A theoretical study of the dielectric solvent effect on vicinal spin coupling constants

A theoretical study of the dielectric solvent effect on vicinal spin coupling constants

Journal of Molecular Structure, 76 (1981) 93-103 THEOCHEM Elsevier Scientific Publishing Company, Amsterdam - Printed A THEORETICAL STUDY OF THE DI...

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Journal of Molecular Structure, 76 (1981) 93-103 THEOCHEM Elsevier Scientific Publishing Company, Amsterdam







Department of Polymer Tokyo (Japan) SHOSUKE Minato







of Technology,




High School


in The Netherlands

of Technology,

19 April 1980;


in final form

20 June





ABSTRACT The dielectric solvent effect on H-C-C-H, H-C-N-H and H-C-N-C spin coupling constants in ethane, tetrachloroethane and trans N-methylformamide has been calculated by finite perturbation theory based on the INDO and CNDO/S approximations incorporating solvaton theory. The available experimental data are interpreted using the calculated variations of spin coupling constants. The effect of dielectric constant on the general form of the Karplus relation is included in the finite perturbation calculations.


Since Karplus’ prediction from valence bond theory [l] of a strong conformational dependence of uicinal proton-proton coupling constants, the relationship between conformation and vicinal couplings of, among others, ethane derivatives and peptide systems, has received much attention [ 21. Workers have investigated the dihedral angle (a) dependence of uicinal spin coupling constants, the form of which is similar to that given by the Karplus relation pit HH


A + B cos @ + C cos [email protected]


where A, B and C are coefficients. The vicinal couplings have been a key factor in the conformational analysis of various systems and NMR spectroscopy has thus been used for determining the conformational states, observations being made in liquid solution. Thus, to correlate precisely the magnitude of vicinal coupling constants with conformation, the effect of the medium often has to be considered. The aim of the present work is to provide a theoretical prediction of the solvent effect of uicinal proton-proton and proton-carbon couplings. Previous theoretical studies on the solvent effect of coupling constants have dealt with molecules in which the relative spatial positions of coupled OlSS-1280/81/0000-0000/$02.50

o 1981






nuclei are fixed by virtue of their structure. Johnston and Barfield have successfully calculated the solvent effect on coupling constants by means of the finite perturbation theory (FPT) [3] using the reaction field model [4], the cubic closest-packed cluster model [ 51 and the rotating point dipole model [6]. Recently, the present authors [7, 81 have calculated the directly bonded 13C-H coupling constants as a function of the dielectric constant, E, of the solvent using the FPT method incorporating solvaton theory [9] ; the solvent effect on the chemical shift of some organic compounds has been satisfactorily interpreted using this method [lo]. In this work the solvent effect on the uicinal coupling constants of molecules which can assume two or more conformations through internal rotation has been investigated by means of the FPT-solvaton theory [ 71 developed by the present authors. In practice, we discuss the effect of aprotic solvent on H-C-C-H coupling constants for ethane and tetrachloroethane, and H-C-N-H and H-C-N-C coupling constants for trans ATmethylformamide. THEORETICAL


In previous papers [lo] , we have developed “solvaton” theory so as to allow inclusion of solvent-interaction in semi-empirical SCF calculations. A solvaton is an imaginary particle representing the oriented distribution of solvents around each atom in a molecule. The requirements for this theory to estimate the solute-solvent interaction are as follows; (i) a number of charges (the solvaton) are induced in an aprotic solvent of dielectric constant E, (ii) one charge is equal in magnitude but opposite in sign to that of the atom to which it is attached, (iii) there are no interactions between the solvatons, and (iv) the solute--solvent interaction is approximated by the Born equation [ll] which represents the free energy of a solvated ion in a dielectric continuum. Next, we consider the calculation of J$& and J$g coupling constants as a function of e by the INDO [ 121 and CNDO/B [13] approximations including the above-mentioned solute--solvent interaction using FPT theory. The calculation for CHCl,CHCl, was made only by the CNDO/2 approximation because of lack of data for the Slate?Condon parameters for the chlorine atom. In this paper, we consider only Fermi contact interaction since it seems to be predominant in Jr’$ and ?n’g coupling constants. The spin-unrestricted SCF equations of the Fbck matrices FEV and FEij for (Y and 0 electrons include both the Fermi contact interaction and the solutesolvent interaction [ 7, 81 .



(2-2) The third term is the solute-solvent interaction which is given by solvaton theory, the fourth term is the Fermi contact interaction, pg the magnetic moment of nucleus B, 6 (rB ) the Dirac delta function representing the contact term between electron and nucleus B, and other symbols have their usual meanings. The charge Q, is defined by assumptions (i)-(iv) given above. rsl is the solvaton-electron distance and is estimated as follows: if the AO’s and the solvaton are associated with the same atomic center the van der Waals’ radius rv of the particular atom is used for the solvaton-electron distance, and if the AO’s and solvaton are associated with different atomic centers and their distance is rR, rsl is approximated as (r$ + r&)112. The expression for vicinal coupling constant between nuclei A and B using the FPT theory [3] becomes JAB




[&z;fAthF3)l ,_=,,

where (4) in which y is the gyromagnetic ratio, ~~(0)’ is the density at the nucleus of the valence S orbital of atom B and PSS!$‘~(hB) is the spin density matrix corresponding to the valence S orbital of atom A. In the numerical calculation, it is important to choose the correct values for the integrals su( 0)’ and s,(O)’ for hydrogen and carbon atoms, respectively. In this work the values of Pople et al. are used [3]. Bond lengths and bond angles used are standard values proposed by Pople and Gordon [ 141, except for bond length C-Cl (1.71 a) [15]. Values used for the effective van der Waals’ radii are 1.20, 1.59, 1.49,1.39 and 1.80 ,& in hydrogen, carbon, nitrogen, oxygen and chlorine atoms, respectively [ 161. An HITAC Ml80 computer at the Computer Center of Tokyo Institute of Technology was used for all the calculations. RESULTS


The dihedral angle @ dependences of Jti and J$ vicinal coupling constants for the molecules under consideration were calculated as a function of dielectric constant, based on the theoretical procedures described above. As an example, the calculated results for CHCl, CHCl, are plotted against dihedral angle in Fig. 1. This figure shows that the calculated J& data are in accord


Fig. 1. Plots of H-C-C-H vicinal coupling constant against dihedral angle, @, in tetrachloroethane, calculated by the FPT CNDO/Z method.

with the Karplus relation (eqn. 1). The calculated data for the remaining molecules also follow this equation. In these calculations the minima are displaced from the 90” and 270” values of @ suggested by Karplus. Maciel et al. [17] have also suggested that the minima are displaced somewhat from @ values of 90” and 270” in their calculation of pi& spin coupling in ethane using the FPT-INDO approximation. The calculated values of parameters A, B and C are given as a function of dielectric constant in Table 1. The absolute values of parameters A, B and C calculated by CNDO/B are smaller than those calculated by INDO through the range of dielectric constants. The CNDO values for H-C-C-H coupling in ethane decrease on substitution of chlorine for hydrogen atoms; for H-C-N-H coupling the values are smaller than those in H-C-C-H coupling. In H-C-N-C coupling the values of parameters A and B are much smaller than those in H-C-C-H and H-C-N-H couplings, and the value of parameter B in the former is somewhat larger than the latter. The calculated absolute values of parameters A, B and C show an increase with increasing dielectric constant (except for parameter C for J$g in trans N-methylformamide in the INDO calculation). They are described by the relation A,Bor





E dependences of parameters A, B and C of the Karplus expression in ethane, tetrachloroethane and tram N-methylformamide, calculated by means of the FPT-solvaton method Compounds

Dielectric 1

constant 2

(E ) 4

Coefficients in eqn. (5) 10





Ethane (Ij-C-C-~) CNDO/B



6.836 -1.869 6.865 8.346 -2.835 7.523

6.985 -1.918 7.028 8.445 -2.870 -7.590

6.986 -1.919 7.029 8.493 -2.889 7.628

6.997 -1.922 7.041 8.516 -2.890 7.628

6.997 -1.922 7.041 8.516 -2.291 7.628

6.997 -1.222 7.041 8.516 -2.291 7.627

0.180 0.059 0.195 0.189 0.061 0.116

6.835 -1.869 6.865 8.346 -2.835 7.523



Tetrachloroethane (~-C-C-II) A CNDOl2 B c

5.150 -1.189 5.324

5.223 -1.223 5.413

5.259 -1.241 5.456

5.281 -1.253 5.483

5.288 -1.256 5.493

5.293 -1.258 5.500

0.145 0.071 0.079

5.150 -1.189 5.324

4.343 -2.745 4.164 4.963 4.944 -4.393 -4.360 5.149 5.124

4.349 -2.778 4.169 4.974 -4.413 5.164

4.351 -2.781 -4.172 4.978 -4.420 5.169

4.352 -2.782 4.174 4.981 -4.425 5.172

0.038 0.062 0.042 0.083 0.132 0.093

4.315 -2.722 4.131 4.899 -4.294 5.080

1.677 -1.026 1.599 1.793 -1.611 2.335

1.683 -1.032 1.604 1.814 -1.626 2.333

1.685 -1.035 1.605 1.822 -1.630 2.331

1.686 -1.036 1.607 1.827 -1.634 2.330

0.036 0.038 0.009 0.110 0.089 -0,004

1.650 -0.998 1.597 1.715 -1.546 2.336


trans N-methylformamidea (H-C-N-II) CNDO/P A 4.315 B -2.722 C 4.131 INDO A 4.899

B (&-C-N-C) CNDO/2







A B c

1.650 1.597 1.715 -1.546 2.336

4.333 -2.743 4.153

1.668 -1.016 1.598 1.765 -1.588 2.335

where a’ and b’ are the coefficients. The values of coefficients a’ and b’ obtained using eqn. (5) are shown in Table 1. The coefficient a’ is a measure of the strength of the dielectric solvent effect on parameters A, B and C. The coefficient b’ is the value of parameters A, B or C at E = 1. These results show that the INDO values are larger than those for CNDO/B except in the case of J$$ in truns N-methylformamide. The vicinal coupling constants calculated as a function of dielectric constant for the truns and guuche conformations of the molecules under consideration are given in Table 2. All the vicinul coupling constants increase with



E dependences of vicinal spin coupling constants in trans and gauche ethane, tetrachloroethane and tram N-methylformamide, calculated method Compounds



conformations in by the FPT-solvaton


(e )


eqn. (6) 1








15.569 2.467 18.704 3.167

15.931 2.511 18.905 3.215

15.931 2.512 19.010 3.235

15.960 2.515 19.034 3.258

15.960 2.515 19.034 3.258

15.960 2.515 19.034 3.258

0.434 0.053 0.366 0.101

15.569 2.467 18.704 3.167

11.663 1.894

11.859 1.905

11.956 1.910

12.017 1.913

12.037 1.914

12.050 1.925

0.393 0.021

11.663 1.894

trans N-methylformamide (H-C-N-I-I) CNDO/Z qr 11.167 4’” 1.779 INDO Jr’” 14.273 4”” 0.212

11.228 1.772 14.429 0.202

11.261 1.768 14.504 0.192

11.281 1.764 14.551 0.185

11.288 1.763 14.568 0.183

11.292 1.763 14.577 0.187

0.126 -0.016 0.309 -9.030

11.167 1.779 14.273 0.212

4.724 0.364 5.689 -0.221

4.301 0.365 5.740 -0.181

4.319 0.365 5.772 -0.166

4.329 0.365 5.783 -0.158

4.329 0.365 5.790 -0.154

0.104 0.004 0.195 0.066

4.225 0.362 5.596 -0.226

Ethane (H-C-C-~) CNDO/B Jy” Jvgic INDO Jyic #” Tetrachloroethane (H-c-c-H_) CNDO/S q” JY

(~-C-N-C) CNDO/Z J’” $y INDO J?f” G”

4.225 0.362 5.596 +I.226

increasing dielectric constant in the CNDO/Z and INDO calculations. The H-C-N-H coupling constants are nearly equal to those of H-C-C-H in CHClz CHCl, . The H-C-C-H coupling constants in ethane are larger than those in CHClz CHClz and trans N-methylformamide. As is expected, the H-C-C-H coupling constants for ethane are larger for INDO than CNDO/B. On the other hand, for the H-C-N-H and H-CN-C coupling constants for the tram conformation INDO > CNDO/2 whereas for the gauche conformation CNDO/B > INDO. We have suggested that the calculated data for directly bonded l&n spin coupling constants in some organic compounds are a function of (E - 1)/e, J=a




where a, b and c are coefficients (in Hz). In the case of vicinal couplings, the first term can be neglected and therefore the calculated data fall on a straight


line against (E - 1)/e. The coefficient b is a measure of the strength of the dielectric solvent effect on uicinal coupling constants, and coefficient c represents the Jyic and JgVicvalues for an isolated molecule (at E = 1). The results for coefficient b are shown in Table 2. The coefficient b is larger for INDO than for CNDO/B calculations and the value for the tram conformations is much larger than that for gauche conformations. We now discuss a comparison of the calculations and observations of vicind couplings. H-C-C-H

coupling constant

Ethane Lynden-Bell and Sheppard [ 181 measured a vicinal coupling constant of 8.0 + 0.2 Hz in CCL solution for the hydrogen nuclei of appropriate isotopic mixtures of ethanes containing one and two 13Cnuclei. Only the average over tram and gauche conformations is available experimentally. However, many authors have reported uicinal coupling constants in ethane calculated using different quantum-chemical methods. For example, average uicinal coupling Ji: = (Jy’” + 2J,“‘“)/3, when the free rotation around C-C bond is assumed, is as follows; Barbier and Berthier [19] : 5.7 Hz (non-empirical method); Kato et al. [20] : 3.2 Hz (non-empirical method); Tow1 and Schaumberg [21] : 10.24 Hz (INDO with triplet CI) and 9.82 Hz (CNDO/B with triplet CI); Pople et al. [3] : 8.38 Hz (FPT INDO) and 6.76 Hz (FPT CNDO/B); and Duval [ 221: 9.3 Hz (Dirac vector method). The results of the semi-empirical calculations are not very far from the experimental value, but the agreement is somewhat poorer for the non-empirical calculations. These calculations were done for an isolated molecule. In this work, the average uicinal constants in Ccl4 [ 231 are 8.493 (FPT INDO) and 6.984 (FPT CNDO/B). The INDO calculation is near the experimental value compared with the CNDO/B calculation. The experimental data on the solvent effect of uicinal coupling constant of this molecule are not available in the literature. Tetrachloroethane Values of Jyic and JgUicfor CHClzCHClz have been determined, e.g. Gutowsky et al. [24] reported JFic = 16.35 + 0.8 Hz and Jgic = 2.01 + 0.08 Hz (in neat liquid); Sheppard and Turner [ 251, Jp = 14 Hz and JgUic= 2.5 Hz (determined using the energy difference between trans and gauche conformations, AE, obtained from IR measurement in n-heptane, neat liquid and CH,NO,); Abraham et al. [26], Juic = 11.2 + 1.0 Hz and JgVic= 1.9 + 0.05 Hz (obtained from solvent and temperature dependences of the average coupling constant by means of an electrostatic theory [ 271 of the medium effect); and Heatley and Allen [28], Jyic = 9.1-13.4 Hz and JgUic= 0.5-1.5 HZ (obtained in various solvents with the Abraham treatment). Our calculated values of Jyic and qic are very near the experimental data of Abraham et al. [ 261, and Heatley and Allen [ 281. Heatley and Allen have reported that


the experimental values of these parameters decrease as the dielectric constant of the solvent increases. Their experimental trends agree with our calculated ones, although the calculated dependence is somewhat smaller than the observed one. (The observed values of b for Jyic and s’gicare estimated to be about 15 and 9 Hz, respectively, for the experimental data of Heatley and Allen. ) In general, it is difficult to obtain exact experimental data on the dielectric solvent effect on H-C-C-H vi&al coupling constants for molecules in which the relative spatial positions of the coupled nuclei are not fixed. Many experimental data on these effects for molecules in which the relative spatial positions of the coupled nuclei are fixed by the structural features have been reported [ 291. For example, the values of Jyic and J$g coupling constants in styrene oxide and styrene sulfide increase slightly with increasing dielectric constant [ 301. This trend is in agreement with that for ethane and tetrachloroethane. However, the sign of the observed solvent-induced change for HC=CH uicinal coupling constants in fluorine-substituted ethylenes [ 291 is opposite to that for the H-C-C-H couplings studied here. H-C-N-H

and H-C-N-C

coupling constants

The H-C-N-H vicinal coupling constant is a key factor in the conformational analysis of peptides. Neel and co-workers [ 31-341, Ramachandran et al. [36] and others [35, 37, 381 have obtained the Karplus relationships for this coupling, using rigid five- and six-membered cyclic compounds. They have suggested that the derived dependence of the Jj$& on the dihedral angle is expressed by eqn. 1. The average values of parameters A, B and C have been reported as follows; Bystrov and co-workers [37, 381: A = 5.1, B = -1.1 and C = 4.5 Hz; Neel and co-workers [34] : A = 4.7, B = -3.2 and C = 4.7 Hz; Schwayzer [35] : A = 4.9, B = -0.42 and C = 4.78 Hz; and Ramachandran et al. [36] : A = 5.05, B = -1.7 and C = 3.55 Hz. Our calculations agree with the results of Neel and co-workers [ 31-341. This substantiates the assumption made in the empirical approach that the coupling constant depends only on the dihedral angle. Quantum-chemical calculations by several workers further support this assumption. For example, Barfield and Gearhart [39] : A = 5.63, B = -4.32 and C = 5.64 Hz (for cis N-methylacetamide by FPT INDO) and A = 6.03, B = -4.48 and C = 6.04 Hz (for tram N-methylacetamide by FPT INDO); and Ostlund and Pruniski [40] : A = 4.595, B = -3.87 and C = 4.465 (for cis N-methylformamide by FPT INDO) and A = 4.905, B = -4.08 and C = 4.835 Hz (for tram N-methylformamide by FPT INDO). Our calculated results show only small differences with these values. In practice, in order to obtain a close comparison between experimental and theoretical estimates of spin coupling some allowance should be made for solvent effect. Our calculation for the dielectric solvent effect on Jyic and JgUiccoupling constants shows that the former increases and the latter


decreases slightly with increasing dielectric constant. Aubry et al. [ 411 have shown for 2-azabicyclo [ 2.2.21 octanone-3-( 3-isoquinuclidone), that the H-C-N-H coupling constant increases by 7% in polar solvents such CDC13, CH&N and (CD3)2S0, and also with CCL,. They explained that the change in the coupling constant is due to the change in the H-N-C bond angle from 120” (X-ray value for the dimer) to 115” (characteristic of non-dimeric packing in the crystal). Such observations, however, could also be interpreted in terms of our theoretical prediction of the dielectric constant dependence For comparison of calculated and experimental averaged vicinal of J$&. coupling constants in amides, our calculated average vicinal coupling constant, Ji$ = (Jy’” + 2J,“‘“)/3, assuming free rotation around the C-N bond, is 4.908 (E = l)-4.939 (E = 50) for the CNDO/B calculation and 4.899 (E = l)-4.980 (e = 50) for the INDO calculation. These values agree with the observed ones, i.e. 4.9 Hz in neat liquid and 5.0 Hz in an aqueous solution of trans N-methylformamide. Considering the solvent dependence of the H-C-N-C coupling constant, our calculations suggest that the general Karplus relation is obeyed as well as in the cases of the molecules already dealt with. Solkan and Bystrov [43] have shown that the H-C-N-C coupling constant calculated using the FPT INDO calculation obeys the Karplus relation of eqn. (1). They have obtained A = 1.05, B = -1.3 and C = 2.25 Hz. Our calculated value (E = l-50) is larger than that of Solkan and Bystrov. Our calculated average coupling constant JiF = ( Jyic + 2Jiic)/3, assuming free rotation around the C-N bond, is 1.650 (E = l)-1.686 (E = 50) Hz for the CNDO/B calculation and 1.715 (E = l)-1.827 (e = 50) Hz for the INDO calculation. These values agree with the calculated value (1.8 Hz) of Solkan and Bystrov. The observed value for tram N-methylformamide in neat liquid is 3.7 Hz which is larger than the calculated value. However, the observed dipeptide constants of Ac(13C)-Ala and Ac(‘~C)AMVD~ in DzO [44] and of Ac-L-Ala-NDCH3 in CD30D [45] are 2.4, 2.2 and 2.5 Hz respectively. These values are near to our calculated values. Our calculation of the solvent dependence of the H-C-N-C constants predicts that the Jfic and JgUicconstants increase with increasing dielectric constant in the CNDO/B and INDO approximations, the solvent-induced change in the latter being larger than that in the former. In the latter calculation qic is negative. As shown above, the vicinal coupling constants change by not more than about 3% in a variety of dielectric constants. At the moment, such a solvent effect is too small to relate significantly to the dielectric solvent-induced conformational change observed. Therefore in order to test these calculations more thoroughly, more exact experimental results of changes in vicinal couplings as a function of dielectric constant are required.

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