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J Coupling

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This page will be devoted to the expansion of the J coupling Hamiltonian (Also known as the Spin-Spin coupling). 

Expansion of the Hamiltonian

Pascals Triangle

Nuclei in different chemical environments up to three bonds away can influence one another’s effective local magnetic field by carrying spin orientational information through bonding electrons.This effect is most prominent among chemically equivalent nuclei, giving rise to the N+1 rule for equivalent protons.  A proton with N protons on contiguous carbon atoms splits into N+1 peaks with intensity pattern. The splitting pattern for A when it is coupled to a number of X nuclides would follow the relation represented by Pascal’s triangle. To be more specific, I will take AX2 for example. AX2 represent a spin system that contains three nuclei, two of which have the same chemical shift and one of which is different (e.g. ClCH2CHCl2). Here A is CH proton and X are CH2 protons. According to table 4 and figure 12, CH proton will be split into 1:1 doublet, while CH2 will give a fine structure of 1:2:1 triplet. The spacing between peaks is defined as coupling constant J, which can be used to describe the degree of coupling.

Table 4. Pascal's triangle according to AX configurations



Figure 12.NMR spectrum of nucleus A in an AX2 spin system.