Proton magnetic resonance of symmetrical molecules

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Abstract
Methods have been developed for the analysis of large-shift A2B2 spectra by perturbation techniques. Modified first-order expressions for the A2X2 transition frequencies are given and two alternative types of second-order correction terms are added. For the first kind of expression the somewhat restrictive conditions pertain that all the coupling constants are to be small as compared to the relative chemical shift, whereas the second kind of expression was derived on the more general assumption that only the coupling constants between chemically shifted nuclei are small. The expressions for the relative intensities have been supplemented with first-order correction terms (i.e. terms on the order of L/(v A − v B) and N/(v A − v B)). As a useful alternative, the very simple expressions obtained in the (AX)2 approximation may be used whenever one of the coupling constants between the chemically shifted nuclei is large in comparison with the other couplings in the spin system. Expressions for the transition frequencies are given to first and second order and for the intensities to first order. The analysis of the proton resonance spectra for a few disubsituted benzenes serve to illustrate the applicability of these perturbation methods.