MULTIPLICITY
High resolution NMR spectrometers can reveal a phenomenon called spin-spin splitting (or 
spin-spin coupling) between non-equivalent hydrogen atoms on neighboring carbon atoms. The multiplicity or splitting of each peak can be explained empirically using the n+1 rule. Each group of equivalent protons can sense the number of protons (n) on a neighboring carbon atom and its peak is separated into n+1 peaks.
| # of equivalent protons to which nucleus is coupled | Name of multiplet | Line intensity |
| 1 | Doublet | 1:1 |
| 2 | Triplet | 1:2:1 |
| 3 | Quartet | 1:3:3:1 |
| 4 | Quintet | 1:4:6:4:1 |
| 5 | Sextet | 1:5:10:10:5:1 |
| 6 | Septet | 1:6:15:20:15:6:1 |
Notice the line intensities of multiplets correlate to the coefficients of a binomial expansion. Go to the Multiplicity Theory page for an explaination of why the line intensities correspond to Pascal’s triangle.
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The spectra of 2-hexanone displays spin-spin splitting nicely. Five inequivalent groups of protons exist in this molecule. The five resonances produced by these protons can be seen in the NMR to the left. Four of these resonance peaks are split by their neighboring protons forming multiplets. The last resonance, corresponding to the terminal methyl group A, appears as a singlet because the neighboring carbon atom does not contain any proton substituents. |
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Correlation of the remaining protons should be straightforward using only your knowledge of chemical shifts and integration. The spin-spin coupling can be used to confirm your assignments. Resonance B appears as a triplet because methylene group B has 2 neighboring protons. The other triplet, upfield at 0.86ppm, clearly corresponds to methyl group E as this group also has two neighboring protons. The remaining methylene groups are split by more than one set of protons. Methylene D has 2 sets of neighboring protons, methyl group E and methylene C, causing it to appear as a group of 6 (sextet). The remaining resonance, C, appears as a quintet (group of 5) due coupling with methylene protons B and D. |
Using the spin-spin coupling rule (n + 1) we can predict the multiplicity of each resonance based on the structure of a molecule. Try to determine the splitting patterns for each set of protons in ethyl bromoacetate. Then test yourself; can you sketch a rough NMR spectra for ethyl bromoacetate? Make sure to include chemical shift, integration and splitting into your answer. Label each peak appropriately.
