NMR Spectroscopy

The n+1 rule fails when protons in a group are magnetically nonequivalent. In these cases, the protons in the group may have different chemical shifts and coupling constants to neighboring protons. The n+1 rule will not apply, and the signals for these nonequivalent protons can be quite complex.

An example of this complex splitting can be seen in styrene oxide. Protons H_a and H_b are not magnetically equivalent, even though they reside on the same carbon atom. H_a and H_b are coupled to each other and coupled to proton H_c by different coupling constants.

Figure 30 contains the NMR spectrum for styrene oxide. In this instance the n+1 rule fails.

Figure 30. Complex coupling in styrene oxide.

In styrene oxide, the 3-membered ring renders protons H_a and H_b nonequivalent; these hydrogens have different chemical shift values, H_a = 2.77 ppm and H_b = 3.12 ppm, and they show geminal splitting with respect to each other. The third proton, H_c, has yet another value of chemical shift, H_c = 3.83 ppm, and is coupled differently to H_a than to H_b.

An analysis of the splitting pattern in styrene oxide is carried out using a tree diagram. Consider hydrogen H_c. First proton H_b splits H_c (³J_bc) into a doublet; second, H_a splits each of the doublet peaks into another doublet (³J_ac). The resulting pattern of two doublets is often called a doublet of doublets. Analysis for protons H_a and H_b can be similarly carried out.

Figure 31 contains the tree diagram for styrene oxide. This analysis can explain the complex splitting patterns observed in this system.

Figure 31. Tree diagram for styrene oxide.

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