Robert M. Silverstein and Robert T. LaLonde SUNY College of Environmental Science and Forestry Syracuse. NY 13210
1
Chemical Shift Equivalence and Magnetic Equivalence in Conformationally Mobile Molecules
Some of the basic concepts of chemical shift equivalence and magnetic equivalence in nuclear magnetic resonance spectrometry (NMR) have been discussed in earlier papers in this Journal (1,2). We should like to refine an earlier discussion (1) and elaborate on these concepts in conformationallv mobile molecules: several definitions are restated here in somewhat modified f d m . This discussion is designed for the oreanic chemist who is involved in interpretation of NMR spectra. The familiar Poole notation is hasedon the concept of sets of nuclei within spin system. A set of nuclei eomists of chemical shift eouivalent (or isochronous) nuclei. A spin system cons& of sets of nuclei that "interact (spin couple) among each other hut do not interact with any nuclei outside the s& system. I t is not necessary for all nuclei withim a spin system to he coupled with all the other nuclei" in the spin system (3).Spin systems are "insulated" from one another; for example, the ethyl protons in ethyl isopropyl ether constitute one snin and the isooro~vl . svstem. . . .. .orotons another. If nuc1t.i are inter~han~eahle by a symmetry operation or a r n ~ i dmerhanism (that is, rapid on the N.MR time srale), they are rhemical shilr equivalent (isorhnmousj; that is, they ha\,e the samechemical shift unrlpr nchiral or racemicconditions. Nuclei are interchangeahle if the structures before and a f er the ooeration are indi.;tinguishahle. Pople decreed that the chemical shift equivalent nuclei he ordered into sets designated As, B, XP,etc. The symmetry operations are (1)rotation about a symmetry axis (C,), (2) inversion a t a center of symmetry (i), (3) reflection a t a olane of svmmetrv (a).or (4) . . hieher orders of rotation about an axis f&owed by reflection in a plane normal to this axis (S.). The svmmetrv element (axis. . . center. or plane) must be; symmetry element for the entire moleche. Nuclei that are interchangeable through an axis of symmetry (C,) are chemical shift equivalent in any environment (solvent or reagent) whether achiral, racemic, or chiral (Y-CH-Y).' Nuclei that are interchangeahle through any other symmetry operation (hut not in addition to a C, operation) are chemical shift equivalent in an achiral or race& environment hut not in chiral environments (Y-CH2-Z).' Nuclei that are not interchaneeahle throueh a svmmetrv operation (nor through ~~
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'The following four terms are based an the concept of separately replacing each of a pair of structurallyidentical ligands with a different ligand; for example, replace H with D. Homotopie. The D for H replacement results in a single product. Compare our C. operation. Enantiotopie. The D for H replacement results in a pair of enantiomers. Compare our interchange through an operation other than C.. I I i ~ i i l o r ~ ~The ~ ~llp for u H replar~mentrewlrs in a pnir of diait+rm,mer; Compare the particular case of ncminterehnnyeabili t ) of n pair nigeminal lignnd- thruuph a .;ymmetr\~operntic~n, or the particular ease of interchange in o ehiral enuironment through an operation other than C2. Heterotopie. The D for H replacement results in a pair of constitmtional isomers. Comoare the particular case of noninterchany e d ~ i l ~ t hy m u g h a iymmctry opetatiw of 9 JimnJ un .1 rsrhnn ,110111w i t h a liyand on snvthcr inrlrm atom, e.g. ~~
a rapid mechanism) are not chemical shift equivalent in any env&onment.' Nuclei that fortuitously absorb at the same position are sometimes classified as chemical shift equivalent, or isochronous, but such coincidence is neither absolute nor fundamental, depending as it does on instrumental resolution Rapid mechanisms involve inter- or intramolecular interchanee between functional erouns . (for . examnle. . . hvdroxvlic" carhoxylic acid proton interchange), conformational interchanee (for examole. axial-eauatorial or rotational). or inversi&(for example, RNH~);these are obviously temperature-dependent phenomena and are usually rapid on the NMR under ordinary conditions. A further refinement involves the concept of magnetic equivalent nuclei. If nuclei in the same set (i.e. chemical shift equivalent nuclei) couple equally to each nucleus (probe nucleus) in every other set of the s& system, they are-magnetic equivalent, and the designations Az, Xz, etc. apply. However, if the nuclei are not magnetic eauivalent. the designations AA'. XX' are used. Magnetic equivalence presupposes chemical shift equivalence. T o determine whether chemical shift equivalent nuclei are magnetic equivalent,. one examines -eeometrical relationshios. If the bond distances and aneles " from each nucleus in relation to the probe nucleus are identical. the nuclei in question are maenetic eauivalent. In other words, two chemical shift equivllent nuclei are magnetic equivalent if they are symmetrically disposed with respect to each nucleus (probe) in any other set in the spin system. This means that the two nuclei under consideration can he interchanged through a plane passing through the probe nucleus and perpendicular to a line joining the chemical shift eqnivalent protons. Note that this test is valid only when the two nuclei are chemical shift equivalent. The latter point bears repeating: only chemkal shift equivalent nuclei are tested for magnetic equivalence. These rules are applied readily to conformationally rigid structures. Thus in p-chloronitrohenzene
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the protons ortho to the nitro group (HAand H A )are chemical shift equivalent to each uther, and the protms ortho to the chlorine atom (Hx and H d are chemical shift equivalent to and JAW are the same, approximately 7 to 10 each other. JAX WL, and J.yx and JAW are also the same but much smaller. approximately U tu 1 Hz. Since H,, and HA coupledifierentlv to another specific proton, they are not magnetic equivalent, and first-order rules do not apply. (Similarly, H x is not magnetic equivalent to Hx..) The system is described as AA'XX', and the spectrum is complex (4). Fortunately, the pattern is recognized readilv because of its svmmetrv and appnrrnt simplicity; under ordinary resolution it resembles an A H oattern of two d~itorteddouhlets. Closer insuecticrn revealsmany additional splittings. As the para suhsiituents become more similar to each other (in their shielding properties), the system tends toward AA'BB'; even these ahsorptions resemble AB patterns until they overlap. The aromatic protons of symmetrically ortho-disubstituted benzenes also ~
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Volume 57, Number 5. May 1980 / 343
give AA'BB' spectra. An example is ortho-dichlorobenzene 1.51.
In confurmationally mohile systems, the situation becomes more complicated. CH., prutons are chemical shift eauivalent. even when the molecule has no symmetry element,-by rapid rotational interchange, and magnetic equivalent by rapid rotational averaging of the coupling constants among identical rotamers, if there is a probe proton in the spin system. Consider, in contrast with the methyl group, a methylene group (a next t o a chiral center as in 1-hromo-1,2-dichloroethane YCHzCHYZ molecule) (Fig. 1). Protons H. and Hb are not
CH2CH2-Y molecule is resolved by examining the coupling of chemical shift equivalent protons to a probe proton. In the anti isomer, H. and Hb are obviously not equally coupled to either H, or Hd. H, and Hh "straddle" H, in one gauche ronot,necessar,ily tamer and Hd in theother. hut H. and coupled equally to the srraddlrd prohe 11 there IS repuli~on between groups Y and Z; the rotamers are shown merely as idealized structures. Attempts to demonstrate equal coupling by averaging couplings among the three rotamers fail because of unequal couplings; thegauche or anti couplings in the anti rotamer are not necessarily the same as those couplings in the gauche forms. Nor are the populations of each of the rotamers equal. The ZCH2CH2Ymolecules are therefore AA'XX'systems, but at the usual resolutions they give apparent A2Xz spectra ( 6 ) ,and in fact they are frequently, though not rigorously described as A2X2 systems. In YCHCYZZ compounds, we have three gauche rotamers, two of them enantiomeric (Fig. 3). In the non-enantiomeric
are
Figure 1. Newman projection 01 the rotamars of I-bro-1,2dichlwoethane. chemical shift equivalent, since they cannot be interchanged h y u symmetry operation or by rapid rotation. The molecule has no axis, plane, center, or reflection axis of symmetry. Although there is a rapid rotation around the carbon-carbon single bond, protons H. and Hb are not interchangeable by a rotational operation, since the rotamers are neither identical nor enantiomeric; the protons in each rotamer are diastereotopic. The question of magnetic equivalence does not arise since there is no chemical shift equivalence; the system is ABX. In ZCH2CH2Ymolecules, we are dealing with an anti rotamer and two enantiomeric gauche rotamers (Fig. 2). (We
Figure 2. Newman projection of the rdamers of a Z-CH2CH2--Y
molecule.
assume that neither Z nor Y contains a chiral element.) In the anti rotamer.. H,- and HAare chemical shift eoivalent bv inof symmetry, as are H, and^^; terchange through a thus there are two sets of enantioto~ic In neither of . ~rotons. . the gauche rotamers is there a symmetry element, but H. and Hb, and H,. and Hd are chemical shift equivalent by rapid rotational interchange between two enantiomeric rotamers. Now we have one chemical shift for H. and Hb in the anti rotamer, and a different chemical shift for Ha and Hb in the gauche rotamers. By rapid averaging of these two chemical shifts, we obtain a single chemical shift (i.e. chemical shift equivalence) for H, and Hb, and of course for H, and Hd. The question of magnetic equivalence in the Z-
344 / Journal of Chemical Education
Y
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H.
Figwe 3. Newman projection of the rotamen of YCH2CHZZ.
rotamer, H, and Hb are chemical shift equivalent by interchange through a plane of symmetry, and in the enantiomeric rotamers, H. and Hb are equivalent by rapid rotational interchange. By rapid rotational averaging of these two chemical shifts, we arrive at chemical shift equivalence in the molecule. Magnetic equivalence of H, and Hb in the non-enantiomeric rotamer is obvious from their geometric relationship to H,. Rapid rotation between the enantiomeric rotamers interchanges the gauche and anti couplings of H. and Ha t o H,. The system is AzX. We shall not attempt to describe all of the possibilities of conformational rotamers, but similar analysis applies. I t turns out that the question of magnetic equivalence in rotamers is readily resolved by examining the individual rotamers in which the protons in question are chemical shift equivalent by a symmetry operation. If they are magnetic equivalent in these rotamers, they are so for the molecule. An extended discussion of internal rotation and equivalence of nuclei is given by Jackman and Sternhell (7). Literature Cited
J.CHEM.EDUC.50.484(19731. J.CHEM. EDUC..11.729(1974). Ed.. p. (41 Eliol,E. L.,J.CHEMEOUC..48,163(19711. (5) Silverstoin, R. M. Barsier. G. C., and Morrill, T C., "SpeNomefrie Identiflmtion of OrganicCompounds," 4th Ed.. Wiley, New York. p. 185.
(1) 8ilventeio.R. M.andSi1berman.R. G., (2) Au1t.A.. (3) Jackman, L. N a n d Sternhell, S,"ApplieationsofNudesrMagnetirResonaneeS~ectrosmpy in Organic Chemis~y: 2nd Pergamon Press, New York, 1969, 12L
(6) Referenee 5, p 184. Fie. 378. (71 Referoner 3. pp. 368-379.
