19F Chemical shift tensor in fluorobenzene compounds

--Cherr&lPhysi&

26 (1977) 123_.130

...

-.

,. .@INorth-Holland fib!ishitig Company _;. :, :

-jQi CHEMICAL SHIFT TENSOR PN FLUOROBENZENE :

COMPOUNDS

.H. RABE&-and M. MEH&G Institut jiir Physik, Universiriit Dortmund, 46 Dorttnund, Germany

.- Received 2.5 May 1977

-’

_Fluorine-19NMR multiple-pulse experiments have been applied to a series of mete-, pan- and orthosubstituted fluoroin the solid state. The principal elements of the lgF chemical shift tensor (LJL~,(rz2, (rss) were deter-

benzene com&unds

mined and the orientation of the tensor axes was infersred from secondary information like molecular motjon. related compounds and liquid crystal studies. Comparison with anisotropies obtained from molecules dissolved in liquid crystals

in the nematic phaseis discussedwheredata are available.Usingthe Gicrke-Rygare approachwe wereable to extract the spin-rotation interaction tensor elementsC,,, CyYand C,, of I9F in sever; 1fluorobenzene compounds.

1. Introduction

The chemical shift tensor in fluorobenzene has attracted much attention in the past [l-l 11. In spite of the numerous investigations, there was a great deal of confusing and conflicting data until the advent of multiple-pulse experiments [ 12-141, which have been applied successfully to fluorine compounds [X]_ hdrew and Tutistall[2] have observed the l9F NMR linewidth in fluorobenzenes.and other compounds at different magnetic fields_ By application of a second moment analysis they were able to extract the order of magnitude of the chemical shift anisotropy [2]. Before reliable tensor data were available, theoreticians had suffered from lacking information and almost any choice of suitable parameters was able to “explain” the isotropic shift data [1,9-l l] ; Karplus and Das [i] h&e obtained suitable.expressions for the local paramagnetic part of the chemical shift tensor.and have applied their theory to the fluorobenzenes. Later other molecular orbital (MO) approachtis have been applied to these compounds in order to investigate trends when different atoms or molecular groups are attached to the benzene ring [g_ll].-

:

Chk and Dubin [S] on the other hand have extracted information about the paramagnetic part of the chemical shift tensor in mtinofluorobenzene from spin-rotational inieractiod, dkte&nined by molecular :

beam experiments. This approach, however, cannot be applied tL the other fluorobenzenes, since already in monofluorobenzene spin rotational interaction is hardly resolved and the data extracted are questionable [S]. It was Snyder and co-workers [3,4], who first applied the liquid crystal method to mono- and hexafluorobenzene, by dissolving these molecules in a nematic solution. Later Nehring and Saupe [6] repeated these measurements and extended them to other fluorobenzene compounds. The shift of the NMR line in the nematic solution onem differs from the shift in the isotropic phase F as [6]

(1) where O= f(a,, + aYv + aJ (2) and where Sii are the elements of the ordering matrix S, which is defined by Sii = ~(3 COS

~j

COS Sj

-

S ji} )

(3)

where Si (i =x,y, z) are the angles between the optic axis of the solution and the molecular i axis. The brackets ( ) denote a th!rmal average. The ordering matrix S may be determined by observing satellite spectra due to dip&r interactions. The sign of the ordering matrix elements Sii, however, ha&to be assumed. This Can bz1 to faulty results [19].

y+ebGcr,. not;..&& only two different values are ob-mined in the liquid &y&l method, namely a,,,~, ahd E and-it isiunexpected, that all six elements of the symmetric chemical shift tensor can be determined. On the contrary only some linear combination of the tensor eleinents uXX,oYY,u,, in the molecular frame is obtained in the llquid crystal study. Only in cases of high enough symmetry, i.e. axialIy symmetric chemical shiit tensor, reliable data are to be expected from such an analysis. Multiple-pulse experiments of the high-resolution type [ 121, however, are capabIe of detennlnlng the symmetric part of the chemical shift tensor fully, i.e. all six elements, three principal values o1 l,02~. o33 and the orientation of the three principal axes can be determined in a single crystal study [ 13,141. Even in a powder sample, the principal eIements u1 l, u22, us3 can be determined unambiguously [S]. For a review about these techniques see refs. [ 13,143. Hexafluorobenzene was one of the fnst compounds investigated by this method [S]. The investigation of other fluorobenzene compounds has been reported previously [14-161 and the intention of this pacer is to summarize all these results and to compare our data with those from liquid crystal studies. The chen&l shift data are analyzed according to Gierke cd Flygare [17] (GF) and spin-rotation interaction tensors are extracted for some of the fluorobenzene compounds investigated. 2. Experimental The compounds investigated were purchased from Merck, Darmstadt and used without further purifica-tion. In order to prevent motional averaging of the chemical shift tensor ah data were taken at liquid nitrogen temperature and are compared with spectra at elevated temperatures. Multiple pulse powder spectra of 19F were taken at 84.6 MHZ(x2.1 14 tesla), while decoupling the protons [ 161 by applying rf pulses at 90.0 MHz as is schematically drawn in fig. 1. ABruker pulse spectrometer SXP 4-100 has been used in combination with a home built double-resonance setup. The rf signals at both frequencies were applied to a single coil by means of a matching network [ 161. The lgF magnetization in the rotating frame was sampled once every cycle, digitized and accumulated in a ‘Varian 620 L computer. The resulting @h-resolution

Fig. 1. Radio-frequency pulse timing&applied to theI((‘gF) and S(‘H) spins in a multiple-pulse experiment including heteronuclear decoupling of the S spins. Observation of the I spin magnetization is favourately accomplished during the. “windows”in the1 and S pulse cycles. Two alternativedecoupling cycles appliedto the S spins are shown. Their advantageand disadvantage concerning the decc&pling efficiency is discus’sed in the text.

free induction decay was qn-line Fourier-transformed_ The corresponding powder spectra were compared with theoretical lineshapes f&the chemical shift tensor elements ull, 022, u33 could be directly obtained from the fitting procedure [14]. Heteronuclear decoupling in combination with multiple pulse experiments has to be performed in a coherent fashion as was outlined previously [ 181. General aspects of heteronuclear decoupling have been discussed recently and.the reader is.referred to refs. [13,14]. The standard procedure would be. to apply a rrpulse to the S spins @rotons.in this case) once every four-pulse cycle as is shown in the top part of fig. 1. In fluorobenzene, however, the llnebroadening due to the protons contributes more to the lmewidth than the homonuclear fluorine broadening; Therefore the proton decoupling hasto be more-efficient, than the fluorine linenarrowing by the four-pulse experiment; Several subcylces of-proton decoupling pulses are .. therefore implementedwithin one-four .pulse cycle as is schematically dratin,m fig. 1..A representative ex: ample of homonuclear and heteronucleardecouplmg, ..

-;

‘. H. Rabei. M. Mehring}lSF chemical shirt tensor in fluoiobenzene compounds

125

demonstrating the different stages of linenarrowing is shown in fig. 2.

3. Results and discus&on

. . . . . . . . . -200

-IL0

-eo-Ld

.

0

40

80

.

I

G

Fig. 2. A typical powder spectrum (lQF in CFsC6HsCOOH at room temperature) showing the different stages of homonuclear- and heteronuclear decoupling. (a) Ordinary “F solid state spectrum; (b) with only the four-pulse sequence [12] applied and (c) with additional proton decoupling according to fig. 1. The chemical shift (ppm) is quoted with respect to C&G.

Preliminary data of chemical shift tensors in tiuorobenzene compounds have been reported previously [14-161. The molecular structure of the different fluorobenzene compounds investigated in this report is schematically drawn in fig. 3. In table 1 we have collected refined data from different fluorobenzene compounds as obtained from multiple-pulse powder spectra [ 161. A pictckial representation of these data is given in figs, 4 and 5. The following orientation of the principal axes is suggested by the temperature dependence of the powder spectra, liquid crystal studies and multiple-pulse single crystal studies of related compounds [19]: (i) The I-axis is perpendicular to the CF bond, but in the molecular plane. (ii) The 2-axis is parallel to the CF-bond. (iii) The 3-axis is perpendicular to the benzene ring. The aii values obtained from the multiple-pulse

(“3

p-Fluoroiolucnc

Fig; 3. Schematic drkfing

.

of the molecular structures of the different fluorobenzene

compounds

investigated in this work.

126

H. Raber, M. Mehring/~lgF chemical shift tensor in fruorolxntene compounds

Table 1..

.: ._ M+yred chk$A shift ten.& elements (~11 =G~zz < 033) &Ippm as obta+d from multiple pulse powder spectra. values tie quoted on an absolute scale [22,23], with i?(C6HsF = 302 ppm). The experimental error is +6 ppm Compound

011

T.22

033

GVG&F3

223 230 247 246 260 270

304 310 310 316 310 304

365 356 350 365 412 408

299 269 232 252 241 240 239 220 222 248

299 307 31.5 328 302 320 327 271 304 299

457 407 357 358 377 350 359 397 359 449

1.3C6H82 C6HsF 1,446H4Fz lP2-C6&F2 1,2,‘k5-C6HzF4 C6F6 o-C6HqFOH mC6H4FOH pC6H4FOH OC6HaFCHg rn-C,jH&&

P-%%FCHa oC6H4FCOOH pCoH4FCOOH tluoranil [S]

-5

297 299

302 309 327 328 352 327 301 313 307 303 308 298 295 332

powder method are within experimental error the un-

ambiguous principal elements of the chemical shift tensor [14]. Note, that our values of oii disagree with most of the data obtained by other methods [2-71. As mentioned above, the liquid crystal study does not

Fig. 4. Pictorial representation of the chemical shift tensor elements QI, 0~2 and 033 of “F in fluorobenzenes as deter- . mined from multiple-pulse experiments. The data are represented on an absolute scale [22,23], where c(C6HsF) = 302 ppm The convention DIL< o22 Q 033 has been used.

250

3w

350

LW dppm!

Fig. 5. Pictorial representation of the chemical shift tensor elements IJ~~,033 and 033 of lgF in different fluorobetizene compounds obtained from multiple-pulse powder spectra. The data are represented on an absolute scale [22,23], where z(C6HsF) = 302 ppm. The convention 011 Cd& 4033 has been used. allow to draw conclusions about the principal values

and axes of the chemical shift tensor without resorting to other information. It is therefore not surprising, that some of the conclusions drawn from the liquid crystal studies concerning the components of the, chemical shift tensor and the chemical shift anisotropy are in error [3,4,6,71. Similar statements apply to the second moment analysis [2]_ However, we have demonstrated recently, that the Iinear combination of chemical shift elements Uii as obtained in liquid crystal investigations could be compared with the same combination of Uii values obtained from multiplepulse experiments [16,20]. In table 2 we compare the linear combination of chemical shift values obtained from the liquid crystal method by Nehring and Saupe [6] on fluorobenzenes with the same combination of our data obtained by the multiple-pulse method. As seen from table Z-the agreement between the data from the different experimental methods is quite convincing. It suggests, that the liquid crystal method does indeed give reliable data in terms of the linear combirkion of chemical shift tensor elements in the molecular frame, whereas any coticlusion about the principal elements of the chemi&l shift tensor as derived from liquid crystal data alone must be corisldered with care. On the other hand, the results of table 2 suggest, that there is not m&h diffecence between the. chemical shift tensorin the. liquid and in the solid

127

H. Raber, M. Mehring/?9F chemical shifttensor in fluorobenzene compounds

Table 2 Comparisorrof the linear combination of chemical shift tensor elements uXX,u,,,,, Q_, obrained from liquid crystal studies [6] with the same combination of oI1. oaa, oaj from multiple-pulse experiments according to table 1. The .zaxis, which is pcrpendicular to the benzene ring coincides always with the 3 axis as is determined by molecular rotation [ 8 j. The comparison favours -the assignment 02s = oyy, placing the 2 axis of the chemical shift tensor along the C-F band Compound

liquid crystal

1,3,%6H&,

296.8

ez.2- :f%

1,3-CeH4F2 C&SF lr4‘CgH& lr2CeH& 1,2,4,5C&F4 C&b

298.9

u,z - 0.250,x -‘o.75uyy

302.0 308.6 327.5 328.4 351.8

uzz - 0.0760,~ - 0.9250yV ozz + OAla,, - 1.470,, czzz- 0.350~~ - 0.65uy), or7 - i?.25exX- 0.750Y,, %z - +Xx + uyy)

+ 9”)

state, i.e. molecular symmetry and configuration instead of crystal symmetry plays a major role for the chemical shift tensor. In molecular crystals the chemical shift tensor can therefore be considered as a local property of the molecule. However, we have observed changes in the isotropic shift of several ppm when going from the liquid into the solid state. These shifts are small compared with the anisotropy and are neglected in our investigation, mainly because they are experimentally unreliable due to a possible change in the scaling factor, when cooling the sample down to liquid nitrogen temperature. Table 2 suggests the assignment crZ2= a,,,, placing the 2 axis of the chemical shift tensor (al,, uZ2. u33) along the C-F bond, whereas the 3 axis is oriented perpendicular to the benzene ring. Note the following general properties of the chetnical shift tensor in fluorobenzene compounds as is evident from figs. 4,s and 6, where ui 1, u22 and ui3 of different compounds are plotted versus the isotropic shift. (i) There is a pronounced “ortho-effect” in the sense that, the a33 component (perpendicular to the ring) is mainly affected, when another fluorine or OH group is placed into an ortho position. A shift of about 50 ppm in the u3 3 component is observed for each ortho-fluorine. Besides the “ortho-effect” the e33 component is fairly independent of substitution. (ii) The uZ2 component (pamlIe to the CF bond) is almost insensitive to substitution. (iii) The ulf_ component (perpendicular to the CF

101 t 1 7224 50 23 f 5 117 c 5 12254 158 +_I

multiple pulse 022 = oyy

022 = ~x.r

105.5 66 44.8 16.1 119.5 112.5 158

105.5 ,106. 98.2 151 134 129.5 158

bond, but in the molecular plane) changes gradually with substitution and even linearly with the isotropic shift 5. Again an “ortho-effect” might be visible in terms of about 25 ppm shift for each ortho-fluorine_ The axial symmetry of the chemical shift tensor in Ce Fe, which seemed to be a puzzling situation before, now appears to be an accidental consequence of the “ortho-effect”. This does not, however, give an explanation for the “ortho-effect” itself. Karplus and Das [I] and others [9-l 1,231, have tried to apply molecular orbital (MO) theories to 19F chemical shifts as noted before. Although some trends could be explained, there are not satisfactory ab inito or even semi-empirical calculations available, which are capable of even roughly describing the experimental observations. In fact the theory of Karplus and Das ]I] has been invoked to “explain” questionable results at different occasions [4,5]. There is some hope, that gauge independent atomic orbital (CIAO) methods [23,24] might give satisfactory theoretical explanation for fluorine chemical shift tensors. One has to await future developments in this field. Since ab initio calculations of the chemical shift tensor of fluorobenzene compounds are not available at this time and other molecular orbital calcuiations are not straightforwardly applicable to these compounds, we are going to apply the semi-empirical approach of Gierke and Flygare [ 171 (GF). The shift tensor u can be separated into two different parts according to Ramsey [21] u=ad+oP,

where

.

. . . .

. . G22

I

-x

x

300

310

Fig. 6. Correlation 022 and 033 with zene compounds. from table 1. The

320

330

360

350

of the chemical shift tensor elements 011, the isotropic shift Zin different fluorobenThe experimental data (symbols) are taken solid lines are inserted as guid&nes.

the diamagnetic and on being the paramagnetic part of the chemical shift tensor. In the GF approach u is expanded into six terms as follows:

with ud being

c&=ItIItIII+IV,

cl,p=x,y,z,

(4)

I = Oatoma II =e?1(2mc2) CZi~i~3(&im,p i

olipi) ,

Here ri = (xi, yi, zi) is the vector from the shielded nucleus to a neighbour atom i, with the atom dipole moment (4 and the atom electronic second moment (p*)i, and with the Kronecker 6,u 5 1 if (Y= p and Sap = 0 if cr# 0. Zi is the atomic number of nucIeus i and the sum Zi runs over all nuclei with the shielded nucleus being omitted_ All terms I-IV can be calculated once the molecular strucutre and the atomic dipolar moments and electronic second moments are known. Term V, however, is related to a different molecular quantity, namely Cap the spin-rotation interaction tensor and where Zap is the corresponding moment of inertia, pu is the nuclear magneton and gf is the nuclearg value of the shielded nucleus. All other parameters have their usual meaning. The tensor crap can be diagonalized and the principal axes and principal elements are readily evaluated, once all the molecular parameters are known. We have calculated terms II-IV acc_ordingto eqs. (5)-(7) for all the fluorobenzene compounds discussed in this work by using the appropriate dipolar moments [17], second moments [17] and the known moIecuIar structure. All angles and bond Iengths have been set to standard values. We note, that the socalled dipolar contribution (term III) amounts to about 1 ppm and may be neglected,in an analysis of this kind. Terms II and VI cancel and reflect the gauge dependence of & and UP respectively. The spin-rotation interaction term V can then be estimated by means of the experimental shift tensor oexp and terms I, III and IV as UP’=v=crexp

- & ) :

.. c-3

where od’=I+IIIfIV.

(9)

The “gauge independent” tensors r# ‘and up’ were

calculated according to eqs. (S), (6), (8) and (9) and

H. Raber, M Mehring/L9F chemical shift tensor in fluorobenzene compourlds

129

:. Tabie.3.. -1 The calculateddiamagnetic part od’ and the paramagnetic part op’ of the chemical shift tensor as derived from the experimental data according to cq: (8) for different fluorobenzene compounds. Note, that the principal axis system of the tensor &’ and oP’ respectively, is rotated about the z axis by the angle 6. For e = 0, (Y= x, p = Y_

1,3,5’AjH3F3 1.3C&Fz CsHsF 1,4-r%%& 1,2-CeH4F, 1,2.4,5CeH2F4

d o,

op 8’

%a d

Ofdegree)

7iP’

&

$,,

4;

0(degree)

463 464 463 463 467 464

493 492 492 493 489 493

459 460 460 460 459 460

0 4 0 0 9 3

-175 -173 -170 -163 -145 -144

-240 -236 -216 -217 -213 -199

-189 -180 -182 -171 -174 -184 -194 -181 -168 -164 -170 -173 -163 -206 -187

-94 -104 -110 -95 - 47 - 52 - 1 -81 -108 -99 - 51 -101 -100 - 59 -99

0 10 0 0 29 3.5 0 24 13 0 38 12 0 22 0

C6F.s

464

494

458

0

-120

-165

oC6H4F-CH3 mCeH4F-CHs p-c&F--CHs o-C6HiF-OH mC6H4F-OH fleH4F-OH

464 463 463 463 463 463 466 463

491 491 491 491 491 491 490 491

458 458 458 458 458 458 456 458

9 5 0 9 5 0 3 0

-164 -168 -163 -144 -170 -158 -173 -173

-231 -226 -224 -207 -233 -211 -253 -24 1

o-C~H~FC%~OH

p-C6H4FCOOH

are listed in table 3 for different fluorobenzene compounds. The tensors are not expected to be diagonal in the “bond frame” (x,y, z) for all compounds, as is indicated by the rotation of the tensors about the z axis by an angle 6, which is determined by the diagonalization procedure. The values of 0 belonging to the paramagnetic tensor should be considered with care, since they rely on the assumption, that the experimental tensor oexp coincides with the bond frame (x,y, z). This is not expected to hold, however, in the compounds, where f3f 0.We therefore quote in table 4 only those values of the spin-rotation interaction tensor Cap, where the bond frame coincides with the inertial frame. The values Caawere obtained from the data of up’ as quoted in table 3 by using eq. (7)_ Note, that od’ is not very sensitive to substitutions on the benzene ring, as can be seen from table 3. This is due to the fact, that the quadrupolar term (IV) in the Gierke-Flygare theory [17J does not depend very much on substitutions “far away” from the nucleaus considered, since this interaction falls of as r-3. It is not expected, that a more rigorous theory would drastically change these numbers. It is therefore justified, that all the experimentally observed variations in the

.

chemical shift tensor are loaded onto an’. Consequently the “ortho-effect” appears as a drastic change in the z and x components of the tensor GP’and the related spin-rotation interaction tensor Cep. The knowledge of the spin-rotation interaction tensor is of considerable interest in molecular physics. . In the case of large molecules like the fluorobenzenes the extraction of the spin-rotation interaction tensor from molecu!ar beam experiments is exceedingly difTable 4 Spin-rotation interaction tensor Co.6of “F in different fluorobenzene compounds, obtained from the paramagnetictensor as listed in table 3 by using eq. (7). All values are in kHz. E = $(Cxx + CYY+ Car) and C2 = & + C;Y + C?,, Compound

Cxx

-2.53 1,3SC&F3 -6.26 C&SF 1,4C&_Fa -6.06 -1.20 CsF.s pCeH4F-CHs -5.82 pC6H4F-OH -5.78 p-C&F-COOK-2.67

CYY

CZZ

C

[Cz]r/z

-1.98 -3.35 -1.86 -1.02 -1.91 -1.75 -1.02

-0.49

-1.16 -0.64 -0.003 -0.70 -0.63 -0.33

-1.67 -3.59 -2.85 -0.74 -2.81 -2.74 -1.34

1.88 4.15 3.68 0.91 3.56 3.50 1.66

ficdt tid even in the most simplest case, namely ‘mono:fluorobenzene no reliable data can.be obtained as is demons&&d by the discrepancy between our .@a a& those of ref. [S J _We therefore hope, that the estimated values of the spin-rotation interaction tensor for fluorobenzene compounds as presented in table 4 are of some use to molecular physicists and chemists. The reliability mainly rests on the validity of the GF approach and the value used for uatom. Recently spin-lattice relaxation of rgF via chemical shift anisotropy and spin-rotation interaction 125-281 has attracted much attention. Here the relation between the reorientational correlation time r2 and the angular velocity correlation time rJ is of considerable interest, concerning different models for molecular motion. A better knowledge of the chemical shift tensor and the spin-rotation interaction tensor may help to elucidate these points.

Acknowledgement We wish to acknowledge the assistence of D. Suwelack in taking part of the experimental data. This work has been financially supported by the Deutsche Forschungsgemeinschaft.

References [ 1) M. Karplusand T.P. Das, J. Chem. Phys. 34 (1961) 1683. (21 ER Andrew and D.P. TunstaU, Proc. Phys. Sot. (London) 81(1963) 986. [3] L.C. Snyder and E.W. Anderson, 3; Am. Chem. Sac. 86 (1964) 5023; J. Chem. Phys. 42 (1965) 3336. [4] LX; Snyder, J. Chem. Phys. 43 (1965) 4041. [S] S.I. Chan and AS. Dubin, J. Chem. Phys. 46 (1967) 174s.

[6] J. ?+&~g and A. Saupe, !; gem Phys, 52 (1970) + 1397:. -[?I C.S. Yannoni, B.P. Dailey and-&i. iis&, j. Che& ._.. : . . .,... Phys. 54 (1971) 4020. (81 M._h$ehring, R.G. Griffii and J.S. W&h, J. C&m. Phys. 55 (1971) 1146; J. Am. Chem. Sot 92 (1970) 7222. [9] F. Pros&and L Goodmann, J. Chem. PhLs. 38 (!963) 374.. [IO] R.W: Taft, F. Prosser, L. Goo$&m and G.T. Da& J. Chem. Phys. 38 (1963) 380. [ll] R.T.C. Brownlee and-R_W_ Taft, J. Am. Chem. Sot. 92 (1970) 7007. [12] J.S. Waugh, L.M. Huber and U. Haeberlen, Phvs. Rev. Letters 20 (1968) 180. [13] U. Haeberlen, Advan. Magn. Resonance ,&ppl. (1976). [ 141 M. Mehring. in: High resolution NMR spectioscopy in solids, Vol. 11 (Springer, Berlin, 1976). .[lS] M. Mehring. H. Rab& and G. Sinning, Proceedings of the 18th. Colloque Ampere (Univ. Nottingham Press,. No&ham, 1974). [16] H. Raber, Doctoral Thesis, Dortmund (1977). [17] T.D. Gierke and W.& Flygare, J. .jm. Chem. Sot. 94 (1972) 7277. [18] M. Mehring, A. Pines, W-K. Rhim and_J.S: Waugh, J. Chem. Phys. 54 (1971) 3239. [19] R.G. Griffin; H.N. Yeung,M.D.LaPradeand H.S.Waugh, J. Chem. Ph?s. 59 (1973) 777. (201 H. Raber and M. Mkhring, Chem. Phys. Letters, 49 (1977) 498. [21] N.F. Ramsey, Phys. Rev. 77 (1950) 567; 78 (1950) 699. 1221 D.K. Hindermann and CD. Cornwell, J. Chem. Phys. 48 (1968) 4148. [23] B.R. Apple& and B.P. Dailey, Advan. Magn. Resonance7 (1974) 231. [24] R Ditchfield and P.D. Ellis, in: Topics in carbon-13 NMR spectroscopy, ed._G.C. Levy (Wiley, New York, i9i4). (251 E. Wolff, Diploma w&k, Dortmund (1977). [26] W.E; Hull and B.D. Sykes, J. Mb. Biol. 98 (1975) 121. 1271 J.H. Chaffin and P.S. Hubbard, J. Chem. Phys. 46 (1967) 1511. [28] T-E. Bull, J. Chem. Phys. 59 (1973) 6173.

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