First-order spectrum

In the early history of high resolution NMR, the theory was developed by use of perturbation theory. First-order perturbation theory was able to explain certain spectra, but second-order perturbation theory was needed for other cases, including the AB system. Spectra amenable to a first-order perturbation treatment give very simple spectral patterns ( first-order spectra), as described in this section. More complex spectra are said to arise from second-order effects.  

FIGURE 6.5 H NMR spectrum of acetaldehyde. Right CH3 resonance, with the two spin states of the aldehyde proton indicated. Left, CHO resonance, with the four spin orientations of the methyl protons indicated. 

From our discussion in the preceding sections, it is clear that this explanation cannot describe NMR spectra in general. However, it is correct and does account for the spectrum provided that two conditions are simultaneously satisfied  

When first-order analysis is applicable, the number of components in a multiplet, their spacing, and their relative intensities can be determined easily from the following rules  

A nucleus or group of nuclei coupled to a set of n nuclei with spin / will have its resonance split into 2nl + 1 lines. For the common case of / = y2, there 

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First-order spectra (mulliplels) are observed when the eoupling constant is small compared with the frequency difference of chemical shifts between the coupling nuclei This is referred to as an A n spin system, where nucleus A has the smaller and nucleus X has the considerably larger chemical shift. An AX system (Fig. 1.4) consists of an T doublet and an X doublet with the common coupling constant J x The chemical shifts are measured from the centres of eaeh doublet to the reference resonance. 

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. 

Fortunately, in a very large number of cases, multiplets can be correctly analysed by inspection and direct measurements. These spectra are known as first order spectra and they arise from weakly coupled spin systems. At high applied magnetic fields, a large proportion of NMR spectra are nearly pure first-order and there is a tendency for simple molecules, e.g. those exemplified in the problems in this text, to exhibit first-order spectra even at moderate fields. 

RULES FOR SPECTRAL ANALYSIS OF FIRST ORDER SPECTRA... 

H NMR-spectroscopy has appeared a powerful method for the recognition of helicenes and for an analysis of their conformations in solution. This is especially due to the appearance of quasi first order spectra for the protons in the terminal rings, even at 90 MHz. 

The simple patterns we have discussed so far give rise to first-order spectra which are very similar to the predictions we have made. First-order spectra are obtained when there is a reasonably large chemical shift difference between the coupling constants of the coupled nuclei, such that equation (4.4) is obeyed ... 

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... 

The experiment is used to separate chemical shifts and J-couplings for homo- and heteronudear systems. In simple cases the chemical shifts and J-couplings may be directly obtained from the 2D spectrum by inspection. For severely overlapped first-order spectra or strongly coupled spin systems the estimated parameters obtained from the spectrum may be used as starting values in a computer assisted spectral analysis as outlined in Modern Spectral Analysis (Volume 3). 

If the matrices which appear in the calculations do not exceed the size of 2 x 2 one can analytically derive the lineshape function, and this tends to make the computation rather trivial. Such cases are represented by all A B exchange processes and some other two-site exchange systems which give first-order spectra, as well as by the mutual AB = BA exchange. The same is possible in calculations on spectral fragments of certain more complicated systems as reported in a previous review in this series by Sutherland. (53)... 

An AB system (Fig. 1.6) consists, for example, of an A doublet and a B doublet with the common coupling constant JAB, where the external signal of both doublets is attenuated and the internal signal is enhanced. This is referred to as an AB effect, a roofing symmetric to the centre of the AB system 2 roofing is frequently observed in proton NMR spectra, even in practically first order spectra (Fig. 1.2, ethyl quartet and triplet). The chemical shifts vA and vB are displaced from the centres of the two doublets, approaching the frequencies of the more intense inner signals. 

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