Journal of Molecular Structure, 76 (1981) 93103 THEOCHEM Elsevier Scientific Publishing Company, Amsterdam

Printed
A THEORETICAL STUDY OF THE DIELECTRIC ON VICINAL SPIN COUPLING CONSTANTS
ISA0
AND0
and TETSUO
Department of Polymer Tokyo (Japan) SHOSUKE Minato
SOLVENT
EFFECT
ASAKURA
Chemistry,
Tokyo
Institute
of Technology,
Ookayama,
Meguroku,
WATANABE
High School
(Received
in The Netherlands
of Technology,
19 April 1980;
Nishishinbashi,
in final form
20 June
Minatoku,
Tokyo
(Japan)
1980)
ABSTRACT The dielectric solvent effect on HCCH, HCNH and HCNC spin coupling constants in ethane, tetrachloroethane and trans Nmethylformamide 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.
INTRODUCTION
Since Karplus’ prediction from valence bond theory [l] of a strong conformational dependence of uicinal protonproton 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]
(1)
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 protonproton and protoncarbon couplings. Previous theoretical studies on the solvent effect of coupling constants have dealt with molecules in which the relative spatial positions of coupled OlSS1280/81/00000000/$02.50
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nuclei are fixed by virtue of their structure. Johnston and Barfield have successfully calculated the solvent effect on coupling constants by means of the finite perturbation theory (FPT) [3] using the reaction field model [4], the cubic closestpacked cluster model [ 51 and the rotating point dipole model [6]. Recently, the present authors [7, 81 have calculated the directly bonded 13CH coupling constants as a function of the dielectric constant, E, of the solvent using the FPT method incorporating solvaton theory [9] ; the solvent effect on the chemical shift of some organic compounds has been satisfactorily interpreted using this method [lo]. In this work the solvent effect on the uicinal coupling constants of molecules which can assume two or more conformations through internal rotation has been investigated by means of the FPTsolvaton theory [ 71 developed by the present authors. In practice, we discuss the effect of aprotic solvent on HCCH coupling constants for ethane and tetrachloroethane, and HCNH and HCNC coupling constants for trans ATmethylformamide. THEORETICAL
ASPECT
In previous papers [lo] , we have developed “solvaton” theory so as to allow inclusion of solventinteraction in semiempirical SCF calculations. A solvaton is an imaginary particle representing the oriented distribution of solvents around each atom in a molecule. The requirements for this theory to estimate the solutesolvent interaction are as follows; (i) a number of charges (the solvaton) are induced in an aprotic solvent of dielectric constant E, (ii) one charge is equal in magnitude but opposite in sign to that of the atom to which it is attached, (iii) there are no interactions between the solvatons, and (iv) the solutesolvent interaction is approximated by the Born equation [ll] which represents the free energy of a solvated ion in a dielectric continuum. Next, we consider the calculation of J$& and J$g coupling constants as a function of e by the INDO [ 121 and CNDO/B [13] approximations including the abovementioned solutesolvent interaction using FPT theory. The calculation for CHCl,CHCl, was made only by the CNDO/2 approximation because of lack of data for the Slate?Condon parameters for the chlorine atom. In this paper, we consider only Fermi contact interaction since it seems to be predominant in Jr’$ and ?n’g coupling constants. The spinunrestricted 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 .
(2l)
95
(22) The third term is the solutesolvent 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 solvatonelectron 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 solvatonelectron 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
=
~h~A~,~2sA(o~zSB(o)
2
[&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!$‘~(hB) is the spin density matrix corresponding to the valence S orbital of atom A. In the numerical calculation, it is important to choose the correct values for the integrals su( 0)’ and s,(O)’ for hydrogen and carbon atoms, respectively. In this work the values of Pople et al. are used [3]. Bond lengths and bond angles used are standard values proposed by Pople and Gordon [ 141, except for bond length CCl (1.71 a) [15]. Values used for the effective van der Waals’ radii are 1.20, 1.59, 1.49,1.39 and 1.80 ,& in hydrogen, carbon, nitrogen, oxygen and chlorine atoms, respectively [ 161. An HITAC Ml80 computer at the Computer Center of Tokyo Institute of Technology was used for all the calculations. RESULTS
AND DISCUSSION
The dihedral angle @ dependences of Jti and J$ 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
96
Fig. 1. Plots of HCCH 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 FPTINDO 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 HCCH coupling in ethane decrease on substitution of chlorine for hydrogen atoms; for HCNH coupling the values are smaller than those in HCCH coupling. In HCNC coupling the values of parameters A and B are much smaller than those in HCCH and HCNH 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 Nmethylformamide in the INDO calculation). They are described by the relation A,Bor
C=a’
(5)
97 TABLE
1
E dependences of parameters A, B and C of the Karplus expression in ethane, tetrachloroethane and tram Nmethylformamide, calculated by means of the FPTsolvaton method Compounds
Dielectric 1
constant 2
(E ) 4
Coefficients in eqn. (5) 10
20
50
a’
b'
Ethane (IjCC~) CNDO/B
A B
C
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
INDO
A B
Tetrachloroethane (~CCII) 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
c
trans Nmethylformamidea (HCNII) CNDO/P A 4.315 B 2.722 C 4.131 INDO A 4.899
B (&CNC) CNDO/2
5.080
A B
0.998
C INDO
4.294
C
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 Nmethylformamide. 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
98 TABLE
2
E dependences of vicinal spin coupling constants in trans and gauche ethane, tetrachloroethane and tram Nmethylformamide, calculated method Compounds
Dielectric
constant
conformations in by the FPTsolvaton
Coefficients
(e )
in
eqn. (6) 1
2
4
10
20
50
b
C
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 Nmethylformamide (HCNII) 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 (HCC~) CNDO/B Jy” Jvgic INDO Jyic #” Tetrachloroethane (HccH_) CNDO/S q” JY
(~CNC) 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 HCNH coupling constants are nearly equal to those of HCCH in CHClz CHCl, . The HCCH coupling constants in ethane are larger than those in CHClz CHClz and trans Nmethylformamide. As is expected, the HCCH coupling constants for ethane are larger for INDO than CNDO/B. On the other hand, for the HCNH and HCNC 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
(q)2+h
(p)
fC
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
99
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. HCCH
coupling constant
Ethane LyndenBell 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 quantumchemical methods. For example, average uicinal coupling Ji: = (Jy’” + 2J,“‘“)/3, when the free rotation around CC bond is assumed, is as follows; Barbier and Berthier [19] : 5.7 Hz (nonempirical method); Kato et al. [20] : 3.2 Hz (nonempirical 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 semiempirical calculations are not very far from the experimental value, but the agreement is somewhat poorer for the nonempirical 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 nheptane, 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 = 9.113.4 Hz and JgUic= 0.51.5 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
100
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 HCCH 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 solventinduced change for HC=CH uicinal coupling constants in fluorinesubstituted ethylenes [ 291 is opposite to that for the HCCH couplings studied here. HCNH
and HCNC
coupling constants
The HCNH vicinal coupling constant is a key factor in the conformational analysis of peptides. Neel and coworkers [ 31341, Ramachandran et al. [36] and others [35, 37, 381 have obtained the Karplus relationships for this coupling, using rigid five and sixmembered 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 coworkers [37, 381: A = 5.1, B = 1.1 and C = 4.5 Hz; Neel and coworkers [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 coworkers [ 31341. This substantiates the assumption made in the empirical approach that the coupling constant depends only on the dihedral angle. Quantumchemical 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 Nmethylacetamide by FPT INDO) and A = 6.03, B = 4.48 and C = 6.04 Hz (for tram Nmethylacetamide by FPT INDO); and Ostlund and Pruniski [40] : A = 4.595, B = 3.87 and C = 4.465 (for cis Nmethylformamide by FPT INDO) and A = 4.905, B = 4.08 and C = 4.835 Hz (for tram Nmethylformamide 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
101
decreases slightly with increasing dielectric constant. Aubry et al. [ 411 have shown for 2azabicyclo [ 2.2.21 octanone3( 3isoquinuclidone), that the HCNH 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 HNC bond angle from 120” (Xray value for the dimer) to 115” (characteristic of nondimeric 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 CN 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 Nmethylformamide. Considering the solvent dependence of the HCNC 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 HCNC 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 = l50) is larger than that of Solkan and Bystrov. Our calculated average coupling constant JiF = ( Jyic + 2Jiic)/3, assuming free rotation around the CN 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 Nmethylformamide 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 AcLAlaNDCH3 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 HCNC constants predicts that the Jfic and JgUicconstants increase with increasing dielectric constant in the CNDO/B and INDO approximations, the solventinduced 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 solventinduced 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.
102 REFERENCES 1 M. Karplus, J. Chem. Phys., 30 (1959) 11. 2 For example; J. W. Emsley, J. Feeney and L. H. Sutcliffe, High Resolution Nuclear Magnetic Resonance Spectroscopy, Vol. 1, Pergamon Press, New York, 1965; 10 (1976) 41; R. J. Abraham and E. Bretschneider, V. F. Brystrov, Prog. NMR Spectrosc., in W. J. OrvilleThomas (Ed.), Rotational Isomerism, J. Wiley, London, Ch. 13, 1974; 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
J. Kowalewski, Prog. NMR Spectrosc., 11 (1977) 1. J. A. Pople, J. W. McIver and N. S. Ostlund, J. Chem. Phys., 49 (1967) 2965. M. D. Johnston and M. Barfield, J. Chem. Phys., 54 (1971) 3084. M. D. Johnston and M. Barfield, J. Chem. Phys., 55 (1971) 3483. M. D. Johnston and M. Barfield, Mol. Phys., 22 (1971) 831. M. Kondo, S. Watanabe and I. Ando, Mol. Phys., 37 (1979) 1521. S. Watanabe and I. Ando, Bull. Chem. Sot. Jpn., 53 (1980) 1257. (a) G. Klopman, Chem. Phys. Lett., 1 (1967) 200. (b) H. A. Germer, Jr., Theor. Chim. Acta, 34 (1974) 145. (a) I. Ando, A. Nishioka and M. Kondo, J. Magn. Reson., 21 (1976) 429. (b) I. Ando, Y. Kato, M. Kondo and A. Nishioka, Makromol. Chem., 178 (1977) 803. (c) I. Ando, M. JallalliHeravi, M. Kondo, S. Watanabe and G. A. Webb, Bull. Chem. Sot. Jpn., 52 (1979) 2240. M. Born, Z. Phys., l(l920) 45. J. A. Pople, D. L. Beveridge and P. A. Dobosh, J. Chem. Phys., 47 (1967) 2026. J. A. Pople and G. A. Segal, J. Chem. Phys., 44 (1967) 3289. J. A. Pople and M. Gordon, J. Am. Chem. Sot., 89 (1967) 4253. L. E. Sutton (Ed), Table of Interatomic Distances and Configuration in Molecules and Ions, Supplement, The Chemical Society, 1965. L. Pauling, The Nature of the Chemical Bond, 3rd edn., Cornell University Press, Ithaca, NY, 1960. G. E. Maciel, J. W. McIver, N. S. Ostlund and J. A. Pople, J. Am. Chem. Sot., 92 (1970) 4497. R. H. LyndenBell and N. Sheppard, Proc. Roy. Sot., London, Ser. A, 269 (1962) 385. C. Barbier and G. Berthier, Theor. Chim. Acta, 14 (1969) 71. Y. Kato, Y. Fujimoto and A. Saika, J. Magn. Reson., 1 (1969) 35. A. D. C. Tow1 and K. Schaumberg, Mol. Phys., 22 (1971) 49. E. Duval, Mol. Phys., 23 (1972) 433. J. A. Riddick and W. B. Bunger, Organic Solvents, WileyInterscience, New York, 1970. H. S. Gutowsky, G. G. Beldford and P. E. McMahon, J. Chem. Phys., 36 (1962) 3353. N. Sheppard and J. J. Turner, Proc. Roy. Sot. London, Ser. A, 252 (1959) 506. R. J. Abraham, M. A. Cooper, T. M. Siveru, P. F. Swinton, H. G. Weder and L. Cavalli, Org. Magn. Reson., 6 (1974) 331. R. J. Abraham, L. Cavalli and K. G. R. Pachler, Mol. Phys., 11 (1966) 471. F. Heatley and G. Allen, Mol. Phys., 16 (1969) 77. M. Barfield and M. D. Johnston, Chem. Rev., 73 (1973) 53. S. L. Smith and R. H. Cox, J. Mol. Spectrosc., 16 (1965) 216. C. M. Thong, D. Canet, P. Grenger, M. Marraud and J. Neel, C.R. Acad. Sci. Ser. C, 269 (1969) 580. M. T. Cung, M. Marraud and J. Neel, Ann. Chim. (Paris), 7 (1972) 183. J. Neel, Pure Appl. Chem., 31 (1972) 201. M. T. Cung, M. Marraud and J. Neel, Macromolecules, 7 (1974) 606. R. Schwayzer, private communication cited by R. J. Weinkem and S. C. Jorgensen, J. Am. Chem. Sot., 93 (1971) 7038. G. N. Ramachandran, R. Chandrasekaran and K. D. Kopple, Biopolymers, 10 (1971) 2113.
37 V. F. Bystrov, S. L. Portnova, T. A. Balashova, S. A. Kozmen, Yu. D. Gavrilov and V. A. Afanasev, Pure Appl. Chem., 36 (1973) 1. 38 V. F. Bystrov, V. T. Ivanov, S. L. Postnova, T. A. Balashova and Yu. A. Qnchinnikov, Tetrahedron, 29 (1973) 873. 39 M. Barfield and H. L. Gearhart, J. Am. Chem. Sot., 95 (1973) 641. 40 N. S. Ostlund and M. J. Pruniski, J. Mag. Reson., 15 (1974) 549. 41 A. Aubry, C. GiessenPrettre, M. T. Cung, M. Marraud and J. Neel, Biopolymers, 13 (1974) 323. 42 A. J. R. Bourn and E. W. Randall, Mol. Phys., 8 (1964) 567. 43 V. N. Solkan and V. F. Bystrov, Isv. Akad. Nauk SSSR Ser. Khim., (1974) 1308. 44 R. U. Lemieux, Ann. N.Y. Acad. Sci., 222 (1973) 915. 45 Yu. D. Gavnilov, V. N. Solkan and V. F. Bystrov, Isv. Akad. Nauk SSSR, Ser. Khim., (1975) 2482.