Addison Ault Cornell College Mt. Vernon, Iowa 52314
Test for Chemical Shift and Magnetic Equivalence in NMR
In nmr spectroscopy it is necessary to be able to tell when magnetically active nuclei may be expected t o have exactly the same chemical shift, and when they may not. Similarly, it is necessary to be able to tell when coupling constants between magnetically active nuclei a t two different chemical shifts may be expected to be exactly the same, and when they may not. The question of chemical shift equivalence depends upon the first distinction,and the question of magnetic equivalence depends upon the The purpose of this paper is to present a straightforward procedure by which these decisions can be made. Test for Chemlcal Shift Equivalence Suppose the question is: Must these two hydrogens atoms have the same, or may they each have a different, chemical shift: must they necessarily be chemical shift equivalent or not? T o answer the question, build two molecular models of the compound and distinguish by some tag or marker one of the hydrogen atoms in the first model and the other hydrogen atom in the second model. Now compare the two models. There can be four possible results. 1) The two models will be identical. If this is the case, the two hydrogen atoms will necessarily be chemical shift equivalent in any solvent: achiral, racemic, or chiral. If this is the result, the two hydrogen atoms may be said to
'Ault, A., J. CHEM.EDUC., 47,812 (1970). 2Silverstein,R. M., and Silberman, R. G., J. CHEM. EDUC., 50,484 (1973).
Mislow, K., and Raban, M., in "Topics in Stereochemistry," Vol. 1, (Editors: Allinger, N. L., and Eliel, E. L.),Academic Press, Inc., New York, 1967, p. 1.
be "equivalent." An example of this would be the hydrogen atoms of dichloromethane
9
H
I
~ k ~ ~ - @
CI.+~
identical
CI
CI
2) The two models will be enantiomers. If this is the case, the two hydrogen atoms will necessarily be chemical shift equivalent in an achiral or racemic solvent. If a chira1 solvent is used, the two hydrogen atoms will not necessarily be chemical shift equivalent. If the models are enantiomen, the two hydrogen atoms are said to be enantiotopic.3 An example of this would be the hydrogen atoms of bromochIoromethane tnmtiomsn
Br
8"
3) The two models will be diastereomers. If this is the case, the two hydrogen atoms will not necessarily be chemical shift equivalent in any solvent. If the models are diastereomers, the two hydrogen atoms are said to be diastereotopic.3 An example of this would be the methylene protons of a molecule containing a chiral center, such as WCH2-CXYZ
Q
+
LC"
4
H I
7% 4
dI88tere0merm
kC,X
Another example would be the protons of l-bromo-l-chlorcethene
Volume 51. Number 71. November 1974
/
729
@ ,
BF
81,
H , di-rromcm
C P y H
C12="\o
4) The two models will he structural isomers. In this case also the two hydrogen atoms will not necessarily he chemical shift equivalent in any solvent. If this is the result, the hydrogen atoms may be said to be "different." An example in which this would be the result is provided by cis-I-bromo-2-chloroethene \'B
H/c%
~ t n r d v aimmrra ~
The trans isomer would also provide an example. Comments
first it may he surprising that enantiotopic atoms or will, in principle, have different chemical shifts in chiral solvents. However, differences in the interaction of enantiotopic groups with chiral solvent molecules is of the same nature as the difference in the interaction of enantiotopic atoms or groups of enzyme substrates with chiral enzyme molemles. For example, the enantiotopic alpha hydrogens of ethanol and the enantiotopic -CH,-COOH groups of citric acid are distinguishable by enzymes
system from CHa-CXYZ, but a t high sample temperatures one would expect the singlet of an As system. This last example shows that the test can be extended to a comparison of three or more nuclei by making three or more models. By comparing these models one can tell which nuclei are "equivalent," which are enantiotopic, which are diastereotopic, and which are "different." As Mislow and Raban have pointed out, some of the confusion over whether or not groups or atoms are equivalent is the result of a tendency to divide stereochemically related sets of groups or atoms into only two categories: distinguishable ("non-equivalent") and indistinguishable ("eq~ivalent").~The problem is that enantiotopic atoms or groups are, in principle, distinguishable when chiral interactions are considered (enzymes, chiral solvents, chiral shift reagents. . etc.) but indistinmishable otherwise. It is therefore necessary to first mak;? the more fundamental distinctions described by Mislow and Raban, and summarized in this paper. The tests described are only one way t o make these distinctions. For example, the distinction between enantiotopic and diastereotopic atoms or groups can be made on the basis of molecular symmetry: atoms or groups which Can be interchanged only by S, (plane of symmetry, a = SI; center of symmetry, i = Sz; or higher improper axis of rotation) are enantiotooic.. while atoms or erouns ~~~~~~, . which cannot be interchanged by any symmetry operation are diastereotopic. However, the tests described require only that one be able to distinguish identical, enantiomeric, diastereomeric. and stmcturallv isomeric models. ~
OH
H-i-H I CH.,
OH
HN-CH,-A-CH~COOH I
eth.nol
CWH
citric acid
While chemical shift differences are expected in principk both for diastereotopic atoms or groups in any solvent, and for enantiotopic atoms or groups in chiral solvents, experimentally observable effects may be quite small, some observed chemical shift differences for diastereotopic protons and diastereotopic methyl groups have heen summarized by M~~~~~and ~~b~~ (footnote 3, pp, 26 and 27), and several examples in which enantiotopic atoms or groups have heen found to have experimentally measur. able differences in chemical shift in a chiral solvent or in the presence of a chiral shift reagent have heen cited by F'i~kle.~ interesting question arises when the models which result from this test are conformational isomers. For example, consider the problem of whether or not the methyl protonsof CH~.CXYZ are chemical shift equivalent. ~h~ test would result in the following models
The question is, then, are these models to he considered to be identical or (in this example) to he diastereomers? I t appears that the answer depends upon the purpose for which the comparison is being made. If the experiment one has in mind takes place rapidly with respect to the rate of interconversion of the conformational isomers, they must be considered to be different (ir and uv spectroscopy; nmr spectroscopy a t low sample temperatures). If the experiment takes place slowly with respect to the rate of interconversion of the conformational isomers, they may be considered to be the same (nmr spectroscopy a t high sample temperatures). Thus a t low sample temperatures one would expect the complex nmr spectrum of an ABC
Kainosho, M.,Ajisaka, K., Pirkle. W. H.,and Beare, S. D., J. Amer. Chem. Soc., 94.5924 (1972). 730
1 Journalof Chemical Education
~
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.
Test for Magnetic Equivalence
Suppose the question is: Are all the possible coupling constants between protons in two sets a t different chemical shifts the same; that is, are all the interset coupling constants equal so that magnetic equivalence is involved? The test to answer this question about magnetic equivalence is analogous to that for chemical shift equivalence. models of the compound and in each model distinguish one atom in one set and another atom in the other set tags Or markers. Make enough SO that every possible combination will be represented. If there are m atoms in one set and n atoms in the other, (m X n) models will be needed. Now compare the models. As there can be four possible results. 1) All the models will he the same. If this is the case, magnetic equivalence must be involved in any solvent. An example for which this would he the result is l,l,l-trifluoroethane
All nine models, of which one is shown, would be the same. We are assuming in this example that it is inappropriate to distinguish conformational isomers. 2) The models can be divided into two sets, the members of the first set being enantiomeric with the members of the second set. If this is the case, magnetic equivalence must be involved if achiral or racemic solvents are used, but magnetic equivalence is not necessarily involved if a chiral solvent is used. An example for which this would be the result is provided by 1,1,2-trichloroethaoe
Q
Q
Another example is given by CHzF2
F'
ct I
Br other set
Other examples could be provided by cyclopmpene and 1,l-difluoroallene. In all examples of this type, models within each set will be identical. 3) The models can be divided into two sets, the members of the first set heing diastereomeric with the members of the second set. If this is the case the two sets of chemical shift equivalent nuclei will not be magnetically equivalent in any solvent. One example for which this would he the result is 1,l-difluoroethene
In all examples of this type, models within each set will be either identical or enantiomeric. 4) The models can be divided into two sets, the members of one set heing structura[ly isomeric with the members of the other set. In this case also the two sets of chemical shift equivalent nuclei will not be magnetically equivalent in any solvent. An example for which this would be the result is given by cis-1,2-difluoroethene
Other examples would include the trans isomer of 1 3 difluoroethene, o-dichlorobenzene, and p-bromochlorobenzene. Comments one set
other set
1-Bromo-2-chloroethane provides a second example
I
Br
I
Br one set
The difficulty which students of nmr spectroscopy have had in persuading themselves that the two sets of methylene protons of 1-X-2-Y-ethane derivatives are not necessarily magnetically equivalent comes from the difficulty of seeing that the relationships between protons in the two methylene groups are diastereomeric, as illustrated by the example of 1-bromo-2-chloroethane. Identical or enantiomeric relationships ensure magnetic equivalence (ex: cept for the latter in chiral solvents), and diastereomeric or structurally isomeric relationships lead, in principle, to magnetic non-equivalence, The test described generates diastereomeric models which correspond to the diastereomeric relationships.
Volume51. Number 11. November 1974 / 731
