J. Phys. Chem. 1994,98, 4517-4521
4517
Hyperfine Scalar Coupling for Attractive Ions in Paramagnetic Solutions. Its Effect on the Tl/Tz Ratio in NMR Relaxation E. Belorizky,'lt P. H. Fries,$ W. Gorecki,? M. Jeannin,* and C. Robys Laboratoire de Spectrombtrie Physique (associb au CNRS), Universitb J. FourierlGrenoble 1, B.P. 87, 38402 Saint- Martin d'Hkres Cbdex, France, CEAIDbpartement de Recherche Fondamentale sur la Matiere Condensbe, SESAMICC, 17 rue des Martyrs, 38054 Grenoble Cbdex 9, France, and DSVIDBMSIRMBM, CEN, 17 rue des Martyrs, 38054 Grenoble Cbdex 9, France Received: January 3, 1994'
We report careful measurements of the relaxation times T1 and T2 of the phosphorus nucleus on the (CH3)4P+ ions in varying concentrations of 'ON (S03)~~anion free radicals in DzO solutions a t 25 O C for a n N M R frequency v1 = 8 1 MHz. The hyperfine scalar coupling between the 31Pnuclei and the free radicals is determined from the frequency shifts of the resonance lines with respect to their position in the diamagnetic solution. It is shown that this interaction has a negligible effect on the longitudinal relaxation time TI, which is governed by the magnetic dipolar intermolecular coupling, but significantly contributes to the transverse relaxation time T2, leading to a ratio, T1/Tz z 1.5, in excellent agreement with experiment. I. Introduction Since the early days of NMR, relaxation rates have been recognized as powerful tools for studying the intra- and intermolecular motions in liquid solutions.1 In particular, the intermolecular relaxation rates depend through various mechanisms on the relative diffusion processes which are correlated to the equilibrium distribution of the pairs of molecules. The theoretical treatment of these dynamical processes has been the subject of increasing interest and of considerable improvement. A large variety of situations has been considered, including nonpolar solutes in nondipolar and dipolar solvents,24 dipolar solutes in nondipolar solvent^,^ and ions in dipolar solvents.6 For ion pairs in water, encouraging results concerning the potentials of mean force, which are simply related to the equilibrium pair distribution, are available for both attractive' and repulsive ions.* Two recent papers9J0 were devoted to a detailed study of the relative dynamical behavior of the *ON (SO3)22- anion free radical (NDS-) with respect to the tetramethylphosphonium (TMP+) cation in dilute D20 solutions at 25 OC. The ions were approximated as charged hard spheres which undergo uncorrelated relative translational and rotational diffusional motions. The water molecules were considered as hard spheres carrying central polarizable point dipoles and tetrahedral quadrupoles. The solvent effects on the interionic behavior were introduced through the solvent averaged potential of mean force at finite concentration (FC) of ions wnFC(R), where R is the distance between the ion centers. The lower indices Z and S refer to the TMP+ cation and to the N D S - anion carrying the nuclear and electronic spins Z and S, respectively. This potential is isotropic. Its infinite dilution limit was calculated within the RHNC" approximation of the integral equation theory of statistical mechanics of interacting classical particles. The ionic screening was taken into account according to the simple Debye-Huckel model.12 The equilibrium pair distribution g,s(R) is deduced from the above potential of mean force using the Boltzmann canonical probability
* Author to whom all correspondence should be addressed.
Universitd J. Fourier/Grenoble 1. CEA. 8 DSV/DBMS/RMBM. Abstract published in Aduonce ACS Abstracts, April 1, 1994.
At the minimal distance of approach 6 i f the ion centers of the attractive pair, gIs(b) takes values of the order of 200 for the typical ionic strengths of our solutions, instead of values between 1 and 5 observed for a solution of uncharged nondipolar molecules. The relaxation rates 1 / T1of the TMP+ protons were measured at four N M R frequencies9.10 and for various concentrations of NDS2- free radicals. The intermolecular dipolar magnetic coupling between the protons Zand the electronic spins Sdominates the relaxation mechanism. The effects of the spin eccentricity on each ion were included. The conditGna1 probability of finding the ion centers atihe relative position R a t time t , given that they were at position Ro at initial time 0, was assumed to satisfy the Smoluchowski diffusion equation
w_hereD is the relative interionic diffusion constant and >(R) = -Va[w1sFC(R)/kr] is an effective force between the ions derived from the R H N C approximation, as explained above. It was then possible to compute this intermolecular relaxation rate for any particular set of ion diameters, of distances between the ion centers and the spins, and of translational and rotational diffusion constants. The R H N C relaxation rates were calculated using measured values of these geometrical and dynamical constants and gave quite good agreement with experimental data without any adjustable parameter. The discrepancy never exceeded 22% at 13 MHz, 12%at 26 MHz, and 5% at 80 MHz. Thesame procedure was appliedconcerninglo theinterpretation of the longitudinal relaxation time of the phosphorus nucleus on the TMP+ at 101 MHz for various NDS2- concentrations. The intermolecular dipolar magnetic coupling is still the dominant relaxation mechanism, but using the same R H N C approximation without any adjustable parameter, we obtained 3lP relaxation rates about 45%lower than the measuredvalues. Thisdiscrepancy was qualitatively explained by the anisotropic shape of the interacting ions, mainly that of the NDS2- molecule, leading to anisotropic collision processes between the ions of the pair. Shorter minimal distances of approach between the 3lP nucleus and the free electron are favored with respect to the hard-sphere model, while only slight modifications can be expected in the proton-free electron minimal distance.
0022-3654/94/2098-45 17%04.50/0 0 1994 American Chemical Society
4518
Belorizky et al.
The Journal of Physical Chemistry, Vol. 98, No. 17, 1994
Another important feature of the NMR of 3lP nuclei in these solutions is the presence of a significant scalar hyperfine coupling with the freeelectron radicals. The averagevalue of this coupling could be easily measured10 from the frequency shifts of the resonance line between the diamagnetic and the paramagnetic solutions. It was shown10 that this hyperfine coupling has a negligible effect on the longitudinal relaxation rate 1/TI. However, it could be expected that this coupling significantly contributes to the transverse relaxation rate 1/T2. In section 11, the general expressions of the longitudinal and transverse intermolecular relaxation rates 1/ T1 and 1/ T2 are summarized for the dipolar magnetic and scalar hyperfine couplings. In the following section, we explain how the measured average value of the resonance frequency shifts in the paramagnetic solutions can be used for calculating the relative contribution of the hyperfine interaction to the intermolecular relaxation rates. Experimental details are given in section IV. Finally, the theoretical ratios T1/T2 are evaluated in the last section and compared to the experimental data. It will be shown that to a large extent these ratios are independent of the relative diffusion constants and of the anisotropic effects.
The latter are the Fourier transforms of the correlation functions g2(t)of the random functions r3Ya(B,4) which are characteristic
of the relative position vector ?(r,O,+) of the interacting spins Z and S:
g2(t) = ( r o 3 ~ ~ , ~ ([rT3 0 ~Y~,~(~,+)I , + ~ ) *) (9) The reduced spectral densitiesj2(w~)also depend on the rotational diffusion constants Df and D.# of the two ionic species and on the eccentricity parameters ( p I / b ) , (ps/b) where P I and ps are the distances of Zand S to the centers of their respective molecules. It has been shown13 thatjl(w7) can be expressed in a power series of these eccentricity parameters, but obviously the leading term j 2 ( 0 7 ) corresponds to the situation where the spins are located at the ion centers. Then, the time correlation function gz(t) reduces to
G 2 0 ) = N s s s g I s ( R o )~ ( * ~ , f i , R03 t ) Y2,q((3~,@~) X
Y,,q(9,9)] d3*, d3R (10)
11. Intermolecular Relaxation Rates
The observed relaxation rates 1/TI and 1 / T2 of a given nuclear species are
(3) -1= -
T2
1 T :
1
+inter T2
(4)
where l/T1O and 1/T20 are the longitudinal and transverse relaxation rates of these nuclei in the absence of any paramagnetic anions (diamagnetic solution). The intermolecular interactions with the free radical electrons yield the main contributions l/Tli"tCr, 1/T2interto the total rates. As explained above, the intermolecular relaxation arises from two mechanisms: (i) the dipolar magnetic interaction between the investigated nuclear spinZand theelectronicspinSof the free radical; (ii) the hyperfine scalar coupling between Zand S when there is some unpaired spin density of the free electron a t the nucleus. The detailed theory giving the corresponding expressions of the relaxation rates was given previously.9,10,13,'4 Let yI and ys be the gyromagnetic ratios of the Z and S spins, respectively. We have ys >> 71. (i) The intermolecular dipolar magnetic relaxation rates are
where ko(Ro,Bo,@o)and k(R,B,@)are the intercenter vec_tor_sat time t = 0 and f , and where the conditional probability p(Ro,R,t) obeys eq 2. The numerical procedure for solving this equation has been described elsewhere.13 (ii) The hyperfine scalar coupling between the radical free electron and the nucleus Z can be written as1 %, = fi A(r)
7.3
(11)
The fluctuations of the coupling function A(r) resulting from the random relative motoins of the interacting spins lead to the following relaxation rates?JOJ9
where the scalar dimensionless spectral densityj,(wT) is defined by
j s ( w ) being the Fourier transform
of the hyperfine correlation function In the above expressions Ns is the number density of the electronic spins, b = 5.1 AistheminimaldistanceofapproachofthecentersI0 of the TMP+ and NDS- molecules considered as hard spheres, T = b 2 / D is the translational correlation time, D = Df + Dsl being relative diffusion constant of both kinds of ions. For our ionic solutions, we estimated10 D = 2.2 X 10-5 cm2 s-* and T = 1.2 X 10-l" s. W I and ws are the Larmor angular frequencies of the spins Zand S . The spectral densitiesjz(w) are dimensionless quantities related to the dipolar spectral densities j,(w) by (7)
of the dimensionless coupling constant a(r) related to A(r) by
The interest of this formulation is to simplify any comparison between the magnetic dipolar and hyperfine contributions. A general method for calculating UT) has been d e ~ c r i b e d . ~ ~ J ~ However, the functions A(r) and a(r) are commonly taken to be proportional to an exponential factor exp(-h,r) which describes the short-range decay of the free radical wave function and
The Journal of Physical Chemistry, Vol. 98, No. 17. 1994 4519
Hyperfine Scalar Coupling for Attractive Ions consequently of the free electron density at a distance r from its mean position. Here, we ass~meI0.'~ that
a(r) = > ~ ( - x J )
(18)
where the factor 1/ r is introduced for mathematical convenience. We can expect a value of A, of the order of 1 A-I, while the factor 1/ r has a much slower decrease than the exponential and has no physical importance. For the particular form (eq 18) of a(r)it was possible to obtain analytical expressions of a(r) in terms of rotational invariants and to easily compute the spectral densityjS(w). Then, the latter is conveniently written as
The observed relative frequency shifts of the protons of T M P in the presence of NDS2- free radicals was in excellent agreement with the predictions of eq 24, showing no measurable hyperfine scalar coupling. On the other hand, for the phosphorus nuclei, we observed10 large departures from expression 24, from which we deduced a ratio
A'hyp V
- Avobs V
"dip lJ
for c, = 0.01 -mol L-I, corresponding to a A(r) = 1.0 X 106 c, rad s-1 or a(r) = -0.67 c,. Then, with the form (eq 18) of the function a(r),the above determined average value is of about 0.1 ppm -
where J(w7) is another dimensionless spectral density. The advantage of writing eq 19 is to show the proportionalityofj,(w.r) to the constant cz. From eq 5,6, 12, and 13 we obtain the following expressions of the total intermolecular relaxation rates:
where the pair equilibrium function gIs has been defined by eq 1. For a reasonable value X,b = 5 , we deduce a value of c/b = -28.8. It can be noted that varying X& between 3 and 10 allows the values of c / b to be modified without altering the quality of the agreement between the observed and the calculated values of Avlv. For A& = 3 and A& = 10, we obtained c / b = -4.17 and c/b = -2060, respectively. Thevalueof the function a(r)at the molecular contact distance b is, for X,b = 5 , C
a(b) = - exp(-X,b) = -0.195 b
111. Frequency Shifts and Hyperfme Coupling
It is well-knonw15 that the introduction of paramagnetic electronic spins in a solution induces a shift of the resonance lines of the various nuclei with respect to their position in the diamagnetic solution. This shift arises from two contributions, the first one from the dipolar magnetic coupling and the other one from the hyperfine scalar coupling. The first one can be easily calculated.16 It is given by
Avdi Y
= -SfXpr,
where Sfis a form factor, which is Sf= -4.1 for a thin tube with a ratio heightldiameter h / d = 10, and xprais the susceptibility of the paramagnetic impurities
For S =
'12
and gs = 2 we obtain
--Y - 1.54 X 10-3 Tcs c, being the free radical concentration in mol L-I. Since the free radical concentrations in our solutions do not exceed 0.1 mol L-I, we see that this shift will be relatively small, less than 0.4 ppm. The hyperfine scalar coupling being a short-range interaction, the induced frequency shift is independent of the sample shape. It leads to a relative shift5J0 for S = l/2:
-
-*%yp - - -1 -hYI A ( r ) V
4%
kT
or, according to the definition (eq 17),
(25)
(29)
which corresponds to A(b) = 2.9 X lo5 rad s-I, according to eq 17. For X,b = 3 and 10, the values of A(b) would be 3.1 X lo5 and 1.4 X 105 rad s-1, respectively. This provides an order of magnitude of the maximum hyperfine coupling which can be compared with the maximum value of the dipolar interaction of the ion pair at the same distance b. The latter is the order of r ~ s h / b 3= 1.5 X 106 rad s-1, i.e. about 1 order of magnitude larger than the hyperfine coupling at the contact distance.
IV. Experimental Section
Ionic Solutions. The dynamic studies of the (CH3)4P+/*ON(SO&*- pair were carried out in heavy-water (Eurisotop, 99.95 atom 9% D, sealed under argon) solutions of tetramethylphosphonium chloride (CH3)dPCl (Aldrich), potassium nitrosodisulfonate K20N(SO& (Aldrich), and sodium carbonate Na2COS. First, Fremy'ssalt K20N(S03)2 was recrystallized in order to remove solid impurities and then dried under vacuum for approximately 48 h. The tetramethylphosphonium chloride was dried in a Buchi oven under vacuum at 80 OC. This procedure is necessary to eliminate any trace of light water, the proton signal of which is superimposed on the NMR signal of the TMP+ protons. The various salt concentrations, 0.1 and 0.5 mol L-1 for TMP+, and 0-0.08 mol L-1 for NDS2-, were weighted and the samples sealed in a drybox under argon. The N D S - concentrations were tested by measuring the absorbance in the visible spectrum at 540 nm using a Perkin-Elmer spectrometer. The purpose of the carbonate is to give a basic solution and hence stabilize the *ON(S03)22-radical, which decomposes rapidly in neutral or acidic solution. It was found18 that 0.05 M of Na2C03 was sufficient to stabilize the *ON(S03)22- radical for approximately 2-3 days at 25 OC, or for approximately 1 week if kept frozen.
Belorizky et al.
4520 The Journal of Physical Chemistry, Vol. 98, No. 17, I994 TABLE 1: Measured Relaxation Times TI and T2 of the 31P Nucleus at Y = 81 MHz and T = 298 K for a 0.1 mol L-1 Solution of (CH3)Q+ Cation in D20 Solution for Various Concentrations c, of the Free Radicals ‘ON(S03)22-. Values of the Intermolecular Relaxation Rates 1/ ?,”’, and 1 Defined by Eqs 3 and 4 Are Also Listed as Well as the Ratio f,ntcr/$p
c, (mol L-I)
TI (SI T2 1 / 7 y (s-l) 1 / T y (s-1)
0 (diamag sol) Tio 11.3 Tzo = 3.5 0 0
Tf”/T,””
0.0185 0.515 0.320 1.85 2.84 1.54
0.037 0.280 0.171 3.48 5.54 1.59
0.055 0.203 0.130 4.84 7.41 1.53
0.075 0.160 0.100 6.16 9.71 1.57
TABLE 2 The Same As Table 1 for a Concentration 0.5 mol L-1 of TMP+ 0.079 0.0215 0.040 c, (mol L-1) 0 (diamag sol) 0.332 0.183 Tio = 12.0 0.560 Ti (s)
~2 (si
l/?yr(S-l)
11T y (s-1) F” irintcr 1 / 2
Tio = 4.75 0 0
0.360 1.70 2.57 1.51
0.212 2.93 4.51 1.54
0.124 5.38 7.85 1.46
TABLE 3: -Values of the Dimensionless Spectral Densities
A ( w ) and j,(or) for a DzO Solution with 0.1 mol L-l of
TMP+ and Various Concentrations c, of NDSZ- Free Radicals at T = 298 K and for a 31PNMR Frequency YI = 81 MHz, Le. o r = 0.06 and 0.g = 97.6. The j ; ( w ~ )Are Given for XA = 5. The Calculated Values of Are Also Reported for Different Values of A&
y/?:tcr
c, (mol L-1)
72(0)
12(w) iz(ws7) X 10’
jI(0) ., wsr) x
Au = 2(2 log 2)1/2(352)’/2= 59.8 Hz
In order to avoid any difficulty concerning the problems of line widths and consequently of the transverse relaxation rates in the multiplet spectra,’ a strong decoupling of the proton resonance lines was performed. Under these conditions we obtained a single exponential decay of the echo amplitude signal, while this is not the case in the absence of decoupling. Note that decoupling has practically no effect on the observed TI relaxation times. V. Results and Discussion The measured relaxation times TI and T2 of the 31Pnuclei at a resonance frequency u1 = 81 MHz and a temperature T = 298 K for concentrations 0.1 and O S mol L-1 of TMP+ are given in Tables 1 and 2, respectively, for concentrations of NDS2- radicals varying between 0 (diamagnetic solution) and c, = 0.08 mol L-I. In each case the values of 1/ Tlintcr and 1/ Tzintcr defined by eqs 3 and 4 are provided, as well as the ratios Tlintcr/Tzinm. We have calculated the various dimensionless spectral densities ~ ~ ( O ) , ~ ~ ( W ~ ) , ~ ~ ( andjs(ws.r) W ~ T ) , ~ appearing ~ ( ~ ) , in eqs 20 and 21. They are given for both kinds of solutions, 0.1 and 0.5 mol L-I of TMP+, in Tables 3 and 4 for the various concentrations c, of NDSZ- used. In these tables we also give the calculated ratio T l i n t W / Tzintcr.It should be emphasized that there are no adjustable parameters in the calculations of the dipolar spectral densities jz(w7). The translational correlation time is 7 = bz/D = 1.2 X 10-10 s with b = 5.1 X 10-8 cm and D = 2.2 X 10-5 cmz s-1, as explained above. In order to calculate thescalar hyperfine spectral densities jS(o7),we chose X,b = 5 . However, varying X,b in,a
0.037 0.574 0.554 0.466 1.055 3.281
0.055 0.550 0.530 0.444 0.978 3.124
0.075 0.528 0.509 0.424 0.907 2.979
1.58 1.56 1.60
1.57 1.55 1.59
1.56 1.54 1.58
1.55 1.53 1.57
g n t c r lp ; t c r
h,b = 5 X,b = 3 X,b = 10
TABLE 4 The Same A> Table 3 for a Concentration 0.5 mol L-1 of TMP+. The j , ( w ) Are Given for A& = 5 0.040 0.079 cs (mol L-1) 0.0215 j2(0)
gWI-4 .@(@87)
NMR Measurements. The phosphorus relaxation times TI of the (CH3)4P+/*ON(S03)2z-pair were measured by the usual 180°-t-900 pulse sequence18 a t 81 MHz using a Brucker-200 WB Spectrometer. The phosphorus relaxation times Tz were measured either by the Hahn spin echo pulse sequencelg or by the CPMG20J sequence (when T2 > 0.2 s) on the same spectrometer. There is an indirect exchange coupling between the 12 equivalent protons and the 31P nucleus of T M P . The value of this coupling was previously given:22 3 J p = ~ -14.4 Hz. We made a new measurement of this coupling in our solution, and we obtained 3 J p = ~ f14.65 Hz. Due to this coupling, the phosphorus high-resolution spectrum had 13 components with one central line and 6 pairs of symmetric satellite lines on each side with relative intensities 1:12:66:220:495:792:924 (central line). The width of the spectrum at half-height is
io3
0.0185 0.604 0.584 0.494 1.157 3.481
JdO)
.
$nter/
10’
x 103
0.469 0.450 0.369 0.725 2.586 1.52
0.459 0.440 0.360 0.696 2.520 1.51
0.442 0.423 0.343 0.646 2.404 1.50
reasonable range between 3 and 10, we checked that the spectral densities are practically not affected although the values of c / b are different. This is due to the fact that an increase of X, means a faster decrease of the function a(r),which is compensated by larger values of the pair correlation function gIs(R). For completeness we give the results of the calculation of Tlintcr/ Tzintcrfor X,b = 3 and X,b = 10 in Table 3. According to the experimental uncertainties on T1 and Tz which are about 3%, the comparison between the observed ratios Tlintm/TzintmofTables 1 and 2 with thecalculated values of Tables 3 and 4 shows a remarkable agreement for all the concentration of NDS-and for both solutions of TMP+. We obtain an unusual value of about 1.5 for this ratio. As far as the absolute values of l/Tlintcrand l/Tzinterare concerned, we obtain relaxation rates which are about 50%lower than the measured values. As explained previously for the longitudinal relaxation rate,1° this is due to the strongly anisotropic collisional process between the ions of the pair. The TMP+ cation has tetrahedral symmetry, and the N D S - is approximately ellipsoidal in shape. Then shorter minimal distances of approach between the nucleus and the free electron will be favored with respect to the hard-sphere model for some relative orientations of the ions. We are now testing this possibility through a Monte Carlo simulation of the ion dynamics in our solutions. This is the reason why we studied the ratio Tlintcr/TZintcr. According to eqs 20 and 21, this ratio only involves the dimensionless spectral densities j z ( w 7 ) and j s ( w r ) . The main uncertainty concerning r/b3 = 1/Db is eliminated. Indeed the anisotropic collision process introduces a large indetermination in the effective value of b. Furthermore, the relative diffusion constant D is not known accurately. Its determination was previously discussed? However, we performed recent experiments through spin echo techniques with pulsed magnetic field gradients in order to measure the absolute diffusion constant Of of the T M P for a fixed temperature. We observed significant variations of Of when theconcentrationof free radicals was increased without any measurable change of the solution viscosity. It seems that Df increases with c,. This phenomenon has not yet been explained, and it increases the difficulty of interpretation of the absolute values of the relaxation rates. It can be argued that the correlation time 7 also appears in the reduced spectral densities. However, as can be seen in Tables 3 and 4,the contributions ofjz(ws7) and jS(ws7) are negligible andjz(wF) is very close tojz(0). Thus, in
Hyperfine Scalar Coupling for Attractive Ions
References and Notes
first approximation we have -=
28j,(O)
The Journal of Physical Chemistry, Vol. 98, No. 17, 1994 4521
+ 5j,(O)
which is obviously independent of T . Finally, several remarks must be pointed out. We have estimated theeccentricity effectsof the freeelectronon theNDS2molecule. Indeed, the free electron is not at the center of the ellipsoid. There is a spin density centered at the midpoint of the NO- bond? leading to an average distance to the center of the anion ps = 1.6 A and to a value ps/b = 0.31. This effect, which has been taken into account in the spectral densities given in Tables 3 and 4, leads to an increase of 15% for l/Tlinterand of 10% for l/Tzinkrwithrespect tothecalculatedvaluesforacentered electronic spin in a spherical molecule. It is interesting to evaluate the contribution of the hyperfine scalar coupling to the total intermolecular relaxation rates. The relative contribution of j8(wSr)to l/Tlinter is absolutely negligible (2.4 X le3). But, as expected, the contribution ofjs(0) to 1/T2jnteris about 25%.This explains the unusual ratio T1inter/T2intCr = 1.5, which is quite different from that expected for a purely dipolar magnetic coupling, which would be 1 in the extreme narrowing case T = = 1.16 at our working frequency. 0 and close to The main result of our work is that the determination of the magnitude of the hyperfine coupling through frequency shift measurements and the contribution of this coupling to the transverse intermolecular relaxation rate give an excellent agreement with the ratio Tlinter/T2inter. This shows the overall validity of our model for describing the dynamical properties of solvents with diluted attractive ions.
(1) Abragam, A. La Principes du Magn6tisme Nuclhire; P U F Paris, 1961. (a) Chapter VIII. (b) Chapter XI. (2) Reisse, J. Nouv. J. Chim. 1986,10,665. (3) Machos, A,; Reisse, J. J . M a g . Reson. 1991, 95, 603. (4) Luhmer, M.; Van Belle, D.; Reisse, J.; Odelius, M.; Kowalewski, J.; Laaksonen, A. J . Chem. Phys. 1993,98, 1566. (5) Dally, E.; Miiller-Warmth, W.Ber. Bunsen-Ges. Phys. Chem. 1977, 81, 1133. (6) Miiller, K. J.; Hertz, G. H. Chem. Script. 1989, 29, 277. (7) Fries, P. H.; Jagannathan, N. R.; Henning, H. G.;Patey, G. N. J. Chem. Phys. 1984,80, 6267. (8) Fries, P. H.; Rendell, J. C. T.; Bumell, E. E.; Patey, G.N. J. Chem. Phys. 1985, 83, 307. (9) Fries, P. H.; Belorizky, E.; Rendell, J. C. T.; Burnell, E. E.;Patey, G.N. J. Phys. Chem. 1990,94, 6263. (10) Jeannin, M.; Belorizky, E.; Fries, P. H.; Gorecki, W. J . Phys. 11 France 1993,3, 1511. (11) Lado, F. Phys. Rev. 1964, 135, 1013. (12) Berry, R. S.; Rice, S. A.; Ross, J. Physical Chemistry; Wiley: New York, 1980; pp 997-1006. (13) Fries, P. H.; Belorizky, E. J. Phys. (Paris) 1978, 39, 1263. (14) Fries, P. H.; Belorizky, E. J. Phys. (Paris) 1989, 50, 3347. (1 5 ) (a) Jesson, J. P. In N M R of Paramagnetic Molecules; La Mar, G. N., Horrocks, W. D., Holm, R. H., Eds.; Academic: New York, 1973; p 1. (b) Swift, T. J. Ibid; p 53. (16) Belorizky, E.; Fries, P. H.; Gorecki, W.; Jeannin, M. J . Phys. 11 France 1991, 1, 527.
(17) Fries, P H.; Rendell, J.; Bumell, E. E.; Patey, G.N. J . Chem. Phys. 1985, 83, 307. (18) Levy, G. C.; Peat, I. R. J. Magn. Reson. 1975, 18, 500. (19) Hahn, E. L. Phys. Rev. 1950,80, 580. (20) Carr, H. Y.; Purcell, E. M. Phys. Rev. 1954, 94, 630. (21) Meiboom, S.; Gill, D. Rev. Sci. Instrum. 1958, 29, 688. (22) Albrand, J. P.; Gagnaire, D.; Martin, J.; Robert, J. B. Bull. Sco. Chim. Fr. 1969, 1, 40.
