Magnetic nonequivalence

Consider a nucleus that can partition between two magnetically nonequivalent sites. Examples would be protons or carbon atoms involved in cis-trans isomerization, rotation about the carbon—nitrogen atom in amides, proton exchange between solute and solvent or between two conjugate acid-base pairs, or molecular complex formation. In the NMR context the nucleus is said to undergo chemical exchange between the sites. Chemical exchange is a relaxation mechanism, because it is a means by which the nucleus in one site (state) is enabled to leave that state. 

There is a second, more complicated and for fluorine NMR spectra more common situation that will lead to second-order spectra, that in which chemically equivalent fluorines (same chemical shift) are magnetically nonequivalent. This occurs when the chemically equivalent fluorines do not have the same coupling constants to specific other nuclei in the molecule. 

Magnetic nonequivalence is not uncommon, often deriving from the constraints of a ring, as in pentafluorophenyl derivatives or other symmetrically fluorine substituted ring systems such as those shown in Scheme 2.10. The fluorine and proton NMR spectra of 1,2-difluoroben-zene are both representative of the appearance of second order spectra of polyfluoroaromatics. They can be found in Chapter 3, Section 3.9.3. 

Another common situation that can lead to second order spectra is an open chain system such as meso-l,2-difluoro-l,2-phenylethane whose magnetically nonequivalent spin system and resultant second order fluorine NMR spectrum (Fig. 2.7) can only be understood by examination of the contributing conformations about its fluorine bearing carbons.10... 

Hexacoordinate, hypervalent sulfur fluorides have an octahedral geometry that is symmetrical for SF6, which appears as a sharp singlet at +56 ppm, but which has magnetically nonequivalent (axial and equatorial, ab4 system) fluorines for compounds of the structure R-SF5. Compounds with the general structure R-SF4-X can exist as cis- and trans-isomers, the former having three types of fluorine, and the latter only one (Scheme 7.17). 

When the crystallography of compounds related by polymorphism is such that nuclei in the two structures are magnetically nonequivalent, it will follow that the resonances of these nuclei will not be equivalent. Since it is normally not difficult to assign organic functional groups to observed resonances, solid state NMR spectra can be used to deduce the nature of polymorphic variations, especially when the polymorphism is conformational in nature. Such information is extremely valuable at the early states of drug development when solved single crystal structures for each polymorph or solvate species may not yet be available. 

If two magnetically nonequivalent nuclei I and K are present in the spin system, the transition frequency of nucleus I is shifted by an additional second order term48 55)... 

Cu(acacen) diluted into Ni(acacen) 1/2 H20 has been chosen as a typical example to demonstrate the separation of magnetically nonequivalent sites in a single crystal by proton EI-EPR. For the specific orientation shown in Fig. 14, the ordinary EPR spectrum of site II is difficult to analyze (Fig. 14 a). In the corresponding EI-EPR spectrum (Fig. 14 b), a high-frequency proton ENDOR line of this site has been used as an observer. Since site I is completely suppressed in the EI-EPR spectrum, the analysis of the hf data of site II becomes straightforward. 

The copper complex Cu(bipyam)2(C104)2 diluted into the corresponding Zn host crystal1055 shows an ENDOR spectrum which is due to four magnetically nonequivalent... 

The first order EPR spectrum of Co(acacen) consists of two sets of eight allowed Ams = 1, Amo, = 0 transitions (I = 7/2, two magnetically nonequivalent sites). This simple pattern, however, was only observed for orientations of B0 near the principal axis gj. If B0 lies near the plane spanned by gy and gz, forbidden Ams = 1, Amo, = 1, 2 transitions occur (Fig. 2 a). 

Fig. 2 a, b. EPR and ENDOR spectrum of the low-spin Co(II) Schiff base complex Co(acacen) diluted into a Ni(acacen) 1/2 H20 single crystal, temperature 8K. a) EPR spectrum the two magnetically nonequivalent sites coincide for this particular orientation (EPR observer is marked by an arrow) b) ENDOR spectrum of H, 13C (enriched) and 14N ligand nuclei vp free proton frequency denote the AmN = 2 nitrogen ENDOR transitions. (From Ref. 12)... 

It is of interest to note that the magnetic nonequivalence of the enantiomers of the a-phosphoryl sulfoxide 49 in the presence of TFMC was observed (88) not only in Hbut also in and NMR spectra. With regard to the accuracy of the NMR method, the P H NMR spectra proved very useful in this case, since only two well-separated singlets that were due to enantiomeric sulfoxides 49 were observed. 

Using NMR spectroscopy, it is also possible to determine the polymer s tac-ticity. The constitutional repeating unit of polymethylmethacrylate (PMMA), for example, possesses three different types of (magnetically nonequivalent) protons with different chemical shifts 6, i.e., the CH2 protons (6 = 2 ppm), the a-CHj protons (6=1 ppm), and the OCH3 protons (6 = 3.5 ppm). 

It is evident that in the racemic diade both -CH2- protons are imbedded into an identical microenvironment. Consequently, they are magnetically equivalent, absorb at the same resonance frequency v (have the same value of 6), and do not couple with each other. Therefore, the proton in a racemic diade appears as a singlet in the NMR spectrum. For the meso diade, on the other hand, it is obvious that the two -CH2- protons have a clearly different micro-environment while has two methyl groups as neighbors, there are the ester groups for proton H. Consequently, the two -CH2- protons of the meso diade are magnetically nonequivalent, absorb at different resonance frequencies Vj, and V , respectively, and couple with each other. Therefore, these protons in a meso diade appear as a set of two doublets in the NMR spectrum. 

We would expect that the spectrum of the latter compound would consist of two signals a two-proton triplet in the vinyl region and a four-proton doublet in the allylic region. This is because the coupling constant, / 3 is zero. It if were not zero, then a more complicated spectrum would result. Thus magnetic nonequivalence can lead to much more complicated spectra. 

Protons that are chemically equivalent but magnetically nonequivalent are indicated by, for example, A A. The examples of such systems given below illustrate the medtod. This system for designating spin systems is merely a labeling device. The appearance of actual spectra will depend on die magnitude of die various J values. Nevertheless this is a convenient and common way of categorizing coupled proton systems. 

Whereas the NMR spectra for the l-(p-anisyl)vinyl cation 403 show magnetically nonequivalent signals for the C2 and C6 ortho and C3 and C5 meta carbon and proton signals, these positions remain equivalent in the 3H and 13 C NMR spectra of the jS-silyl-substituted cation, even at the lowest temperatures. 

In a cation such as the (2,4-di-ferf-butyl-6-methyl)benzyl cation 147, a high rotational barrier around the v/r-hybridized atom is observed. The methylene protons are found magnetically nonequivalent in the1H NMR spectrum.356 Recent combined experimental and theoretical studies for the related cation 143 suggest357 that structure 143b is an important resonance contributor. 

This outcome derives from the fact that the carbon that bears the fluorine is chiral, which makes the two vicinal hydrogens diastereotopic and thus magnetically nonequivalent. In such a case, the two diastereotopic protons will not only appear as separate signals (an AB system), but they usually will also couple to vicinal fluorines (and hydrogens) with different coupling constants. Examining Figure 2.8b, which represents... 

Magnetic nonequivalence is not uncommon, often deriving from the constraints of a ring, as in pentafluorophenyl derivatives or other... 

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