Non-first-order spectra

Let us now look at what happens when the chemical shift difference between the coupled nuclei is small and the simple patterns become distorted, i.e. non-first-order spectra. The simplest example of this is an AB spin system. Remembering that an AX system will give a pair of doublets, we will now look at a system in which the chemical shift difference is relatively small, so that the spin system is now described as... 

Particularly striking examples of non-first-order spectra are those of compounds that contain aUcyl chains. Fignre 10-23 shows an NMR spectrnm of octane, which is not first order because all nonequivalent hydrogens (there are fonr types) have very similar chemical shifts. All the methylenes absorb as one broad mnltiplet. In addition, there is a highly distorted triplet for the terminal methyl gronps. 

When the chemical-shift difference between coupled hydrogens is comparable to their coupling constant, non-first-order spectra with complicated patterns are observed. 

Ester-type dimers illustrate the four-step approach for identification of carbohydrate structural elements in the oligosaccharide cores by NMR spectroscopy. Eor these type of compounds, edited NMR sub-spectra have permitted the assignment of all of the resonances in both monomeric units (22, 78). Spectroscopic simulation of the coupling constants can be deduced for proton resonances with a non-first-order resolution. Figure 2 illustrates this approach for batatin 1 (230) the... 

Figure 9.10. Predicted and observed 60-MHz H ABC spectra of compound 9-3. (a) Predicted first order spectrum (b)-(d) multiplet slanting due to second-order effects (e) observed spectrum [From Prediction of the Appearance of Non-First-Order Proton NMR Spectra, by R. S. Macomber, Journal of Chemical Education, 60, 525 (1983). Reprinted by permission.

There are some exeeptions to this simple picture, for instance if there is magnetic non-equivalence, or if the chemical shift difference for the nuclei is not much greater than the mutual coupling constant. The spectra will then be second order, and will not be simple multiplets. Methods of analyzing second-order spectra are discussed briefly in Section 4.9.1. For now, we consider only first-order spectra arising from spin-1/2 nuclei. 

In extreme cases, the simple rnles devised in Section 10-7 do not apply any more, the resonance absorptions assnme more complex shapes, and the spectra are said to be non-first order. Although such spectra can be simnlated with the help of computers, this treatment is beyond the scope of the present discnssion. 

No attempt is made here to give the theoretical reasoning or predictive methods for these non-first-order patterns [16-18], but you should be able to recognize them as you analyze spectra and know what structural meaning they have. 

The quadrupolar effects of order higher than two (7) are usually assumed to be negligible, especially at high magnetic fields. However, once the first- and second-order effects are removed, the measurement of third-order contributions becomes realistic. It can be easily shown that, similar to the first-order case, the CT and all symmetric MQ transitions (q = 0) are free of the third-order contribution, which thus can be safely ignored in DAS, DOR, and MQMAS experiments [161,162]. This is not the case for transitions between non-symmetric spin states, such as the STs. Indeed, numerical simulations of the third-order effect have explained the spectral features that have been observed in 27A1 STMAS spectra of andalusite mineral [161]. 

A rigorous theoretical treatment of the non-alternant and heterocyclic indolizine is extremely difficult and, even for the related isoconjugate hydrocarbon, far from conclusive. Many questions, however, in which experimentalists are interested may be answered in a satisfactory way on the basis of a perturbational treatment. This approach has been used for a discussion of the electronic spectra of indolizine and some azaindolizines (63JCS3999). Following first-order PMO theory the 7r-stabilization which follows from aza substitution at the different positions of the model molecule depends on the ir-electron density qt as well as the change in electronegativity Sat (B-75MI30801). The perturbations caused by aza substitution of the indenyl anion are depicted in Scheme 1. 

Raman spectra as a function of temperature are shown in Fig. 21.6b for the C2B4S2 SL. Other superlattices exhibit similar temperature evolution of Raman spectra. These data were used to determine Tc using the same approach as described in the previous section, based on the fact that cubic centrosymmetric perovskite-type crystals have no first-order Raman active modes in the paraelectric phase. The temperature evolution of Raman spectra has indicated that all SLs remain in the tetragonal ferroelectric phase with out-of-plane polarization in the entire temperature range below T. The Tc determination is illustrated in Fig. 21.7 for three of the SLs studied SIBICI, S2B4C2, and S1B3C1. Again, the normalized intensities of the TO2 and TO4 phonon peaks (marked by arrows in Fig. 21.6b) were used. In the three-component SLs studied, a structural asymmetry is introduced by the presence of the three different layers, BaTiOs, SrTiOs, and CaTiOs, in each period. Therefore, the phonon peaks should not disappear from the spectra completely upon transition to the paraelectric phase at T. Raman intensity should rather drop to some small but non-zero value. However, this inversion symmetry breakdown appears to have a small effect in terms of atomic displacement patterns associated with phonons, and this residual above-Tc Raman intensity appears too small to be detected. Therefore, the observed temperature evolution of Raman intensities shows a behavior similar to that of symmetric two-component superlattices. 

The key result is the appearance of first order Raman scattering (forbidden in centrosymmetric paraelectric phase) by optical phonon modes (TO2, LO3, TO4, and LO4) in all the film systems. These phonon peaks are weak in the nearly stoichiometric MBE-grown film, and are the strongest in the non-stoichiometric (Sro.9Ti03 x) film with intentionally introduced large Sr deficiency. The nominally stoichiometric PLD-grown SrTiOs films also exhibit strong first order Raman peaks nearly identical behavior was observed in both 50- and 1000-nm-thick films. The temperature evolution of Raman spectra (Eig. 21.13b) clearly indicates... 

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