Second-order spectra

In Section 4.7, the first-order splitting patterns arising from coupling between nuclei with / 7 0 are described, but in some circumstances so-called second-order spectra are observed, and these are more complicated to interpret. Second-order spectra can be observed in cases where the coupling between two nuclei is greater than or comparable to their chemical shift difference (in terms of frequency). The effect is to change the 

For some spin systems, analysis of spectra can be achieved with the aid of equations for transition frequencies and intensities. It is not possible to go into spectral analysis in detail here, but the subject is usually covered fairly thoroughly in the major NMR textbooks, and there are some publications 

NMR spectrum of S(Pp2)2- The spectrum is centrosymmetric and half of the total intensity falls in the two most intense lines, which are truncated in the figure- 

Specifically devoted to it [29]. The other approach is to use a computer program devised for the purpose, referred to in Section 2.11.4. Suffice it to say that the analysis yields chemical shifts and coupling constants as usual, but could also give the relative signs of some of the coupling constants, which is usefid additional information. 

Finally, it should be noted that spectra appearing at first sight to be first-order could in fact show some second-order characteristics, which often causes confusion. If an unexpected small splitting is found, or the 

FIGURE 2.13. 19F NMR spectrum of pseudo-p-dinitro-l,l,2,2,9,9,10,10-octafluoro-[2.2]paracyclophane 

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 

when fluorine and/or proton NMR spectra do not appear as simple as you might think they should, it is generally because of a second-order phenomenon resulting from one of those factors described above. 

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Graphite exhibits strong second-order Raman-active features. These features are expected and observed in carbon tubules, as well. Momentum and energy conservation, and the phonon density of states determine, to a large extent, the second-order spectra. By conservation of energy hut = huty + hbi2, where bi and ill) (/ = 1,2) are, respectively, the frequencies of the incoming photon and those of the simultaneously excited normal modes. There is also a crystal momentum selection rule hV. = -I- q, where k and q/... 

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... 

There is still another situation that leads to second order spectra and this one usually cannot be anticipated. For example, take a look at the proton spectrum of 3,3,3-trifluoropropene in Fig. 2.9. This spectrum is not the simple one that one would expect for a monosubstituted ethylene. However, the second order nature of this spectrum can be understood after examining the fluorine-decoupled spectrum, which is given in Fig. 2.10. The decoupled spectrum displays the expected multiplets from the ABC system, each proton appearing as a doublet of doublets. The second order spectrum seen in Fig. 2.9 derives from the fact that the protons at 5.98 and 5.93 are seen from the 19F frequency as... 

In the case of a number of vicinal difluoro systems, such as 2,3-difluoro-2,3-diphenylethane or 2,3-difluorosuccinic acid derivatives, the coupling systems are AA XX, which means that they will produce second-order spectra (see Chapter 2, Section 2.3.5). A case in point is the fluorine and proton spectra of 1,2-difluoroethane, which have been... 

It is fortunate that most applications devolve into one of two camps small molecules or proteins. In the former case, the size of these molecules has stayed fairly constant and the inexorable rise in magnetic fields has meant that the number of incidences of second-order spectra has decreased (although complications will always exist with virtual couplings). It is therefore pertinent to examine methods, which are not only designed to extract couplings from first-order spectra, but are also amenable to automation. 

Each chemically distinct nucleus is assigned a letter and a numerical subscript is used to indicate the number of such nuclei. If the chemical shift difference between two sets of nuclei is large compared with the coupling constant between them (3i - S2 > > Jn), letters that are well apart in the alphabet are used A, X, M. Such systems are first order and give rise to simple multiplets in the NMR spectra. On the other hand, if the chemical shift difference is of the same order of magnitude as the coupling constant between the two nuclei ( 1 - 2 J12), then consecutive letters are used A, B, C,. . . , X, Y, Z. The latter systems give rise to second-order spectra with complex multiple patterns. 

The cyclophosphinophosphonium ions Me(PR) ( = 3, 4, 5) (see Section 11.3.1.2 and Scheme 11.2) provide an informative example of magnetic inequivalence. Whereas the P H NMR spectra for the three-membered ring 3.12a and the four-membered ring 3.12b are essentially first order (A2X and A2MX, respectively), the five-membered architecture of 3.12c results in magnetic inequivalence of the two pairs of phosphorus atoms that, in solution, are related by a C2 axis. Consequently, complex second-order spectra resulting from an AA BB X spin system are observed. 

Second-order spectra are characterized by peak spacings that do not correspond to coupling constants, by nonbinomial intensities, by chemical shifts that are not at the midpoints of resonance multiplets, and by multiplicities that do not follow the n + 1 rules. (See Figures 4-1, 4-2, and 4-3.) Even when the spectrum has the appearance of being first order, it may not be. Lines can coincide in such a way that the spectrum assumes a simpler appearance than seems consistent with the actual spectral parameters (a situation called deceptive simplicity). For example, in the ABX spectrum, the X nucleus is coupled to two nuclei (A and B) that are themselves closely coupled. When is extremely small, the A and B... 

The pulse sequence, as a variant of the spin echo experiment, also refocuses the spread of frequencies caused by field inhomogeneity, so that some improvement in resolution is obtained. The inset at the lower right of Figure 6-18 shows the normal ID spectra of H-4 and H-5 at the top (Figure 6-18c and e) and the unrotated projection of the 2D J-resolved spectra at the bottom [Figure 6-18d and f, extracted from the projected spectrum (Figure 6-18a) at the top of the 2D display]. The much higher resolution of the 2D resonances is clearly evident. Thus, the procedure is an effective way to measure J accurately, particularly when J is poorly resolved in the ID spectrum. The experiment fails for closely coupled nuclei (second-order spectra). 

Arithmetic analysis of four spin systems is very limited. First-order spectra (AX3, A2X2) provide no difficulty. Of the second-order spectra, however (AA XX, AA BB, ABXY, ABCX, ABCD, etc.), only the AA XX can be analyzed readily. This common pattern, which is second order only because of magnetic nonequivalence, is determined by six parameters vx, JaaS - xx Ax (= A xO and Ax (= A x)- that such a spectrum... 

The most important spin system parameters can often be obtained directly from a NMR spectrum by simply measuring the signal positions, the line separation in multiplets and the line widths. It must be stressed that a molecular parameter measured directly from a NMR spectrum, particularly in second order spectra, is not necessarily the same as the spin system parameter. 

Harris and Sheppard (1961) measured the line width in the fast-exchange limit, which has been shown to be a satisfactory procedure by Alexander (1962, 1963) provided second-order spectra at low-... 

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