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On the origin of magnetic non-equivalent of diastereotopic nuclei in NMR spectroscopy
Volume 43, number 1
CHEMICAL PHYSICS LETTERS
ON THE ORIGIN OF MAGNETIC NON-EQUIVALENCE IN NMR SPEaROSCOPY
’ October 1916
OF DIASTEREQTOPXC NUCLEl
P.J. STILES ResearchSchool of Chemistry, Austrahn National University, Canberra, A. C. T. 2600, Australia Received 30 June 1976
Long range chiral shielding is found to be proportional to the product of spectroscopic parameters which characterke the site chirality of the Sensor nucfeus and the rotatory strengths of the dissymmetric perturbing group. it falk away as the invczse sixth power of the distance between the nucleus and the perturbing group. Such shielding is extremely small but fs zcsponsiblc for the proton non-equivalence which survivcs/rce rotation about the cazbon-carbon bond in rigid-rotor ethanes of the type CH2U-CXYZ.
1. Introduction Magnetic tlon-equivalence, as measured by anisochronism in nuclear magnetic shielding, of diastercotopic nuclei such as the protons H, and Hb in substituted ethanes of the type CHaHbU-~XYZ has attracted a lot of attention [l-9]. Similar interest surrounds the magnetic non-equivalence of nuclei in corresponding sites of diastereoisomers [IO- 12 f . By 1961 Waugh and Cotton [2] (see also Pople (31) had demonstrated with the aid of symmetry arguments that diastereotopic nuclei in asymmetric substituted ethanes remain magneticaliy nonequivalent even when the internal rotation is free. Such non-equivalence can be attributed to intrinsic dirrstereotopic discrimination. Rigorous theories for nuclear magnetic shielding derived by Lamb [ 13 J and Ramsey [ 141 fail to exhibit chirality dependent terms directly and previous inves-
chirahty dependent nuclear magnetic screening and hence to intrinsic diastereotopic discr~~ation.
2. A theory for choral shielding The system of interest is divided into sensor groups (fj) and perturbing groups (P) which can be entire molecular species or individual functional groups. The perturbing group must be dissymmetric but the onIy criterion for the sensor group is that the sensor nuclei are at chiral sites. The latter requirement does not de: mand that the sensor group as a whole be chit& For example, the tetrahedral CH,HbU- group of CH,Hr,UCXYZ has a plane of symmetry but its two protons are enatttiotopic [S J - they are at chiral sites of opposite handedness. This point is illustrated below.
tigations of electric [ 15,161 and magnetic [ 17) through-space shielding mechanisms and of inductive
and resonance through-bond mechanisms have neglected chirality dependent screening altogether. In this letter we show how dispersive or electron-conelation interactions between the chiral electronic distribution about the nucleus of interest in the sensor group and that of the perturbing group can lead to
As first noted by Ogston [IS] a chiral perturbing group renders enantiotopic sites diastereotopic and therefore discriminates between them. 23
For simplicity we confine our attention to chirality dependent shielding associated with the diamagnetic or Lamb (131 component of the total shielding. In diamagnetic organic molecules this contribution to the shielding is larger than the paramagnetic term [ 141. The isotropic diamagnetic shielding of nucleus NQ in the sensor group Q of the composite system PQ in its electronic ground state 10) is [ 131, in c.g.s. units, oc’vQ) = (e2,3m,c2)~0,,&r;1
IO>,
(01Fl
(2)
in which direct shielding of nucleus NQ by the electrons in P [ 171 is neglected. The influence of interactions between P and Q on the ground state IO) is readily assessed if electron exchange between the groups can be disregarded. These interactions perturb the simple product wavefunctions Iqp) appropriate to the uncoupled ccmplex formed by taking species Q in state i@ with P in state I@. The lezding chiral contributions to nuclear magnetic shielding are obtained by expanding the composite ground state 10) to second order in the dipolar pertirbation (19) pQ = -R-3
[~~(Q)r,&$p)
(3)
+ m,(Q)r,m,(P)l.
Here R = Rk is the position vector of the origin in group P r?!ative to nucleus NQ, p(Q) is the electric dipole operator of Q, m(Q) the magnetic di$oie operator of Q, and the qmmetric tensor foa = 3R& - 6, measures the angular dependence of dipole-dipole coupling. Summation over the Cartesian components of repeated Greek suffKes is implied. We find the leading diamagnetic contribution to the isotropic chiral shieldinn is dlM
%
= Im(o(Q)I~,(Q)I~(Q))(9(Q)Imp(Q)IO(Q)) = Im p*rnz’ a
(5)
of the CJ+ 0 transitran of frequency Eqo/h, and introduces a new quantity the site chirality strength,
sy*(Np) = _
e2
3m_2 c
Im
~*‘rn$q+p$rnp”‘“J a’
(c)iri
-1
*
’
(6)
at nucleus N in group Q. The difference between the diamagnetic shielding at nucleus NQ when Q is in its qth excited state and in its ground state is denoted by
?!&!p#O C +P LFo--jf Pool($) =Y tp)
R6
(Epo+Eq())2
The operators p, m and r;t in eqs. (5)-(7) refer to nucleus NQ as origin and the state vectors are those of the isolated sensor group Q. The chiral shielding ochti falls away as the inverse sixth power of the distance between the sensor nucleus and the chiral perturbing group. It is sensitive to the mutual orientation of the sensor and perturbing groups. The rotatory strength 9@ has a pseudo-scalar mean value 32@ = 392% which is independent of origin but non-zero only when the sensor group as a whole is dissymmetric. Thus the mean rotatory strength c)2W of the achiral sensor group CH,&,Uis always zero but 3Q@ has individual components which can be equal in magnitude and opposite in sign when referred to local right-handed axis systems at the enantiotopic protons. By contrast, the site chirality strength S@q’ has a pseudo-scalar mean value S&q = jS%g which is origin dependent and non-zero wherever the local site symmetry is chiral. It follows that S@q’(H,) = -*q’(Hb). Because uchiral is proportional to the product of chiral properties of both the sensor and the perturbing groups it discriminates between diastereotopic nuclei. One diamagnetic component of the intrinsic diastereotopic discrimination which survives free rotatiori about the C-C axis Of CH,&,U-CXYZ comes from the equal and opposite chiral shieldings associated with the pseudo-scalar mean values of the site chirality strengths at H, and Hb and of the rotatory strengths
(4) 24
strength [20] components
n CQ)
f#?IO)= (01IFi f,?IO),’
&“Q) i-
Eq. (4) invokes the rqtatory
(1)
where e is the proton charge, m, the electronic mass, c the velocity of light in vacua and ri the distance of electron i from nucleusN. The total number of electrons !I = n(Q) + ,2(P). We now make the approximation n
1 October 1976
CHEMICAL PHSYICS LETTERS
Volume 43. number 1
of the perturbing’group
-CXYZ.
contribution to the intrinsic non-equivalence from eq. (4) as
This
follows
Volume 43, number 1
,(Ha)_,(Hb)
= -2”
R6
CHEMICAL PHYSICS LEITERS
c
~~P(-cxyz)
PZO
dq”(Ha) - f qqq (EpO+Eq~p;-' other
more complicated free rotation.
(8) terms from (4) also survive the
3. Discussion Our analysis indicates that chirality dependent shielding of a sensor nucleus by a chiral perturbing group is at least ten.thousand times weaker than the conventional dispersive shielding [ 161 of the same nucleus by the same perturbing group. The latter rarely exceeds several parts per million for fluorine and carbon nuclei which in turn are more strongly shielded than protons. Thus the experimental observation of intrinsic diastereotcpic discrimination imposes an extremely severe test of instrumental resolution. Magnetic non-equivalence due to intrinsic diastereotopic discrimination survives in the high temperature free rotation limit. This limit is never achieved in studies of substituted ethanes at temperatures available to NMR spectroscopists. It might be attained in measurements on analogously substituted but-2-ynes 12’). Gutowsky [4], Raban (61, and Binsch et al. [8,9] have found a component of the total diastereotopic discrimination that persists when all possible rotamers of asymmetrically substituted ethanes are equally populated. Since chiral shielding is so small we conclude that these residual non-equivalences are due to standard chirality independent shielding mechanisms like those responsible for the anisochronism of the geminal protons in mono-substituted ethylenes. Nonequivalence due to chirality independent shielding mechanisms reflects inequalities among the six angles in the Newman projection of each rotamcr. Thus, the observations above [4,6,8,9] provide evidence of geometric non-idealities such as deviations from 60” staggerings.
1 October 1976
Magnetic non-equivalence in intermolecular contexts is found when shieldings of corresponding nuclei in meso and racemic isomers are compared [ 101. Splittings in the observed shieldings of corresponding nuclei of enantiomers interacting with a chiral shift reagent [ 111 or a chiral solvent [ 121 can be classified similarly. Because the time-average structures of diastereoisomers formed by inter-group [lo], solute-solute [ 1 I I or solute-solvent [ 12) interactions are not simply related, standard chirality-independent shielding mechanisms [ 15- 171 can account for the observed splittings [ 12, 221. Although chirality dependent shielding, the diamagnetic component of which is given by eq. (4), also contributes to the splittings its influence is probabIy negligible. Paramagnetic contributions te chiral shielding will be described elsewhere.
4. Conclusion Our analysis provides a theoretical basis for interpreting nuclear magnetic shielding that depends on the absolute configurations of interacting molecular sites. It suggests that intrinsic disstereotopic discrimination in nuclear magnetic shielding is extremely smalI and experimentally insignificant for nuclei of low atomic number. Previously observed nonequivalence of diastereotopic nuclei in molecules with appreciably hindered internal rotation owes its existence to the molecular asymmetry but can be attributed to standard chirality-independent shielding mechanisms.
Acknowledgement I thank Professor D.P. Craig and Dr. W.P. Healy for helpful discussions.
References [ I] J.J. Drysdalc and W.D. Phillips, 1. Am. Chcm. Sot 79 (1957) 319.
[ 2] J.S. Wnugh and F.A. Cotton, J. Phys. Chcm. 65 (1961) 562. [ 31 J.A. Pople, Mol. Phyn 1 (1958) 3. [4] H.S. Gutowsky. J. Chcm. Phys. 37 (1962) 2196. [S] K. hlisiow and M. Raban. Topics Stereochcm. I (1967) 1. (61 hl. Raban. Tetrahedron Letters (1966) 3105.
25
Votun-e 43. number
1
CHEMICAL
[7] M. van Corkom and G.E. ita& Quart Rev. 22 (1968) 14; W.B. Jennings. Chcm. Rev. 75 (1975) 307. IS] R.D. Norris and G. Binsch, J. Am. Chem. Sot. 95 (1973) 182, and references therein. 191 G. Binsch and G.R. Franzen. J. Am. Chcm. Soe. 91
(1969) 3999;
[IO]
[ 11 J 1121 1131
26
G.R. Franren and G. Binsch, J. Am. Chem. Sot. 95 (1973) 175; 1. McKenna. J.M. McKonna and B.4. Wcrby, Chcm. Commun. (I 970) 867. A.A. Bothncr-By and C. NaarColin. J. Am. Chem. Sot. 84 (1962) 743; F.A.L. Anct, J. Am. Chem. Sot. 84 (1962) 747; C.J. Carman, A.R. Tarpley and J.H. Goldstein!, J. Am. Chcm. Sot. 93 (1971) 2864. G-M. Wbitesidcs and D.W. Lewis, J. Am. Chem. Sot. 92 (1970) 6979. W.H. Pirkleand S.D. Bcsre, 1. Am.Chem. Sot. 91 (1969) 5 150, and refcrenas therein. W. Lamb. Phys. Rev. 60 (1941) 817.
PHSYICS LETTERS
I October
1976
[ 14 j N.F. Ramsey, Phys. Rev. 78.(1950) 699. [ 15 1 A.D. Buckingham, Can. J. Chcm. 38 (1960) 300. [ 161 W.T. Rqvws, A.D. Buckingham and H.J. Bernstein, J. Chem. Phyt 36 (1962) 3481; F.H.A. Rummcns, in: NMR basic principfcs and progress, Vol. 10 (1975) p. 1, and references therein. 1171 H-M. McConnell, J. Chem. Pbys. 27 (1957) 226; P.J. Stiles, Chcm. Phys. Letters 30 (1975) 259; Proc. Roy. Sot. A346 (1975) 209. and rcfcrences therein; J.W. Perram and P.J. Stiles. Proc. Roy. SOC. A349 (1976) 12s. (18) A.G. Opston, Nature 162 (1948) 963. [ 19 1 C. Mavroyannis and M.J. Stephen, Mol. Phys S (1962) 629; D.P. Craig, E.A. Power and T. Thirunamachandran, Proc. Roy. Sot. A322 (1971) 165. (201 A.D. Buckingham and P.J. St&s, Accounts Chcm. RCS. 7 (1974) 258. j21 1 E.I. Snyder, J. Am. Chcm. Sot. 88 (1966) 1165. [ 221 L.L. Morozov. E.I. Fedin and MI. Kabachnik, Russian J. Phys. Chem. 48 (1974) 6.
CHEMICAL PHYSICS LETTERS
ON THE ORIGIN OF MAGNETIC NON-EQUIVALENCE IN NMR SPEaROSCOPY
’ October 1916
OF DIASTEREQTOPXC NUCLEl
P.J. STILES ResearchSchool of Chemistry, Austrahn National University, Canberra, A. C. T. 2600, Australia Received 30 June 1976
Long range chiral shielding is found to be proportional to the product of spectroscopic parameters which characterke the site chirality of the Sensor nucfeus and the rotatory strengths of the dissymmetric perturbing group. it falk away as the invczse sixth power of the distance between the nucleus and the perturbing group. Such shielding is extremely small but fs zcsponsiblc for the proton non-equivalence which survivcs/rce rotation about the cazbon-carbon bond in rigid-rotor ethanes of the type CH2U-CXYZ.
1. Introduction Magnetic tlon-equivalence, as measured by anisochronism in nuclear magnetic shielding, of diastercotopic nuclei such as the protons H, and Hb in substituted ethanes of the type CHaHbU-~XYZ has attracted a lot of attention [l-9]. Similar interest surrounds the magnetic non-equivalence of nuclei in corresponding sites of diastereoisomers [IO- 12 f . By 1961 Waugh and Cotton [2] (see also Pople (31) had demonstrated with the aid of symmetry arguments that diastereotopic nuclei in asymmetric substituted ethanes remain magneticaliy nonequivalent even when the internal rotation is free. Such non-equivalence can be attributed to intrinsic dirrstereotopic discrimination. Rigorous theories for nuclear magnetic shielding derived by Lamb [ 13 J and Ramsey [ 141 fail to exhibit chirality dependent terms directly and previous inves-
chirahty dependent nuclear magnetic screening and hence to intrinsic diastereotopic discr~~ation.
2. A theory for choral shielding The system of interest is divided into sensor groups (fj) and perturbing groups (P) which can be entire molecular species or individual functional groups. The perturbing group must be dissymmetric but the onIy criterion for the sensor group is that the sensor nuclei are at chiral sites. The latter requirement does not de: mand that the sensor group as a whole be chit& For example, the tetrahedral CH,HbU- group of CH,Hr,UCXYZ has a plane of symmetry but its two protons are enatttiotopic [S J - they are at chiral sites of opposite handedness. This point is illustrated below.
tigations of electric [ 15,161 and magnetic [ 17) through-space shielding mechanisms and of inductive
and resonance through-bond mechanisms have neglected chirality dependent screening altogether. In this letter we show how dispersive or electron-conelation interactions between the chiral electronic distribution about the nucleus of interest in the sensor group and that of the perturbing group can lead to
As first noted by Ogston [IS] a chiral perturbing group renders enantiotopic sites diastereotopic and therefore discriminates between them. 23
For simplicity we confine our attention to chirality dependent shielding associated with the diamagnetic or Lamb (131 component of the total shielding. In diamagnetic organic molecules this contribution to the shielding is larger than the paramagnetic term [ 141. The isotropic diamagnetic shielding of nucleus NQ in the sensor group Q of the composite system PQ in its electronic ground state 10) is [ 131, in c.g.s. units, oc’vQ) = (e2,3m,c2)~0,,&r;1
IO>,
(01Fl
(2)
in which direct shielding of nucleus NQ by the electrons in P [ 171 is neglected. The influence of interactions between P and Q on the ground state IO) is readily assessed if electron exchange between the groups can be disregarded. These interactions perturb the simple product wavefunctions Iqp) appropriate to the uncoupled ccmplex formed by taking species Q in state i@ with P in state I@. The lezding chiral contributions to nuclear magnetic shielding are obtained by expanding the composite ground state 10) to second order in the dipolar pertirbation (19) pQ = -R-3
[~~(Q)r,&$p)
(3)
+ m,(Q)r,m,(P)l.
Here R = Rk is the position vector of the origin in group P r?!ative to nucleus NQ, p(Q) is the electric dipole operator of Q, m(Q) the magnetic di$oie operator of Q, and the qmmetric tensor foa = 3R& - 6, measures the angular dependence of dipole-dipole coupling. Summation over the Cartesian components of repeated Greek suffKes is implied. We find the leading diamagnetic contribution to the isotropic chiral shieldinn is dlM
%
= Im(o(Q)I~,(Q)I~(Q))(9(Q)Imp(Q)IO(Q)) = Im p*rnz’ a
(5)
of the CJ+ 0 transitran of frequency Eqo/h, and introduces a new quantity the site chirality strength,
sy*(Np) = _
e2
3m_2 c
Im
~*‘rn$q+p$rnp”‘“J a’
(c)iri
-1
*
’
(6)
at nucleus N in group Q. The difference between the diamagnetic shielding at nucleus NQ when Q is in its qth excited state and in its ground state is denoted by
?!&!p#O C +P LFo--jf Pool($) =Y tp)
R6
(Epo+Eq())2
The operators p, m and r;t in eqs. (5)-(7) refer to nucleus NQ as origin and the state vectors are those of the isolated sensor group Q. The chiral shielding ochti falls away as the inverse sixth power of the distance between the sensor nucleus and the chiral perturbing group. It is sensitive to the mutual orientation of the sensor and perturbing groups. The rotatory strength 9@ has a pseudo-scalar mean value 32@ = 392% which is independent of origin but non-zero only when the sensor group as a whole is dissymmetric. Thus the mean rotatory strength c)2W of the achiral sensor group CH,&,Uis always zero but 3Q@ has individual components which can be equal in magnitude and opposite in sign when referred to local right-handed axis systems at the enantiotopic protons. By contrast, the site chirality strength S@q’ has a pseudo-scalar mean value S&q = jS%g which is origin dependent and non-zero wherever the local site symmetry is chiral. It follows that S@q’(H,) = -*q’(Hb). Because uchiral is proportional to the product of chiral properties of both the sensor and the perturbing groups it discriminates between diastereotopic nuclei. One diamagnetic component of the intrinsic diastereotopic discrimination which survives free rotatiori about the C-C axis Of CH,&,U-CXYZ comes from the equal and opposite chiral shieldings associated with the pseudo-scalar mean values of the site chirality strengths at H, and Hb and of the rotatory strengths
(4) 24
strength [20] components
n CQ)
f#?IO)= (01IFi f,?IO),’
&“Q) i-
Eq. (4) invokes the rqtatory
(1)
where e is the proton charge, m, the electronic mass, c the velocity of light in vacua and ri the distance of electron i from nucleusN. The total number of electrons !I = n(Q) + ,2(P). We now make the approximation n
1 October 1976
CHEMICAL PHSYICS LETTERS
Volume 43. number 1
of the perturbing’group
-CXYZ.
contribution to the intrinsic non-equivalence from eq. (4) as
This
follows
Volume 43, number 1
,(Ha)_,(Hb)
= -2”
R6
CHEMICAL PHYSICS LEITERS
c
~~P(-cxyz)
PZO
dq”(Ha) - f qqq (EpO+Eq~p;-' other
more complicated free rotation.
(8) terms from (4) also survive the
3. Discussion Our analysis indicates that chirality dependent shielding of a sensor nucleus by a chiral perturbing group is at least ten.thousand times weaker than the conventional dispersive shielding [ 161 of the same nucleus by the same perturbing group. The latter rarely exceeds several parts per million for fluorine and carbon nuclei which in turn are more strongly shielded than protons. Thus the experimental observation of intrinsic diastereotcpic discrimination imposes an extremely severe test of instrumental resolution. Magnetic non-equivalence due to intrinsic diastereotopic discrimination survives in the high temperature free rotation limit. This limit is never achieved in studies of substituted ethanes at temperatures available to NMR spectroscopists. It might be attained in measurements on analogously substituted but-2-ynes 12’). Gutowsky [4], Raban (61, and Binsch et al. [8,9] have found a component of the total diastereotopic discrimination that persists when all possible rotamers of asymmetrically substituted ethanes are equally populated. Since chiral shielding is so small we conclude that these residual non-equivalences are due to standard chirality independent shielding mechanisms like those responsible for the anisochronism of the geminal protons in mono-substituted ethylenes. Nonequivalence due to chirality independent shielding mechanisms reflects inequalities among the six angles in the Newman projection of each rotamcr. Thus, the observations above [4,6,8,9] provide evidence of geometric non-idealities such as deviations from 60” staggerings.
1 October 1976
Magnetic non-equivalence in intermolecular contexts is found when shieldings of corresponding nuclei in meso and racemic isomers are compared [ 101. Splittings in the observed shieldings of corresponding nuclei of enantiomers interacting with a chiral shift reagent [ 111 or a chiral solvent [ 121 can be classified similarly. Because the time-average structures of diastereoisomers formed by inter-group [lo], solute-solute [ 1 I I or solute-solvent [ 12) interactions are not simply related, standard chirality-independent shielding mechanisms [ 15- 171 can account for the observed splittings [ 12, 221. Although chirality dependent shielding, the diamagnetic component of which is given by eq. (4), also contributes to the splittings its influence is probabIy negligible. Paramagnetic contributions te chiral shielding will be described elsewhere.
4. Conclusion Our analysis provides a theoretical basis for interpreting nuclear magnetic shielding that depends on the absolute configurations of interacting molecular sites. It suggests that intrinsic disstereotopic discrimination in nuclear magnetic shielding is extremely smalI and experimentally insignificant for nuclei of low atomic number. Previously observed nonequivalence of diastereotopic nuclei in molecules with appreciably hindered internal rotation owes its existence to the molecular asymmetry but can be attributed to standard chirality-independent shielding mechanisms.
Acknowledgement I thank Professor D.P. Craig and Dr. W.P. Healy for helpful discussions.
References [ I] J.J. Drysdalc and W.D. Phillips, 1. Am. Chcm. Sot 79 (1957) 319.
[ 2] J.S. Wnugh and F.A. Cotton, J. Phys. Chcm. 65 (1961) 562. [ 31 J.A. Pople, Mol. Phyn 1 (1958) 3. [4] H.S. Gutowsky. J. Chcm. Phys. 37 (1962) 2196. [S] K. hlisiow and M. Raban. Topics Stereochcm. I (1967) 1. (61 hl. Raban. Tetrahedron Letters (1966) 3105.
25
Votun-e 43. number
1
CHEMICAL
[7] M. van Corkom and G.E. ita& Quart Rev. 22 (1968) 14; W.B. Jennings. Chcm. Rev. 75 (1975) 307. IS] R.D. Norris and G. Binsch, J. Am. Chem. Sot. 95 (1973) 182, and references therein. 191 G. Binsch and G.R. Franzen. J. Am. Chcm. Soe. 91
(1969) 3999;
[IO]
[ 11 J 1121 1131
26
G.R. Franren and G. Binsch, J. Am. Chem. Sot. 95 (1973) 175; 1. McKenna. J.M. McKonna and B.4. Wcrby, Chcm. Commun. (I 970) 867. A.A. Bothncr-By and C. NaarColin. J. Am. Chem. Sot. 84 (1962) 743; F.A.L. Anct, J. Am. Chem. Sot. 84 (1962) 747; C.J. Carman, A.R. Tarpley and J.H. Goldstein!, J. Am. Chcm. Sot. 93 (1971) 2864. G-M. Wbitesidcs and D.W. Lewis, J. Am. Chem. Sot. 92 (1970) 6979. W.H. Pirkleand S.D. Bcsre, 1. Am.Chem. Sot. 91 (1969) 5 150, and refcrenas therein. W. Lamb. Phys. Rev. 60 (1941) 817.
PHSYICS LETTERS
I October
1976
[ 14 j N.F. Ramsey, Phys. Rev. 78.(1950) 699. [ 15 1 A.D. Buckingham, Can. J. Chcm. 38 (1960) 300. [ 161 W.T. Rqvws, A.D. Buckingham and H.J. Bernstein, J. Chem. Phyt 36 (1962) 3481; F.H.A. Rummcns, in: NMR basic principfcs and progress, Vol. 10 (1975) p. 1, and references therein. 1171 H-M. McConnell, J. Chem. Pbys. 27 (1957) 226; P.J. Stiles, Chcm. Phys. Letters 30 (1975) 259; Proc. Roy. Sot. A346 (1975) 209. and rcfcrences therein; J.W. Perram and P.J. Stiles. Proc. Roy. SOC. A349 (1976) 12s. (18) A.G. Opston, Nature 162 (1948) 963. [ 19 1 C. Mavroyannis and M.J. Stephen, Mol. Phys S (1962) 629; D.P. Craig, E.A. Power and T. Thirunamachandran, Proc. Roy. Sot. A322 (1971) 165. (201 A.D. Buckingham and P.J. St&s, Accounts Chcm. RCS. 7 (1974) 258. j21 1 E.I. Snyder, J. Am. Chcm. Sot. 88 (1966) 1165. [ 221 L.L. Morozov. E.I. Fedin and MI. Kabachnik, Russian J. Phys. Chem. 48 (1974) 6.