First Order Spin Systems

Any such collection of sets insulated from all other sets, is a spin system. The following are examples of first-order spin system AX (two doublets), A2X (doublet, triplet), A2X2 (two triplets), A3X2 (triplet, quartet). The reasoning is obvious In A2X for example, the A2 set is split into a doublet by the n + 1 neighboring protons in this case there is one proton in the X set the two protons in the A2 set account for the triplet. 

With two or more sets, there is the complication of several coupling constants. Thus nitropropane can be described as follows since the N02 group spreads out the three sets  

The A and X groups couple with the M group but the A group does not couple with the X group. The analysis is presented in Section 3.8.1.1 after discussion of some relevant material. At this point, we note only that the spectrum consists of two triplets with slightly different coupling constants, and a sextet with slightly broadened peaks. 

Beyond these spin systems are those containing magnetically nonequivalent protons, which are quite common and have an unpleasant aspect They cannot become first-order systems by increasing the magnetic field. These spin systems are discussed in Section 3.12. 

There are collections of calculated spectra that can be used to match complex, first-order, splitting patterns (see references to Wiberg 1962 and Bovey 1988). Alternatively, these spin systems can be simulated on the computer of a modern NMR spectrometer. For example see the NMRSIM computer program available from Bruker BioSpin. 

---

First-order spin systems Not very specific term used to describe spin systems where the difference in chemical shift between coupled signals is very large in comparison to the size of the coupling. In reality, there is no such thing as a completely first-order system as the chemical shift difference is never infinite. See Non-first order spin system. 

The 600 MHz spectrum in Figure 3.33 consists of a simple first-order spin system, as does the 300 MHz spectrum but with minor distortions. The 60 MHz spectrum consists of a higher order spin system. A spin system may consist of one or more higher-order multiplets, in which case it is difficult to determine all of the <5 value, coupling constants, and multiplicities by inspection. Figure 3.50 offers an example even at 600 MHz. ... 

Further Examples of Simple, First-Order Spin Systems... 

With an understanding of simple first-order spin systems and of the Pople notations, we can consider the following example. 

In addition to the above requirements for a first-order spin system, we now consider the concept of magnetic equivalence (or spin-coupling equivalence) by comparison with the concept of chemical-shift equivalence. 

In Fig. 3.3 the roof effect, a typical indication of strongly coupled spins, can be observed for the AB spin system, whereas the line intensities of the AX spin system indicate that it may be analysed on a simple first order basis. Normally a first order spin system can be assumed if the chemical shift difference in Hz for the coupled spins i and k is a lot greater than the scalar coupling constant Jj. ... 

Computer programmes applicable to intermolecular exchange in non-first-order spin systems have been developed and their scope has been illustrated with reference to the equilibrium ... 

Once the protonated carbons and nonprotonated carbons are determined (quaternary carbons can be deduced through a combination of the multiplicity edited HSQC and the ID C data) a good approach is to begin the analysis of the COSY data (see Figure 33). This will allow the spectroscopist to look for the presence or absence of contiguous IH spin systems. While much of this can be deduced from a detailed understanding of the ID H NMR data the use of the COSY data will both confirm previous data as well as enable one to look at spin system that have non-first-order spin systems. 

Figure 2 High-field region of the H NMR spectrum of strychnine. The automatic interpretation results in an identification of peak patterns and the analysis of first-order spin systems. If the identification of a first-order system is not possible, the signal group is denoted a multiplet (M). The symbols ( , -h, , —) are symmetry descriptors for the considered multiplet...

---