Robert M. Silverstein SUNY College of Environmental Science and Forestry Syracuse, New York 13210 and Robelt G. Silberman suNY Colleae at Cortland Cortland, New York 13045
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Troublesome Concepts
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in NMR Spectrometry
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Students generally have difficulty with the following concepts in nmr spectroscopy: spin system, set of nuclei, chemical shift equivalence, magnetic equivalence, and virtual coupling. We offer the following definitions and explanations, and suggest references (1-5) for further discussion. 1) A spin system consists of sets of nuclei that "interact (spin couple) among each other hut do not interact with any nuclei outside the spin system. It is not necessary for all nuclei within a spin system to be coupled to all the other nuclei" within the system (4). 2) A set of nuclei consists of chemical shift equivalent nuclei. 3) If nuclei are interchangeable by a symmetry operation or a rapid mechanism, they are chemical shift equiualent; that is, they have exactly the same chemical shift under all conditions. 4) Nuclei are rnogneticolly equiualent if they couple to all other nuclei in the system in exactly the same way. Chemical shift equivalence is presupposed. 5 ) Virtual coupling is a concept that only becomes necessary if part of a spin system is incorrectly considered as a separate entity,and the "break" occurs between strongly coupled nuclei.
Figure 1. trans-1.2-Dichloracyclapropane showing axis of symmetry and effect of rotation around the axis.
We begin with the concepts of chemical shift equivalence and magnetic equivalence as the basis for describing systems. Chemical Shift Equivalence If the two concepts expressed in the chemical shift equivalence rule are stated separately, we can illustrate them more clearly Nuclei that can be interchanged thrugh a symmetry operation are chemical shift equivalent in an achiral solvent. The interchange may occur in any reasonable conformation of the maleeule. 2) Nuclei that can be interchanged mare rapidly than about once in 10W3 sec are chemical shift equivalent. 1)
The symmetry operations referred to are: rotation about a symmetry axis, reflection a t a center of symmetry, reflection a t a plane of symmetry, or higher orders of rotation about an axis followed by reflection in a plane normal to this axis. The symmetry element (axis, center, or plane) must be a symmetry element for the entire molecule. The term "interchange" will be clarified by the examples below. Chemical shift equivalent nuclei are ordered into sets designated by capital letters near the beginning, middle, or end of the alphabet (ABC . . . MNO . . . XYZ) depending on the strength of coupling between them. If the ratio of shift difference in Hz and the coupling constant ( A u l d is less than about 10 or so, the nuclei are said to be strongly coupled, and they are designated by letters close together in the alphabet. Note that "counline streneth" deoends both on Au and J. Protons a and h in trans-l,2-dichlorocyclopropaneare chemical shift eauivalent. as are the orotons c and d (Fia. 1). The molecule has a n axis of symmetry passing through C3 and bisecting the CI-C2 bond. Rotation of the mole-
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Figure 2. Newman projections of staggered and eclipsed conformers of a molecule with a methyl group attached to an optically active center.
cule by 180" around the axis of symmetry interchanges proton H, and Hb and H, and &. If the protons were not labelled, it would not he possible to tell if the symmetry operation had been performed merely hy inspecting the molecule before and after the operation. The second concept can be illustrated by the rapidly exchanging protons on some heteroatoms and by protons in molecules that are rapidly changing conformations. If the exchanee is raoid enough. u " . a single - oeak . will result from, say, the carhoxylic acid proton and the hydroxylic nroton of a hvdroxvcarboxvlic acid. Chemical shift eauivalence of protons on a CH3 group results from rapid rotation around a carbon-carbon single bond. Figure 2 shows Newman projections of the three staggered and three eclipsed conformers of a molecule containing a methyl group attached to another sp3 carbon atom having three different substituents, i.e., an optically active center. In any single conformation, protons H,HbH, are not chemical shift eauivaleut because the protons cannot be interchanged by a symmetry operation. However, the protons are raoidlv chaueine oosition. The time w e n t in anv one conforka
