Equivalence of Nuclei in High-resolution Nuclear Magnetic Resonance Spectroscopy By M. van Gorkom and G. E. Hall UNILEVER RESEARCH LABORATORY VLAARDINGEN NETHERLANDS UNILEVER RESEARCH LABORATORY SHARNBROOR BEDFORD Since free rotation about a single bond is generally easy two identical atoms or groups attached to a common atom (e.g. the protons of a CH group) are often assumed to be indistinguishable. In practice they may be chemically or magnetic- ally distinguishable. A proper three-dimensional consideration of molecular structure allows an understanding of otherwise unexpected non-equiva1ence.l The aim of this Review is to reduce the confusion surrounding the concept of equivalence of nuclei. The principles involved are of value to organic and inorganic chemists in appreciating stereochemical subtleties and in interpreting even the simplest high-resolution nuclear magnetic resonance (n.m.r.) spectra in terms of chemical structures; to the physical chemist investigating barriers to chemical changes or the interaction forces between groups; and to the biochemist requiring to distinguish two similar groups and trying to understand the niceties of enzymic action.1 Definitions A. Chemical Non-equivalence.-Two atoms of the same isotopic species in a molecule are chemically non-equivalent if there is no molecular symmetry axis of rotation relating the two atoms. Citric acid (1) has been shown to react enzymically in such a way that the two indicated carboxyl groups are distinguishable. The ‘three-point attachment’ theory which attributes the enzyme with special features was suggested2 as an explanation of this observation.These features are however not a unique3 y x - c - x F H02C.CH2-y-CH;.C02H (1) 2 (2) C0,H b&!! H,‘ OH (4) HB K. Mislow and M. Raban in ‘Topics in Stereochemistry’ ed. N. L. Allinger and E. L. Eliel John Wiley New York vol. I ch. I. 8 A. G. Ogston Nature 1948 162 963. * G. Popjiik and J. W. Cornforth Biochem. I. 1966,101 553. 14 van Gorkom and Hall condition for a stereospecific reaction. Conside#s5 a molecule Cxxyz (2). Looking from the ‘left-hand’ x group towards the rest of the molecule the clockwise sequence is y-x-z. From the right-hand x group the clockwise sequence is y-z-x. The x-groups are enantiotopicl because they are situated in enantiomeric environments! Consequently the approach of an asymmetric reagent will be affected by the direction of approach and the x groups may react at different rates.With a highly asymmetric reagent such as an enzyme the differentiation may be complete. Further consideration shows5 that for two otherwise identical groups to be chemically non-equivalent (distinguishable) the relevant criterion is one of rotational symmetry. Chemically non-equivalent atoms require an optically active reagent for their chemical differentiation only if the molecule has a rotation-reflection axis such as a plane of symmetry relating these atoms as in (2). B. Isochronous Nuclei.-Nuclei which experience equal magnetic shielding have identical chemical shifts; such nuclei are termed’ isochronous. Chemically equivalent nuclei are isochronous but the reverse is not necessarily true.For example the two x nuclei of (2) are isochronous since a plane of symmetry relates them. C. Magnetic Non-equivalence.-Two atoms (or groups of atoms) are magnetic- ally equivalent if they are isochronous and if the constants (J) for the coupling to any other atom are identical. In catechol(3) the nuclei labelled B are chemic- ally shifted (non-isochronous) from those labelled A. They are magnetically non-equivalent in the chemical-shift sense. Also the coupling between A and B is through three bonds whilst between A’ and B it is through four bonds; the coupling constants must therefore be expected to be different. Consequently A and A’ are magnetically non-equivalent in the spin-coupling sense (this is an example of isochronous magnetic n~n-equivalence~). The aromatic ring proton spin system is described in the usual convention* as AA’BB’.On the other hand the atoms labelled B in resorcinol (4) are isochronous and do have identical values for the coupling constants with either nuclei C or A. They are therefore magnetically equivalent and this spin system is described as AB,C. This analysis ignores any coupling between the ring protons and the hydroxyl protons. D. Accidental Magnetic Equivalence.-The above arguments are based simply on considerations of symmetry without recourse to experimental data. If in (3) by some quirk of fate it had transpired that J(AB) =J(A’B) and J(AB’) =J(A’B’) P. Schwartz and H. E. Carter Proc. Nat. Acad. Sci. U.S.A. 1954,40,499. 6 H. Hirschmann J. Biol. Chem. 1960 235 2762. K. Mislow M. A. W. Glass H. B. Hopps E. Simon and G.H. WahI J. Amer. Chem. SOC. 1964 86 1710. (a) A. Abragam ‘The Principles of Nuclear Magnetism’ Oxford University Press 1961 p. 480; (b) E. I. Snyder J. Amer. Chem. Soc. 1963,85,2624. 8 E.g. J. W. Emsley J. Feeney and L. H. Sutcliffe ‘High Resolution Nuclear Magnetic Resonance Spectroscopy’ Pergamon Press Oxford 1965 p. 283. 15 Nuclei in High-resolution Nuclear Magnetic Resonance Spectroscopy then A and A' would be said to be accidentally magnetically equivalent. Two atoms may appear to be equivalent if the operating conditions are insufficient to resolve the appropriate peaks. For example the acetylenic and methyl protons in propyneQ are accidentally isochronous at 60 Mc./sec. and produce a one-line spectrum. E. Time-averaged Equivalence.-If a configurational or conformational change occurs rapidlylo compared with the inherent time scale of the n.m.r.experiment then two atoms may become equivalent by averaging if each spends the same time in each particular environment. Table 1 The possible combinations of chemical and magnetic equivalence Relationship of the two CE IS ME Fluorine nuclei in 1,l -difluoroallene CE IS MNE Fluorine nuclei in 1,l -difluoroethylene CNE IS ME Protons in chlorofluoro- methane CNE IS MNE Protons in tetraethyl-lead CNE NIS MNE aand/?Protonsin (groups of) nuclei Example pyridine Spectrum type A2X2 AA'XX' A2X A J 2 X A A' B B'C Ref. a a b C d C(N)E = chemical (non-)equivalence (N)IS = (non-)isochronous M(N)E f magnetic (non-)equivalence a H. M. McConnell A. C. McLean and C. A. Reilly J. Chem. Phys. 1955,23 1152; Ref. 8; C E. B.Baker J . Chem. Phys. 1957,26,960; W. G. Schneider H. J. Bernstein and J. A. Pople Ann. New York Acad. Sci. 1958 70 806. Table 1 lists all the possible combinations of chemical and magnetic equival- ence with examples. Further examples are given both later and elsewhere.",18 2 Temperature-independent Magnetic Non-equivalence Any factor which locks two nuclei in different magnetic environments will cause them to be magnetically non-equivalent. In the isotopically unusual form (5) of trans-1 ,Zdichloroethylene the protons exhibitlS magnetic non-equivalence which since there is no reaction causing exchange should be temperature- N. s. Bhacca L. F. Johnson and J. N. Shoolery 'N.M.R. Spectra Catalog' National Press New York 1962 vol. 1 Spectrum 16. lo J. E. Anderson Quart. Rev. 1965 19 426.l1 F. A. Bovey Pure Appl. Chem. 1966,12 525. l2 M. L. Martin and G. J. Martin Bull. Soc. chlm. France 1966,2117. l3 A. D. Cohen N. Sheppard and J. J. Turner Proc. Chem. Soc. 1958 118. 16 van Gorkom and Hall independent. Similarly the two methylenedioxy rings of the tetradehydro-otobain (6) have sharp proton n.m.r. lines.14 The plane of the molecule evidently bisects the <HCH angle of the two methylene groups and the two protons in each Cl \’3 12/ HA ,c=c\ Cl HA’ (5 1 ,A-a A-a ’NH -7H-5- Me 0 a’c ‘A w ‘a-A’ (9). A=S-alanyl residue o =R-alanyl residue group are equivalent. This is not so for otobain (7) itself; the methylenedioxy- group on ring c shows a singlet but the two protons of the other methylenedioxy ring (attached to ring A) exhibit non-equivalence as an AB quartet.It is also interesting that the protons at 2’ 5’ and 6’ of otobain are accidentally magnetic- ally equivalent and have a single proton n.m.r. signal. The corresponding protons of the dehydro-compound (6) are non-equivalent. Diastereoisomers may also have sufficiently different magnetic environments at particular atoms for distinguishable spectra to be observed. As an example the proton n.m.r. spectra of ~-[Co(en),-~-ala]Cl and ~-[Co(en),-~-ala]Cl are different. These complexes involve cobalt(m) ethylenediamine (en) and alanine (ala). On the other hand the n.m.r. spectra of ~-[Co(en),-c-ala]CI and ~-[Co(en),-~-ala]Cl should be identicaP5 because they are enantiomeric com- pounds ( i e . mirror images). Cycloenantiomers16 must also have the same n.m.r. spectra. The cyclohexapeptides (8) and (9) are mirror images of each other; although they have the same distribution of chirall’ (i.e.asymmetric) centres they differ by virtue of the ring direction which is indicated by the arrows. Such compounds are termed cycloenantiomers. As expected their n.m.r. spectra are identical and their optical rotations are equal and opposite. On the other hand each methyl group of either compound ‘sees’ a different sequence of R- and S-chiral centres from those ‘seen’ by the other five and the proton spectrum contains six methyl doublets. Cyclodiastereoisomers,la which have an identical l4 T. Gilchrist R. Hodges and A. L. Porte J . Chem. SOC. 1962 1780. l6 D. A. Buckingham S. F. Mason A. M. Sargeson and K. R. Turnbull Inorg. Chem. 1966 5 1649. l6 V. Prelog and H. Gerlach Helv.Chim. Acta 1964 47 2288; H. Gerlach J. A. Owtschin- nikow and V. Prelog ibid. p. 2294. l7 R. S. Cahn C. Ingold and V. Prelog Angew. Chem. Internut. Edn. 1966,5,385. 17 Nuclei in High-resolution Nuclear Magnetic Resonance Spectroscopy sequence of chiral centres and differ only in the ring direction but are not mirror images are expected to give distinguishable n.m.r. spectra. 3 Magnetic Non-equivalence with Both Temperature-dependent and -independent The substituted ethanes form the basis of the following discussion not only for historical reasons; the principles involved can be clearly demonstrated and then used for the understanding of related instances of magnetic non-equivalence. (i) Ethanes. In 1957 the 30 Mc./sec. room-temperature fluorine-19 n.m.r. spectrum of CF2Br.CHBr.C,H was reported.ls It was clear that the fluorine atoms are magnetically non-equivalent on two counts; they are chemically shifted and they couple with the vicinal proton to different extents.The fluorine spectrum of CF,Br.CBrCl on the other hand is down to -3O”c a singlel9 sharp line. It is thus unlikely20 that restricted rotation is the cause of the observed non-equivalence the origin of which can be understood in the following way. Consider a compound of the general formula HxYZC.CHAHBR. In general the energy barriers to rotation will be sufficiently small that at ordinary tempera- tures free rotation occurs. The eclipsed forms21 correspond to potential maxima Contributions. The ‘Ethane Type’ have very short residence times and may be ignored. There are then three dis- tinguishable rotational forms represented2 as (10)-(12).The environment of HA in (1 1) is such that it is ‘opposite’ Z and has Y and R to one side and HB and Hx to the other. Magnetic anisotropy in the bonds can23 cause significant differences in magnetic shielding. In none of the conformers (10)-(12) does HB have exactly that same environment. In (10) HB is opposite Z but it has R and Hx to one side and Y and HA to the other. Even if HA and HB spent equal times in each of the three possible conformations the average environments can never be exactly identical and a chemical shift can therefore be expected. This pos- sibility has not been recognised by some a ~ t h o r s . ~ ~ ~ (It should be noted that either Y or 2 may be the same as RCH,. in which case the two RCH,. groups are chemically and the two protons within each group magnetically non- J.J. Drysdale and W. D. Phillips J . Amer. Chem. SOC. 1957 79 319. lS P. M. Nair and J. D. Roberts J . Amer. Chem. SOC. 1957,79,4565. *O E. 0. Bishop Ann. Reports 1961 58,67. a1 D. H. R. Barton and R. C. Cookson Quart. Rev. 1956,10,44. a8 M. S. Newman ‘Steric Effects in Organic Chemistry’ John Wiley New York 1956. 24 H. Finegold J. Amer. Chem. SOC. 1960,82,2641; R. Freymann Compt. rend. 1965 261 2637. L. M. Jackman and N. S. Bowman J. Amer. Chem. SOC. 1966,88 5565. K. Deutsch and I. Deutsch Ann. Physik 1965 16 30. 18 van Gorkom and Hall equivalent. If neither Y nor Z is RCH,. then optical isomerism arises.) The non-equivalence within one group arises by its interaction with another of low symmetry (in this case a carbon atom with either three or four different sub- stituents).Although magnetic non-equivalence always arises by virtue of some form of low symmetry in the molecule the term intrinsic asymmetry26 is reserved for this special case. Two atoms (or groups) such as HA and HB which reside in diastereomeric environments and cannot be interchanged by symmetry operations are said to be diastereotopic? Since populations of excited vibrational and solvation states probably influence chemical shifts and coupling constants only slightly the intrinsic asymmetry effect is generally assumed to be temperature-independent. The temperature- dependent effect which results from unequal populations (i.e. residence times) of the conformers must however be allowed for. As we have already seen the environments of HA and HB in any one of the conformers (1 0)-( 12) are different.Consequently if the populations are unequal a weighted average must be computed. Since the populations will vary with temperature there results a temperature-dependent contribution. At ordinary temperatures this is normally more important than the intrinsic asymmetry effect. Various simplified mathe- matical have been given. In one method a least-mean-square analysis allows an estimation of the rotamer populations and of all the coupling constants. These calculations have been made for several and in the case of protons the gauche and trans coupling constants (about 2 and I6 c./sec. respectively) compare favourably with those obtainedz8 by the analysis of the carbon-13 satellite proton spectra. All methods agree that as the tempera- ture is raised the chemical shift differences should approach a limiting value owing to the intrinsic asymmetry.At infinite temperature the populations of all three rotamers will be equal and so this limiting value should be the average of the chemical shifts within each rotamer. For the geminal fluorine atoms in CF,Br.CFBrCl the limiting value was found29 to be 0.11 p.p.m. At very low temperatures the three possible (f)-rotamers can be frozen out:* and. the fluorine-19 spectrum is the superposition of the spectra of these three forms. Analysis of these spectra gives the chemical shift between the geminal fluorine atoms for each rotamer and their average (0.09 ~.p.m.)~l agrees well with the above figure. An interesting compound is the phthalide (13) for which the measured temperature-independent chemical shift (0.73 p.p.m.) between the methyl groups is said32 to be due to intrinsic asymmetry.A temperature-independent spectrum 8* G. M. Whitesides F. Kaplan K. Nagarajan and J. D. Roberts Proc. Nat. Acad. Sci. 27 J. N. Shoolery and B. Crawford J. Mol. Spectroscopy 1957,1,270; J. A. Pople Mol. Phys, 1958 1 3. 2a N. Sheppard and J. J. Turner Proc. Roy. Soc. 1959 A 252 506. as H. S. Gutowsky J. Chem. Phys. 1962,37,2196; H. S . Gutowsky G. G. Belford and P. E. McMahon ibid. 1962 36 3353. so R. A. Newmark and C. H. Sederholm J. Chem. Phys. 1963,39 3131; 1965,43,602. *l M. Raban Tetrahedron Letters 1966 3105. u.s.A. i962,4a 1112. G. C. Bnunlik R. L. Baumgarten and A. I. Kosak Nature 1965,201 388. 19 Nuclei in High-resolution Nuclear Magnetic Resonance Spectroscopy Y A Y A R-Y-O-y-Ph Ph-$-0-7-R (14) HB (15) 0 can actually be observed2' in three circumstances (1) if one rotamer has a much lower energy than the others; (2) if all possible rotamers have almost equal energies; (3) if the energy barriers between the rotamers are high.Some interest- ing spectral types are shown in Table 2. Table 2 Some possible spectral types for substituted ethanes Proton spectrum type Fast rotation Fast rotation populationsb populationsa Substituted ethane Slow rotationa unequal equal * CHS-CXYZ ABCC A3 A3 * CHZU-CHXY 3 x ABCd ABC CH2U-CXYZ 3xABd AB * ABC AB * * CHUV-CHXY 3 x ABd AB AB a Not temperature-dependent; Three over- lapping spectra; * Indicate possible asymmetric carbon atoms. Enantiomers of each formula give identical spectra.Table 2 is based upon that given by J. A. Pople Mol. Phys. 1958 1 3. Temperature-dependent ; C Not yet reported; In the case of longer substituted chains many conformational isomers become possible. An example is 2,3,5-tricyano-2,3,5-trimethylhexane all five methyl groups of which can be magnetically non-equivalent. More interestingly though the chemical shift between the methylene protons increases33 in many solvents on increase in temperature. This presumably means that a low temperature favours a conformation in which these protons experience almost identical shieldings. It is now possible to generalise the conditions which must be satisfied in order that magnetic non-equivalence may be observed (a) There must be no molecular symmetry operation which relates the nuclei concerned but not those nuclei to which they are spin-coupled.The plane of symmetry which relates A and A' 88 P. Smith and J. J. McLeskey Canad. J. Chem. 1965 43,2418. 20 van Gorkom and Hall in catechol(3) also relates B and B’ to which the protons A are coupled; A and A’ are thus magnetically non-equivalent. (6) Any molecular motions which are occurring rapidly compared with the n.m.r. time scale must not both correspond to such a symmetry operation and allow the nuclei to reside in the same environ- ments for comparable times. (c) There must be a field gradient between the nuclei. In other words the previous two conditions having been satisfied if the (average) environments are insufficiently dissimilar then no magnetic non- equivalence will yet be observed. The effect leading to satisfying condition (c) appears to be transmitted mainly spatially.The number of bonds is in itself not significant and the interacting sites may be quite far apart and not necessarily involve carbon atoms. In other words non-equivalence of geminal nuclei can always be expected if there is present somewhere in the molecule a carbon atom with three different substituents. A selection of examples25 is given in the following sections. (ii) Oxygen-containing compounds. The two interacting groups may be separated by a bivalent atom such as oxygenM as in (14) and (15). The difficulties encoun- tered in studying the various conformations of such compounds are considerably increased by the oxygen; the ether linkage has been insufficiently studied in this respect% for the possible conformers confidently to be predicted.The compounds (14) and (15) were however studied to help determine the manner in which an asymmetric centre exerts its influence. In (14) the chemical shift between A and B appears to increase the larger the group R which is a saturated alkyl chain; in the compounds (15) this is not so. Steric size at the chiral centre therefore plays some part. Roberts and his co-workers3Qs3B considered that the shielding differ- ences between A and B would result from two general effects. These are electronic differences in the two carbon-hydrogen bonds concerned and differences in shielding by more distant parts of the molecule and solvent. Now the protons in the methylene groups of diethyl s~lphoxide~~ and diethyl ~ u l p h i t e ~ ~ exhibit magnetic non-equivalence The constants for the coupling between the methylene carbon-13 and each of the protons are said% to be equal in these cases.But for acetaldehyde diethyl acetal there are two distinct39 such coupling constants which are a sensitive indication of the bond character. They may therefore provide a new criterion for non-equivalence since they should be39 largely unaffected by the magnetic shielding contributions which complicate the interpretation of chemical shifts. They therefore probably reflect the first of the two effects considered by Roberts and his co-workers and indicate that there are electronic differences in the two carbon-hydrogen bonds concerned. Of the various factors considered possibly to affect shielding differences (the G. M. Whitesides D. Holtz and J. D. Roberts J.Amer. Chem. SOC. 1964 86 2628. S. C. Abrahams Quart. Rev. 1956 10 407. 36 G. M. Whitesides J. J. Grocki D. Holtz H. Steinberg and J. D. Roberts J. Amer. Chem. SOC. 1965 87 1058. 37 K. Mislow M. M. Green P. Laur J. T. Melillo T. Simmons and A. L. Ternay J. Amer. Chem. SOC. 1965 87 1958. 3* F. Kaplan and J. D. Roberts J. Amer. Chem. SOC. 1961 83 4666. 39 L. S. Rattot L. Mandel and J. H. Goldstein J. Arner. Chern. SOC. 1967 89,2253. 21 Nuclei in High-resolution Nuclear Magnetic Resonance Spectroscopy second effect) interactions with the solvent are significant. Chemical shift differences therefore form an unreliable measure of conformational equilibria.' It has been shown*O that for substituted ethanes the energy differences between the rotamers are not constant but are a function of both the dielectric constant and the temperature of the medium.A change of solvent may therefore affect the observed non-equivalence by altering conformer populations. However the ring current41 of the aromatic ring attached to the methylene group in (14) was considered the most important factor. This would mean that the chiral centre affects the conformation of the benzyl group in such a way that the two protons are in different positions relative to the aromatic ring. The experimental data do not suffice to decide whether the effects discussed are altering conformer popula- tions or the intrinsic asymmetry contributione or both. Various families of optically inactive compounds may contain nuclei which meet the conditions for observable magnetic non-equivalence. Diethyl acetals sucN12 as (1 6) and triglycerides such as triacetin (1 7) have a molecular symmetry plane and consequently are optically inactive.However this plane does not bisect the connecting line of the geminal protons which are magnetically non- Me A I HO Me B Ph\ a / O-CHAHBMe/ CHAHgO. COMe O.CHgHe,Me Me-CH CH I .O*COMe ,,CH- C-0-Ce (18) (16) CHA. He; 0-COMe (17) ,OMe ' Me equivalent. This is manifested by the relative complexity of the AA'BB'X type proton spectrum of the glyceryl moiety of triacetin (Figure). Similar magnetic non-equivalence can be induced across an ester bond; e.g. the two methyl groups of the isopropyl ester (18) area non-equivalent. (iii) Nitrogen-containing compounds. The asymmetry effect in a molecule can be transmitted across a nitrogen atom similarly to the way it is transmitted across an oxygen.The methylene protons of (19) areu non-equivalent probably for this reason. However non-equivalence may be caused by the nitrogen atom itself. One cause may be a sufficiently slow inversion of a trigonal nitrogen atom. The two methylene protons of the substituted hydroxylamine (20) are non- equivalent at low temperatures and this can be explained on the assumption of 40 R. J. Abraham L. Cavalli and K. G. R. Pachler MoZ. Php. 1966 11,471 ; R. Freeman and N. S. Bhacca J Chem. Phys. 1966,453795. 41 H. P. Figeys Tetrahedron Letters 1966,4625; J. I. Musher J. Chem. Phys. 1965,43,4081. 43 P. R. Shafer D. R. Davis M. Vogel K. Nagarajan and J. D. Roberts Proc. Nat. Acad. Sci. U.S.A. 1961 41,49. 43 N. S. Bowman D. E. Rice and B. R. Switzer J. Amer.Chem. SOC. 1965,87,4477; C. van der Vlies Rec. Trav. chim. 1965 84 1289. 44 T. H. Siddall J. Phys. Chem. 1966 70,2249. 22 van Gorkom and Hall The 100 McJsec. spectrum of the glycerylprotons of triacetin. a non-planar nitrogen atom as in the conformers (21)-(23). The energy barrier to umbrella inversion was found45 to vary inversely with the dielectric constant of the medium. X - Y Y x v - Y X Y Y A (24) R (25) (26) 46 D. L. Griffith and J. D. Roberts J. Amer. Chem. SOC. 1965,87,4089. 23 Nuclei in High-resolution Nuclear Magnetic Resonance Spectroscopy However although a non-planar nitrogen atom probably introduces a greater asymmetry a planar nitrogen (or a nitrogen atom pseudo-planar owing to rapid inversion) may introduce sufficient asymmetry for observable magnetic non- equivalence.There is confusion in the l i t e r a t ~ r e ~ ~ ~ ~ ’ as to the conformations in which a compound containing a planar trisubstituted atom exists. However by arguments similar to those used to demonstrate that the average environments of A and B in (10)-(12) are not identical it may be seen that A and B in the conformers (24)-(26) have differing average environments. The compound (27) in which the methylene protons are48 magnetically non-equivalent may be an example of such a situation. It appears that before invoking a slow nitrogen inversion on the basis of magnetic non-equivalence some independent evidence ought to be obtained. (iv) Phosphorus-containing compounds. Other multivalent atoms may introduce the requisite degree of low symmetry into a molecule.For example the tetraco- ordinated approximately tetrahedral phosphorus atom can induce magnetic non-equivalence. Proton n.m.r. spectra49 of (28) and its analogues show that the two methyl groups are non-equivalent. In compounds (29) if R = 2-propyl the two methyl groups may similarly44 be non-equivalent even if R2 = R1 [since the phosphorus atom has three different groups attached to it; see Section 3 (i)]. If R2 # R1 then the two R groups can also be distinguishable as there is then no symmetry plane relating these two groups on each phosphorus. A trico-ordinated phosphorus atom may50 also introduce magnetic non- equivalence in a molecule. (v) Allenes biphenyls and other aromatic compounds. The examples discussed so far have been concerned with compounds in which the required low order of symmetry is related to a chiral centre.Other types of chirality1’ may cause 46 Ref. 21 p. 50; J. A. Elvidge in ‘Nuclear Magnetic Resonance for Organic Chemists’ ed. D. W. Mathieson Academic Press London 1967 p. 39; I. S. Showell Progr. Chem. Fats and Other Lipids 1965 8 275. 47 E. L. EIiel ‘Stereochemistry of Carbon Compounds’ McGraw-Hill New York 1962 p. 155. 40 A. H. Lewin J. Lipowitz and T. Cohen Tetrahedron Letters 1965 1241. 4g T. H. Siddall and C. A. Prohaska J . Amer. Chem. Soc. 1962 84 2502 3467. T. H. Siddall C. A. Prohaska and W. E. Shuler Nature 1961 190,903. 24 van Gorkom and Hall magnetic non-equivalence. The allenes (30) serve as examples of axial chirality the methylene protons of the ethyl group being5l non-equivalent. The (hydroxy) methylene protons of the biphenyl (31) are5% similarly non-equivalent.If the stable biphenyl conformers occur with the aromatic rings at right-angles to one another then such magnetic non-equivalence can only be observed if rotation around the bond between the rings is slow since a rotation through 180” ex- changes the environments of the two protons in the methylene groups. This rotation is the process by which an optically active biphenyl would be racemised. Consequently a temperature study of the spectra of a compound such as (31) can yield information on the racemisation process52 without recourse to optical resolution. The protons of the unsubstituted ring in monoacetyl-ferrocene mthenocene and -0smocene produce a sharps singlet. This is due to the fast rotation of the five-membered ring as is typicalM for metallocenes.However non-equivalence of the methylene protons in the side-chain of the ferrocene derivative (32) is55 observed. This observation is presumably related to the non-equivalence of the methylene protons of NN-dimethylben~ylamines~~ with ortho or meta sub- Me / Ph a) R=*CO-CH \CH,OH stituents lacking symmetry. A similar example is the non-equivalence of the two methyl groups of an isopropyl residue5’ attached to a highly substituted naph- thalene nucleus. The exact cause of such magnetic non-equivalence has not been established but may be explicable in terms of conformers such as (24)-(26) in which X-Y would represent the asymmetrically substituted aromatic nucleus. However not only interspatial effects but also the influenceM of asymmetry induced in the molecular electronic system might be important.(vi) Vicinal atoms. The previous examples have been concerned with demon- strating that some low order of symmetry may cause two geminal (groups of) nuclei to be magnetically non-equivalent. Similar effects can be observed with two vicinal groups. One example of this is the non-equivalence of protons A and B in (33a) and their equivalence in (33b).58 52 M. L. Martin R. Mantione and C. J. Martin Tetrahedron Letters 1965 3185. sz (a) W. L. Meyer and R. B. Meyer J . Arner. Chern. SOC. 1963,85,2170; (b) D. M. Hall and T. M. Poole J. Chem. SUC. (B) 1966 1034. 5s M. D. Rausch and V. Mark J . Org. Chem. 1963 28 3225. 64 M. Rosenblum and R. B. Woodward J. Amer. Chem. SOC. 1958 80 5443. 65 P. Smith J. J. McLeskey and D. W. Slocum J . Org. Chern.1965 30,4356. 58 J. C. Randall J. J. McLeskey P. Smith and M. E. Hobbs J. Amer. Chem. SOC. 1964 86 3229. 67 F. Conti C. H. Eugster and W. von Philipsborn Helv. Chirn. Acta 1966 49,2267. 68 S. R. Johns and J. A. Lamberton Chern. Comrn. 1965,458. 25 Nuclei in High-resolution Nuclear Magnetic Resonance Spectroscopy 4 Temperaturedependent Magnetic Non-equivalence in other than Ethane-type Any process which effectively exchanges the environments of two nuclei will cause time-averaged equivalence of the nuclei if the process is fast on the n.m.r. time scale. If the rate of the process is temperature-dependent and comparable with the n.m.r. time scale (which is a function of the magnetic field strength employed) the spectra and any magnetic non-equivalence observed will be a function of temperature.Molecules A. Intramolecular Processes.-Owing to the partial double bond between and hence the restricted rotation around the carbonyl-nitrogen bond of NN- dimethylformamide (34) two methyl signals may be observed. These correspond M e o w (35) OMe to methyls cis and trans to the carbonyl group. As the temperature is raised the ratelO~~~ of the relevant rotation increases the spectra alter and finally no non-equivalence is observed. The phenanthrene derivative (35) exists as two distinct molecular species which giveeo overlapping spectra. These species one of which has the methyl group cis to the carbonyl and the other the methyl trans are interconverting by rotation. There is thus an important difference between this example and dimethylformamide in which non-equivalence of the two methyl groups occurs within the single molecular species.Valence isomerisation can cause similar effects. The proton spectrume1 of bullvalene one form of which is shown in (36) at low temperatures consists of two bands corresponding to the six olefinic and the four allylic protons. As the temperature is raised the Cope rearrangements become easier and at room temperature only a single resonance close to the weighted average of the other two is observed. Organometallic compounds also undergo processes which can affect the appearance of the n.m.r. spectra. An X-ray crystallographic analysis sB L. W. Reeves in ‘Advances in Physical Organic Chemistry’ ed. V. Gold Academic Press London 1965 vol. 3 p. 196; W. D. Phillips Ann. New York Acad. Sci. 1958 70 817. O0 S. R.Johns J. A. Lamberton and A. A. Sioumis Chem. Comm. 1966 480. G. Schroder Angew. Chem. 1963 75,722. 26 van Gorkom and Hall of (37) has showns2 the structure to be that given; the second C,H group is present as a normal a-bonded 2,4-cyclopentadienyl group. In solution at room temperature the proton spectrum consists of two singlets. The five protons of this second C,H group are evidently all equivalent. A study of this resonance as a function of temperature has led to the conclusion that a rapid intramolecular reorientation process occurs possibly by repeated 1,2-shifts. Such organometallic compounds ('sterically non-rigid') are thus phenomenologically related to the 'fluxional' structures typified by bullvalene. Similar averaging processes have also been postulateda to occur in trisallylrhodium to account for some other- wise fortuitous magnetic equivalences.B. Intermolecular Processes.-If a molecule containing two or more equivalent nuclei interacts with the solvent or with some third material magnetic non- equivalence may arise either by conversion into a new species or by conforma- tional changes. Clearly the reverse may also occur. Since the extent of interaction is ordinarily a function of temperature the spectra observed will change with temperature. (i) Solvent eflects. There has been considerable interest recently in inducing non-equivalence by the use of a suitable solvent. The magnetic anisotropy of aromatic compounds such as benzene p ~ r i d i n e ~ ~ and quinolines5 is normally exploited for this purpose. The technique has been frequently employed in the steroid field.gp Orientation occursse in the collision complex and so different parts of the molecule may experience different shielding effects.For example the C(12) axial and equatorial protons in 2p-epoxy-5a-androstan-1 l-one have practically identical chemical shifts in deuteriochloroform but in benzenes4 solution are non-equivalent. The method has been extended to distinguish two enantiomers. Racemic 2,2,2-trifluoro-l-phenylethanol (38) gives two overlapping spectras7 in an optically active base. The two types of collision complex formed between the base and the two forms of the alcohol are diastereomeric and consequently 6a M. J. Bennett F. A. Cotton A. Davison J. W. Faller S. J. Lippard and S. M. Morehouse J. Amer. Chem. SOC. 1966 88 4371 ; P. von R. Schleyer J.J. Harper G. L. Dunn V. J. Dipasquo and J. R. E. Hoover J . Amer. Chem. SOC. 1967,89 698. 68 J. K. Becconsall and S. O'Brien Chem. Comm. 1966 720. 84 N. S. Bhacca and D. H. Williams 'Applications of N M R Spectroscopy in Organic Chemistry' Holden-Day San Francisco 1964 ch. 7. 65 A. P. Tulloch J. Amer. Oil Chemists' SOC. 1966 43 670. 68 J. Ronayne and D. H. Williams Chem. Comm. 1966,712. 67 W. H. Pirkle J. Amer. Chem. SOC. 1966,88 1837; J. C. Jochens G. Taigel and A. Selinger Tetrahedron Letters 1967 1901. 27 Nuclei in High-resolution NucZear Magnetic Resonance Spectroscopy the trifluoromethyl groups are in different environments. This means that the presence of optical isomers can be established without optical resolution and the optical purity checked by the relative intensity of the overlapping spectra.Normally high-resolution n.m.r. experiments are deliberately obtained under conditions in which both the solute and solvent molecules are tumbling rapidly. In this way direct dipoledipole interactions are averaged. However a new field may be opened up if liquid crystalssa are used as the anisotropic solvent. Such nematic phases as pp’-di-n-hexyloxyazoxybenzene cause largescale ordering of the solute molecules andsg additional lines due to intramolecular dipoledipole interactions are observed. (ii) Reaction with a third material. If the solute reacts with some other compound in the solution the molecular symmetry may be altered. For example the methylene protons of the benzylamines are generally equivalent. However in the presence of trifluoroacetic acid the protonated species (e.g.39) is formed,7o and the protons A and B are magnetically non-equivalent. Again diethyl sulphide gives a normal 1 3 3 1 quartet for the methylene protons but it reacts with borane to give an addition compound (40) of reduced symrnetry7l and the methylene protons A and B of this adduct are magnetically non-equivalent. If dimerisation of a compound occurs in solution72 similar spectral changes may be observed. As an example the meso protons of certain72 porphyrin tetramethyl esters give the expected singlet signals in dilute solution but in concentrated solutions extra signals owing to dimerisation. (iii) Exchange reactions. The copper-63 resonance of a mixture of the copper(1) and copper(I1) ions in water consists73 of a single peak. This is due to a rapid electron-transfer reaction between the two types of ion which then appear to be equivalent.On the other hand the rate of exchange between bulk water mole- cules and water molecules bound to cobalt(r1) ions may be slow at certain temperatures. In this case two signals may be observed for the oxygen-17 reson- ance of the water molecules74 and the relative areas of the resonances give an indication of the hydration number of the cobalt(r1) ion. 5 Interpretation of Spectra Before concluding it is worth drawing attention to some pitfalls that can be met in certain circumstances. The concept of magnetic equivalence is not absolute but is briefly an observational property. In this way it is a somewhat negative 68 G. W. Gray ‘Molecular Structure and the Properties of Liquid Crystals’ Academic Press London 1962; D.Chapman Science Journal 1965 Oct. 1 32. 60 A. Saupe 2. Naturforsch. 1964 19a 161; S. Meiboom and L. C. Snyder J . Amer. Chem. SOC. 1967,89,1038; R. A. Bernheh and B. J. Lavery ibid. p. 1279; J. 1. Musher J. Chem. Phys. 1967 46 1537. 70 W. F. Reynolds and T. Schaefer Canad. J. Chem. 1964 42 21 19. 71 T. D. Coyle and F. G. A. Stone J. Amer. Chem. SOC. 1961 83,4138. 72 R. J. Abraham P. A. Burbidge A. H. Jackson and D. B. Macdonald J. Chem. SOC. (B) 1966,620. 73 H. M. McConnell and H. E. Weaver J. Chem. Phys. 1956,25,307. 74 J. A. Jackson J. F. Lemons and H. Taube J . Chern. Phys. 1960,32,553; 1. R. Lantzke and D. W. Watts Austral. J. Chem. 1967 20 173. 28 van Gorkom and Hall feature since its validity may depend on the experimental conditions such as the operating magnetic field strength and homogeneity.As an example the aromatic protons of toluene and cumene give an unsplit singlet at 60 Mc./sec. but well- resolved75 analysable resonance lines at 200 Mc./sec. It is therefore dangerous to rely on negative n.m.r. evidence; apparent equivalence must not be interpreted as proving the nuclei involved to be identical. It is also dangerous to assume that measured splittings necessarily correspond to the coupling constants involved since the first-order interpretation rules76 may only be applied to groups of magnetically equivalent nuclei. The ABX system has been fully disc~ssed'~ in this respect. Faiiure of first-order rules is sometimes manifested by virtual coupling.78 When in three sets of nuclei the first set is coupled to the second which is also coupled to the third the spectrum of the first set of nuclei may appear more complicated owing to virtual coupling with the third set even if the real coupling is zero.6 Conclusion The magnetic non-equivalence which has been the main concern of this Review arises from quite subtle differences in (average) environment or conformer populations. The existence of these differences does not aecessarily lead to observable non-equivalence. So far most workers have attempted to accentuate such potential differences by means of a magnetically anisotropic group such as cyan0 or phenyl. Any resulting magnetic non-equivalence can normally be qualitatively explained on topological grounds after observation but quantitative prediction is virtually impossible. More research is required regarding inter- action between groups.An awareness of the possibility of otherwise unexpected magnetic non-equivalence is important in spectral interpretation. When two atoms (or groups) are distinguishable in an n.m.r. spectrum they may sometimes be differentiated chemically. For example the methylene protons of methyl benzyl sulph~xide~~ are magnetically non-equivalent and on reaction with sodium deuteroxide the resonances due to the lower-field proton disappear more rapidly than those of the higher-field proton. The fact that the two protons of a methylene group in biologically important materials such as triglycerides can be distinguished may assist in showing enzymic preference for one particular proton. 76 F. A. Bovey F. P. Hood E. Pier and H. E. Weaver J. Amer. Chem. SOC. 1965,87,2060. 76 E. D. Becker J . Chem. Educ. 1965,42 591. 77 J. D. Roberts 'An Introduction to the Analysis of Spin-Spin Splitting in High Resolution Nuclear Magnetic Resonance Spectra' W. A. Benjamin New York 1962 p. 71. 78 J. I. Musher and E. J. Corey Tetrahedron 1962,18 791; D. L. Hooper N. Sheppard and C. M. Woodman J. Chem. Phys. 1966,45 398. 70 A. Rauk E. B u d R. Y. Moir and S. Wolfe J. Amer. Chem. SOC. 1965,87 5498. 29