J. Phys. Chem. 1981, 85, 3883-3887
the NOz plane. For NO2-vycor, AA, is again virtually unchanged while AA, = -18.7 and AA, = +32.8, or the same trends as for neon but less pronounced. This is to be expected for NO2 above the surface rather than sandwiched between layers. (We note that the molecular orbital analyses’”l7 rely on configuration interaction to interpret the inequality of AA, # AA, induced by the medium.) Last of all, we wish to comment that, as the NOz rotates about the y axis above the Vycor surface, one may anticipate that A (and g) may be modulated by interaction with the surface (as we noted above). In fact, one might envision a cooperative rotation of the NOz about its y axis with a small bond angle variation33 with the rotation and with a small variation in the distance of its center of mass from the surface in order to accommodate this motion. Finally, one may speculate on a surface structure in which both oxygens have weak van der Waals bonds to the surface, which could allow a partial rotation of the NOz about its y axis to include the two conformers in which the NO2 plane is parallel to the surface and the conformer in which the oxygens point to the surface, while at the same time suppressing rotation about the molecular x and y axes. (Note that a 180’ rotation about is sufficient to average out second-rank tensor C#J
3883
components g, -g, and A , - A,, cf. ref 29.) This should be the subject of further investigation.
V. Conclusions The NO2 molecule adsorbed on Vycor displays a predominantly axial rotation about the y axis (parallel to the 0-0 internuclear axis) below 77 K but above this temperature the motion becomes more nearly isotropic probably due to a translational diffusion mechanism. The line shape analysis is reasonably consistent with this picture, except for some discrepancies in detail for 77 K and below, which are worthy of further study. From consideration of quantum models for the rotation, it is suggested that this y axis aligns parallel to the surface, but further work with 170labeling is recommended.
Acknowledgment. We thank Dr. G. Mor0 and Ms. L. Schwartz for their help and advice. This research was supported by Grant No. DE-AC02-80ER04991 from the Office of Basic Energy Sciences of the DOE, by NSF Grant CHE 80-24124, and by the Cornel1 Materials Science Center (NSF), and acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support.
Temperature and Density Dependence of the Proton Lifetime in Liquid Water W. J. Lamb, D. R. Brown, and J. Jonas* Department of Chemistry, School of Chemical Sciences and Materials Research Laboratory, Unlverslty of Illinois, Urbana, Illinois 6 180 1 (Received: June 22, 198 1)
The NMR TIptechnique is developed to determine the average residence time, T,, of a proton on a water molecule in liquid water. The temperature and density dependence of 7,is measured in the range 0-100 “C and at densities up to 1.125 g cm-3 (pressure range, 1bar to 5.6 kbar). The T1, technique is compared to other NMR methods such as the T1 and TZ techniques also used to determine T ~ .The anomalous behavior of T~ with compression at temperatures below 40 “C parallels changes in other physical properties of liquid water.
Introduction Ever since Meiboom’s original paper,l there has been considerable effort to determine the rate constants governing proton transfer between H30+( k l ) and OH- (k,) ions and neutral water molecules. However, a review of the literature2+ since 1961 reveals that the values of kl and k2 and the corresponding activation energies for these rates are still in dispute. More recently, work has centered on the measurement of the average time that a proton spends on a water molecule (7,)in bulk neutral water and in occluded water. Woessner7has measured 7,’s for preferentially ordered water molecules in minerals and porous clays. Pintar et a1.8 have determined 7, values for bulk (1) S. Meiboom, J. Chen. Phys., 34,375 (1961). (2) A. Loewenstein and A. Szoke,J. Am. Chem. SOC.,84,1151 (1962). (3) Z. Luz and S. Meiboom, J. Am. Chem. SOC.,86, 4768 (1964). (4) R. E. Glick and K. C. Tewari, J. Chen. Phrs., 44, 546 (1966). (5) S. W. Rabideau and H. G. Hecht, J. Chem. Phys., 47,544 (1967). (6) D.L. Turner, Mol. Phys., 40, 949 (1980). (7) D. E. Woessner, J. Magn. Reson., 16, 483 (1974).
0022-3654/81/2085-3883$0 1.25/0
neutral water from NMR spin-spin relaxation (T2)measurements, and Noack et aln9have determined 7,by using the field-cycling technique to measure spin-lattice relaxation (T,) at very low Ho fields. In this work we present the first direct application of NMR spin-lattice relaxation measurements in the rotating frame (T1J to determine the temperature and density dependence of 7,. Meibooml has shown that the Bloch equations modified for proton exchange may be solved provided certain assumptions are made. For our experimental conditions these assumptions are valid, and the expression relating the proton lifetime to the difference in relaxation rates is
Pis: 1 _1 _ _ TI 7et:1 + 7,2(8? + 012) TI,
(1)
where 7e is the average time that a proton is bonded to a given oxygen atom, Pi is the relative intensity of the ith (8) R. R. Knispel and M. M. Pintar, Chern. Phys. Lett., 32,238 (1975). (9) V. Graf, F. Noack, and G. J. BBn6, J. Chem. Phys., 72,861 (1980).
0 198 1 American Chemical Society
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The Journal of Physical Chemistry, Vol. 85,No. 25, 1981
line, 6iis the frequency difference between the ith line and the dominant central line, and w1 = yH1 is the angular frequency in the rotating frame. The sum is carried out over the sextet proton resonance that arises because of spin-spin interaction between the spin 5/2 170(-3% 170H2in our case) and the spin 1/2 'H. The difference in the relaxation rates is due to the slow proton exchange process (-10 kHz) occurring between 160H2and 170H, molecules in the liquid state. This low-frequency modulation of the protons local field lowers T1, but does not affect T1. The right-hand side of eq 1 is the contribution to the TlPrelaxation due to the slow exchange process. Equation 1 may be further simplified by using the approximation that uI2 >> 6 t . For an 170/'H spin-spin splitting constant of J = 90 Hz'O and a dim= = 56 = 5 ( 4 , this approximation is valid for H1 2 0.05 G. Equation 1 then becomes
where A = ( 3 5 / 1 2 ) p ( 2 ~ &(ref ~ 11) and p is the fraction of 170H2present in the sample. A similar expression has been used by Burnett et al.1° to measure the temperature and pH dependence of J in liquid water and by Deverell et a1.12 to study the temperature dependence of the chair-to-chair isomerization in cyclohexane. The goal of this work is to develop the T1,technique for the study of proton exchange and to determine the affect of temperature and density on the average proton lifetime in bulk neutral water.
Experimental Section NMR Measurements. The automated pulsed NMR spectrometer has been described in detail e1~ewhere.l~ The temperature dependence of re along the saturated vapor pressure (svp) line was obtained in the high-temperature NMR probe. The pressure dependence of re was obtained in an externally heated high-pressure NMR probe.14 For both probes, the temperature gradient across the sample was never more than 0.5 "C. All proton NMR measurements were performed at 60 MHz (14.1 kG) in a wide-gap (9.5 cm) electromagnet. The proton Tl was measured by using the inversion recovery pulse sequence (18Oo-7-9O0). The proton TI, was determined from the height of the magnetization following a series of spin-locking pulses of duration r. The fixed field (Ho)resolution was at least 1.5 ppm, and Van Putte'sle A parameter for H1homogeneity estimation was typically 0.03. The experimental range of spin-locking fields used was 0.05 < H1< 2.5 G. In all cases H1>> AHo so that magnetization was not lost due to dephasing. Samples. Samples containing 3-4% 170Hzand natural deuterium abundance were prepared by diluting 20% 170H2(Merck & Co., Inc., St. Louis, MO) with glass-distilled low-conductivity water. If necessary, the pH of the sample was adjusted to 7.0 f 0.1 at T = 22 "C by the addition of small amounts of 0.001 N NaOH or HC1. On the basis of proton chemical shift measurements in liquid water,16 we can estimate that the low concentration of the structure making Na+ or C1- ions added should not sig~~~
(10)L. J. Burnett and A. H. Zeltmann, J. Chem. Phys., 60,4636 (1974). (11)Z. Luz and S. Meiboom, J . Chem. Phys., 39,366 (1963). (12)C. Deverell, R.E. Morgan, and J. H. Strange, Mol. Phys., 18,553 (1970). (13)D. M.Cantor and J. Jonas, Anal. Chem., 48, 1904 (1976). (14)J. Jonas, D. L. Hasha, W. J. Lamb, G. A. Hoffman, and T. Eguchi, J . Magn. Reson., 42, 169 (1981). (15) K. Van Putte, J. Magn. Reson., 2, 174 (1970). (16)C.Deverell, Prog. Nucl. Mugn. Reson. Spectrosc., 4,235 (1969).
nificantly affect the value of re. During the course of the measurements, four samples were diluted and pH was adjusted if necessary. The percent of 170H2in these samples varied because of differences in the starting fraction of 170H, (-20%), dilution errors as the volumes were small, and exchange of I7OHz with atmospheric water vapor during the dilution and pH adjustment. The different fraction of 170H2in each sample resulted in differences in the value of A ( A a p ) , but the value of reis independent of this fraction and was the same for each sample (see the discussion in the next section). All NMR measurements were performed in carefully cleaned quartz sample tubes. For the temperature study, the sample was degassed and sealed on a vacuum line. Only one sample was required for the temperature study. Several samples were required for the pressure study as a sample had a limited lifetime due to any leaching from the sample cell assembly or contamination by the pressurizing fluid. Sample purity following a pressure run was verified by reproducing the 7, value a t 1bar. All samples used in the pressure study were not degassed. Paramagnetic Impurities. Even after careful degassing, the T1 of the prepared 170H2sample was -15% lower than the literature value.17 We suspect that the low value was due to dissolved paramagnetic ions present in the 20% 170Hzsample as the water used for the dilution gave the correct Tl. To check whether these paramagnetic centers had an affect on re, we measured lifetimes for a degassed sample and another sample containing dissolved air (OJ. The Tl's of these samples differed by -40%, but the measured lifetimes were the same. This result was expected since any paramagnetic center undergoing rapid motion in liquid water should increase the rate of Ti and TlPrelaxation equivalently. The difference in these rates still reflects the low-frequency proton exchange process. Errors. There are several sources of error involved in the determination of re. The approximations necessary to solve the modified Bloch equations are explicitly stated in Meiboom's original paper.' Experimentally, the measurement accuracy of T1,Tlp,and the HI field strength is f 5 % . As the calculation of re involves a fit to ol2,errors in the value of H1are the most severe. In addition, there is the possibility of pH drift during the measurement as the samples were not buffered. The approximate overall error in the measured lifetimes is estimated to be -&20%. N
Results and Discussion Returning to eq 2, we can see that a dispersion relationship exists between l/Tipand Hi = q / y . Physically, as the frequency in the rotating frame (7H1/2r)comes into resonance with the rate of proton exchange (l/re),l/Tlp decreases as spin-locking energy is exchanged. Equation 2 predicts that ( l / T l - (l/T1JZ- = A(l/Tlp) = r J ; hence, the width of the dispersion is directly proportional to the lifetime provided A is a constant (see the discussion later in this section). The pressure data at 90 "C shown in Figure 1 demonstrates these features. At 90 "C the lifetime is such that the whole dispersion relationship is observed for our range of Hi fields. Once the T1 is measured and the TlSis determined as a function of the spin-locking field, a linear fit to eq 2 is performed. Only the T1, data in the sloping dispersion region is used since this is the region where u1 = yH1/2r is in resonance with 1Ire. In Figure 2 we show the results for the 90 "C pressure data. From the slope and the intercept of the line, we can determine both 7, and A. (17)J. C. Hindman, A. Svirmickas, and M. Wood, J . Chem. Phys., 59, 1517 (1973).
The Journal of Physical Chemistry, Vol. 85,No. 25, 198 1 3885
Proton Lifetime in Liquid Water
TABLE 11: Experimental Density Dependence of the Average Proton Lifetime in Water
T, "C
P, bar
0
1 526 1817 3545
30
1
90 05
GI
1.0
30
laglOH, (goussl
Figure 1. Proton Ti, dispersion for -3% "OH2 water at 90 O C and various constant densities: (0)p = 0.965; (0) p = 1.025; (A) p =
1.075; (V)p = 1.125. i
I
I
g cm-3
1.000 1.025 1.075 1.125 0.996 1.025 1.075 1.125 0.983 1.025 1.075 1.125 0.965 1.025 1.075 1.125
705 2164 4017 1 1125 2767 4900 1 1551 3251 5630
60
c05
p:
T, ms
10-4A,bs-'
0.53 0.56 0.55 0.46 0.35 0.30 0.34 0.29 0.21 0.18 0.11 0.081 0.12 0.081 0.042 0.024
0.72 1.4 1.6 1.8 2.1 2.6 2.0 2.6 2.8 2.7 2.9 3.0 2.9 3.1 3.1 3.7
a Value taken from ref 1 8 and 20. Several samples were used so the fraction of "OH, is not constant. For details, see the text.
I 06-
- 03-E bW
w f x IO-* (rad2/se&
Figure 2. Plot of (l/T,,, - l/T,)-' vs. w,' for -3% i 7 0 H , at 90 OC and various constant densities: (0)p = 0.965; (0)p = 1.025; (A) p = 1.075; (V) p = 1.125.
TABLE I: Experimental Temperature Dependence of the Average Proton Lifetime of Water Under Its Own Vapor Pressure
02-
01Oo8
b
10
Jb
I 30
410
LO T
1 60
; 70
EO
90
IbO
IT)
Figure 3. Plot of 7,vs. Tfor liquid water along the svp line: (0)this work; (0)ref 9; (A) ref 8.
mentioned that for the longer lifetimes only the high HI field part of the dispersion was observed since HImax was T , "C pf g 1 0 - ~ ~ s, b- ~ r e , 171s 0.05 G. However, enough points were obtained so that a 0 1.00 0.53 0.72 linear fit could be obtained. 0.46 10 1.00 0.87 A plot of the temperature dependence of 7, along the 0.39 20 0.998 1.5 svp line is shown in Figure 3. Within the error, log 7, is 30 0.996 0.35 2.1 a linear function of temperature. Also shown in the figure 0.26 40 0.992 2.5 0.22 50 0.988 2.5 are the average values of 7, found by Pintar et a1.8 from 60 0.983 0.21 2.8 T z dispersion data and the values of T , found by Noack 70 0.17 0.978 2.8 field Tl diset al.9 from a three-parameter fit to low H,, 0.14 3.1 80 0.972 persion data. The agreement between the three NMR 90 0.12 2.9 0.965 measurement techniques (Tip, T2,TI) is good; however, the 100 0.958 0.099 3.0 Tz results appear to be less accurate. Pintar et a1.8 find a Values taken from ref 19. All of the data were obT, = 0.027 ms at 94 "C, which appears to be low and could tained from one sample so the fraction of "OH, is conbe caused by a bad sample. stant. For details, see the text. A plot of the density dependence of 7, at constant temperature is shown in Figure 4. The lines drawn through Similar plots were constructed and fits were made to the data are the best smooth curves. The figure reveals determine T, and A at each temperature and density. The that 7,changes by a factor of 5.0 at 90 "C and a factor of experimental temperature data along the svp line from 0 2.6 at 60 "C. Although the anomalies observed at 30 and to 100 O C are presented in Table I, and the pressure data from 0 to 90 "C and from 1to 5600 bar ( p to 1.125 g ~ m - ~ ) 0 "Care barely outside experimental error, it is interesting to qualitatively compare 7,to other physical properties for are presented in Table 11. The PVT were taken from liquid water. The s e l f - d i f f u s i ~ n ,the ~ ~ -v~i~s ~ o s i t y ,the ~~,~~ Burnham et a1.,18 Kell,19and Kell et aL20 It should be (18)C.W. Burnham, J. R. Holloway,and N. F. Davis, Am. J.Sci., 267, 70 (1969). (19)G.S. Kell, J. Chem. Eng. Data, 12, 66 (1967).
(20) G. S. Kell and W. Whalley, J. Chem. Phys., 62, 3496 (1975). (21)D. J. Wilbur, T. H. DeFries, and J. Jonas, J. Chem. Phys., 65, 1783 (1976).
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The Journal of Physical Chemistry, Vol. 85, No. 25, 1987
080 - 0
20
40
60
80
IO0
T ("C)
o'010.95
1.0
1,05
1,l
Figure 5. Plot of JM vs. temperature along the svp line: (0)this work: (0) ref 1; (A)ref 9.
1.15
p (g ~ r n - ~ )
Figure 4. Plot of
T,
as a function of density at constant temperature.
spin-lattice and the chemical shiftz7exhibit similar behavior. At 0 "C, the initial application of pressure up to -2 kbar results in an anomalous change of each property. A t 30 "C, pressure has little effect on these properties until -3000 bar. This result is explained qualitatively by using a simple physical picture based on the competition between optimal hydrogen bond geometry and increases molecular packing.28 It is interesting that these pressure trends are qualitatively similar for the proton lifetime. A word on an Arrhenius rate law fit to the data is in order. Within the experimental scatter, the svp temperature data can be fit to an Arrhenius rate equation with a preexponential factor of 9.65 X lo6 and an activation energy of 3.45 kcal mol-'. However, plots of log ( l / ~ ,vs. ) 1/T at constant density for p = 1.025, 1.075, and 1.125 are distinctly curved and reveal that the picture of an activated model for proton exchange in water is too simplistic. Such non-Arrhenius behavior is also observed for D, 9, and 7 ~ i , l for liquid water in the low temperature region.29 Now let us turn our attention to the value of A = (35/12)p(2ra2. As mentioned earlier, only one sample was used for the temperature study so the 170H2fraction was constant. An inspection of Table I reveals that the value of A is temperature dependent. Above 60 "C A is a constant within the error, but below 60 "C the value steadily decreases. Meibooml recognized that the decrease in J = 8/71. is due to frequency averaging caused by 170relaxation before proton exchange. This averaging is most severe a t lower temperatures where the T f O decreases and the T , increases. Using Hindman's Tl data30 and our values of 7,, we can calculate the average number of proton exchanges before 170relaxation. At 0, 50, and 100 "C the respective values are 6, 54, and 274. Hence, the leveling off of the value of A above 60 "C is reasonable. Using the average value of A = 2.92 X lo4 s2 above 50 "C and the value of J = 90 Hz, we can calculate that the sample used for the temperature study contained 3.1% ~
(22)T. H.DeFries and J. Jonas, J. Chem. Phys., 66, 5393 (1977). (23)K.Krynicki, C. D. Green, and D. W. Sawyer, Faraday Discuss. Chem. Soc., 66,199 (1979). (24)T.H.DeFries and J. Jonas, J. Chem. Phys., 66,896 (1977). (25)K. E. Bett and J. B. Cappi, Nature (London),207, 620 (1965). (26)J. Jonas, T.H. DeFries, and D. J. Wilbur, J.Chem. Phys., 65,582 (1976). (27)J. W.Linowski, Nan-I Liu, and J. Jonas, J. Chem. Phys., 65,3383 (1976). (28)J. Jonas, NATO Adu. Study Inst. Ser., Ser. C , 41,65-110(1978). (29)F. Franks, Ed., "Water, A Comprehensive Treatise", Vols. 1-6, Plenum Press. New York. 1972-1979. (30) J. C . Hindman, A. J. Zielen, A, Svirmickas, and M. Wood, J . Chem. Phys., 54,621 (1971).
170H2 To compare our result with others, we can calculate a JeffIJ using the measured value of A a t each temperature and the known percentage of 170H2 The results are presented in Figure 5. Our results agree nicely with those of Meibooml and Noackg with the exception of Noack's value at 10 "C. Pintar'@ results are not shown since for his reported 4% 170Hzsolution all values of Jeff are above 120 Hz. It is not meaningful to look a t trends in the density dependence of A at constant temperature as the reported values in Table I1 are average values determined from one or more sample batches and runs. However, the observed values are reasonable. At 60 and 90 "C where Tll'O >> T ~ , all A values fall within the error between the limits 2.8 X lo4 s - ~(3% 170H2)and 3.7 X lo4 c2(4% 170H2). At 30 "C, we would expect that is nearly density independent,26 so the differences in A are due to varying percents of 170H2(p). At 0 "C, the large increase in A is due to an increase in p and T;O. If we assume that l/T:O Kq/T and use our density dependence of K," viscosity data from ref 25, and data from ref 30, we can estimate that T1"O increases from ca. 3.1 ms (1bar) to 4.4 ms (3500 bar) a t 0 "C. The value 4.4 ms is about the value of at 10 "C30which from Figure 5 increases Jefffrom ca. 44 to 56 Hz. We also know from the svp results that the sample for the temperature study contained 3.1% 170H2.For a 4% solution at 0 "C and 3500 bar, the value at 1 bar would increase by A = (0.72 X lo4 ~-~)(0.040/ 0.031)(56/44)2= 1.5 X lo4 s2. Hence, the increased values at higher pressure are reasonable. It is interesting to compare the value of T , in bulk neutral water to that found by Woessner7 for water in cation-exchanged chabazites and in porous clays. In the temperature range from 20 to 100 "C, the T , values for the chabazites range from 0.01 to 10 msec and depend on the cation (Caz+,Na+, K+, LP). The temperature dependence of 7,in all of the chabazites is stronger than in bulk water by a factor of -3. The values of 7, for the Li+ chabazites (0.01 < 7, 1ms) are closest to the values found for bulk neutral water. The water in the porous clay, calcium vermiculite, exists in sheets two layers thick.7 In the temperature range from 50 to 100 "C, the 7, values in this clay range from 0.13 to 0.033 ms. The temperature dependence of 7,in this clay is a factor of -2 stronger than bulk water. However, it is remarkable that the proton lifetime in these materials is comparable to bulk neutral water. As mentioned earlier, Burnett et al.1° used the T1, technique to measure J in liquid water, They found that J was independent of pH and temperature provided T?O >> 7,. Using their results, we can calculate approximate values of T , for a buffered solution of pH 9.21: 0.07 ms (4 "C), 0.02 ms (25 "C), and 0.006 ms (46 "C). When comQ
J. Phys. Chem. 1981, 85,3887-3891
pared to neutral water, these short values indicate that 7, is a strong function of the OH- (or H+) concentration. In addition, the results show that 7, is a function of temperature at constant pH. Obviously the proton lifetime in liquid water depends on several interacting factors. The separation of the contributing factors would require a
3887
considerable amount of further study. Acknowledgment. This research was partially supported by the Department of Energy under Contract DE-ACO276ER01198 and the Air Force Office of Scientific Research under Grant AFOSR-81-0010.
Quadrupolar Relaxation. The Multiquantum Coherences Lawrence Werbelow” Department of Chemistry, New Mexico School of Mines, Socorro, New Mexico 8780 1
and Guy Pouzard Centre de St. Jerome, Universite de Provence, 13397 Marseille Cedex 4, France (Received: June 24, 1981)
The appropriate time evolution equations for the n quantum coherence of a spin I nucleus relaxed by quadrupolar interactions are developed and discussed. The contrasting behaviors for the extreme narrowing and nonextreme narrowing regimes for both isotropic and anisotropic spin environments are examined. The influence of rank-one-type interactions and second-order dynamic frequency shifts are also considered.
I. Introduction The recent development of various multidimensional NMR experiments has stimulated much intrigue and has resulted in numerous applications of practical imp0rtance.l But perhaps the most exciting aspect of these multipulse techniques is the ability to observe (albeit indirectly) the creation and subsequent destruction of multiquantum coheren~e.~-~ As beautifully illustrated by Wokaun and the study of intensive processes which are responsible for the loss of multiquantum coherence provides an important complement to conventional relaxation studies. For example, certain spin correlations which do not affect the observable quantities in conventional “TI”and “Tz” studies do indeed affect the relaxation behavior of the multiquantum c ~ h e r e n c e .Likewise, ~~~ the measurement of the loss of single quantum coherence (lQC), double quantum coherence (2QC), ..., and n quantum coherence (nQC) often provides linearly independent combinations of spectral density term^.^-^ This can greatly aid in the isolation and identification of the large assortment of factors responsible for effecting nuclear spin thermalization. In this paper, we examine the simplest of spin systems that exhibits multiquantum coherence-the isolated multipolar nucleus relaxed by quadrupolar interactions. Of course, for systems at thermal equilibrium, all coherences of all order vanish. However, we shall assume that multiquantum coherence can be produced and monitored (e.g., with a 90°-~-900-~1-“look” pulse-digitize ( T ~ pulse ) sequence). Our immediate interest is the quantification of the disappearance of coherence subsequent to creation. We will consider only the case where the anisotropic quadrupolar Hamiltonian is averaged (not necessarily to zero) in a time short compared to the reciprocal rigid lattice quadrupolar splitting (motional narrowing), and the case where the anisotropic quadrupolar Hamiltonian is averaged in a time short compared to the reciprocal Zeeman splitting *Visiting Professor, Physics Department, Universite de Provence, 13397 Marseille, Cedex 4,France.
(7
