Symmetry of spin wave functions

FIGURE 6.6 Repetitive first-order splitting analysis applied to a simulated spectrum of cis-CH3CH=CHCN. 

Coupling between nuclei within a magnetically equivalent set does not affect the spectrum. 

For sets of magnetically equivalent nuclei, first-order analysis is usually considered applicable when (vA — r,u)//AB — 7. [When 7 (vK — Pb)/Jab 20, there is some distortion of intensities from the pattern given in Table 6.2, but the multiplet is still recognizable.] The deviation in intensities always occurs in the direction of making the lines near the center of the overall spectrum more intense and those toward the edges less intense. 

When two or more couplings are present that may be treated by the first-order rules, a repetitive procedure can be used. For example, Fig. 6.6 gives an illustration of the repetitive application of first-order analysis. Usually it is convenient to consider the largest coupling first, but it is immaterial to the final result. 

The presence of symmetry in a molecule imposes severe restrictions on many chemical and spectral properties. Often the existence of symmetry permits considerable simplification in the analysis of NMR spectra. 

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