic fields. All the investigated lanthanide solutions show an increase of relaxivity at high magnetic fields. The increase is dramatic for Dy, Er,and Ho aqua ions. When the temperature is increased, the relaxivities at high fields decrease substantially, while at low magnetic fields they decrease much leas. Ouantitative interuretation of the Droton relaxation data needs some careful analysis of the influenck of several parameters. The first is the chemical exchange. As it has already been shown extensively,15J6 this factor often hampers the obtainment of
100
10
1
0.1
[
37c
1 +w;7:
+ 1 +w&: 77c
3
(3)
where (+)is called the geometric factor. It is the inverse sixth power of the average distance between the metal and coordinated water protons with the assumption of a point dipole. The difference between the N M R and the crystallographic distance is due to covalency effects whereby the distributionof the unpaired electronsover the ligand orbitals brings about an increaseof their dipolar interactionwith the p r o m relative to the electron-nuclear dipolar However, the ligand-centered dipolar contributions have been shown to be essentially not operative in lanthanide c o m p l e x ~ a . So ~ ~ ~the ~ ~metal-hydrogen distance estimated from X-ray structural data can be used without introducing large errors. The dipoldpole relation (eq 3) holds in the absenceof ZFS,whichisnot thecasein the present systems. ZFS has been shown to cause a decrease in nuclear relaxation as long as the Zteman energy is smaller than the ZFS.This may introduce some indetermination in the evaluation of 7s which, however, is not so severe. The correlation time which modulates nuclear relaxation is given by TC-1
= 17;
+
7;'
+
TM-l
The order of magnitude of the electronic relaxation time (except
The Journal of Physical Chemistry, Vol. 97, No. 24, 1993 6353
Water Proton Relaxation for Some Lanthanides
TABLE I: Dynamic and Structural Parameters for Some Lanthanide Aaea Ions Pr Ho DY Sm ~~~
298K word no.
4P4 dps)
298K
~~
308K
~
~~
298K
308K
9 1.58
3.208 63 49 0.082 0.082
3.166 67 53 0.079 0.075
63 0.39
Large induced magnetic moments may cause nuclear relaxation through dipolar coupling upon rotation. This is called Curie relaxation. It is important at high magnetic field and slow rotational correlation times. In particular in proteins the effect on NMR line width has often been observed. In the case of lanthanides, Curie relaxation effects on T2 had been observed also in small complexes.' 1,12 The nuclear longitudinal relaxation enhancement due to the Curie contribution is24,2s
with all the symbols having the same physical meaning as above. The total paramagnetic relaxtion rate is the sum of the two contributions: -1
= TIM(dip)-l + TIM(Curic) We begin to fit the NMRD profiles of Dy, Er, and Ho aqua ions with eqs 4 and 5. We only keep the electronic relaxation time and the rotational correlation time as parameters for the best fitting, where the X-ray data have been used to estimate the Ln-H distances. The experimental magnetic moments for the crystalline Ln2(S0&3H20 have been used.26 The coordination number of water molecules of lanthanide ions in solution is still a puzzling problem. In previous works, this parameter for the whole series was tacitly assumed to be nine.lO Recently, Helm and Merbach pointed out that this parameter changes from 9 to 8 from Ce(II1) to Yb(II1) by using the neutron scattering technique and 1 7 0 NMR.27 Accordingly, we use 9 for the lanthanide ions in the first half and 8 for the second half of the series. We found that this model fits the experimental data very well (Figures 1 and 2). The parameters coming out of the fit are quite consistent with what is expected (see Table I). The values of rotational correlation time for the lanthanide ions Dy, Er, and Ho are the same for the same temperature, and are very similar with what has been reported for Gd(II1) aqua ion.lS The high field increase in relaxivity is due to Tl~(~,,ri~)-l which depends on the square of the external magnetic field. For the Pr, Yb, and Sm aqua ions, very little field dependenceof the nuclear relaxation is observed at high magnetic fields. This is because these ions have relatively small magnetic moments. If we take 1 as the Curie contribution to the overall relaxation in the case of Dy3+, it is only 0.17 for Yb3+, 0.11 for Pr3+, and 0.02 for Sm3+if the electronic relaxation is assumed to be constant from one ion to another.
Er 308K
298K
65 0.27
Yb 308K
298K
9.4
3.101 49 0.27
61 0.31
308K 8 4.3
8
8 10.4
3.111 51 0.38
G d 9 is 8: the contribution of chemical exchange and of the rotational correlation time to the overall correlation time can thus be neglected. The term pB2gJ2J(J4- 1) in eq 3 is more properly replaced by the experimental per? value. So, eq 3 can be rewritten as
TIM-l
298K
8 10.3
9 3.47
czrr(c's)28
r(A)
308K
~
3.083 46 0.30
68 0.22
3.065 49 0.22
TABLE Jk Calculated 298K T~ Values (ps) without and with Inclusion of ZFS Effects datasource Pro+ Sm3+ Dy3+ Ho3+ Er3+ YV+ prcviouswork10 0.062 0.053 0.34 0.22 0.28 0.16 present work 0.082 0.079 0.39 0.27 0.31 0.22 presentworkwith 0.25 0.16 0.99 0.81 0.78 0.48 ZFSeffects This is to our knowledge the first time that a field dependence of nuclear longitudinal relaxation due to Curie relaxation has been observed and quantitated, whereas Curie relaxation effects on T2 are well-documented. Indeed, Curie relaxation on small complexes (7, = s) can only be expected when T, > Zeeman energ~).~~.~O The latter case, with J substituting for S, should also be operative for lanthanides all over the magnetic field range investigated here. The strong zero-field splittingcase can be generalized by taking into account that the ws-containingterm in the Solomon equation is dispersed down everytime the electronic transition occurs between zero-field split levels, i.e. at an energy much larger than the Zeeman energy. For integer J the U Sterm totally disappears, whereas for half-integer J only the l / 2 -l/2 transition retains a transition energy equal to the Zeeman energy. As suggested by Koenig,3l the contribution of this transition to the total OS dispersion is proportional to the fractional oscillator strength of the l / 2 -l/2 tran~ition.~~
-
-
-
-
The coefficients of the os and 01 dispersions in the low field limit can be generalized on the basis of our previous work29*30 to give
6354 The Journal of Physical Chemistry, Vol. 97, No. 24, 1993
Bertini et al. the electrons. It should be noted that the electron relaxation times in solution are not largely affected by temperature.
1)- 1/2(1/2-
J(J
1)
+ 1) - M,(Mj - 1)
for half-integer J, and
for integer J. Similar modificationsof the ws term were previouSly proposed for 3d metal ions.31 By using the above equations in the place of the Solomon equation to analyze the present data, the same best fit curves are obtained with the same values of the parameter T~ involved in the Curie term, but with TS values 2-3 times longer than in the previous case (Table 11). As a final comment we may add that, since the electronic relaxation times of these systems are very short, a convenient way to investigate them in solution at room temperature is through NMR relaxation measurements. The ground J level is split by the crystalline field to provide a set of closely spaced energy levels. Thus, the Orbach mechanism could well be dominant.33 Indeed, when lanthanide ions are doped in lanthanum salts, a large body of experiments have shown that the electrons relax through an Orbach mechanism when the temperature is low.34335 At high temperature Gd3+probes doped into lanthanide crystals experiencebroadening of the EPR signals. From the broadening, estimates of the lanthanide electron relaxation times are provided which are somewhat shorter than, but sufficiently consistent with, our data.36937The discrepancy may be due to solid-state effects but also to the presenceof spin-spin interactions in the nondiluted lanthanide crystal lattice. The Occurrence of efficient Raman mechanisms in addition to Orbach mechanisms is sometimes invoked on the basis of the temperature dependenceof the electron relaxation times.36~3~ The analysis presented here was based on the assumption (verified a posteriori) that the electronic relaxation times for lanthanideions (except Gd(II1))arenot magnetic field dependent. The electronic relaxation time for an Orbach mechanism is not field dependent. The present finding points out again the need for a physical model for solutions which substitutes the phonon model of the solid state, and which allows the coupling of the electron magnetic moment with lattice motions. The electron relaxation rates are too short to indicate that the latter motions are rotations or translations. It is possible that librations and vibrations involving a certain number of molecules (at the level of an instantaneous microcrystal as proposed by Al'tsch~ler~~) provide short-range phonons capable of exchanging energy with
Acknowledgment. Z.X.and G.N. would like to acknowledge B r a m Industria Chimica S.p.A. for providing the scholarships that allowed them to carry out this research.
References and Notes (1) Bertini, I.; Luchinat, C.; Brown, R. D., III; Koenig, S. H. J. Am. Chem. Soc. 1909,111,3532. (2) Bertini, I.; Banci, L.; Brown, R. D., 111; Koenig, S. H.; Luchinat, C. Inorg. Chem. 1988,27,951. (3) Bertini, I.; Luchinat, C.; Xia, Z . Inorg. Chem. 1992,31,3152. (4) Bertini, I.; Xia, 2.;Luchinat, C. J. Mugn.Reson. 1992,99,235. (5) Luchinat, C.; Xia, 2. Coord. Chem. R N . 1992,120,281. (6) Koemg,S. H.; Brown, R. D., III;Progr.Nucl. Mugn.Reson.Spzctrosc.
1990,22,487. (7) Koenig, S. H.; Brown, R. D., I11 NMR specrroscopy of Cells und Organisms; Gupta, R. K. Ed.; CRC Press: Boca Raton, 1987;Vol. 11. (8) Banci, L.; Bertini, I.; Luchinat. C. Inorg. Chim. Aero 1985,IW173. , (9) Koenig, S. H.; Brown, R. D., 111; Bertini, I.; Luchinat, C. Biophys. J . 1983,41, 179. (10) Alsaadi, B. M.; Rossotti, F. J. C.; Williams, R. J. P. J. Chem. Soc., Dulron Truns. 1980,2147. (11) Burns, P. D.; La Mar, G. N. J. Mugn.Reson. 1982,16,61. (12) A h e . S.:Barbero.. L.:. Botta. M.: Erm0ndi.G. J. Chem.Soc..Dulron Trans.. 1992,225. (13) Hausser, R.; Noack, F. Z . Phys. 1964,182,93. (14) Bertini, I.; Capozzi, F.; Luchinat, C.; Xia, 2.J. Phys. Chem. 1993, 97,1174. (15) Koenig. S.H.; Eptein, M. J. Chem. Phys. 1975,63,2279. (16) Koenig, S. H.; Brown, R. D., I11 J. Mugn.Reson. 1985,61, 426. (17) Reuben, J.; Fiat, D. Chem. Commun. 1967,729. (18) Reuben, J.; Fiat, D. J. Chem. Phys. 1969,51,4909. (19) Peters, J. A.; Nieuwcnhuizcn, M. S.; Raber, D. J. J. Mugn.Reson. 1985,65,417. (20) Solomon, I. Phys. Rm. 1955,99, 559. (21) Kowalewski,J.;Nordenskiiild, L.; Benetis, N.; Westlund, P.-0. Progr. Nucl. Mum. Reson. Soectrosc. 1985. 17. 141, (22) gelding, R. hi.; Pascual, R. 0.;McGarvey, B. R. J. Mugn.Reson. 1982. 46. 406. @3) Golding, R. M.;Pascual, R. 0.;Hoare, I. C. J. Mugn.Reson. 1984, 58,219. (24) Vega, A. J.; Fiat, D. Mol. Phys. 1976,31, 347. (25) Gueron, M. J. Magn. Reson. 1975,19,58. (26) Shannon, R. D.; Prewitt, C. J. Acta Crysrullogr. 1969,E25,925. (27) Helm, L.; Merbach, A. E. Eur. J. Solid Stare Inorg. Chem. 1991, 28, 245. (28) Gysling, H. J.; Tsutsui, M. Adv. Orgummet. Chem. 1970,9,361. (29) (a) Bertini, I.; Luchinat, C.; Mancini, M.; Spina,0.J . Mugn.Reson. 1984,59,213.(b) Banci, L.; Bertini, I.; Briganti, F.; Luchinat, C. J. Mugn. Reson. 1986,66,58. (c) Bertini, I.; Luchinat, C.; Mancini, M.; Spina, G. Mugneto-Strucrurul Correlurion in Exchunge Coupled Systems; Willet, R. D.; Gatteschi, D.; Kahn, 0.. Eds.; D. Reidel Publishing Company: Dordrccht, Holland, 1985. (30) Banci, L.; Bertini, I.; Luchinat, C. Nuclear and Electron Relaxation; VCH Weinheim, Germany, 1991. (31) Koenig, S. H. J . Mugn.Reson. 1978,31,1. (32) Abragam, A.; Blcaney, B. Electron Purumugnetic Resonunce of Trunsition Ions; Clarendon Press: Oxford, 1970. (33) (a) Finn,C. B. P.;Orbach,R.; Wolf, W. P. Proc. Phys.Soc. (London) 1961,77,261. (b) Orbach, R. Proc. Phys. Soc. (London) 1961,A77, 821. (34) Larson, G. H.; Jeffries, C. D. Phys. R N . 1966,141,461. (35) Cowen, J. A.; Kaplan, D. E.; Browne, M. E. J . Phys. Soc. (Jupun)
1962,17,465. (36) Misra. S. K.: Orhun. U.Solid Srure Commun. 1987. 63. 867. (37) Malhotra, V.'M.; Buckmaster, H. A.; Dixon, J. M. J. Phys C: Solid Srure Phys. 1980,13,3921. (38) Al'tschuler, S . A.; Valiev, K. A. Souiet Phys. JETP 1959,35, 661.
